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EXPERIMENTS IN MASS EDUCATION 2000-2010
EXAMINATION & COMMON SENSE ORIENTED MNEMONIC FAIRY TALES








OUR STUDENTS ARE VERIFIERS OF SOLUTIONS!!!!!!


THE SOLVERS OF PROBLEMS DO NOT EXIST!!!!!!



DRAFT
METAMATHEMATICS DEMYSTIFIED ver 3.0 (with pictures and fancies)

click here for: TEXT ONLY-NO FANCIES-NO PICTURES
A FAIRY TALE CONCERNING THE P=NP PROBLEM
(A Computational problem predating the Ages of Man)
(Computation in all Environments predating all Ages, all Revolutions, all Civilizations)
(Competing with Michelangelo)




[Note:- Being sporadically updated directly online on the server using pidgin-HTML and weak, unreliable, sporadic internet connectivity.]

[Note:-The use of pidgin-HTML enables translation and cultural adaptation across cultures, civilisations and the The Four Waves. The use of pidgin-HTML enables easy modification by K-12 and adult literates in all walks of life, in all cultures, in all Waves. The use of pidgin-HTML like the "Emperor's Old Clothes" enables leapfrogging into the Fourth Wave of the Cloud. A possible extension is to use pidgin-HTML + pidgin-JavaScript + pidgin-PHP for all purposes.]

SCROLL DOWN A WEE BIT FOR THE STORY WITH PICTURES






CHARLES DICKENS: BILL STUMPS HIS MARK
(Rip Van Winkle visits The Pickwick Papers after two centuries)

THE MODERN VERSION: BILL STUMPS HIS MARK


OMAR KHAYYAM'S VERSION: BILL STUMPS HIS MARK

A SOLUTION: BILL STUMPS HIS MARK


SEARCH FOR A SOLUTION: BILL STUMPS HIS MARK

SEARCH FOR A SOLUTION: BILL STUMPS HIS MARK



METAMATH EMATICS
SIX BLIND MEN AND THE ELEPHANT

SIX BLIND MEN AND THE ELEPHANT

SIX BLIND MEN AND THE ELEPHANT




METAMATH EMATICS
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O NE BLIND M AN LEADIN G ANOTHER
SIX BLIND MEN AND THE ELEPHANT



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SCROLL DOWN FURTHER A WEE BIT FOR THE STORY

O F THE DUMM IES
FOR TH E DUMMIES
BY THE DUM MIES




DRAFT
METAMATHEMATICS DEMYSTIFIED
A FAIRY TALE CONCERNING THE P=NP PROBLEM

(Computation in all Environments predating all Ages, all Revolutions, all Civilizations)

CONTEN TS


PART I
"IT WAS THE BEST OF TIMES"

PART II
"IT WAS THE WORST OF TIMES"

PART III
"THE WILDERNESS OF THE ETERNAL QUEST"

PART IV
"COMPUTATION PREDATES THE AGES OF MAN"
(Computation in all Environments predating all Ages, all Revolutions, all Civilizations)

COMMENTS AND NOTES


DETAILED CONTENTS





A hypothetical, naive, simplistic, procrustean model using specious metamathematics


"COMPUTATION PREDATES THE AGES OF MAN"
(Computation in all Environments predating all Ages, all Revolutions, all Civilizations)


METAMATH EMATICS
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O F THE DUMM IES

FOR TH E DUMMIES

BY THE DUM MIES

PART I
"IT WAS THE BEST OF TIMES"






PROLOGUE


When we were in our centuries of sleep an interesting thing happened in the world. In a far off land about two centuries ago a delegation of children led by Winnie the Pooh and Tigger met the Emperor.


THE DELEGATION


THE EMPEROR



THE STATEMENT OF THE PROBLEM


They complained about the horrid mathematics subject they had to study and the birch of the mathematics teacher. The Emperor recalled having had similar problems when he was young.


THE PROBLEM OF THE BIRCH OF MATHEMATICS




THE EMPEROR INITIATES STEPS FOR A SOLUTION

The Emperor was pleased to order the Prime Minister to find a Solver for a permanent solution with the rider that he (i.e. the Emperor), the children and their leaders would be Verifiers of the solution.


THE PRIME MINISTER IS TO FIND A SOLUTION




THE PRIME MINISTER AND HIS FRIGHT


The Prime Minister was frightened. The Emperor may cut off his head if he failed. He asked the courtiers for help.
In the meantime he asked the children to play.


THE CHILDREN PLAY IN THE PALACE AND AWAIT THE SOLUTION



THE STRATEGY FOR THE SOLUTION

A suave courtier suggested the strategy for a solution.
Like the alchemists of old had tried to do in their area mathematics had to be distilled and its essence found. This could be encapsulated and converted to a sugar coated pill. The pill could be swallowed with milk and honey. The mathematicians and mathematics teachers can be shown the door. A mathematics teacher can be left in the wilderness to use his birch on himself.


THE DISTILLATION OF MATHEMATICS




THE ESSENCE OF MATHEMATICS



THE SUGAR COATED MATHEMATICS PILL



AWAY WITH THE MATHEMATICS TEACHER-THE CHILDREN CAN PLAY!


THE OTHER USES OF THE SOLUTION
PRACTICE WHAT YOU PREACH

Another suave courtier convinced everyone that the mathematics pill will explain all the mysteries of the Universe and the High Priest and his minions can be bundled off. The High Priest could be left in the desert and can listen to his own sermons.


AWAY WITH THE HIGH PRIEST-THE CHILDREN CAN PLAY!



STILL OTHER USES OF THE SOLUTION
PHYSICIAN HEAL THYSELF

Another suave courtier convinced everyone that the mathematics pill will explain all the mysteries of sickness. The horrid Royal Physician and his minions can be expelled. The Royal Physician could be left in the Artic wilderness and can swallow his own bitter medicines, to heal himself.


AWAY WITH THE DOCTORS-THE CHILDREN CAN PLAY!



THE COURTIERS SING A SONG

The courtiers went on and on. They were all in the pay of a foreign scoundrel.


THE CHILDREN ARE ASKED TO CONTINUE PLAYING


THE SEARCH FOR THE SOLVER

A high power Search Committee was formed and messengers were sent full speed in all directions to find the Solver.


THE SEARCH FOR THE SOLVER




THE SOLVER ENTERS THE STAGE


Half a century later a legendary scoundrel named Procrustes descended from the legends of ancient Greece and entered Mathematics with an aim to reform it, distill it, get its essence and create the sugar coated pill.


PROCRUSTES THE SOLVER




THE STRATEGY OF THE SOLVER


Procrustes had a reputation for having a magic bed which he said would fit anyone.


THE MAGIC BED OF PROCRUSTES




THE METHODS OF FOR THE SOLVER

Procrustes seems to have taken a leaf out of a course in Programming Languages. If a person was bigger than the bed he employed 'narrowing' and lopped of the limbs etc. till the person could fit his bed. If a person was too short he employed 'widening' and stretched the person's limbs so that he could fit into his bed.


THE METHODS FOR FINDING THE SOLUTION




THE NEW BED OF PROCRUSTES THE SOLVER

Procrustes now had a new bed which he called Arithmetic and claimed all mathematics would fit into it.


THE NEW BED OF PROCRUSTES

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THE SOLVER IS EMPLOYED


Procrustes was employed by the Emperor on the recommendation of the courtiers and charged with the task of taming mathematics. He was to be paid a penny a day for his efforts. He was given a Piggy Bank to store his money.


THE EMPLOYMENT & THE WAGES OF PROCRUSTES



THE EASY PART OF THE SOLUTION


Procrustes left Algebra and Geometry alone. Much to his disgust a century of effort by the mathematicians he had employed showed that Algebra & Geometry could be put into various knots & contortions and actually fit into his bed.


ALGEBRA IS FOUND TO BE TIMID BUT GEOMETRY IS TROUBLESOME


THE STRATEGY FOR GEOMETRY



Geometry did create some trouble, till one used the ancient proverb: "Once a goon always a goon".
In any Geometry there are invariants which do not basically result in any change to a goon when applied to the goon. Once these are isolated it seems possible to reduce that Geometry to Arithmetic.


GEOMETRY IS MADE TO FIT INTO THE BED USING INVARIANTS



THE HARD PART OF THE SOLUTION


Analysis was a troublesome affair. It depended on the continuum which seemed to be a model for the Universe.


THE PROBLEM WITH ANALYSIS, THE UNIVERSE AND THE VOID



PROCRUSTES AND THE VOID

Procrustes started with the Void as the Universe. By 'narrowing' he declared the Universe is the Void.


THE UNIVERSE IS THE VOID DECLARES PROCRUSTES


POINTS DO NOT EXIST IN THE CONTINUUM

Procrustes widened the Universe to a massive lump where there was no such thing as a point.


THE UNIVERSE IS A MASS WHERE THERE IS NO POINT



THE CREATION OF A POINT

By 'narrowing' Procrustes reduced the Universe to a mathematical point. By 'widening' he said this point was eternal, immortal but 'dumb'. It could not do anything by itself.


THE MASS IS A MATHEMATICAL POINT



ENTER ARISTOTLE


Procrustes 'narrowed' the concept of differing points of view allowed to the human race to two valued logic, putting the blame on Aristotle. He claimed that for every statement he was correct and the other person wrong.
By 'narrowing' he did not allow suo motto change by the immortal truth values for an eternal amount of time.


TWO VALUED LOGIC IS CREATED
MULTIVALUED LOGIC IS SUPPRESSED
CONTRADICTION IS BANNED
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THE EXPULSION OF THE CRETEAN


The ancient ambassador from Crete had serious objections on this two valued logic business. He said he was a bonafide ambassador and all ambassadors were liars, who lie for the good of their country. He was promptly expelled to ancient Crete to eternally contemplate on the validity of his objections. He was excommunicated by the High Priest. He was by Royal Proclamation declared as nonexistent. He was declared to be a figment of one's imagination. All records pertaining to him were expunged from all archives.



THE EXPULSION AND SUPPRESSION OF THE CRETEAN




PROCRUSTES AND THE SERPENT

Procrustes had a frightening dream. He saw a fearful spotted Snake in the continuum. He woke up with a Divine Inspiration and by 'narrowing' claimed there was something called a real number line/curve in the continuum.



THE DIVINE INSPIRATION OF THE EXISTENCE OF THE REAL NUMBER LINE



PROCRUSTES CREATES POINTS IN THE CONTINUUM

Procrustes considered the Universe of the single eternal, immortal, dumb point. He 'widened' it to an infinite collection of distinct eternal, immortal, dumb points. By 'narrowing' he did not allow suo motto birth, death or change in any point.


THE INFINITE NUMBER OF POINTS IN THE CONTINUUM



PROCRUSTES AND HIS PIGGY BANK

Procrustes had a dream that he was taking stock of his piggy bank where he kept his pay.
Starting with a penny, he kept on adding another penny as a successor, and found out that he had progressively increasing small but tidy sum.


THE GROWING PIGGY BANK AND THE CONCEPT OF INTEGERS


PROCRUSTES INVENTS THE NATURAL NUMBERS-I

Procrustes woke up with a Divine Inspiration that God created the natural numbers and all else is the work of Procrustes.


THE NATURAL NUMBERS ARE INVENTED


PROCRUSTES DREAMS OF THE OVERLOADED CAMEL

Procrustes had a dream that he was in the desert. He saw a hungry, starved, old camel with a heap of straw on its back. Its master kept on adding straw after straw to the load on the back of the camel. Nothing seemed to happen to the camel.


THE BACK OF THE CAMEL WILL NOT BREAK?


PROCRUSTES INVENTS THE NATURAL NUMBERS-II



Procrustes woke up with a Divine Inspiration that God created an infinite 'bunch' the natural numbers and all else is the work of Procrustes.


WITH GOD GIVEN INTEGERS EVERYTHING IS THE WORK OF PROCRUSTES
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PROCRUSTES CREATES THE INTEGERS AND OPERATIONS ON THEM



Procrustes applied his dream.
Starting with a single immortal, eternal, dumb integer representing the Universe by 'widening ' he created an unlimited number of immortal integers.


THE INTEGERS AND OPERATIONS ON THEM ARE CREATED



THE SUPERNATURAL PROPERTIES OF INTEGERS

He 'widened' the integers and declared they were immortals and eternal. By 'narrowing' he did not allow birth, death, suo motto changes.


THE INTEGERS ARE IMMORTAL AND ETERNAL



OPERATIONS ON INTEGERS

He 'widened' many operations on integers and declared by 'narrowing' that they and their results could be defined. He used 'widening' to declare that they were immortal and eternal entities.


THE RESULTS OF OF OPERATIONS ON INTEGERS ARE IMMORTAL AND ETERNAL



PROCRUSTES STARTS COUNTING


He 'narrowed' the collection of points in the continuum and said it consisted of distinct points that could be described by 'bunches' of integers or combinations of them. By 'narrowing' he did not allow suo motto change by the immortal points for an eternal amount of time.


THE CONTINUUM 'KOWTOWS' TO THE BUNCHES OF INTEGERS



PROCRUSTES AND THE TORTOISE

Procrustes dreamt that he saw a person called Zeno traveling on a tortoise. The tortoise claimed that the points in the continuum cannot be assigned numbers, or 'bunches' of numbers.


THE TORTOISE CLAIMS: THE POINTS IN THE CONTINUUM CANNOT BE DESCRIBED BY NUMBERS



THE ARGUMENT OF THE TORTOISE - I

The tortoise could never travel to any point from any other point, by traveling a fraction of the remaining distance in a stage of its journey.
The tortoise claimed that there was no such thing as length in the continuum.


THE TORTOISE CLAIMS: THERE IS NO SUCH THING AS LENGTH IN THE CONTINUUM



THE ARGUMENT OF THE TORTOISE - II

The tortoise claimed that in a suitably overcrowded metropolis everyone's house extends and includes his neighbor’s houses in all directions.
This was the situation in the continuum. Every point includes all the points adjacent to it. Any mapping to integers will show that.


THE TORTOISE CLAIMS: THE POINTS IN THE CONTINUUM ARE ALL BUNCHED TOGETHER, THEY CANNOT BE SEPARATED



THE ARGUMENT OF THE TORTOISE - III

The continuum cannot be described by natural numbers or integers.
This was the stand of the tortoise.
There is only one house in a suitably overcrowded metropolis, and thus just one point in the continuum.


THE TORTOISE CLAIMS: THE CONTINUUM IS JUST ONE POINT



THE ARGUMENT OF THE TORTOISE - IV

There is no such thing as infinity claimed the tortoise.
Only a finite number of natural numbers and integers exist.
Even if infinity exists the finite cannot comprehend or comment on the infinite.
This is as per the fable of the mother bullfrog taking deeper and deeper breaths to become as big as the Ox. It can at most burst.
A visitor to a house is a welcome guest. Longer he stays the happier we are. He cannot stay forever. Then he is evicted. A guest is different from the member of a house.
Lollipops are stimulants for a child. More lollipops the better. All lollipops mean the child collapses. Similarly the natural numbers are stimulants for mathematics. More numbers the better. All natural numbers means mathematics collapses.



THE TORTOISE CLAIMS: THERE ARE ONLY A FINITE NUMBER OF NUMBERS & THERE IS NO INFINITY



THE ARGUMENT OF THE TORTOISE - V

The tortoise threatened to descend into the Empire and complain to the Emperor that Procrustes was all bogus.


THE TORTOISE THREATENS TO COMPLAIN TO THE EMPEROR



THE TORTOISE IS PUNISHED

The tortoise was banished to hold up the entire Earth on its back eternally.
It was condemned to be the eternal Beast of Burden in all Screensavers dedicated to children the world over.






THE TORTOISE IS PUNISHED


PROCRUSTES BEGS THE QUESTION

Procrustes further 'narrowed' the points in the continuum to a class of immortal 'computable' real numbers. By 'narrowing' he did not allow suo motto change by the 'computable' real numbers for an eternal amount of time.


THE COMPUTABLE REAL NUMBERS ARE BUNCHES OF INTEGERS



PROCRUSTES VISITS THE BOTTOMLESS PIT


Procrustes had a dream that he was cast into the Bottomless Pit. Hurtling down the pit he met friendly Titans who were also hurtling down the pit. They would hurtle down for an infinite amount of time, throughout eternity. He found out that they were basically a friendly, simple lot who had been taken for a ride by some unscrupulous youngsters.

PROCRUSTES MEETS THE TITANS IN THE BOTTOMLESS PIT



PROCRUSTES TAMES THE INFINITIES

Procrustes woke up and claimed Divine Inspiration insofar as infinity was concerned.
He 'narrowed' infinity and reduced it to some kindly, harmless, naive, simple old persons next door. They were simple persons, perhaps a little foreign, but just like us. By 'narrowing' he did not allow suo motto changes by any of the infinities for an eternal amount of time.


THE INFINITITES DECLARED & ARE MADE USER-FRIENDLY



PROCRUSTES REACHES INFINITY

Procrustes dreamt his pennies were adding up. It was just a matter of time till his Piggy Bank reached, overtook Croesus and then reached some infinity.



THE PIGGY BANK WILL GROW AND GROW TILL INFINITY



PROCRUSTES IN THE CIRCUS


Procrustes dreamt that the Emperor had thrown him into the Arena. Herds & herds of herds, of wild animals were chasing him. They were rushing in from all the waterholes in the deep interiors of Africa. There were herds of bison chasing him. There were herds of tigers, elephants, pandas, penguins, kangaroos, kites, vultures, eagles, etc. etc. all after him.
He woke up with a sudden start and claimed by Divine Inspiration that there were some things called 'sets' which were fundamental to all mathematics.




THE HERDS OF ANIMALS CHASING PROCRUSTES

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THE PROPERTIES OF SETS - I

Procrustes naively 'narrowed' the concepts of sets and operations on them till they behaved themselves, and 'widened' their attributes by granting them immortality.
By 'narrowing' Procrustes did not allow suo motto change by sets at any time throughout eternity.



THE HERDS OF ANIMALS ARE SETS THAT ARE ETERNAL AND IMMORTAL




THE PROPERTIES OF SETS - II

Procrustes said a set is a collection of objects just as a Zoo is a collection of animals.
A Zoo can contain Zoos which can contain Zoos and so on.
A new Zoo can be formed from two Zoos by including the animals in both Zoos.
A new Zoo can be formed from two Zoos by taking only the animals they have in common.
A new Zoo can be formed from a Zoo containing the animals not in the Zoo.
One can talk of a Zoo of all Zoos.
One can determine if an animal is in a Zoo.

A ZOO IS A COLLECTION OF ANIMALS



A SET IS A COLLECTION OF OBJECTS LIKE ANIMALS




THE PROPERTIES OF SETS - III

Procrustes pompously talked of a Set of All Sets and compared himself to it. He said any goon can determine if he belongs to a gang.
He wrote a voluminous treatise showing that if a child is given one lollipop for the left hand and one lollipop for the right hand the child ends up with two lollipops.
He proclaimed he had laid the rock foundations of mathematics.



A ZOO OF ALL ZOOS OR A SET OF ALL SETS IS ANNOUNCED




THE ROYAL BARBER OBJECTS


The powerful royal Barber of all Barbers had some serious objections. He protested by putting up a board that he would shave anyone who does not shave himself. He was promptly banished to the Antarctic wilderness to eternally contemplate on the dignity of shaving himself. He was formally excommunicated by the High Priest. He was by Royal Proclamation not to be mentioned or included in any set of decent persons.


THE ROYAL BARBER OF ALL BARBERS OBJECTS TO THE SET OF ALL SETS AND IS EXPELLED




THE PROPERTIES OF SETS-I
OR
ATTEMPTS TO TACKLE THE ROYAL BARBER

Procrustes was shaken up by the behavior of the barber. He further 'narrowed' the concepts of sets and operations on them to avoid all troublesome barbers.
He 'widened' their attributes by retaining their immortality.
By 'narrowing' Procrustes did not allow suo motto change by sets at any time throughout eternity.
The Problem of the Royal Barber of Barbers still persisted.

THE TROUBLESOME ROYAL BARBER OF ALL BARBERS HAS CREATED A MESS





THE PROPERTIES OF SETS-II
OR
ENTER HAMMURABI OF BABYLON

Procrustes was shaken up by the behavior of the sets. He consulted the courtiers out of desperation.
A suave courtier advised him that the solution to the problem was to consider a set as a collection of goons. They have to civilized. They needed a Code of Conduct.
Hammurabi of Babylon had a code. This was preserved on ancient clay tablets. A sample commandment of the code was: If a child's lollipops are 'pinched' by its neighbor, then the child should 'pinch' the neighbor’s lollipops.
All other codes were mere refinements and variations of the above code. He suggested that Procrustes should 'narrow' the concepts of sets and operations on them by defining a Code of Commandments to avoid all troublesome barbers.
Considering the Visibility of the Project the courtier volunteered to be Chairman of the Law Givers of the Code. His 'cronies' would be the Directors of the Board of Law Givers.

A CODE OF LAWS FOR THE GOONGANGS



A CODE OF LAWS FOR HERDS OF ANIMALS IN ZOOS



THE SETS NEED A CODE OF CONDUCT




THE PROPERTIES OF SETS-III
OR
THE CREATION OF THE CODE OF CONDUCT FOR SETS

Procrustes thought 'long and hard' about the problem and the suggested solution.
He recalled the advice of Bluto of The Sailors his childhood Mentor in Mathematics, that mathematics is best left to mathematicians.
He kept a legion of mathematicians in chains in GoonLand supervised by mercenary Sumo Wrestlers. For half a century they were to toil, slave and evolve a minimal sets of commandments using sets for all the mathematics they thought was mathematics. They were Mentored and Guided by The Beagle Boys in their efforts.

THE VISIONARY

THE MATHEMATICIANS IN GOLD CHAINS

THE MATHEMATICIANS IN BRONZE CHAINS

THE MANAGER

THE MENTORS AND GUIDES

THE CODE OF CONDUCT FOR SETS IS CREATED



THE CODE OF THE GOONS IS CREATED





THE PROPERTIES OF SETS-IV
OR
THE PROCLAMATIONS OF THE CODE OF CONDUCT FOR SETS

His Proclamation of Commandments for Sets or Goons was issued from time to time. For a sample......


THE CODES ARE REGULARLY PROCLAIMED THROUGHOUT THE EMPIRE





THE PROPERTIES OF SETS-V
THE DEMOCRATIC LAND OF SETS AND GOONS

A. Everything is a set. Every goon is a set, every gang of goons is a set and one can determine membership in a set or a goon gang.


GOONGANGS ARE SETS - EVERYTHING IS A GOONGANG





THE PROPERTIES OF SETS-VI
THE COMMANDMENT OF THE NULL SET OR EMPTY GANG

B. Procrustes allowed the Void to exist as the empty set of goons or empty set.


IF ALL THE GOONS ARE LOCKED UP THE EMPTY GOONGANG REMAINS





THE PROPERTIES OF SETS-VII
THE COMMANDMENT OF THE INFINITE SET OR INFINITE GANG OF GOONS

C. Procrustes allowed an infinite set of goons which starting with the empty set adds an element or a goon at a time, just like his Piggy Bank starting from being initially empty had a penny added to it every day.
The gang of goons can grow eternally like the Piggy Bank can grow eternally reaching Croesus, leaving him in tears, and rushing along to infinity.


GOONGANGS CAN GROW AND GROW TILL INFINITY





THE PROPERTIES OF SETS-VIII
THE COMMANDMENT OF PAIRS OR THE GANG OF PAIR OF GOONS

D. Procrustes banned the 'gestalt' concept when combining sets, but allowed the combination to result in a set.
If a goon helps himself to the music player from one neighbor’s house and a compact disc from another then all that he has is a set of two items. His enjoyment of music is not counted.
ALTERNATIVELY
If a new gang of goons is formed by taking a distinct element from two sets of goons, then all we have is the set of two goons in the new set. They do not do anything extra special because they are together. There is no synergistic effect.


NEW GOONGANGS FROM OLD ONES





THE PROPERTIES OF SETS-IX
THE COMMANDMENT OF EXTENSIONABILITY OR EQUALITY OF GANGS OF GOONS

E. Procrustes banned the class concept and enforced Socialism in sets.
If the Royal Prince and the Plebian Pauper Fisherman went fishing, and had the same catch, then Royal basket of fish and the Plebian basket were equal sets.

ALTERNATIVELY
If the miserly Grand Mughal Emperor Aurangzeb weaves baskets to sell at fancy prices to his courtiers and the lowly weaver of baskets weaves some baskets to eke out a miserable living, and both weave the same number and type of baskets, the sets of baskets they weave are equivalent.

ALTERNATIVELY
Two goon gangs which have the same members are always equal, regardless of their individual experience and toil in life. A gang of goons learns nothing from experience. It is basically dumb.


TWO GOONGANGS ARE EQUAL IF THEY HAVE THE SAME MEMBERS





THE PROPERTIES OF SETS-X
THE LEGALITY OF NEW GOON GANGS FROM OLD ONES

F. Procrustes allowed new sets to be created by goons from existing sets.



THE PROPERTIES OF SETS-XI
THE GOON GANGS CAN LEGALLY GROW

1. A goon moves into an empty house in some locality, and finds the well furnished houses of his two neighbors have different sets of things with nothing in common. The goon can create a new set by helping himself to items from both his neighbors.
ALTERNATIVELY
A new goon gang can be formed by drawing goons from different gangs, which have no goon in common.


GOONGANGS FORM FROM GOONGANGS





THE PROPERTIES OF SETS-XII
THE COMMANDMENT OF THE POWER SET OR THE POWER SET OF GOON GANGS

2. An instance of the creation of the power set consists of all the different ways the goon can help himself to the belongings of one of his neighbors.
ALTERNATIVELY
All the ways goons from a goon gang can gang up together is the power set of the gang of goons. It is also a set.


THE POWER SET OF A GOONGANG - ALL THE WAYS GOONS CAM MERGE





THE PROPERTIES OF SETS-XIII
THE COMMANDMENT OF SEPARATION OR THE GOON HELPS HIMSELF

3. A function is defined as follows. The goon treats the items in his neighbor’s house as the domain of the function. The goon's house is the range of the function. The range is restricted to the items the goon transfers to his house from his neighbor’s house. Paradoxes are to be avoided.


THE WAYS OF THE GOONS





THE PROPERTIES OF SETS-XIV
THE COMMANDMENT OF THE BLACK SHEEP OR THE BANNED GOON

G. Procrustes banned a set from being a member of itself. The Barber was under permanent exile.

THE ROYAL BARBER OF ALL BARBERS IS UNDER PERMANENT EXILE





THE PROPERTIES OF SETS-XV
THE COMMANDMENT OF THE FOUNDATION OR THE ORIGINAL GOON

H. Procrustes demanded a nonempty set of goons to have a goon as a member who is distinct from the set itself. Only the empty set is bankrupt and a nonempty set has some assets.
ALTERNATIVELY
An empty mother Kangaroo has no babies in her pouch. A nonempty mother Kangaroo has at least one baby in her pouch.
This was a case of Kanga without Roo on one hand, and Kanga with Roo peeping out on the other.


THE ORIGINAL GOON





THE PROPERTIES OF SETS-XVI
THE COMMANDMENT OF UNIQUE UNION OR THE UNION OF ALL GANGS

I. Procrustes demanded that given a set of goons a set of a goon gang can be formed that included all the goons. Like in Nursery & KG every goon is included in the party, everybody wins the race and everybody gets a prize.


THE UNION OF GOONGANGS





THE PROPERTIES OF SETS-XVII
THE COMMANDMENT OF REGULARITY OR THE LEAST IMPORTANT GOON

J. Procrustes demanded that from a set of goons one should be able to choose any subset of them as a sub gang. A strict linear hierarchy can be imposed on this sub gang and the least important goon isolated.
ALTERNATIVELY
Given a nonempty set of goons. A drill master asks some of the goons to 'fall in line' by ascending height. The shortest goon in the line can be isolated.


THE LEAST IMPORTANT GOON IN A GOONGANG





THE PROPERTIES OF SETS-XVIII
THE COMMANDMENT OF CHOICE OR THE 'MAMOOL' OF THE GOON

K. Procrustes demanded that a goon moving into a neighborhood with nonempty neighbors can "wet his beak". He can help himself to exactly one item from each of his nonempty neighbors’ house.


THE GOONS CAN 'WET THEIR BEAKS'





THE PROPERTIES OF SETS-XIX

L. The above Axioms for Acceptable Goons were Verified formally by various demonstrations. Read the history of any ancient civilizations and the set of friendly visitors they had as 'goon' or 'gang of goons' for a real life Example of Verification.


THE CODE FOR ACCEPTABLE & CIVILISED GOONGANGS





THE PROPERTIES OF SETS-XX


Procrustes now claimed by narrowing that the sets following his commandments were all that mattered. They were his rock foundation for mathematics. Any set found violating his commandments could join the Royal Barber in the wilderness of Antarctica and have the penguins for company.



GOONGANGS VIOLATING THE CODE ARE EXPELLED TO THE WILDERNESS




PROCRUSTES TAMES MATHEMATICS


Coming back to the continuum, Procrustes now said by 'narrowing' that what was left of the butchered universe, the 'bunch' of immortal points described by his contortions of integers and sets of integers was all that mattered.


THE BUTCHERED CONTINUUM IS WHAT MATTERS



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ANALYSIS IN THE BED OF PROCRUSTES

He had thus by 'narrowing' reduced the Universe and hence the continuum to computable real numbers, and hence to integers, and hence Analysis was reduced to arithmetic.


ANALYSIS REDUCED TO ARITHMETIC IN THE NEW BED OF PROCRUSTES





MATHEMATICS IN THE BED OF PROCRUSTES

So now he had put the lid on mathematicians & mathematics and reduced everything to Arithmetic.


MATHEMATICS REDUCED TO ARITHMETIC IN THE NEW BED OF PROCRUSTES


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THE SUPPRESSION OF DISSENT


There were some complaints on the way the continuum was butchered, the use of his Proclamation of Commandments for Sets seemed farfetched, and the cavalier treatment of infinity did not go down well in some quarters. However, dissent was put down with a strong hand. The damp, leaking dungeons and the dusty, rusted torture chambers were renovated. They were painted with all the unpleasant colors of the Rainbow. This for housing dissenters of the commandments relating to sets. Multiple instances of straw filled Pits and Pendulums of bamboo shoots were installed and commissioned.




THE RUTHLESS SUPPRESSION OF DISSENT


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THE CANNIBALS ARE EXCITED


The cannibals at the edge of the Empire were excited when they saw the butchered continuum. They asked it to guess correctly as to whether it would be roasted alive or boiled alive.

THE CANNIBALS EYE THE BUTCHERED CONTINUUM




THE CANNIBALS ARE CONFUSED

The Cannibals had a strong lobby, but Procrustes managed to put them into an eternal loop. The army was called out to drive them into the deepest interiors of the Island Continent. They were left to eternally contemplate on the confusion created in their confused minds.


THE CANNIBALS ARE SENT PACKING




PROCRUSTES LAUNCHES THE WORLD WARS


One thing leads to another, perhaps unintended consequences. A hypothetical view can be taken, that this Denial of the continuum and 'narrowing' of infinity, resulted in the human race declaring itself as 'gangs' of supermen out to control gangs of 'super dunces'. The human race merrily rolled downhill for half a century.




THE WORLD IS DESTROYED AND REJUVENATED



PROCRUSTES DEFINES COMPUTATION


Procrustes 'narrowed' the purpose of the Universe to something indulging eternally in 'computation' describable by arithmetic and hence encompassing mathematics.


THE PURPOSE OF THE UNIVERSE IS ARITHMETIC





THE CREATION OF A MONSTER-I


Procrustes had a frightening dream. He was being chased by the monsters Grendel and his family. He ran and ran and ran with the monsters behind him. He fled through the Pampas of South America into the deep Jungles of the mighty Amazon with the monsters right behind him. He sought out Beowulf the Hero who destroyed the monsters and saved him.


THE MONSTER GRENDEL WITH FAMILY




THE CREATION OF A MONSTER-II


Procrustes woke up with a start and created an unspeakable horror called the Turing machine to frighten future generations of naughty children.


THE UNSPEAKABLE HORROR - THE TURING MACHINE

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THE MONSTER AS DR.JEKYLL


A first acquaintance with the Dr Jekyll like machine gave it naive, user friendly toy like characteristics. It seemingly had a kindergarten type vocabulary, literacy and manipulative ability.


THE MONSTERS CREATED BY PROCRUSTES IN THE GUISE OF DR JEKYLL





THE MONSTER ENGAGES ITSELF
OR
THE CHURNING OF THE MILK OCEAN

The monster indulged in simple activities like simulating picking up the Pacific Ocean and transferring it to the Atlantic Ocean.


THE SEARCH FOR THE POT OF NECTAR





THE METHODS OF THE MONSTER
OR
THE POT OF NECTAR IS FOUND

The monster used a thimble to simulate the transfer of water: a thimbleful of water at a time.
It carried on the process for eons of time.

THE POT OF NECTAR FOR IMMORTALITY





THE MONSTER AS MR. HYDE


Procrustes exhibited its true Mr. Hyde character.


THE MONSTERS AS MR HYDE




THE MONSTER AS A SUPERNATURAL
OR
THE MONSTERS SCRAMBLE FOR THE POT OF NECTAR

Procrustes 'widened' the capabilities of his machine by endowing it with immortality, infinite reliability, and the ability to compute eternally, much beyond Odin's feast or Shiva's dance of Death.


THE ETERNAL IMMORTAL MONSTERS




THE MULTI-HEADED MONSTER

It could by metamorphosis convert itself into a multi-headed hydra or a ferocious multi-headed demon descending directly the from myths and legends, of many cultures the world over.


THE MULTIHEADED UNSPEAKABLE HORROR




ARCHIMEDES COUNTS THE HEADS OF THE MONSTER
OR
THE SERPENTS WITH FORKED TOUNGES

The number of heads and their associated tapes could be more than the number of grains of sand Archimedes estimated to be in all the beaches of the world.


THE HEADS AND TAPES CAN BE COUNTED BY ARCHIMEDES




THE BOTTOMLESS PIT OF THE MONSTER

The monster had a digestive system that was a bottomless pit for a never ending, voracious consumption of food.


THE INSATIABLE PIT OF THE MONSTER




THE FOOD OF THE MONSTER

The monster had a very simple staple diet of ink and tape. Take away its ink and the monster would become a simple, well-behaved, regular tamed household toy or dumb pet.


THE STAPLE DIET OF THE MONSTER



THE MONSTER IS ETERNALLY ACTIVE
THE PERPETUAL MOTION MACHINE

The monster did not require any energy for its operation, unlike the voracious demands for power of other computing devices like a Google server farm.


THE PERPETUAL MOTION OF THE MONSTER




THE MONSTER IS A LINGUIST

The monster was comfortable with all the symbols of all languages in the world, past, present and the foreseeable future.


THE LINGUISTIC CAPABILITIES OF THE MONSTER




THE MONSTER AND SYMBOLISM

The monster was comfortable with all the symbols, of all stereotypes, of all the cultures, past, present and the foreseeable future.




THE MONSTER HAS INSATIABLE APPETITE AND TOLERANCE FOR SYMBOLS




THE MONSTER IS A SCHOLAR

The monster had a finite control which could store the entire library of Alexandria, all the libraries of the world, all the information, knowledge and associations of the human race in the past, present and possible future. It could compete with Odin in its thirst for knowledge.


THE SCHOLARLY MONSTER




THE MONSTER CHALLENGES ALL SEARCH ENGINES

The monster could organize, store and retrieve this information from its finite control with a speed surpassing that of light, in fact instantaneously.


THE MONSTERS BEAT ALL SEARCH ENGINES




THE MONSTER AND GOOGLE

The monster should make any Google search engine, past, present or future end up with a strong inferiority complex.


SEARCH ENGINES FEEL INFERIOR TO THE MONSTERS




COOKING FOOD FOR THE MONSTER

Procrustes used 'widening' to allow any entity to be encoded as a symbol or sequence of symbols even if the entity had immortal, eternal or infinite characteristics.



THE VOCABULARY OF THE MONSTER



EDIBLE FOOD FOR THE MONSTER

By 'narrowing' Procrustes demanded the sequence represent a sequence computable by his monsters. He now called these monsters his machines.


THE FOOD OF THE MONSTER



THE MONSTER AS A CANNIBAL

In particular his machines could be encoded as a sequence of symbols.
This sequence could be fed to his machine.


THE MONSTERS ARE CANNIBALS




THE MONSTER SOLVES THE PROBLEMS OF INDUSTRY


Procrustes 'widened' the capabilities of all industries & businesses, of all civilizations and cultures the world over, from cottage industries to MNCs, from supermarkets to grocery stores, by granting them their dreams. By 'widening' he granted them infinite reliability.


THE MONSTERS ARE IDEAL BUSINESS PROPOSITIONS




THE MONSTER AS THE IDEAL CUSTOMER

Industry would find in the Turing machines an eternal captive market of satisfied customers. They can supply tape and ink eternally to these immortal, eternal customers who will never complain.


THE MONSTERS ARE DREAM CUSTOMERS FOR ALL INDUSTRY




THE FINANCES OF INDUSTRY BECOME SOUND

Procrustes 'widened' the capabilities of the environment of his machines to reliably settle the invoices raised by industry & business the world over.


INDUSTRY HAS UNLIMITED POTS OF MONEY




THE COLLECTION AGENTS ARE OUT OF BUSINESS

Industry could do without the use of horrid collection agents who would like to auction the machines for a fat commission.


THE COLLECTION AGENCIES WIND UP




PROCRUSTES DEFINES EFFECTIVE COMPUTATION


Procrustes 'narrowed' the concept of computation to 'effective computation'.






THE CONCEPT OF AN EFFECTIVE PROCEDURE FOR COMPUTATION




MODELS OF EFFECTIVE COMPUTATION

Procrustes took a leaf out of Ovid’s Metamorphoses and demonstrated, for about half a century that his multi-headed hydras of machines, can effortlessly change into many different models of effective computation.






MANY MANY EQUIVALENT UNSPEAKABLE HORRORS OF EFFECTIVE COMPUTATION




THE MODEL FOR EFFECTIVE COMPUTATION

Procrustes declared by 'narrowing' that the concept of 'effective computation' was identical to the capability of his machines.


THE MONSTERS AS DR JEKYLL ARE DECLARED TO BE THE MODEL FOR EFFECTIVE COMPUTATION - CHURCH'S THESIS





THE MONSTERS LOVE THEMSELVES


Procrustes found his machines ended up contemplating their own descriptions, and some of them got into trouble as a result of the same.


THE MONSTERS KEEP ON LOOKING AT THEMSELVES




THE MONSTER CAN REPRODUCE ITSELF


Procrustes found that some of his machines could reproduce themselves.


THE MONSTERS BECOME MORE AND MORE MONSTERS




THE MONSTER OF MONSTERS


Procrustes found that among his machines there was one that could simulate the behavior of any other machine. He called it a Universal Machine.


THE MONSTER OF MONSTERS




THE MONSTER OF MONSTERS
SETS AN EXAMPLE-I


Procrustes announced by 'narrowing' that if anyone had pencil, paper and the ability to simulate the Universal machine one could do all 'mathematics'.


THE MONSTER OF MONSTERS CAN REPLACE ANY MONSTER



THE MONSTER OF MONSTERS
SETS AN EXAMPLE-II


Procrustes announced by 'narrowing' that if anyone had pencil, paper and the ability to simulate the Universal machine one could do all 'computation'.


THE MONSTER OF MONSTERS MODELS COMPUTATION




THE MONSTER OF MONSTERS
SETS AN EXAMPLE-III


Procrustes announced by 'narrowing' that if anyone had pencil, paper and the ability to simulate the Universal machine one could do all 'computation'.
By 'narrowing' one can simulate whatever mattered in the Universe.


THE MONSTER OF MONSTERS SEEMS TO BE THE BOSS OF THE UNIVERSE




THE MONSTER OF MONSTERS
SETS AN EXAMPLE-IV


Procrustes announced by 'narrowing' that if anyone had pencil, paper and the ability to simulate the Universal machine one could do all 'mathematics'.
The mathematicians and mathematics teachers can seemingly be shown the door.


THE MONSTER OF MONSTERS CAN SEEMINGLY SHOW MATHEMATICIANS THE DOOR




THE MONSTERS GET INTO A LOOP
OR
THE FIRST ENCOUNTER WITH INCOMPLETENESS


Procrustes found that when asked to solve some problems in mathematics his machines ended up in a loop, and an eternal beating around the bush sometimes. They did not know when to stop and announce failure.






SOME OF THE MONSTERS END UP IN A LOOP SOMETIMES




THE MONSTERS ARE STUMPED-I
OR
THE MONSTERS ARE SHY


Procrustes found that when asked to solve some problems in mathematics his machines declined to volunteer.







ALL THE MONSTERS RUN AWAY FROM SOME PROBLEMS




THE MONSTERS ARE STUMPED-II
OR
THE SECOND ENCOUNTER WITH INCOMPLETENESS


Procrustes found that when asked to solve some problems in mathematics, the machines one by one declined to solve the same. The problem had no takers.







ALL THE MONSTERS WILL SHY AWAY FROM SOME PROBLEMS




THE MONSTERS ARE STUMPED - III


Procrustes wanted to know why him machines were stumped.
Why when asked to solve some problems in mathematics his machines declined to volunteer.







WHAT IS THE PROBLEM THE MONSTERS HAVE??




THE MONSTER OF ALL MONSTERS LOVES ITSELF
OR
THE FAMILY ASTROLOGER IS CONSULTED


Procrustes found his machines ended up contemplating their own descriptions, and some of them got into trouble as a result of the same. He used 'widening' and equipped the machines with an oracle.


THE ORACLE IS CONSULTED BY THE MONSTERS




THE MONSTERS STILL LOVE THEMSELVES
OR
THE ASTROLOGER IS STUMPED


Procrustes found his machines with an an oracle ended up contemplating their own descriptions, and some of them got into trouble as a result of the same. He used 'widening' and equipped the machines with another oracle.


THE SECOND ORACLE IS CONSULTED BY THE MONSTERS




THE MONSTERS CONTINUE TO LOVE THEMSELVES


Procrustes found his new machines with two oracles still ended up contemplating their own descriptions, and some of them got into trouble as a result of the same. He used 'widening' and equipped the machines with yet another oracle.


THE THIRD ORACLE IS CONSULTED BY THE MONSTERS




THE MONSTERS KEEP ON LOVING THEMSELVES
OR
HIERARCHIES OF ASTROLOGERS ARE STUMPED


Procrustes found his machines with three oracles still ended up contemplating their own descriptions, and some of them got into trouble as a result of the same. He used 'widening' and equipped the machines..........




HIERARCHIES OF ORACLES ARE CONSULTED BY THE MONSTERS




PROCRUSTES CONSULTS ORACLE AFTER ORACLE
HIERARCHIES OF UNDECIDABILITY

Procrustes then used 'widening' and equipped the machines with another oracle. He then used 'widening' and equipped the machines with yet another oracle. He then used 'widening' and equipped machines .........




HIERARCHIES OF ORACLE MONSTERS ARE 'STUMPED'




THE FINAL SOLUTION

Procrustes announced that now he had his tool of mathematics to explain the Universe by simulation.



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PROCRUSTES WANTS A MEDAL


Procrustes declared his contraption to be the greatest intellectual achievement of not only the century, but for all time throughout eternity.





THE ACHIEVEMENT OF THE CENTURIES

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PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - I
THE MONSTERS RUN AMUCK

Procrustes faced a problem. The Monsters were all over the Empire. It was worse than the Jurassic Park with all types and sizes of Dinosaurs.


THE MONSTERS CREATED BY PROCRUSTES ARE TOO NOISY AND UNRULY






PROCRUSTES FACES THE INVASION OF THE OMEGAS - I
ENTER THE GRAND WIZARD OF OMEGAS

The 'racket' created by the Monsters woke up the Spirit of Diophantus, an ancient Mathematician.
He complained to the Grand Wizard of the Omega tribe that his repose was disturbed.
This was a primitive tribe deep inside the Jungles of the Mighty Amazon river.
The Grand Wizard of the Omega tribe consulted all the oracles in sight.





HIERARCHIES OF ORACLE MONSTERS ARE CONSULTED BY THE GRAND WIZARD OF OMEGAS





PROCRUSTES FACES THE INVASION OF THE OMEGAS - II
THE INVASION OF THE OMEGAS

The Grand Wizard of the Omega tribe sent an army of ferocious monsters called Omegas, Super Omegas, Super Super Omegas, Super...Super Omegas to attack the Monsters created by Procrustes.

THE HORRID OMEGA AND SUPER OMEGA MONSTERS ATTACK





PROCRUSTES FACES THE INVASION OF THE OMEGAS - III
THE MONSTERS ARE NO MATCH FOR THE OMEGAS

The horrid Omegas could not be tackled. Procrustes found his Monsters running up and down the Pampas of South Americas chased by the Omegas. The rushed across the Andes into ancient Chile. They appealed desperately to the Ancient Inca civilization for help.
The Wizards of the Incas informed Procrustes that the Omegas and Super Omegas were mathematical problems that his Monsters could not tackle. However they gave the Monsters some oracles to combat the Omegas and Super Omegas.
A fierce war broke out but the Super Omegas aided by Conquistadors had the upper hand. The Monsters crossed the Pacific Ocean in a raft and ended up in the Land of Oz.
They appealed to the Wizard of Oz for help.



THE WARS OF THE MONSTERS





PROCRUSTES FACES THE INVASION OF THE OMEGAS - IV
THE MONSTERS ARE GIVEN ORACLES

The Wizard of Oz consulted to Wizard of the Maoris’. He explained to Procrustes that the Omegas and their tribe were problems in Mathematics that the Monsters could not handle. He suggested that the Monsters be equipped with oracles.
This helped the Monsters tackle some of the Omegas and Super Omegas.
The Monsters still could not tackle the Super Omegas which chased the Monsters to Egypt.



THE FIERCE & HORRID OMEGA AND SUPER OMEGA MONSTERS



THE MONSTERS CREATED BY PROCRUSTES ARE FRIGHTENED






PROCRUSTES FACES THE INVASION OF THE OMEGAS - V
THE MONSTERS ARE GIVEN ORACLES

In Egypt there was the Sphinx. This was a monster which was half a lion and half a woman.
The Sphinx helped the Monsters combat the Super Omegas by giving the Monsters some more oracles. The Super Omegas destroyed the Sphinx and it was converted to stone.
Before being destroyed the Sphinx advised Procrustes to 'throw' the remaining Omegas and Super Omegas into the Bottomless Pit. They represented mathematical problems that were beyond the capabilities of his Monsters.



THE ADVICE OF THE SPHINX WAS TO SEND THE OMEGAS TO THE BOTTOMLESS PIT




THE END OF THE FIERCE & HORRID OMEGA AND SUPER OMEGA MONSTERS





PROCRUSTES FACES THE INVASION OF THE OMEGAS - VI
THE SUPER OMEGAS ARE DESTROYED

Procrustes used 'narrowing' and threw the Super Omegas into the Bottomless Pit.
They represented 'hordes' of problems in mathematics that the Monsters could not solve. They were all encounters with the Incompleteness of Mathematics.
Procrustes declared by 'narrowing' that Mathematics as defined by his Monsters was all that mattered.
By Imperial Proclamation the Omegas, Super Omegas and their tribe were declared nonexistent and irrelevant.



THE MONSTERS CREATED BY PROCRUSTES ARE SAVED






PROCRUSTES FINDS HIS MONSTERS CELBRATING THEIR VICTORY
THE MONSTERS ARE NOISY

The Monsters celebrated their victory over the Omegas and Super Omegas. They ran wild all over the Empire, consuming a lot of ink and tape in their wild parties.
They had run amuck in their noisy celebrations.
They declared they were Supreme.



THE MONSTERS CREATED BY PROCRUSTES BECOME TERRIBLY NOISY






PROCRUSTES FINDS HIS MONSTERS HAVE BAD EATING HABITS - I
THE MONSTERS ARE GREEDY

The Comptroller and Auditor General of the Empire complained about the cost of feeding the Monsters. The Imperial treasury was being drained. The economy was facing a collapse.



THE MONSTERS WERE RUINING THE ECONOMY WITH THEIR EATING HABITS






PROCRUSTES FINDS HIS MONSTERS HAVE BAD EATING HABITS - II(a)
A MONSTER IS ON HUNGER STRIKE
THE EMPTINESS PROBLEM

Procrustes dated a Monster chosen randomly. They went out to eat. He found he could not determine beforehand in a finite amount of time whether the Monster would eat anything at all or was on a hunger strike and would eat nothing.



DATING A MONSTER: WILL THE MONSTER EAT ANYTHING AT ALL?





PROCRUSTES FINDS HIS MONSTERS HAVE BAD EATING HABITS - II(b)
WILL A MONSTER EAT THE DISH SERVED TO IT?
THE MEMBERSHIP PROBLEM

Procrustes dated a Monster chosen randomly. They went out to eat. He found he could not determine beforehand in a finite amount of time whether the Monster would eat the dish given to it.



DATING A MONSTER: WILL THE MONSTER EAT WHAT IT IS SERVED?






PROCRUSTES FINDS HIS MONSTERS HAVE BAD EATING HABITS - III
A MONSTER IS ENORMOUSLY HUNGRY
DOES A MONSTER EAT AN INFINITE NUMBER OF DISHES?

Procrustes dated a Monster chosen randomly. They went out to eat. He found he could not determine beforehand in a finite amount of time whether the Monster would eat an enormous amount, an infinite variety of things and run up a huge bill.



DATING A MONSTER: WILL THE MONSTER RUN UP AN INFINITE BILL?





PROCRUSTES FINDS HIS MONSTERS HAVE BAD EATING HABITS - IV
A MONSTER IS A GLUTTON
WILL THE MONSTER EAT UP EVERTHING AND ANYTHING?

Procrustes dated a Monster chosen randomly. They went out to eat. He found he could not determine beforehand in a finite amount of time whether the Monster would eat everything in sight and run up a huge bill.



DATING A MONSTER: WILL THE MONSTER EAT EVERYTHING IN SIGHT?





PROCRUSTES FINDS HIS MONSTERS HAVE BAD EATING HABITS - V
A MONSTER DEMANDS 'MORE'
WILL THE MONSTER STOP EATING SOME TIME?

Procrustes dated a Monster chosen randomly. They went out to eat. He found he could not determine beforehand in a finite amount of time whether the Monster would eat everything in the menu and 'demand more' or be satisfied with what was in the menu.



DATING A MONSTER: WILL THE MONSTER DEMAND 'MORE' LIKE OLIVER TWIST?




PROCRUSTES FINDS HIS MONSTERS HAVE BAD EATING HABITS - II(c)
A MONSTER IS ON HUNGER STRIKE
THE EQUIVALENCE PROBLEM

Procrustes dated two Monsters chosen randomly. They went out to eat. He found he could not determine beforehand in a finite amount of time whether the Monsters would eat the same dishes.



DATING TWO MONSTERS: WILL THE TWO MONSTERS EAT THE SAME DISHES?





PROCRUSTES FINDS HIS MONSTERS HAVE BAD EATING HABITS - II(d)
A MONSTER IS ON HUNGER STRIKE
THE CONTAINMENT PROBLEM

Procrustes dated two Monsters chosen randomly. They went out to eat. He found he could not determine beforehand in a finite amount of time whether one Monster would eat at least the same dishes as the other Monster.



DATING TWO MONSTERS: WILL A MONSTER EAT AT LEAST THE SAME DISHES AS THE OTHER ONE?






PROCRUSTES FINDS HIS MONSTERS HAVE BAD EATING HABITS - VI
ENTER A SAGE NAMED RICE

Procrustes was educated by a Sage that only trivial things about Monsters can be determined beforehand in a finite amount of time. This pertains to questions concerning all Monsters or no Monsters.



DATING A MONSTER: ONLY THE EATING HABITS OF ALL MONSTERS OR NO MONSTER CAN BE DECIDED






PROCRUSTES FINDS HIS MONSTERS HAVE BAD EATING HABITS - VII
ENTER RICE'S THEOREM

Procrustes was educated by a Sage that any nontrivial trivial thing about Monsters cannot be determined beforehand in a finite amount of time. This pertains to questions concerning some of the Monsters only.
It was thus not possible to budget the cost of what the unruly Monsters would eat.



DATING A MONSTER: THE EATING HABITS OF ONLY SOME OF THE MONSTERS CANNOT BE DECIDED






PROCRUSTES FINDS THE DEVIL’S ADVOCATE FOR THE MONSTERS-1!!

Procrustes was educated by a Sage that in real one finds it difficult to enumerate the good qualities of other people. It is far easier to be negative and enumerate the bad invalid qualities. Being the Devils’ Advocate is a far easier job than the job of advocating Deification.


THE MONSTERS HAVE THEIR DEVIL'S ADVOCATE






PROCRUSTES FINDS THE DEVIL’S ADVOCATE FOR THE MONSTERS-2!!
NO MAN CAN SERVE TWO MASTERS

The same applies to the Monsters.The invalid computations of a Monster are easy to describe. The valid computations are very difficult to describe. For the valid computations of a Monster to be described one has to jointly check that two or more simple codes of conduct are simultaneously adhered to. This means two or more pliable Masters must be simultaneously served.
As the proverb says-“No man can serve two Masters”. Serving two conflicting Masters will have disastrous effects.


THE MONSTERS HAVE THEIR DEVIL'S ADVOCATE






PROCRUSTES FINDS THE DEVIL’S ADVOCATE FOR THE MONSTERS-3!!

A lot of problems the Monsters cannot decide in a finite time can be related to the problem the Monsters have in serving two or more pliable Masters simultaneously. Alternatively this is like demanding that the Monsters adhere to two or more different simple codes of conduct simultaneously.
If one pliable Master is satisfied the other may end up as a Devil's Advocate.


THE MONSTERS HAVE THEIR DEVIL'S ADVOCATE





PROCRUSTES FINDS THE DEVIL’S ADVOCATE FOR THE MONSTERS-4!!
THE POWER OF THE DEVIL'S ADVOCATE

In fact ALL the problems the Monsters cannot decide in a finite time can be related to the problem the Monsters have in serving two or more pliable Masters simultaneously. Alternatively this is like demanding that the Monsters follow two or more different simple codes of conduct simultaneously.
If one pliable Master is satisfied the other may end up as a Devil's Advocate.


THE MONSTERS HAVE THEIR DEVIL'S ADVOCATE




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - II
THE MONSTERS HAD TO DO SOMETHING USEFUL

Procrustes was summoned by the Parliament and asked to see that the Monsters do something Useful instead of just gobbling up tape and ink at enormous expense to the Empire and the Imperial Treasury.







THE MONSTERS SHOULD DO SOMETHING USEFUL LIKE HERCULES




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - III
THE MONSTERS SHOULD DO SOME USEFUL THINGS

Procrustes was given suggestions as to what his Monsters could do.
One solution was to put the Monsters down to work building Pyramids for all the Courtiers and their families, as in Ancient Egypt.
An alternative was to make Terracotta Soldiers and Terracotta Citizens of all the soldiers and citizens of the Empire.
Another alternative was to build a series of Great Walls around the Empire to keep the Cannibals out.
They could tackle problems like the Human Genome project or continue the work of Alchemists of converting base metals to gold efficiently and so on.






THE MONSTERS SHOULD DO SOMETHING USEFUL TO JUSTIFY THEIR EXPENSE




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - IV
THE CENSUS OF THE MONSTERS IS INITIATED

He was ordered by the Parliament to take a Census of the Monsters. All of them had to be Enumerated and their Capabilities determined and Recorded.



THE MONSTERS SHOULD BE ENUMERATED AND ASSIGNED SOME USEFUL TASK




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - V
THE CENSUS OF THE MONSTERS IS INITIATED

Procrustes formed Census Committees consisting of groups of Mathematicians. One group was created for each Model of Effective Computation, i.e. a variety of Monsters.
The group was ordered by the Parliament to take a Census of the Monsters. All of them had to be Enumerated and their Capabilities determined and Recorded.
In case of doubt they had to refer to Procrustes who told them, "I will decide who is a Monster around here!!".



THE CENSUS OF THE MONSTERS STARTS



PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - V(b)
THE CENSUS OF THE MONSTERS IS UNDERWAY

Procrustes declared that he was the Head of the Unique Identification Authority.
Every bona-fide Monster in the Empire would be given a Unique ID. This ID could be used to record the capabilities of the Monsters and then they could be put down to work.



THE CENSUS OF THE MONSTERS - UNIQUE IDENTIFICATION




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - VI
THE CENSUS OF THE MONSTERS RUNS INTO TROUBLE
THE PROCEDURES CAN BE EFFECTIVELY ENUMERATED

His committees found that while they could enumerate all the Monsters, they could not determine the Useful Ones. They could not decide when any Monster would Stop Eating and Start Working. They could not decide when any Monster would "Stop Talking and Start Working".
He reported the matter to Parliament and was ordered to take a Census of the 'Useful' Monsters only.
All of them had to be Enumerated and their Capabilities determined and Recorded.



ALL THE MONSTERS CAN BE ENUMERATED-INCLUDING THE USELESS ONES




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - VII(a)
THE CENSUS OF THE MONSTERS RUNS INTO TROUBLE
THE ALGORITHMS CANNOT BE EFFECTIVELY ENUMERATED

His committees found that any Census Strategy to enumerate all the Useful Monsters failed. Some Useful Monster escaped enumeration.
They could not decide when any Monster would Stop Eating and Start Working. They could not decide when any Monster would "Stop Talking and Start Working".
This was as in realife. Any attempt at a Unique Identification of the population will find some persons who will, 'not file the first tax return' or 'not open the first bank account' or 'will escape any Unique Identification Scheme'. These persons evade the tax net and the prying, victimizing eyes of the State.
He reported the matter to Parliament and was ordered to take a Census of the 'Useful' & 'Well-behaved manageable' Monsters only.
All of them had to be Enumerated and their Capabilities determined and Recorded.



THE USEFUL MONSTERS ALONE CANNOT BE ENUMERATED




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - VII(a)
THE CENSUS OF THE MONSTERS RUNS INTO FURTHER TROUBLE
THERE EXITS A TAX EVADER FOR ANY TECHNIQUE
THERE EXISTS A MONSTER THAT CANNOT BE GIVEN A UID

His committees found that any Census Strategy to enumerate all the Useful Monsters failed. Some Useful Monster escaped enumeration regardless of enumeration technique used.
It could be shown that any enumeration technique will fail. It will show some Useful Monster that is outside the enumeration.
In any enumeration technique some Useful Monster can be demonstrated that does not get a Unique Identification Number(UID).
He reported the matter to Parliament and was ordered to take a Census of the 'Useful' & 'Well-behaved manageable' Monsters only.
All of them had to be Enumerated and their Capabilities determined and Recorded.



A MONSTERS PLAYS 'HOOKEY'




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - VII(c)
THE CENSUS OF THE MONSTERS RUNS INTO DEEP TROUBLE
THERE IS A 'IDEAL' TAX EVADER WHO CAN NEVER BE CAUGHT
THERE EXISTS A NUMBER OF FINITE PRECISION THAT CAN NEVER BE DESCRIBED

His committees found that any Census Strategy to enumerate all the Useful Monsters failed.
There existed some Useful Monster that can be demonstrated to exist but can never be isolated and given a Unique ID.
Even if an oracle or astrologer is used it cannot be isolated.
Even if a finite hierarchs of oracles or astrologers are used it cannot be isolated.
Even is an infinite hierarchy or oracles or astrologers are used it cannot be isolated or described.
In other words there will always be a Tax Evader in any scheme of Tax Collection, even with hierarchies of astrologers, who is known to exist, but can never be described or isolated. There is no ideal Tax Net.
In other words the grey market can never be fully eradicated. It will always contain a member, who is known to exist, but can never be described or isolated. There will always be a Swiss Bank or its equivalent.
He reported the matter to Parliament and was ordered to take a Census of the 'Useful' & 'Well-behaved manageable' Monsters only.
All of them had to be Enumerated and their Capabilities determined and Recorded.



THERE IS A MONSTER THAT ESCAPES ENUMERATION




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - VII(d)
THE CENSUS OF THE MONSTERS RUNS INTO DEEP TROUBLE
THERE EXISTS A USEFUL MONSTER THAT CANNOT BE ISOLATED OR DESCRIBED
THERE EXISTS A NUMBER OF FINITE PRECISION THAT CAN NEVER BE DESCRIBED

His committees found that any Census Strategy to enumerate all the Useful Monsters failed.
There existed some Useful Monster that can be demonstrated to exist but can never be isolated.
Procrustes declared by 'widening' that this showed the limitations of all Dictators. No program or method by any Dictator can eradicate life or the human spirit.
Even if an oracle or astrologer is used it cannot be eradicated.
Even if a finite hierarchs of oracles or astrologers are used it cannot be isolated and eradicated.
Even is an infinite hierarchy or oracles or astrologers are used it cannot be isolated and eradicated.
He concurred with James Thurber's The Last Flower, and declared that there will always be 'One Man, One Woman and One Flower' that can never be described, isolated and destroyed.
He reported the matter to Parliament and was ordered to take a Census of the 'Useful' & 'Well-behaved manageable' Monsters only.
All of them had to be Enumerated and their Capabilities determined and Recorded.



THERE EXISTS AN EVASIVE MONSTER




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - VIII
ENTER THE GRAND SAGE OF COMPLEXITY

Procrustes was at a loss as to how to proceed.
A wise old courtier advised him that in the Baltic States there was a Grand Sage of Complexity. In ancient times he had studied and classified the Complexities and Capabilities of all the Baltic Monsters. Even Homer had made references to this in the Iliad which had its origin in the Baltic States.
He should follow the fable of The Fox and the Crow carefully. If in all humility he petitions the Grand Sage of Complexity he would receive the directions to prepare porridge. When consumed hot this porridge would give him the Courage and Wisdom to face all Monsters throughout Eternity.
The Wizard of Oz had used this porridge effectively to give courage to the Cowardly Lion.


THE HORRID BALTIC MONSTERS



THE MONSTERS SHOULD BE CLASSIFIED




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - IX
THE GRAND SAGE OF COMPLEXITY EDUCATES PROCRUSTES

Procrustes sent a messenger to the Baltic States, in sack cloth and ashes, and humbly petitioned the Grand Sage of Complexity for a solution to his problem.
He obtained the ingredients and directions required to prepare the magic porridge. He prepared a bowl of porridge but found that with his limited capabilities, he could consume only a few spoonfuls of it.
He now suddenly found himself full of knowledge and courage to tackle all Monsters.



PROCRUSTES CONSUMES THE MAGIC PORRIDGE




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - X
THE MONSTERS ARE A BIZARRE LOT

Procrustes considered the Monsters with his new Wisdom and Insight gained from consuming the magic porridge.
He saw that the Monsters were an unruly, uncivilized bizarre lot. Some believed in breaking an egg at the Big End, some at the Small End and some in the center. Some swallowed it whole. They had no standard, no discipline, no Code of Conduct.
Given enough time some Monster who was a slow coach could do things that a busy beaver Monster cold not do.
The first step would be to Standardize the Monsters with a Code of Conduct.



THE MONSTERS NEED A CODE OF CONDUCT





PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - X(b)
THE MONSTERS THAT WILL NEVER HALT ARE EXPELLED

Procrustes considered the Monsters with his new Wisdom and Insight gained from consuming the magic porridge.
He had legions of Dog Catchers in the Empire retrained as Monster Catchers. A Committee was formed to use the help of the Universal Monster and an Oracle to determine the Monsters that always keep Talking and never get down to Working. They were to be caught and thrown out of the Empire.



THE MONSTERS THAT WILL NEVER WORK ARE PACKED OFF




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - X(c)
THE MONSTERS HAVE A DRESS AND BEHAVIOURAL CODE

Procrustes considered the Monsters with his new Wisdom and Insight gained from consuming the magic porridge.
He had a Code of Conduct drawn up for the Monsters that would terminate sometime. How they were to look, and what they should do in some situation was all standardized.
The old method of using multiple tapes, with multiple heads in all directions was banned.



THE MONSTERS HAVE A DRESS CODE & ARE SENT TO A BEAUTY PARLOR




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS -XI
THE SPEED UP AND TAPE REDUCTION THEOREMS

Procrustes determined that if a Monster is consuming a Mountain of Food in chunks of some size, the Monster could be made to consume the food in larger chunks. He called it the Speed Up Theorem. The Monster could consume the food faster, in a fewer number of munches.
Procrustes determined that if a Monster is consuming a Mountain of Food, the Mountain can in reduced in size like concentrated food. After a lot of concentration only a pill size food has to be consumed. He called this the Tape Reduction Theorem.
What actually mattered was the 'intrinsic' purpose of the Monster's activity.


THE HARE OBJECTS TO THE SPEEDUP AND TAPE REDUCTION THEOREMS AND IS SUPPRESSED




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XII
THE MONSTERS FOR TIME AND SPACE COMPLEXITY

Procrustes considered the Monsters with his new Wisdom and Insight gained from consuming the magic porridge.
If the authorities wanted to know about the number of munches a Monster would take to polish off a mountain of food, then its user interface and behavior in any situation had to follow a Code of Conduct for Munches.
If the authorities wanted to know about the sizes of the munches a Monster would take to polish off a mountain of food, then its user interface and behavior in any situation had to follow a Code of Conduct for Munch Sizes.



THE DRESS CODES & THE BEAUTY PALOR




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XIII
THE INTRINSIC WORTH OF A MONSTER

Procrustes considered the Monsters with his new Wisdom and Insight gained from consuming the magic porridge.
He had four Merchants of Commerce visiting him.
The Gold Merchant advised him to purchase a small nugget of gold with his Piggy Bank.
The Silver Merchant advised him to purchase a brick of silver with his Piggy Bank.
The Copper Merchant advised him to purchase a big pot of copper with his Piggy Bank.
The Lead Merchant advised him to purchase a small hillock of lead with his Piggy Bank.






THE CONCEPT OF INTRINSIC VALUE




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XIV
THE INTRINSIC WORTH OF A MONSTER(revisited)

Procrustes was advised by a Wise Courtier that he should not be carried away by First Impressions.
He should consider the long term effects of his investments.
With inflation only the intrinsic value matters. The gold nugget will overtake the silver brick in the long run.
The silver brick will overtake the big pot of copper in the long run.
The big pot of copper will overtake the hillock of lead in the long run.
He should see that in the very long run only the intrinsic value matters.






THE CONCEPT OF INTRINSIC VALUE




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XV
THE INTRINSIC WORTH OF A MONSTER(revisited again)

Procrustes decided to keep his Piggy Bank as Cash.
He applied the concept of intrinsic worth to the Monsters.
He announced that the intrinsic worth comes from the Problem and not from the Monster.






THE INTRINSIC VALUE OF THE MONSTER ALONE MATTERS




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XVI
THE WELL-BEHAVED FUNCTIONS

Procrustes formed a Committee of Mathematicians to determine the intrinsic difficulty of functions.
The committee suggested that one need not consider all functions, as some of them are notoriously ill-behaved and like the monsters are a bizarre lot.
One should standardize on well-behaved functions, which have nice aesthetic behavior. More the input the bigger the output becomes and this goes on and on. Also the functions are what generations of mathematicians have considered well-behaved.



THE WELL-BEHAVED MONSTERS




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XVI
THE INTRINSIC WORTH OF A MONSTER(revisited again)

Procrustes had a Proclamation made that all Monsters whose behavior was ill-behaved would be caught by the Monster-catchers and expelled from the Empire.
Given a mountain of food to consume a Monster would be studied. If it does not finish its consumption within the limits predicted by a well-behaved function it will be expelled from the Empire.



THE ILL-BEHAVED MONSTERS SHOULD BE EXCLUDED




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XVII
THE ARGUMENTS OF THE HARE -I

Procrustes had a dream that he was confronted by a Hare.
The Hare found fault with the concept of well-behaved functions.
Everything the Hare claimed had a Beginning, Middle and an End.
For small amounts of food or input sizes a Monster may behave in one way, like a child, as something in the Beginning.
For medium amounts of food or input size a Monster may behave in another way, like a grown up, as something in the Middle.
For very large amounts of food or input size a monster may behave in another way, like a person in old age, as something in the End.
One cannot classify the behavior of a Monster throughout its life in a Uniform Way by a well-behaved function.




THE HARE OBJECTS TO THE ASYMPTOTIC CONCEPT




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XVIII
THE ARGUMENTS OF THE HARE - II

Procrustes was confronted by the Hare.
The Hare pointed out that for small amounts of food or input sizes Monsters will behave in a strange way. This is how well-behaved functions are. For small inputs an inefficient way of doing things is better. One does not fly around in one's house in a helicopter, one walks. One runs to the park, one does not take a rocket to cover the small distance.
It is not possible to extrapolate behavior when the amount of food or input size fills up the solar system or become vanishingly small. So there is an error in assuming that "the good days will last forever" or that "the bad days will never end".

The Hare quoted in support of its point of view from an ancient Nursery Rhyme....
This is the way the ladies ride: clippety, clippety, clop
This is the way the gentlemen ride: trippety, trippety, trot
This is the way the farmer rides: bumpety, bumpety, bump
This is the way the huntsman rides: a gallop,....., a gallop, over the hedge and into the ditch!

The Hare threaded to descend to the Empire and complain to the Emperor that Procrustes was all bogus.




THE HARE CLAIMED THAT FUNCTIONS COLLAPSE AFTER SOME POINT




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XIX
THE HARE IS PUNISHED

Procrustes had the Hare punished. It was banished to join the Tortoise.
The Hare and the Tortoise were condemned to eternally race with each other.






THE HARE & THE TORTOISE ARE PUNISHED: THEY HAVE TO ETERNALLY RACE WITH EACH OTHER




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XX(a)
THE DISCOVERY OF COMPLEXITY CLASSES

Procrustes learnt that the Grand Sage of Complexity had determined that Monsters whose behavior is restricted to well-behaved functions are a very decent lot when compared to the entire class of Monsters.
The fall into complexity classes like rings of asteroids, or planets with moons, orbiting around the Sun.
These complexity classes are like the energy levels of electrons in the nucleus of an atom.
The complexity classes are like the great Periodic Table of Chemistry to classify the chemical elements.




THE WELL BEHAVED MONSTERS FALL INTO COMPLEXITY CLASSES




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XX(b)
THE COMPLEXITY CLASSES EXPLAINED

Procrustes learnt that the Grand Sage of Complexity had determined that Monsters whose behavior is restricted to well-behaved functions are a very decent lot when compared to the entire class of Monsters.
An example is when the abilities of some children are to be classified as per some activity.
The activity can be how good is the child at playing 'hooky', how good it the child in 'hooking doughnuts', how good the child is in Reciting Poetry, or how good is child is in playing Hide and Seek.
A good grading system is like placing the child in various classes properly. No child should fall between two grades. Every child should fit 'snugly' into some class.
The children fall into complexity classes like belts of asteroids around the Sun.



THE MONSTERS ARE CLASSIFIED




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XX(c)
THE COMPLEXITY CLASSES FURTHER EXPLAINED

Procrustes learnt that the Grand Sage of Complexity had determined that Monsters whose behavior is restricted to well-behaved functions are a very decent lot when compared to the entire class of Monsters.
Another example will be the classification of 'Ducks'.
First the bonafide 'Ducks' that are well-behaved are isolated as per the rule: If something looks like a 'Duck', walks like 'Duck' and quacks like a 'Duck' then it is a 'Duck'.
A classification scheme then is imposed on the 'Ducks' following 'well-defined' uniform criteria for judging. They are classified as 'Super Ducks', 'Regular Ducks', and 'Dumb Ducks'.
The three classes are distinct and no 'Duck' falls between the classes. Thus there are gaps between the classes. The classification is "Perfect".
The well-behaved Monsters thus fall into complexity classes with large gaps between classes. No well-behaved Monster falls between in gaps between the classes.



THE MONSTERS: SUPER DUCKS-GAP-REGULAR DUCKS-GAP-DUMB DUCKS




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XX(d)
THE COMPLEXITY CLASSES FURTHER EXPLAINED

Procrustes learnt that the Grand Sage of Complexity had determined that Monsters whose behavior is restricted to well-behaved functions are a very decent lot when compared to the entire class of Monsters.
Another example will be the classification of 'Gooses' which are related to many practical problems.
First the bonafide 'Gooses' that are well-behaved are isolated as per the rule: If something looks like a 'Goose', walks like 'Goose' and quacks like a 'Goose' then it is a 'Goose'.
A classification scheme then is imposed on the 'Gooses' following 'well-defined' uniform criteria for judging. They are classified as 'Super Gooses', 'Regular Gooses', and 'Dumb Gooses'.
The three classes are distinct but some 'Goose' falls between the classes. Thus there are no gaps between the classes. The classification is "Perfect".
The well-behaved Monsters thus fall into complexity classes with perhaps large gaps between classes.



THE MONSTERS: SUPER GOOSES- gooses - REGULAR GOOSES - gooses - DUMB GOOSES




PROCRUSTES HAS PROBLEMS WITH THE MONSTERS - XXI
THE CENSUS COMMITTEES ARE HAPPY

Procrustes by 'narrowing' had the duties of the Census Committees of the Monsters modified. They were only to consider Monsters as per some well-behaved function or some Complexity Class.
The Census of the Monsters was now easy once a Complexity Class is defined.
A Bouncer was created to expel Monsters that did not behave as predicted by the well-behaved functions in the Complexity Class. This was just as in the Pub or the Ctrl+Alt+Del to terminate a computation.



THE MONSTERS SHOULD BLOOM IN THE CLASS WHERE THEY ARE PLANTED




PROCRUSTES DETERMINES COMPLEXITY CLASSES - I
THE CLASS P

Procrustes by 'narrowing' identified some Complexity Class which he said stood out.
He concentrated on Monsters which do not have any choice as to what to do in any situation.
He considered the Complexity Class associated with finding the shortest path from one's house to a selected Pub in the world.
An associated problem is finding the shortest distances to all the Pubs in the world form one's house.
Another associated problem is finding the shortest distances between all pairs of Pubs in the world, to enable easy 'Pub Hopping'.
A Monster capable of doing this job 'well' he called a Champion of the Gold Class.
In the terminology of the classification of 'Gooses' these are the 'Super Gooses'.
The Monster solving the problem 'easily' is called a TRACTABLE Monster.



THE POPULAR GOLD CLASS TRACTABLE MONSTERS




PROCRUSTES DETERMINES COMPLEXITY CLASSES - II
THE INTRACTABLE CLASS

Procrustes by 'narrowing' identified some Complexity Class which he said stood out.
He concentrated on Monsters which do not have any choice as to what to do in any situation.
He considered the Complexity Class associated with finding all the paths from a child's to school via the parks, the malls, the zoo(s), the movie theatres etc. etc. on the way.
He announced that a Monster capable of doing this job 'well' would be called a Champion of the Silver Class. It is not as clever as a Monster of the Gold Class.
In the terminology of the classification of 'Gooses' these are the 'Regular Gooses'. However there are "Gooses" between the "Regular Gooses" and "Super Gooses"
The Monster solving the problem 'properly' is called an INTRACTABLE Monster.



THE UNPOPULAR SILVER CLASS INTRACTABLE MONSTERS




PROCRUSTES DETERMINES COMPLEXITY CLASSES - III
THE seemingly INTRACTABLE CLASS

Procrustes by 'narrowing' identified some Complexity Class which he said stood out.
He concentrated on Monsters which do not have any choice as to what to do in any situation.
He considered the Complexity Class associated with transporting the Mountain of Gold that Big Jim and Charlie Chaplin found in The Gold Rush.
A Monster is to determine the 'minimum' number of sacks of 'fixed' size required to transport the Mountain of Gold.
All Monsters that have been attempted for the purpose or similar purposes over countless centuries, by geniuses, by the hoi polloi, by people from all walks of life have ended up being Champions of the Silver Class.
It is not known if a Monster that is Champion of the Gold Class can solve the problem or cannot solve the problem.
It is not known if we will ever know the answer to problem.
All attempts to solve the problem turn out to cost much much more that the value of the Mountain of Gold itself.
In the terminology of 'Gooses' the problem seem to be seemingly that of a 'Regular Goose' but it is suspected that a 'Super Goose' exists that can solve the problem.
Birdwatchers are searching for the 'Super Goose' which can solve the problem but it is elusive, and it is not known whether it exists in the first place. It is not even known whether it will ever be known that it 'exists' but the birdwatchers will never find it. It may be that it 'exists' but it can never be sighted.
The Monster solving this problem is called a seemingly INTRACTABLE Monster.




THE SEEMINGLY INTRACTABLE MONSTERS THAT SHOULD BE CIVILISED



PROCRUSTES DETERMINES COMPLEXITY CLASSES - IV
THE horribly INTRACTABLE CLASS

Procrustes by 'narrowing' identified some Complexity Class which he said stood out.
He concentrated on Monsters which deal with Search. Combinations of Search patterns or Search strings in a Search Engine are required, where they must satisfy some of the patterns/ strings and 'not' satisfy some patterns/strings.
The resulting Search results require a horribly inefficient Monster.
He called a Monster computing the result a Champion of the Copper Class.
In the terminology of 'Gooses' the problem requires a 'Dumb Goose' which will slave for eons of time.
The resulting Monster solving the problem is said to provably INTRACTABLE.



A CLASSIFICATION


TRACTABLE

SEEMINGLY TRACTABLE

INTRACTABLE

HORRIBLY INTRACTABLE


THE COMPLEXITY CLASSES OF SOME INTEREST



PROCRUSTES SAYS HE'S DONE AND WANTS A MEDAL


Procrustes declared his contraption(s) to be the greatest intellectual achievement of not only the century, but for all time throughout eternity.
Mathematics and mathematicians can be shown the door. They can be replaced by Universal Monster of Monsters. These in turn can be replaced by a child scribbling 'systematically' with pencil and paper. This in its turn can be replaced by a child systematically 'whitewashing a fence', and finally, this could be replaced by a child 'systematically' playing on the beaches of the world with a stick in hand.
Ultimately what is required is as per James Thurber's The Last Flower - one man, one woman, one flower and one child 'systematically scribbling' with a stick on the beaches of the world.
He sent a message to the Prime Minister that he was prepared to present his results to the Emperor in Open Court and wanted a Big Prize.



PROCRUSTES SUMMARISES HIS ACHIVEMENTS



THE UNIVERSAL MONSTER OF MONSTERS RULES


UNIVERSAL COMPUTATION - CHILD WITH PENCIL AND PAPER


UNIVERSAL COMPUTATION - WHITEWASHING A FENCE


REJUVENATING UNIVERSAL COMPUTATION - THE LAST FLOWER


PROCRUSTES WANTS A BIG PRIZE

METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS
METAMATH EMATICS









PART II
"IT WAS THE WORST OF TIMES"


PROCRUSTES IS GIVEN A PRIZE
The Emperor took the advice of Obelix the Gaul his childhood mathematics peer and classmate. He presented a very large block of the finest Italian marble to Procrustes.
As a prize Procrusteswas allowed to personally carve a "PERFECT" statue of himself.
He was commanded to exhibit the result along with his "PERFECT" statue in the Court in a short span of a few decades of time.

THE PRIZE



PROCRUSTES MEETS MICHELANGELO
Procrustes had a dream that he saw Michelangelo carving a statue of David in a jiffy. Michelangelo told him it was a trivial affair to look at the block of marble, see the image of the statue of David in it and chip away the unnecessary parts. It was child's play, anybody could do it, was Michelangelo's comment.

THE MODEL OF SUCCESS


PROCRUSTES IMITATES MICHELANGELO
Procrustes woke up and looked and looked and looked at his block of marble. He could see no image of the statue of himself inside the block of marble.


A GAME SANS GUIDE



ENTER THE MANDARIN
The Emperor of the Land of Sleeping Giants sent a wise Mandarin as an Ambassador to the Empire.


THE MANDARIN



PROCRUSTES CONSULTS THE MANDARIN-I
The Mandarin advised Procrustes that it was not necessary to follow Michelangelo’s methods. Just list out the steps and follow the procedure to carve the statue. If a mistake occurs use another block of marble.


"IF AT FIRST YOU DON'T SUCCEED - TRY TRY AGAIN"



PROCRUSTES CONSULTS THE MANDARIN-II
The Mandarin however cautioned Procrustes that it would take a lot of time and a lot of blocks of marble to follow the procedures. He advised him to get himself(i.e. Procrustes) a government job with indefinite tenure as a safety measure to keep his head firmly on his shoulders. Unfriendly persons may make fun of the time taken and the wastage of marble to get the final statue.


"SEE THAT YOUR HEAD REMAINS FIRMLY ON YOUR SHOULDERS"



PROCRUSTES FINDS THE CLOCK TICKING AWAY
Procrustes contacted Obelix the Gaul for a large number of blocks of marble. After supplying for a few decades Obelix the Gaul told him that only menhirs of granite blocks and lime stone blocks were available. The 'powers that be' in Italy had banned the export of marble blocks.
PROCRUSTES now wanted to follow the method of Michelangelo. He was running out of time. He was desperate. br

A STREAM OF MARBLE BLOCKS



PROCRUSTES LEARNS ABOUT THE DRUIDS
PROCRUSTES was advised by a suave courtier that in the Land of Gaul there were some Druids who could give him a magic potion. This potion when consumed will make him the equal of Michelangelo.


THE MAGIC POTION OF THE DRUIDS



PROCRUSTES SEEKS OUT THE DRUIDS
PROCRUSTES dispatched an army of messengers and goons full speed to Gaul, to search high and low for the magic potion. The Emperor of the Land of Gaul had banned all intoxicants and hence the magic potion was in the grey market. All the messengers and goons were caught. Their heads were cut off with a brand new instrument designed for the purpose.
Procrustes kept waiting and hoping.


THE SEARCH FOR THE DRUIDS



PROCRUSTES AS A DOUBTING THOMAS-I
PROCRUSTES wanted to know if he was as clever as Michelangelo. He asked his Monsters for advice. He granted them an oracle. He ordered them to work within the framework of his various promulgated Proclamation(s) of Finite Commandments for Sets.




THE MONSTERS ARE TO USE AN ORACLE AND STAY WITHIN THE CODE OF GOONS AND FIND THE ANSWER



PROCRUSTES AS A DOUBTING THOMAS-II
P=NP is valid
One bunch of Monsters reported back to Procrustes that within the framework of his various promulgated Proclamation(s) of Finite Commandments for Sets he was as clever as Michelangelo.



THE MONSTERS REPORT(1): PROCRUSTES IS AS CLEVER AS MICHELANGELO, ONLY HE IS A SLOW COACH



PROCRUSTES AS A DOUBTING THOMAS-III
P=NP is not valid
One bunch of Monsters reported back to Procrustes that within the framework of his various promulgated Proclamation(s) of Finite Commandments for Sets he was 'dumb' compared to Michelangelo.



THE MONSTERS REPORT(2): PROCRUSTES IS DUMB COMPARED TO MICHELANGELO



PROCRUSTES AS A DOUBTING THOMAS-IV
P=NP STUMPS THE MONSTERS
One bunch of Monsters reported back to Procrustes that within the framework of his various promulgated Proclamation(s) of Finite Commandments for Sets perhaps all his Monsters were too 'dumb' & confused to answer the question.




THE MONSTERS REPORT(3): THE MONSTERS ARE TOO DUMB TO ANSWER THE QUESTION DEFINITIELY AND THEY ARE CONFUSED



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-I
OR
ENTER THE FIRST VISITOR

The Palace was all excited. A Visitor from the Land of Man Made Mountains was expected. In knowledge the Visitor was superior to Odin.
Procrustes consulted the Visitor and complained about the confused behavior of his Monsters.
He wanted to know if he was as clever as Michelangelo.




PROCRUSTES COMPLAINS ABOUT THE MONSTERS TO THE WISE MAN FROM THE WEST



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-II(a)
OR
THE MONSTERS AS DEVAS AND BHEESHMAS
The Visitor listened patiently to Procrustes and clarified the matter.




THE WISE MAN FROM THE WEST EDUCATES PROCRUSTES ON THE CONFUSION OF HIS MONSTERS



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-II(b)
OR
THE MONSTERS AS DEVAS AND BHEESHMAS
In ancient days there was a Sage: The Grand Master of the Incomplete.
He had considered the capabilities of different classes of Monsters.
He considered the Superior Monsters who followed Procedures. These Monsters could choose when to stop 'computing'.
There was no independent party who with Ctrl+Alt+Del could preempt the computation. There was no Bouncer to throw them out of the Bar. Whenever like Oliver Twist they asked for more of anything they were given more. The catch was that some of the Monsters could compute 'for ever'.
He had predicted in ancient times that the immortal Monsters that Procrustes had created, or their equivalents by Metamorphoses would be intellectually 'stunted'. They would be 'stumped' by some problems. The Monsters were intellectually Incomplete.
There were problems that no Monster would volunteer to solve. There were problems that would lead some monsters to confusion and they will not be able to announce failure. They will keep on trying for ever.
He had determined that mathematics based on the famous Proclamation for Commandments of Sets was Incomplete. Just like a totally drunken person trying to proclaim he is sober it could not prove its own consistency.
These predictions along with their proofs were recorded by Fate in Plates of Bronze.


THE SISTERS FATE





THE MONSTERS ARE INCOMPLETE AND WILL BE STUMPED BY SOME PROBLEMS




PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-II(c)
OR
THE MONSTERS AS BHEESHMAS
The Grand Master of the Incomplete had considered removing the immortality attributes of the Monsters.
He now had Inferior Monsters who followed Algorithms. These Monsters however could choose when to stop 'computing'.
There was no independent party who with Ctrl+Alt+Del could preempt the computation. There was no Bouncer to throw them out of the Bar. Whenever like Oliver Twist they asked for more of anything they were given more. The catch was that all the Monsters had to 'end' their computation.


THE RESTRICTED INFERIOR MONSTERS MUST STOP COMPUTING SOME TIME



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-II(d)
OR
THE MONSTERS AS BHEESHMAS
Among human beings there were the creative ones who could seemingly solve combinatorial problems like crossword puzzles, Sudoku games, etc. in any area in a jiffy. They could see the answer in a Vision and a simple Monster can Verify the guess.
The bulk of the human race had no Vision to help them and had to try all possibilities for a solution.
A Monster simulating the bulk of the human race and trying to solve the combinatorial problem for large inputs the long way took eons of time.
If however an oracle existed which could give a yes/no answer to a possible solution for an instance of the problem, then life becomes easy.
The oracle can dictate step by step the solution to the problem. Alternatively the person/agent determining the solution could query the oracle for the correctness of each step. The problem is 'easily solved'.
Does a monster exist which can 'easily' do the job of the oracle?



THE RESTRICTED INFERIOR MONSTERS MUST SOLVE THE ETERNAL GAME WITHOUT THE GUIDE OR WITH A SIMPLE GUIDE



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-II(e)
OR
THE MONSTERS AS EKALAVYAS?
The Grand Master of the Incomplete suspected that the problem encountered by Procrustes, or similar ones, would 'stump' all Monsters, all mathematics and mathematicians.
Does a creative person exist for all sizes of a problem? Can the infinite union of creative persons for a problem be simulated by some creative person? The problem is to determine if creativity can be acquired by the hoi polloi, in all cases, in all walks of life. Can a dummy be trained in any problem by a creative person who can then be sacked? Can a creative person be replaced by an Expert System, which can serve as an effective MEMEX for a dummy to use? Can an effective (Software Engineering?) process be found for all problems without those troublesome creative visionaries who cannot be managed easily? Like the concept of Programmer Scope in Software Engineering, is there a size limit for a combinatorial problem beyond which no creative person can have a Vision? Can a super programmer be replaced by ordinary programmers? Do creative persons have a problem size limit like the last straw on the camel's back? Can the monsters with a finite lifetime comment on the infinite?
However in this case the Vision of the Grand Master of the Incomplete failed him. He had suffered from the Joan of Arc syndrome. He could not resolve the problem.
He suspected it to be a 'finite analog' of the Incompleteness syndrome of the immortal monsters. We can suspect he smelt Incompleteness lurking in this problem also, but we cannot be sure. His views were recorded by Fate in Plates of Bronze.
These Bronze Plates have been preserved by Fate in places dedicated to Advanced Study for future generations.

\

THE PLATES OF BRONZE PREPARED BY FATE



THE ETERNAL PROBLEM WILL STUMP EVERYBODY IN SIGHT



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-III
OR
THE GRAND SLAVE OF THE CELTIC MONSTERS

The Visitor from the Land of Man Made Mountains had a suggestion for Procrustes.
In the Land of Celts there was a famous mathematician. He was the Grand Slave of the Celtic Monsters. For eons of time, as a result of an ancient curse he had to continuously 'visit' and 'kowtow' to all the Celtic Monsters. His activity was subject to some constraints.
The Visitor suspected that a study of the curse and the associated activity would help resolve the problem Procrustes faced.

THE CELTIC MONSTERS AND AN ANCIENT CURSE



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-IV
OR
THE GRAND SLAVE IS INVITED

An Imperial Invitation, conferring the status of a State Visit, was sent to the Grand Slave of the Celtic Monsters.

THE GRAND SLAVE OF THE CELTIC MONSTERS IS INVITED



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-V
OR
THE HAMILTONIAN CYCLE PROBLEM
The Grand Slave of the Celtic Monsters arrived. He was asked about the Ancient Curse.
In the ancient times as a result of a misspent youth he had in an inebriated state damaged the nose of the Sphinx and illegally entered the Pyramids of Egypt. This was 'taboo' and an eternal Curse was upon him by Isis and her son Horus whose repose he had disturbed.
The Curse was a case of eternally "Going around the Mulberry Bush".
In the center of Land of the Celts there was a Mulberry Bush. The Celtic Monsters were continuously moving around the bush. They travelled in many directions on the roads around the bush.
Whenever the Sun was eclipsed, he had to make a circuit starting from his house, visit all the Celtic Monsters, without visiting the same monster twice, 'kowtow' to each monster, and finally return to his house. He had to undertake the journey provided the circuit existed around the Mulberry Bush connecting all the Celtic Monsters.
In simple terms he had to continuously go "round and round the mulberry bush" visiting all the Celtic Monsters that were connected by roads around the bush exactly once.
The vast mass of Celtic Monsters, who were subject to birth and death, were always on the move, but when the Sun was eclipsed they froze in their places.
Just like Joan of Arc had her Visions, in this case when the Sun was eclipsed and the Monsters froze in their places the Grand Slave had a Vision of the circuit, if it existed, and could execute his journey satisfying the Curse.
Just as in the case of Joan of Arc, sometimes the Grand Slave's Vision failed him. Then he had to spend eons of time to determine the circuit by trying all possibilities. Many times he had given up in vain, and he was severely punished by the Furies as per the terms of the Curse.
He had tried in vain to find a simple way to determine the circuit when his Vision failed. The futile tears and sweat he had generated in the process had sunk the great continent of Atlantis and the Atlantic Ocean had formed.
He was unable to determine whether a 'simple way' to determine the circuit existed or not, or whether perhaps he will never know.


THE CURSE OF THE GRAND SLAVE OF THE CELTIC MONSTERS



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-V
OR
A SOLUTION TO THE HAMILTONIAN CYCLE PROBLEM
The Grand Slave of the Celtic Monsters said a solution to the Curse was suggested by the Grand Master of the Incomplete.
The solution is to treat the problem as a game. A game children in all cultures, all civilizations and all ages have been playing from time immemorial and is called "Blind Man's Buff". Here the blindfolded child is guided to the target at each step by a Guide or Oracle. Alternatively if the child goes off on the wrong track, or is on the right track, it is guided after some steps have been taken.
A variation of the solution in the Blind Man's Buff was what he needed. Here the Vision he had was the Oracle or Guide. The problem was when the Guide or Vision was not there.
He had tried in vain to find a simple way to determine the solution when his Vision failed. He tried for a simple way of replacing his Vision or Guide or Oracle. This could be done by appealing to a reputable/disreputable local/international terrestrial/extraterrestrial Consulting/Technology/Outsourcing organization/group/person/procedure to find a simple method. The efforts were futile. The futile tears and sweat he had generated in the process had resulted in undersea volcanic activity and sunk the great continent of Atlantis and the Atlantic Ocean had formed.
He was unable to determine whether a 'simple way' to determine the circuit existed or not, or whether perhaps he will never know.
An eclipse was due and the Grand Slave hastily departed to serve the Celtic Monsters.


THE CELTIC MONSTERS SUMMON THE GRAND SLAVE


THE ETERNAL GAME OF THE CHILDREN IS THE SAME AS THE CURSE OF THE GRAND SLAVE OF THE CELTIC MONSTERS



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-VI
OR
THE DIRECTIONS OF THE VISITOR FOR A SOLUTION

The Visitor form the Land of the Man Made Mountains advised Procrustes that both the problems were similar and related. They were the problems the Grand Master of the Incomplete was talking about.
He promised Procrustes that he would convince the Wise Man from the Land of the Redwood Trees to 'drop in' and elaborate on similar problems.
He opined that the Mathematical tools to resolve the problems have not been found as yet. The foundations of Mathematics must be examined all over again with a fresh clear mind.
The Visitor from the Land of Man Made Mountains departed. He had learnt all that was to be learned.

THE ETERNAL GAME OF THE CHILDREN IS THE SAME AS THE CURSE OF THE GRAND SLAVE OF THE CELTIC MONSTERS


THE FOUNDATIONS OF MATHEMATICS MUST BE EXAMINED ANEW TO RESOLVE THE PROBLEM


PROCRUSTES CONSULTS THE MATHEMATICAIANS
Procrustes consulted the Mathematicians. They slyly told him to refer the problem to the children and their leaders who were responsible for his employment in the first place. They were the fresh young minds needed to resolve the problem.

THE FOUNDATIONS OF MATHEMATICS MUST BE EXAMINED ANEW TO RESLOVE THE PROBLEM
THE MATHEMATICIANS PASS THE BUCK TO WINNIE THE POOH, TIGGER AND THE CHILDREN

PROCRUSTES PASSES THE BUCK-I
Procrustes saw Winnie the Pooh and Tigger, playing in the corridors of the Palace along with some children. They were playing Blind Man's Buff by continuously going around a Mulberry Bush that was in a Big Wonky Pot in the center of the corridors. He asked them to solve the problem: Was he as clever as Michelangelo?

THE GAME OF THE CHILDREN


PROCRUSTES TO THE CHILDREN ---“AM I AS CLEVER AS MICHELANGELO?”



PROCRUSTES PASSES THE BUCK-II
Winnie the Pooh and Tigger, along with the children, could not control their laughter at the seemingly stupid question by a stupid person. Procrustes fiercely ordered them to solve the problem with a mathematical proof: Was he as clever as Michelangelo?—OR NO SUPPER, AND ONLY STALE BREAD AND WATER.


PROCRUSTES TO THE CHILDREN---“NO SUPPER TILL YOU CAN PROVE YOUR ANSWER TO THE QUESTION!”


PROCRUSTES TO THE CHILDREN ---“AM I AS CLEVER AS MICHELANGELO?”



WINNIE THE POOH, TIGGER AND THE CHILDREN DECAMP
In a few days time, Winnie the Pooh and Tigger along with the children got tired of stale bread and water and decamped to a Land flowing with Milk and Honey.


THE CHILDREN AND THEIR LEADERS DECAMP IN A FEW DAYS TIME


THE CLOCKTICKS ON RELENTLESSLY
Half a century passed. The remaining Monsters were still computing the answer. There was no sign of the children or their leaders. The Visitor from the Land of the Man Made Mountains had departed. The Mandarin went home to the Land of Sleeping Giants. The Mathematicians slyly reminded the Courtiers of the delayed Mathematics Pill.


THE SLY MATHEMATICIANS REMIND THE COURTIERS



PROCRUSTES IS HECKLED
The suave Courtiers hinted about Universal pills to Procrustes and hinted that he had to exhibit his statue in Court in a few years time for all to see.


PROCRUSTES IS HECKLED BY THE COURTIERS



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-VII
OR
ENTER THE SECOND VISITOR

The Palace was all excited. A Visitor from the Land of Wanderers was expected. In knowledge the Visitor was only inferior to Odin.
Procrustes consulted the Visitor and complained about the confused behavior of his Monsters, and the raw deal the children and their leaders had given him.
He wanted to know if he was as clever as Michelangelo.

PROCRUSTES ASKS THE SECOND WISE MAN FROM THE WEST ---“AM I AS CLEVER AS MICHELANGELO?”



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-VIII
OR
THE DESIDERETA IS CONSULTED FOR FINDING A SOLUTION

IP=PSPACE
The Visitor advised Procrustes not to compare himself to Michelangelo. He advised him from the Desiderata, "If you compare yourself with others you will become vain and bitter".

THE WISE MAN ADVISES PROCRUSTES NOT TO COMPARE HIMSELF WITH MICHELANGELO



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-IX
IP=PSPACE
The Visitor claimed the solution was to employ Michelangelo, not compete with him. He is the Solver, so let him slave it out. Let him do the job or 'if possible' be the Consultant for some hare brained sculptors doing the job, whose queries he had to continuously answer and whose mistakes he had to continuously correct.
He can use the method suggested by the Grand Master of the Incomplete:-
1. He can take the role of an oracle and dictate the solution step by step.
2. He can alternatively guide a 'dumb' sculptor by answering it the 'next step' contemplated is correct.
Another strategy is to use the Interactive Verifier=Solver syndrome for a large set of problems:- He can be used as a Solver by a 'dumb' Interactive Verifier. They can carry on a conversation, and even if Michelangelo tries to be evasive or mislead the 'solution' can easily be found.
Procrustes was the boss, the Verifier. He only has to Verify the result.
A better solution was for Procrustes to be the nagging boss. He could continuously audit Michelangelo, harass him, and test him by misleading him and so on.
Procrustes could various the titles for himself, like "Interactive Verifier", "Auditor-General","Director", "Manager" or just plain "Boss".
To Manage creative persons like Michelangelo & Co was easy. Any Allosaurus with a brain of a few grams in its tail can do the job of Management in such a situation.

SOLUTION IS TO OUTSOURCE THE JOB TO MICHELANGELO AND MANAGE HIM!!!
SEARCH FOR A NARROW PROOF AND A NARROW SOLUTION!!



PROCRUSTES TRIES TO ENSLAVE MICHELANGELO-I
IP=PSPACE
Procrustes wanted to capture Michelangelo. He decided to catch him in his (i.e. Procrustes's) dream, and drag him down to the Empire in chains. The Legion of Monstrous Weight Boxers along with Sumo Wrestlers would 'soften' & tame Michelangelo. He can then be put down to work and managed.

PROCRUSTES TIRES TO CAPTURE MICHELANGELO AND TAME HIM



PROCRUSTES TRIES TO ENSLAVE MICHELANGELO-II
IP=PSPACE
Procrustes slept and slept. He had dream after dream. No Michelangelo was sighted.
Procrustes took sleeping pill after sleeping pill. He slept and slept. He had dream after dream. No Michelangelo was sighted.
Procrustes became desperate.

PROCRUSTES IS UNABLE TO FIND MICHELANGELO EVEN IN HIS DREAMS



PROCRUSTES TRIES TO ENSLAVE MICHELANGELO-III
THE MEMEX AND IP=PSPACE
Procrustes slept and slept. He had dream after dream. No Michelangelo was sighted.
In a dream within a dream, on a Christmas Eve, the Kindly Spirit of an Ancient Sage from the Land of Great Lakes advised Procrustes that he cannot capture Michelangelo in a dream. Perhaps consulting the Memex and outsourcing will help him if Michelangelo exists in "flesh and blood".
Either he could 'isolate & buy' Michelangelo's services or if that fails he should use the fable of The Fox and the Crow effectively.
Procrustes became desperate.

PROCRUSTES IS ADVISED TBY A KINDLY SAGE TO USE THE MEMEX TO SEARCH FOR, CONTACT AND USE THE SERVICES OF MICHELANGELO IN FLESH AND BLOOD



THE CLOCK FURTHER TICKS ON RELENTLESSLY
Half a century passed. No Michelangelo 'in flesh and blood' was found anywhere. Only legends of him were found. He only appeared in dreams and dreams within dreams.
The remaining Monsters were still computing the answer. There was no sign of the children or their leaders. The Mandarin had gone home to the Land of Sleeping Giants. The Visitor from the Land of the Man Made Mountains had departed. The Visitor from the Land of Wanderers had departed. The Mathematicians slyly reminded the Courtiers, who in their turn slyly reminded the Prime Minister of the delayed Mathematics Pill.

NO MICHELANGELO EXCEPT THE ONE IN LEGENDS IS FOUND



PROCRUSTES IS WORRIED
The Prime Minister sent a message to Procrustes that the Emperor would be pleased to see the statue in Court in a few months time.


THE PRIME MINISTER TAKES PROCRUSTES TO TASK


PROCUSTES PASSES THE BUCK-III
Procrustes sent a message to the Prime Minister that he was awaiting an answer from Winnie the Pooh and Tigger, along with the children. He petitioned in all humility for time.

PROCRUSTES BLAMES THE CHILDREN FOR THE DELAY



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-X
OR
THE THIRD VISITOR ARRIVES

The Palace was all excited. A Visitor was expected from the Land of The Redwood Trees. In knowledge the Visitor was the peer of Odin.
Procrustes consulted the Visitor and complained about the confused behavior of his Monsters, the raw deal the children and their leaders had given him, the elusive Michelangelo, the petty politics of the petty mathematicians etc. etc.
He wanted to know if he was as clever as Michelangelo.
He wanted to know how to become as clever as Michelangelo.

PROCRUSTES CONSULTS THE THIRD WISE MAN FROM THE WEST---“AM I AS CLEVER AS MICHELANGELO?”



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XI
OR
THE GIFT OF THE VISITOR

The Visitor told Procrustes that he had brought a Can along with him. The contents would explain the problem.
When Thor went to the Land of the Giants he quenched his thirst by drinking from a Horn. He could not see the bottom of the Horn and ended up almost emptying the oceans in a draught or two. The Can was created from that bottomless Horn.
The original purpose of the Can was to house the progeny of the Midgard Serpent.





THOR AND THE MIDGARD SERPENT - THE MAGIC CAN



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XII
OR
THE CAN OF WORMS

The Visitor gave Procrustes a large Can of Worms. The can was so large that its bottom was not visible.
Each worm in the can had a unique search string associated with it. One could use any decent Search Engine, the search string and the MEMEX for the details of the problem associated with a worm.

THE CAN OF WORMS



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XIII
OR
THE EXCLUSIVE CLUB OF WORMS

The Visitor told Procrustes that half a century of effort had gone into collecting the worms.
Initially the Can was empty and various worms claim to have started the club.
The Visitor however said he preferred to consider the Adam of all the worms was the one representing the Curse of the Grand Slave of the Celtic Monsters.
This started the club and the membership exploded.
Archimedes and his assistants had counted and catalogued 3000 worms so far, but the end was not in sight.
His problem also corresponded to one of the worms.
The worms represented nontrivial problems in practically all activities of the human race, and perhaps Nature itself.

THE HIGH STATUS OF THE WORMS IN THE CAN



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XIV(a)
OR
THE ATTRIBUTES OF A WORM IN THE CAN

The Visitor told Procrustes that just as in Ovid's Metamorphoses, all the worms in the can were simple transformations of each other. In fashionable terms the problems they represented were computationally related to each other. They could be 'easily' transformed among themselves.
If the term 'easily' is varied liberally a different club of worms may result. This was now standardized to represent only the Can of worms he had presented.
Each worm represented a COMPLETE-problem which a creative person like Michelangelo can guess the answer in a jiffy and Verify it 'easily'.
A COMPLETE-problem beyond a small size, takes a normal person trying all possibilities, and all errors, eons of time to Solve.
To claim the 'COMPLETE-' status a problem has some restrictions. Like the Jinn of the desert or Rakshasas of the Subcontinent, the normal person is allowed to make many copies of himself. One of these copies closely simulates a creative person solving the problem 'easily'. However one does not know beforehand which copy is the 'simulator'.

THE '-COMPLETE' WORM OR WORM OF ALL WORMS



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XIV(b)
OR
THE HIGH STATUS OF A WORM IN THE CAN

If the problem represented by any of the worms can be solved 'easily' in a reasonable amount of time, by a normal person, without Vision, using only the routine steps of a procedure, then all the worms represent simple problems.
In the latter case the obnoxious creative persons can be shown the door.
In such a case the statue in question can be carved in a very short span of time, by any ordinary person, simply by following the steps of a procedure. Michelangelo & Co can join the lists of unemployable, unemployed persons.

THE POWER OF THE WORM OF ALL WORMS



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XIV(c)
OR
THE ETERNAL TOM AND JERRY SHOW
The worms represented problems mirroring the eternal never ending Tom and Jerry shows. The worms were a legion of Jerries. The countless human beings who for centuries expended tears, toil and sweat to find a simple solution to any one of the worms were a legion of Toms. The show just keeps going on with the legion of worms having the last word and last laugh.

THE ETERNAL STRUGGLE



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XIV(d)
OR
HOW TO BECOME A WORM IN THE CAN

Membership to the Can of worms was exclusive and by invitation. For a Candidate worm to qualify for membership it should be declared a Peer by a reputable bonafide member of the Can. There should be a creative person who can guess the solution to the problem represented by the Candidate worm in a jiffy, and some 'simple' Monster should Verify it easily. A normal human being or 'simple' monster duplicating like a Jinn for each possibility should have a copy simulating the creative version 'easily'.

HOW TO BECOME A WORM OF ALL WORMS



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XIV(c)
OR
THE DIFFICULTY OF MEMBERSHIP IN THE CAN

Membership to the Can of worms can be a tedious process. It had taken decades for some worms to obtain membership. Some are waiting for decades.
A worm which had been trying for centuries, employing all devious methods and tactics, to obtain membership was declared bogus in the Land of the Five Rivers and its membership banned. It represented the problem of primality.
A worm created in ancient times, and studied in ancient Babylonian, ancient Indian, and ancient Moorish civilizations was attributed to Diophantus of Alexandria. It membership in the can could not be proved from time immemorial. Half a century ago it was exposed in The Land of Leo Tolstoy. It was shown that it was not a worm at all. It was just as in the fable the Ass in the Lion's skin. Its membership application was turned down.

THE DIFFICULTY OF BECOMING A WORM OF ALL WORMS

PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XV(a)
OR
THE 'snappy' iMonster ENTERS THE PICTURE

The Visitor as a 'parting gift' gave Procrustes a Scroll made of the finest Silk woven with the richest and most intricate weaving knowledge of South East Asia. It contained details about the evolution and difficulty of the problem Procrustes faced.
It was a small scroll with a huge big red wax ball on it with the Seal of the Visitor.
It was called "THE CHRONICLES OF THE 'snappy' iMonster".
He was to read it at leisure.

THE SCROLL OF THE SNAPPY iMONSTERS



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XV(b)
OR
THE CAPABILITIES OF THE 'snappy' iMonsters DEFINED

The Scroll dealt with the technologies as to how a vast mass of 'easy going persons' called 'snappy' iMonsters, can organize themselves in various 'structures'; 'easily' cooperate, 'easily' communicate and 'easily' broadcast harmoniously among themselves; implement oracles 'easily' by using the 'outsourcing' concept; use 'easy' approximations, 'easy' trial and error methods and 'perhaps' resolve the problem Procrustes faced 'easily' in 'eons' of time given enough 'easily' determinable resources.

THE SNAPPY iMONSTERS YIELD PSPACE



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XV(bb)
OR
IP=PSPACE=AP WITH THE TOWER OF BABEL RESTRICTION

The 'snappy' iMonsters are however not as powerful as the Inferior Monsters. They have a communication bottleneck which demands that they 'easily' communicate. This like all concurrent computation ends up like the Tower of Babel with everybody talking and nobody really listening. This restricts the 'snappy' iMonsters.

THE SNAPPY iMONSTERS HAVE THE TOWER OF BABEL PROBLEM



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XV(c)
OR
THE iMonsters and IP=PSPACE

THE 'snappy' iMonsters were modular. They could scale up 'easily' in computation. The basic module did its job 'easily'. It used outsourcing and communicated with the 'parties' only an 'easy' number of times. The outsourcing also was to an iMonster which was built modularly with 'easy' components.
Everything about it was based on the 'easy' paradigm. Everybody has an 'easy' time.
Any entity like a 'dumb' number, or set, or any 'dumb' entity can have meaning or 'semantics' attached to it by a 'snappy' iMonster. This is in any situation, any mathematical system.
Even if the outsourcing to a 'snappy' iMonster did not exercise "Due Diligence" and was given to unreliable parties who did the wrong computations one third of the time, the iMonsters could solve the problem Procrustes faced 'easily' provided one did 'NOT' count the outsourcing cost, effort and time.
This was one way to satisfy what the Grand Master of the Incomplete wanted.

OUTSOURCING TO THE SNAPPY iMONSTERS MAKES LIFE EASY



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XV(d)
OR
THE iMonsters and the P=NP PROBLEM

If one dealt only with reliable 'snappy' iMonsters and had outsourcing parties which were reliable then a lot of effort can be saved. The levels of outsourcing then is only the number of primes in the input.
With unreliable outsourcing parties discussed earlier the levels were in the worst case equal to the number of primes in the entire computation. Also one had to continuously interact with the outsourcing parties.
In the case also where "Due Diligence" has been exercised and reliable outsourcing parties have been found the problem Procrustes faced is 'easily' solved provided one did 'NOT' count the outsourcing cost, effort and time.
This was another way of satisfying the requirements of the Grand Master of the Incomplete.

OUTSOURCING RELATED TO THE P=NP PROBLEM



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XV(e)
OR
THE NICKELS ADD UP TO TRILLIONS

The Visitor as 'parting advice' told Procrustes that even if one considers outsourcing by one 'snappy' iMonster to another 'snappy' iMonster as costing 'just a wee bit' one ends up in a problem. Outsourcing to one 'snappy' iMonster for a simple problem may cost a pittance like a nickel, but when a mass of them operate concurrently to solve a problem like the one he faced they nickels add up. Like rich Search Engines making money, the nickels add up to trillions in no time at all. Then the trillions add up to trillions of trillions and so on. No Piggy Bank, even that of Croesus, can afford this cost.

THE SNAPPY iMONSTERS ARE DECEPTIVELY CHEAP



PROCRUSTES CONSULTS THE WISE MAN FROM THE WEST-XV(f)
OR
THE DIRECTION FOR A SOLUTION

The Visitor as 'parting advice' told Procrustes that he concurred with the Visitor from the Land of Man Made Mountains that the mathematical tools to solve the problem have not yet been found. Fresh minds were required. The foundations of Mathematics must be examined from new viewpoints.



THE ETERNAL STRUGGLE HAS TO CONTINUE



THE CLOCK FURTHER TICKS ON MOST RELENTLESSLY
Half a century passed. The remaining Monsters were still computing the answer. There was no sign of the children or their leaders. The Mandarin had gone home to the Land of Sleeping Giants. The Visitor from the Land of the Man Made Mountains had departed. The Visitor from the Land of Wanderers had departed. The Visitor from the Land of the Redwood Trees had departed. The Mathematicians slyly and repeatedly reminded the Courtiers, who in their turn slyly reminded the Prime Minister of the delayed Mathematics Pill.


NO SOLUTION IN SIGHT--THE ETERNAL STRUGGLE HAS TO CONTINUE



PROCRUSTES IS MOST WORRIED
The Prime Minister sent a message to Procrustes that the Emperor would be pleased to see the statue in Court in a few DAYS time.


THE PRIME MINISTER IS RESTIVE



PROCUSTES PASSES THE BUCK-IV
Procrustes sent a message to the Prime Minister that he was awaiting an answer from Winnie the Pooh and Tigger, along with the children. He petitioned in all humility for time.

PROCRUSTES BLAMES THE CHILDREN FOR THE DELAY




PROCUSTES IN THE TAVERN OF BACCHUS
Procrustes rushed off to the Tavern of Bacchus to 'drown his sorrow'. In the Tavern of Bacchus he saw a Stranger. This was a Man in Flowing Robes.

THE WORLD OF POTS STARTS SURFACING




PROCUSTES MEETS OMAR KHAYYAM
Procrustes was asked by the Kindly Stranger, who introduced himself as Omar Khayyam, as to why he had the "Lost Looks'.
Procrustes 'wept on the Stranger's shoulder' and told him the whole history as how he had been taken for a ride. He felt everybody excluding himself was at fault and up to tricks.



THE WORLD OF POTS SHOWS ITSELF



OMAR KHAYYAM EXPLAINS HIS ANCIENT PROBLEM
Procrustes was enlightened by Omar Khayyam.
For countless tens of thousands of years, from time immemorial, his long line of ancestors starting from Adam, had tried to solve a problem.
A human being (or any being), like himself, feels like a 'wonky' Pot. Other human beings (or any beings) are like beautiful, carved Pots. This is particularly applicable to 'beautiful', 'gifted' and 'creative' persons. The questions were whether the 'Hand of the Potter shook' in making him, whether he is 'worse off' than the beautiful Pots, how can he become a beautiful Pot, and finally why some beautiful Pots end up becoming 'wonky'.




THE BEAUTIFUL POTS AND THE ‘WONKY’ POTS



OMAR KHAYYAM TRIES TO SOLVE HIS PROBLEM
Procrustes was told by Omar Khayyam, that decades of effort and struggle with "Doctors and Saints" like Odysseus of old had only led to more confusion and chaos.
His problem was identical to the problem Procrustes was facing.



IDENTICAL PROBLEMS



OMAR KHAYYAM FINDS THE SOLUTION
Procrustes was then informed by the Kindly Stranger, the Great Omar Khayyam, about the solution.
Omar Khayyam had sold off his property, and invested in Baskets of Grapes. These were then placed in a large Caravan.
The Caravan was heading for a distant Oasis of Lotus Eaters, in a far off desert, deep inside the Continent of Circle.
He planned to relax, "take the cup in hand...." and concentrate on drinking "Iced Grape Juice" for the rest of his life.
He invited Procrustes to join him in the Party and bring his overflowing Kiddy Bank with him.


OMAR AND ICED GRAPE JUICE





PROCRUSTES IS WORRIED THAT THE MONSTERS MAY PINE FOR HIM
PROCRUSTES thought deeply about what he was advised. Then he sadly announced that he just could not ‘decamp’ leaving his Beloved Monsters in the lurch. They would pine for him and may fall sick if he deserted them. He just could not live without them or they without him.

THE MONSTERS MAY PINE FOR PROCRUSTES IF HE DECAMPS

PROCRUSTES CAN SIMULATE THE TURING MACINE
Omar Khayyam pointed out a solution. It was not necessary to be with the Monsters. PROCRUSTES can ‘simulate’ the Monsters. The Emperor would continue paying PROCRUSTES his wages of a penny a day indefinitely. It is this unlimited resource that will allow PROCRUSTES to carry out the simulation.


THE WAGES OF PROCRUSTES WILL ALLOW HIM TO SIMULATE THE MONSTERS



PROCRUSTES TRIES SIMULATION OF UNIVERSAL COMPUTATION USING FOUR STACKS WITH A MULTITUDE OF SYMBOLS
PROCRUSTES had his Piggy Bank. Omar Khayyam had his Piggy Bank. They could purchase one more Piggy Bank each. They could exchange their pennies for a multitude of coins in various currencies. They could ‘stack’ up the coins in the four Piggy Banks. With the ‘four’ stacks of coins they can simulate any Monster.


FOUR PIGGY BANKS WITH STACKS OF COINS OF MANY TYPES CAN SIMULATE THE MONSTERS



PROCRUSTES TRIES SIMULATION OF UNIVERSAL COMPUTATION USING FOUR STACKS AND TWO TYPES OF COINS
PROCRUSTES said a multitude of coins will lead to confusion and ‘mixing of accounts’ which is a situation no self-respecting Accountant will stand. There will be problems with the ‘light fingered’ Taxman. Omar Khayyam said two types of coins will do. With two types of coins any Monster can be simulated with their ‘four stacks’ of coins in their four Piggy Banks.


FOUR PIGGY BANKS WITH STACKS OF TWO TYPES OF COINS CAN SIMULATE ALL MONSTERS


PROCRUSTES TRIES SIMULATION OF UNIVERSAL COMPUTATION USING TWO STACKS AND TWO SYMBOLS
PROCRUSTES was still worried and suspicious. Images of the Taxman and Mixed Accounts leading to brawls worried him. He strenuously objected to the expense of an additional Piggy Bank. Omar Khayyam said two ‘stacks’ of coins with two types of coins were sufficient. The expense of an additional Piggy Bank could be avoided.


TWO PIGGY BANKS WITH STACKS OF COINS OF TWO TYPES CAN SIMULATE ALL MONSTERS



PROCRUSTES TRIES SIMULATION OF UNIVERSAL COMPUTATION USING FOUR COUNTERS
PROCRUSTES pointed out that Foreign Exchange regulations were a bad affair. If one goes to a Bank to get another type of coin in exchange, then the contents of the Piggy Bank become White Money. The notorious Taxmen and the still more notorious local goons will move in. Omar Khayyam said one could avoid going to the Bank and the hassle of exchanging the money with light fingered Bankers. One could just stack the coins in four Piggy Banks. The stacks of coins could be used as counters. Each of them would have to acquire an additional Piggy Bank.


FOUR PIGGY BANKS WITH JUST PENNIES CAN SERVE AS FOUR COUNTERS TO SIMULATE ALL MONSTERS



PROCRUSTES TRIES SIMULATION OF UNIVERSAL COMPUTATION USING TWO COUNTERS
PROCRUSTES strenuously objected to the expense of an additional Piggy Bank. Omar Khayyam thought about the matter and said the additional expense was unwarranted. Two Piggy Banks with stacks of pennies could be used as two counters. They can simulate whatever any Monster does.


TWO PIGGY BANKS WITH JUST PENNIES CAN SERVE AS TWO COUNTERS AND SIMULATE ANY MONSTER



PROCRUSTES TRIES THE DEVELOPMENT OF THE TURING MACHINE
PROCRUSTES wanted the mixing of accounts to be avoided. He just wanted the accounts of the Piggy Banks to be separate. Omar Khayyam said there was a solution. PROCRUSTES could exchange half his unlimted supply of pennies for a different type of coin. He would have two types of coins now. He could draw a table of 1 row and many columns on the long road using chalk pieces. He could add columns at either end as required. He could populate his table with coins. With this he could simulate the computation of any Monster.


JUST TWO TYPES OF COINS FROM THE PIGGY BANK LAID OUT IN A ROW CAN SIMULATE ALL MONSTERS



PROCRUSTES TRIES USING THE SANDS OF THE DESERT TO SIMULATE UNIVERSAL COMPUTATION
PROCRUSTES wanted to do away with the chalk. Drops of water make an ocean and thus the cost of the chalk pieces will in due course add up to an astronomical sum. Omar Khayyam had a solution. PROCRUSTES could take a twig. With this he could draw the squares of the table in the desert. He could use two different types of pebbles to fill up the squares, He could play around with the pebbles ‘systematically’ in different ‘moods’ and ‘state of mind. With this he could simulate any Monster. He did not need his Piggy Bank or those ‘stupid’ coins at all!!!,br.


AWAY WITH PIGGY BANKS!!! JUST PEBBLES OF TWO TYPES IN A ROW IN THE DESERT CAN SIMULATE ALL MONSTERS



PROCRUSTES TRIES USING MULTIDIMENSIONAL TABLES IN THE DESERT
Omar Khayyam said PROCRUSTES could draw and use a multidimensional table in the desert. He could add rows and columns a desired at the end. With this multidimensional table, two types of coins and granted enough ‘moods’ and ‘states of mind’ PROCRUSTES can simulate any Monster.


AWAY WITH PIGGYBAMKS!! JUST TABLES OF PEBBLES OF TWO TYPES IN THE DESERT CAN SIMULATE ALL MONSTERS!!



PROCRUSTES TRIES USING MULTIPLE TABLES
PROCRUSTES can split his multidimensional tables to individual tables. Again with three types of coins and granted enough ‘moods’ and ‘states of mind’ he can simulate any Monster.


AWAY WITH THE PIGGY BANK!!! JUST A TABLE WITH THREE TYPES OF PEBBLES CAN SIMULATE ANY MONSTER THAT IS SIMULATEDD BY A TABLE!!!



PROCRUSTES TRIES REDUCING MULTIPLE TAPES TO ONE TAPE
If the number of individual independent tables of one row is to be reduced to a single table of one row the time taken to simulate the Monster is squared in the worst case.


AWAY WITH THE PIGGY BANK!!! MULYIPLE TABLES OF PEBBLES CAN BE REDUCED TO TWO TABLES WITH PEBBLES TO SIMULATE ANY MOMSTER!!!



PROCRUSTES TRIES REDUCING MULTIPLE TAPES TO TWO TAPES
If the number of individual independent tables of one row of a multitape Original Monster is to be reduced to two tapes of one row in a Copycat Monster the time taken to simulate the Original Monster is to be multiplied by the number of digits in the time taken by the Original Monster.


AWAY WITH THE PIGGY BANK!!! MULTIPLE TABLES OF PEBBLES SIMULATING A MONSTER CAN BE REDUCED TO TWO TABLES



PROCRUSTES GETS ADVICE: ENTER THE FIRST MONK IN SAFFRON ROBES
PROCRUSTES suddenly realized that in the dim lighting of the Pub of Bacchus there was another person at the table. This was a Monk in saffron robes, who spoke up now. He said he was a Follower of The Enlightened One. There were other models of Computation to simulate the Monsters. He said he would elaborate on the legendary Mouse RASP.


PROCRUSTES HEARS ABOUT THE CREATION OF THE MONSTER BIG IRON
In ancient times after a dismal struggle of ten years the Greeks manufactured the Trojan Horse and used it to sack the ancient city of Troy. Every ingot of metal was collected as booty. The High King of the Greeks wanted the victory to be eternally remembered. He had all the Iron ingots and articles in the booty melted and created a MONSTER BIG IRON. This ponderous Monster was given life by PROCRUSTES . It was a regular Monster capable of Universal Computation. It was capable of reproducing itself. The BIG IRON MONSTER wandered around the Rich Countries and Economies of the World, like the Dinosaurs of old.


PROCRUSTES HEARS ABOUT THE CREATION OF THE Mouse RASP
In ancient times the Grand Sage of Complexity had created a tiny Monster called Mouse RASP. PROCRUSTES gave life to this tiny Monster and Mouse RASP was capable of Universal Computation.


PROCRUSTES HEARS THAT The MONSTER BIG IRON and Mouse RASP met at a party.
MONSTER BIG IRON held forth on its Mighty Capabilities. Much to its merriment Mouse RASP claimed equal status. MONSTER BIG IRON laughed so much that the chair on which it was sitting collapsed. Mouse RASP said they were both capable of Universal Computation.



PROCRUSTES HEARS THAT Mouse RASP OUTPERFORMS MONSTER BIG IRON
Mouse RASP said there were problems for which there was no such thing as an efficient Algorithm. It was a case of the proverb-“there is always scope for improvement”. MONSTER BIG IRON guffawed loudly!!! There were problems which Mouse RASP doing something with rests of half a century, can overtake MONSTER BIG IRON grinding away doing millions or zillions of things per second. It was a case of the proverb-“every dog has its day”. MONSTER BIG IRON could not control its merriment on hearing such ‘counter intuitive’ seemingly ridiculous statements!!!



PROCRUSTES HEARS THAT THE OWL SPEAKS UP FOR Mouse RASP
The Wise Owl who was at the party cautioned MONSTER BIG IRON. It recapitulated the ancient fable of the Lion and the Mouse. Long ago in the Deep Interiors of the Dark Continent the humble mouse wanted to make friends with the Mighty King Lion who had caught it. The Lion laughed and let it off condescendingly. The mouse told the King Lion that someday it would repay & help the Great King. The Lion just laughed. Some time later King Lion got caught in the Wicked Hunter’s Net. It was trapped. The humble mouse came along and saw the net. It called all its relatives and friends . An army of mice appeared and chewed up the net. The Lion was saved. The Lion remained the eternal friend of the mouse.


PROCRUSTES HEARS THAT MONSTER BIG IRON IS BUSY MAKING DATE STAMPS
MONSTER BIG IRON was the busiest being on earth. It recorded every activity, looked up its huge stack of calendars, and gave a date stamp to everything in sight.


PROCRUSTES HEARS ABOUT MONSTER BIG IRON AND ITS PRIZED DATABASES
It then marched to the Land of the Vikings. It selected a lake in a part of the Land of Vikings where there are more lakes than people. The lake was hundred miles wide, hundred miles long and hundred miles miles deep. It deposited a date stamp as a drop of water. It was very proud of its massive lake of Date Stamps. It gave it the name-“Legacy Databases”.


PROCRUSTES HEARS THAT MONSTER BIG IRON ECONOMISES
The lake was turning out to be too small so MONSTER BIG IRON abbreviated the dates without the ‘century’ being recorded.


PROCRUSTES HEARS THAT MONSTER BIG IRON IS CAUGHT IN A NET
At the end of the century, when the century changed MONSTER BIG IRON fell into the lake. It got caught in a net meant to catch Monstrous Sharks and was in despair. It was also caught in a bog at the same time. It bellowed like a huge ‘gang’ of Blue Whales. Its bellowing was heard in all corners of the world.



PROCRUSTES HEARS THAT Mouse RASP RESCUES MONSTER BIG IRON
Mouse RASP heard from afar the bellowing of MONSTER BIG IRON. It called all its relatives and friends and chewed the horrid net away. MONSTER BIG IRON was saved by the army of humble Mouse RASPs.


PROCRUSTES HEARS THAT MONSTER BIG IRON OUTSOURCES
MONSTER BIG IRON was over the period of half a century attacking larger and larger problems. It broke up the problems into small pieces that iMonsters could handle. Once it became ‘chummy’ with Mouse RASP it found it can take up any large problem, break it up into tiny pieces, that iMonsters or Mouse RASPs can handle (and do it for a pittance).


PROCRUSTES HEARS THAT THE WHOLE WORLD OUTSOURCES (IP=PSPACE)
This snowballed in no time into everyone in the world breaking up problems to tiny problems that can be outsourced to iMonsters or Mouse RASPs (who would do it for a pittance).


PROCRUSTES HEARS THAT UTOPIA CREATED WITH IP=PSPACE
Everyone in the world ideally has an easy time. Everyone would stop working. Anything to be done is outsourced, for a pittance, to somebody else equipped with iMonsters or Mouse RASPs. If one was lucky one hunted for a Michelangelo on the Memex and put him down to work for ‘low cost’.


PROCRUSTES IS ADVISED: ENTER A SAGE NAMED POST
In the dim lighting of the Pub of Bacchus PROCRUSTES saw another person. It was A Sage named Post.


PROCRUSTES IS ADVISED: THE ADVICE OF THE SAGE POST -I
Post advised Procrustes that Computation could be carried out in other ways. One only needed text documents and FIND & REPLACE. FIND & REPLACE with text documents can simulate the Computation of any Monster. FIND & REPLACE allows Computation involving massive parallelism of identical Monsters to be simulated. If additionally one had a CUT, COPY & PASTE facility one can speed up the simulations of the Computation. All documentation (in any media) recording any aspect of any natural or human activity is a simulation of the activity. This means it is a Computation by itself. With the use of FIND & REPLACE it can simulate any computation. This means simulation simulations of the Computation is equivalent to the actual Computation. “One can live in a world of comfortable illusion”. Simulating the simulations of eating is equivalent to eating!!!!


PROCRUSTES IS ADVISED: THE ADVICE OF THE SAGE POST -II
Procrustes objected to the heavy use of pencil and paper. In remote parts of the world & universe they were not available easily. Sage Post advised that text documents were not essential. One can use any objects real or abstract, natural or man made, concrete or imaginary and line them up simulating a text document. A child in the Nursery can use a line of toys, the housekeeper can use a line of objects in the house. To this line of objects one can apply FIND & REPLACE, CUT, COPY & PASTE to simulate the computation of any Monster. Just as in FIND & REPLACE with text documents one allows the line to grow indefinitely or shrink. So Computation could be carried out in other ways. One did not need the Monsters. They only had to be simulated.


PROCRUSTES IS ADVISED: ENTER THE SECOND MONK IN SAFFRON ROBES
In the dim lighting of the Pub of Bacchus PROCRUSTES saw another weird, wild looking monk in saffron robes. He was carrying a Trishul. He spoke up now. He said there were other models of Monsters for Universal Computation.


PROCRUSTES IS ADVISED: ENTER THE HUMBLE GRAND SAGE OF THE LAND OF DIKES
He said that in ancient times there was the Humble Grand Sage of the Land of Dikes. In his youth he had handled some of the fiercest monsters and tamed them all.


PROCRUSTES IS ADVISED: THE COMPUTATIONAL MODEL OF THE HUMBLE GRAND SAGE OF THE LAND OF DIKES
Towards the latter half of his residence on earth he scorned all hard-wired Monsters. He believed in computation using Programming Languages. Just as the telescope is not essential in the study of Astronomy, the Monsters were not essential to study Computation---this was his famous dictum.


PROCRUSTES IS ADVISED: THE FURTHER RELEVANCE OF THE COMPUTATIONAL STRATEGY OF THE GRAND SAGE OF THE LAND OF DIKES
Most of the computation of the MONSTER BIG IRON was in a language called COBOL. This was a very user friendly affair. The computation could be easily be understood by any dell but literate person without the MONSTER BIG IRON hanging. This made it easy for Mouse RASP and iMonsters to bail out MONSTER BIG IRON.


PROCRUSTES IS ADVISED: ENTER THE GRAND SAGES OF ALGORITHMS
In the dim lighting of the Pub of Bacchus PROCRUSTES saw a Red Man. The Red Man said he was a descendent of an ancient prophet named Hiawatha. He elaborated on the problem. Some noted Grand Sages from the land of Hiawatha developed on the ancient concepts of Algorithms to specify computations. It started as a cookbook for Programmers and ended up as a cook book for Computation via Algorithms.


PROCRUSTES IS ADVISED: THE BASIC TWO SCORE ALGORITHMS
All Algorithms were reduced to a basic collection that was less than two score in number. If they could be described by ‘efficient’ algorithms we have whatever Computation can achieve within the framework of known Mathematics, within the Finite Laws of Commandments for Sets.


PROCRUSTES IS ADVISED: THE MONSTERS ARE AN IRRELEVANT LOT IN ALGORITHMS
The problems had intrinsic value or complexity like platinum, diamonds, gold, silver, bronze, copper, tin and lead. The Monsters implementing them did not matter in the long run. The study of Algorithms is independent of the Monsters. The Monsters did not have to hang around.


PROCRUSTES IS ADVISED: LIVING WITHOUT THE NOISY MONSTERS
The solution to PROCRUSTES ’s problem of having to carve his statue did not therefore require any Monster to hang around. PROCRUSTES could quietly retire to his Oasis in the Desert.


PROCRUSTES IS ADVISED: THE TOOLS FOR SOFTWARE OUTSOUCING ARE CREATED
Here were models for all the countries and economies of the world that did not have access to the MONSTER BIG IRON or the scantily dressed MONSTER SUPER MINI & MONSTER MINI. One could learn to program without the Monsters hanging around.


PROCRUSTES IS ADVISED: THE MONSTERS GANG UP
Over a period of time the Monsters ended up forming gangs. Initially they were loners but they ended up in networks. This could be locally within a building, over the town/city, over the country, and finally all over the world. One could learn how to program and compute on these Gangs of Monsters by simulation.


PROCRUSTES IS ADVISED: THE SITUATION WHEN THE MONSTERS INVADED THE ENTIRE EARTH
When the Monsters were accessible ubiquitously and easily one merely tested out one’s computation. The world of outsourcing was born.


PROCRUSTES IS ADVISED: THE ADVICE OF OBELIX THE GAUL
In the dim lighting of the Pub of Bacchus PROCRUSTES saw another person. It was Obelix the Gaul.


PROCRUSTES IS ADVISED: THE GRAND SAGE OF COMMON SENSE
Obelix the Gaul lectured PROCRUSTES . He had met a Grand Sage who had created the ‘Case Construct’ in Programming Languages to help Omar Khayyam choose from a variety of Pubs & made everybody and everything point to the ‘Eternal Void’. Obelix the Gaul was advised by the Grand Sage that all Computation was Common Sense. It was merely finding Common Sense Solutions to problems that could be described by Common Sense. The Monsters were an overhead in Computation. PROCRUSTES should concentrate on finding a ‘Common Sense’ way of carving his statue and forget about his Monsters.


PROCRUSTES IS ADVISED: THE ADVICE OF THE MEDICINE MAN FROM THE DARK CONTINENT
I n the dim lighting of the Pub of Bacchus PROCRUSTES saw another person at the table. This was a Medicine Man from the Deep Interiors of the Dark Continent.


PROCRUSTES IS ADVISED: A SOLUTION THE PROBLEMS IN THE CAN OF WORMS
He said that a couple of decades ago he had contacted Sibyl the Prophetess about PROCRUSTES ’s problem. He had also consulted the “Three Witches” who were the ‘chums’ of Macbeth in the forgotten past two decades ago. He was advised that the problem of the Grand Slave of the Celtic Monsters is trivially subexponential. A truly marvelous simple demonstration of the same is possible.


PROCRUSTES IS ADVISED: THE CURSE ON THE SOLUTIONS TO THE PROBLEMS IN THE CAN OF WORMS
However the problem suffers from an ancient curse. Any one having a solution is considered to be crying Wolf! Wolf! like the Shepherd Boy in the fable. It suffers from the Cassarandra syndrome. Though it is trivially subexponential only an ‘authorized’ and ‘anointed’ person can announce it in proper ‘form’. It is taboo for the laity to involve themselves. It does not matter for anyone can rediscover the solution in a ‘jiffy’ or like Fermat’s Last Theorem it may take a while.


PROCRUSTES IS ADVISED: THE CURSE OF COMBINATORIAL PROBLEMS
The problems in the Can of Worms are like Jerry the Mouse. An attempt by Tom the Tomcat to get the better of him invariably ends up in a disaster at the end for ‘poor’ Tom. The same may apply to any subexponential algorithm. The worm in the can will suddenly pop some ‘spinach’ into itself and send any claimed ‘solution’ for a spin. The worms in the Can have all of the ‘wicked temper’ of the Midgard Serpent.


PROCRUSTES IS ADVISED: MONSTER BIG IRONLAUGHS AT THE iMonster
When the iMonster was created it charged around like Mouse RASP and told MONSTER BIG IRON that it was its equal. MONSTER BIG IRON guffawed!! The iMonster said it could do things MONSTER BIG IRON could not do however hard and fast MONSTER BIG IRON worked. MONSTER BIG IRON could not control its laughter at such ludicrous, counter intuitive claims!!


PROCRUSTES IS ADVISED: THE iMONSTER WINS A RACE AGAINST MONSTER BIG IRON
The existence of a subexponential algorithm for solving the Curse of the Grand Slave of the Celtic Monsters for a small collection , shows that a garden variety iMonster can do what MONSTER BIG IRON or its relatives SUPER MONSTERS BIG IRON could not do.


PROCRUSTES IS ADVISED: THE POWER OF CLOUDS OF iMonsters
A cloud of iMonsters can completely dispose of 100 Celtic Monsters in the problem of the Grand Slave as easily as Tom Sawyer polished off the doughnut he had ‘hooked’. Apparently in a computation spanning a few decades of time a Cloud of garden variety iMonsters can completely dispose of 500 Celtic Monsters.


PROCRUSTES IS ADVISED: CAN iMONSTERS REDUCE THE PROBLEMS IN THE CAN OF WORMS TO EACH OTHER?
The conjecture of the Grand Sage of Complexity as to whether a iMonster can convert the ‘-complete’ problems in the Can of Worms to each other remins unsolved.


PROCRUSTES IS ADVISED: THE CONFUSION OF THE MONSTERS IS NOT RESOLVED
The confusion of the Monsters, operating with an oracle and staying within the framework of the Finite Commandments for Sets, remains as solid as ever.


PROCRUSTES IS ADVISED: DOES AN iMONSTER EXIST TO SOLVE PROCRUSTES ’S PROBLEM?
There is still scope for improvement in the subexponential algorithm. It may still be that an iMonster exists to solve the problems in the Can of Worms, though we may not be able to describe the iMonster.


PROCRUSTES IS ADVISED: THE GENERIC SUBEXPONENTIAL ALGORITHM WITH SEMANTICS
All the problems in the Can of Worms can be tackled with a standard strategy. A generic scaffolding is created and attributes and semantics are added, just as in XML or Syntax Directed Translation. The attributes and semantics are for a particular worm in the can. The strategy can uniformly handle all the ‘residents’ of the Can of Worms, to obtain a subexponential algorithm.


PROCRUSTES IS ADVISED: THE CURSE OF COMBINATORIAL PROBLEMS
The problems in the Can of Worms are like Popeye. An attempt by Bluto to get the better of him ends up in a disaster at the end. The same may apply to any subexponential algorithm. The worm in the can will suddenly pop some ‘spinach’ into itself and send any claimed ‘solution’ for a spin.


PROCRUSTES IS ADVISED: THE ADVICE OF THE MEDICINE MAN
The Medicine Man advised PROCRUSTES that he could contemplate on the problem to resolve his ‘statue’ problem.


PROCRUSTES IS ADVISED: THE ADVICE OF THE AVADHANI
In the dim lighting of the Pub of Bacchus Procrstes saw another person. He was a ‘half naked fakir’ from a distant land. He told PROCRUSTES that in his country there were persons with enormous combinatorial memories and abilities. Their performance in challenges corresponded to perfect and total solutions to problems in the Can of Worms. They were not approximation algorithms but total solutions to the problems.


PROCRUSTES IS ADVISED: THE AVADHANAM
For over a thousand years they demonstrated their memory and combinatorial skills in congregations called Avadhanams. They are not allowed access to pencil, paper or any Monster. They should operate only with their memory. They are to operate in the presence of artificially created noise, distraction and asynchronous interrupts involving events like the ringing of a bell. They are restricted to one of the areas in the languages Kannada, Sanskrit or Telugu, which are Indian languages. They are further restricted to Literature, Mathematics, Dancing, Poetry, etc. They are questioned, perhaps for days on end, by knowledgeable persons in their chosen area and language. Their performance should be perfect. All the answers should be correct. No approximation is allowed. This can be modeled as total solutions to problems in the Can of Worms. Approximation algorithms are out.


PROCRUSTES IS ADVISED: THE ASHTAVADHANI OR COMBINATORICS WITH 8 ELEMENTS
There are the Ashtavadhanis who can track eight things. Normal human beings can keep track of 5 to seven things at most. This was rediscovered by Software Professionals/Industry in their concepts of fan-in, fan-out and scope of control. Combinatorial skills involving eight or more items is not common.


PROCRUSTES IS ADVISED: THE DASHTAVADHANI OR COMBINATORICIS WITH 100 ELEMENTS
There are the Dashtavadhanis who can track 100 things. Here combinatorial skills of 100 items are to be demonstrated. This is much rarer and nears the problem of chess if brute force solutions are attempted. However with partitioning or with the subexponential algorithms this can be handled by ordinary persons with iMonsters. A garden variety iMonster should be enough for the job if a valid, accepted and proven subexponential algorithm is found.


PROCRUSTES IS ADVISED: THE SHASRAAVADHANIS OR COMBINATORICES WITH 1000 ELEMENTS
There are the Sahasravadhanis who can track 1000 things. Here the combinatorics involves 1000 items. Such persons rely on experience and combine their earlier experiences with 100 items. They ‘Reuse’ their earlier results.


PROCRUSTES IS ADVISED: RELATING THE PROBLEM TO THE MONSTERS
This can be extended to the Monsters which ‘learn by experience’. The problems in the Can of Worms are highly self-referential to an obnoxious degree. This allows modularization of small instances of the problems. Reuse involves modification whose effects can be localized as far as possible. Polymorphism can be used by adding attributes to various components. The high self-referential nature of the problem allows massive parallelism allowing easy use of the Cloud for the purpose.


PROCRUSTES IS ADVISED: RELATING THE PROBLEM TO MEGA PROJECTS
Solutions to these problems are akin to the mega construction projects spanning centuries like the Great Wall of China, the South Indian Temples, the Rheims Cathedral in France, the Pyramids of Egypt or the Terracota soldiers of China.


PROCRUSTES IS ADVISED: THE FUTURE OF OUTSOURCING
This shows that the human race time and gain, culture after culture, civilization to civilization falls back on the likes of Michelangelo, herds of serfs/slaves/workers, or masses of iMonsters/Mouse RASPS. As the ancient saying goes—“Somebody has to do the job” or “A mass of Somebodies has to do the job”.


PROCRUSTES IS ADVISED: BEYOND THE SAHASRAAVADHANIS
In Avadhanam there are rare persons who can track 10,000 things. This is very rare and involves combinatorics of 10,000 items. High degree of Reuse of earlier results involving small instances of the problem are used here. This can be related to monolithic mega projects with networks of masses of serfs/slaves/Monsters/iMonsters/Mouse RASPs.


PROCRUSTES IS ADVISED: APPICATION TO THE PROBLEMS IN CAN OF WORMS
This means problems like the Curse of the Grand Slave of the Celtic Monsters can in principle be solved for 8, 100, 1000 or 10,000 Celtic Monsters roaming around. It involves massive reuse with modification of situations involving 100 or less Celtic Monsters. For 200+ and above Monsters exact solutions span decades and centuries, just like the mega-projects of old.


PROCRUSTES IS ADVISED: THE END OF THE TUNNEL
It is a matter of time before his Monsters learn how to do all this to aid PROCRUSTES . They no longer need the help of PROCRUSTES . It is the other way around. He needs their help. It is thus conceivable that PROCRUSTES could carve his perfect statue, with the help of Monsters rather than the elusive Michelangelo.


PROCRUSTES IS ADVISED: LEGENDS WILL REMAIN LEGENDS
However Michelangelo will remain Michelangelo. MONSTER BIG IRON will remain MONSTER BIG IRON.


PROCRUSTES IS ADVISED: HE MAY GET AWAY SCOT FREE FROM THE MATHEMATICIANS
Till the time taken for the Monsters to mature, everyone at the table said PROCRUSTES should lie low to ensure his head is firmly on his shoulders.


PROCRUSTES IS ADVISED: THE ADVICE OF BLUTO THE MENTOR
In the dim lighting of the Pub of Bacchus PROCRUSTES saw another person. It was Bluto of the Sailors his childhood Mentor in Mathematics. Bluto of the sailors said he has consulted the Grand Sage of Concurrency from the Land of the Danes. As a result of the same he had some advice for PROCRUSTES .


PROCRUSTES IS ADVISED: AVOID THE BUSY WAIT METHOD
Bluto of the Sailors advised PROCRUSTES to take it easy. The ’busy wait’ method of waiting, waiting and waiting for something to happen is expensive on resources.


PROCRUSTES IS ADVISED: SET UP A SEMAPHORE AND GO TO SLEEP
PROCRUSTES should put up an Ad on the Memex(perhaps by a broadcast),. He could say he was on the lookout for a Michelangelo or a Monster to solve his problem. He can then quietly go to sleep or concentrate on his iced grape juice.


PROCRUSTES IS ADVISED: THE SEMAPHORE IS USED TO WAKE UP PROCRUSTES
When a large bunch of Monsters and Michelangelo-hopefuls turn up in response to the Ad, the Memex will wake up PROCRUSTES .


PROCRUSTES IS ADVISED: SYNCHRONISATION OF THE CANDIDATES FOR THE INTERVIEW
An interview date can be broadcast to the Monsters and Michelangelo-hopefuls who have applied and thus they are ‘synchronised’ to turn up at the same time on some day for their credentials to be examined.


PROCRUSTES IS ADVISED: THE USE OF A MONITOR TO IMPLEMENT MUTUAL EXCLUSION
He can interview them one at a time for the job. He can employ a ‘Sumo Wrestler’ as a ‘Monitor’ to see that the Monsters and Michelangelo-hopefuls do not gatecrash when an interview is going on. The Sumo wrestler will ensure that the interview is going on for one candidate only at a time. He implements ‘mutual exclusion’. An interview is a serious affair. It is called a ‘critical region’. When a candidate is being interviewed the others should lie low. The ‘Monitor’, the Sumo wrestler, ensures this. Only one candidate can be in the ‘critical region’.


PROCRUSTES IS ADVISED: THE SCHEDULING OF THE INTERVIEWS
If there are too many applicants from the ‘crowd’ of Monsters/Michelangelo-hopefuls Scheduling problems will surface in allotting interview times.


PROCRUSTES IS ADVISED: SCHEDULING PROBLEMS & THE CAN OF WORMS
As most scheduling methods and strategies are also members of the Can of Worms, PROCRUSTES should ensure that the Sumo wrestler does not gang up with the Beagle Boys and make a pile from the candidates. The solution is to employ ‘honest’ Sumo wrestlers who associates only with ‘reformed’ Beagle Boys.


PROCRUSTES IS ADVISED: THE DANGERS OF DEADLOCK
Bluto of the Sailors had a parting word of advice for PROCRUSTES . In case he employs more than one Monster/Michelangelo-hopeful to do the job, he should be careful to avoid ‘Deadlock’. What could happen is that one Monster/Michelangelo-hopeful will pick up the chisel, another the hammer , a third one will grab the block of marble and the remaining Monsters/Michelangelo-hopefuls will cry foul. No Monster/Michelangelo-hopeful will let go of what has been grabbed. Each one expects the others to let go. These situations are very difficult to control. Just as in the case of traffic jams a lot of ‘beefy’ policemen are required to beat up everybody in sight and get the situation back to normalcy.


PROCRUSTES IS ADVISED: THE STRATEGY TO BE FOLLOWED
In short an Ad had to be put up and PROCRUSTES can relax after that.


PROCRUSTES IS ADVISED: THE FINAL ADVICE ON THE STRATEGY TO BE FOLLOWED
The last person at the in the dim lighting of the Pub of Bacchus now spoke up. It was Jumbo the Elephant.


PROCRUSTES IS ADVISED: ENTER THE GRAND SAGE OF MULTICS
Jumbo said he was aware of the problem PROCRUSTES was facing. He had consulted the Grand Sage of Multics on the matter.


PROCRUSTES IS ADVISED: THE MONSTERS ARE JUST TECHNOLOGY
He was advised that the Monsters were ‘technology’ which varies from place to place, age to age, culture to culture.


PROCRUSTES IS ADVISED: COMPUTATION IS UNIVERSAL
PROCRUSTES ’s problem was a problem of Computation. Computation is the same everywhere. Computation predates the Ages of Man. There is only ‘one’ Computation.


PROCRUSTES IS ADVISED: THE MONSTERS CAN BE DISPENSED WITH
The Monsters can be dispensed with. PROCRUSTES can quietly abscond.


PROCRUSTES IS ADVISED: COMPUTATION CAN BE DONE WITH ANY RESOURCE IN ANY ENVIRONMENT
The Monsters will take care of themselves. He could be mentally with them wherever he is in the world or Universe and ‘simulate’ their behavior. He could do with just the resources Nature has provided. He can make perhaps life easier for himself with some man-made items. He could also buy problems as a result of the same.


PROCRUSTES IS FRIGHTENED
On his way home Procrustes saw the fierce Head Executioner vigorously sharpening his sword. He could make out that his head was being eyed by the sly mathematicians and the Head Executioner.


THE EXECUTIONER IS ACTIVE & THE SLY MATHEMATICS ARE GRINNING




PROCRUSTES DECAMPS


Procrustes quietly absconded like the weavers of the Emperor's magic clothes. He left no address but took his Piggy Bank with him.


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PROCRUSTES RESURFACES
OR
PROCRUSTES AS RIP VAN WINKLE


It is understood that Procrustes has surfaced again of after a couple of decades and tried new types of 'narrowing' like quantum computation.
He found that if a number of small sticks of standard size are glued together in groups, or groups of groups ...of groups, to form a big stick he can determine the joints of the groups of sticks easily.
He can do this even if the sticks are 'beautifully' glued together.
This allows one to break into the Imperial Treasury.
He tried applying this new form of computation to solve his problem. The attempts were in vain.
This new form of computation was a case of his 'good old' Monsters parading in a new dress. It was a case of “old wine in a new bottle".
The mathematicians informed the Secret Agents of the Empire who almost got hold of Procrustes. He fled from the Empire and rushed off to the Oasis.



PROCRUSTES RESURFACES WITH QUANTUM COMPUTATION AND IMMEDIATELY ABSCONDS

PART III
"THE WILDERNESS OF THE ETERNAL QUEST"



THE MONSTER IS CONFUSED


Needless to say using Procrustean mathematics to model and explain reality resulted in coils of undecidability springing up. Even asking Procrustean mathematics to speak up for itself resulted in coils of undecidability. This was just as in the Tower of Babel.
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THE FAMOUS PROBLEM


Oracle after oracle was desperately consulted but enigmas like the generalizations of the P=NP problem surfaced. Very few seem to understand their nature and implications clearly.





THE ETERNAL ENIGMA OF IDENTICAL PROBLEMS




ATTEMPTS TO SOLVE THE PROBLEM


Toil, tears and sweat for over a century were of no avail in solving the problem. This applies to numskulls like me, the hoi polloi, the glitterati and the geniuses.





FIND AN EASY GUIDE!!




DENYING THE PROBLEM


Attempts to deny the problem as in the fable of the Fox and the Grapes does not seem to solve the problem. It keeps on surfacing everywhere.







DENYING THE PROBLEM STOPS THE GAME?--NO!




USING PROCRUSTEAN MATHEMATICS
FOR SIMULATION


The problem is that simulation is a very dangerous game. Procrustean mathematics can be used to specify computations to simulate the Universe.
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THE DANGERS OF SIMULATION


In simulation we end up with a situation like the multiple choice examination and know all the wrong answers.


KNOWING ALL THE WRONG ANSWERS SOLVES THE PROBLEM!


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THE SOLVER DOES NOT EXIST


There is no such thing as a Solver of problems. We end up as Verifiers of solutions, and experts in knowing what is not the Universe. We will know all the wrong answers.




WE SOLVE THE PROBLEM BY VERIFYING THE SOLUTION!


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THE DIFFICULTY OF PROVING
THE EXISTENCE OF THE SOLVER


We end up working very hard and come up with something trivial. We end up in learnedly knowing everything about nothing. We end up beating around the bush and making never ending excursions to the periphery, but never to the center. Whatever Procrustes may try his brand of mathematics can only simulate something not create anything. Simulating eating is different from eating.


THE LEARNED GAME: BILL STUMPS - HIS MARK


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THE SOLVER OF PROBLEMS MAY EXIST AFTER ALL


There seems to be a catch. Dreaming up something is different from reality. Or is it???? In case Procrustes succeeds to find a suitable model of mathematics, then the time immemorial 'eternal quest' of the environment will end.
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THE VERIFIER IS SUPREME


So it is not clear if Verifiers of solutions are as good as Solvers of problems.
In the limiting case of using a computing device for the simulation of anything in the Universe the Solver vanishes. Solvers just degenerate to Verifiers when Procrustean mathematics is used as a tool.
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RESTATEMENT OF A FAMOUS PROBLEM


Provers=Verifiers??? simplifies to (a procrustean) P=NP???? simplifies to are all equally clever in Verifying solutions???.



EVEN MICHELANGELO SAW THE IMAGE AND FINALLY VERIFIED HIS SOLUTION



WE ARE ALL VERIFIERS PLAYING THE GAME!


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THE SOLUTION TO THE PROBLEM


At the present moment it has been left as an exercise for future generations of children led by Winnie the Pooh and Tigger to solve the problem.


THE CHILDREN ARE SOLVING THE PROBLEM AT PRESENT


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THE USE OF THE SOLUTION


When the children and their leaders report back to us we will Verify the solution so that it can be presented to the Emperor of that far off land.


WE WILL VERIFY THE SOLUTION TO KEEP THE EMPEROR HAPPY




SOLACE AND CONSOLATION


We can take solace in the consolation given in a canonical book on computation by the legendary Prof. Marvin Minsky.
When describing the computable real numbers, to numskulls like me, he has consolingly remarked in his book: "Nobody understands it terribly well anyway."


NOBODY UNDERSTANDS IT TERRIBLY WELL ANYWAY!


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THE EMPEROR'S ROYAL PROCESSION


The show must go on, and the Emperor dressed as a swineherd must keep on parading in his new magic clothes, with the mathematics people bringing up the rear with their birches.


THE EMPEROR PARADES WITH THE SOLUTION


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EPILOGUE

"Whether or not it is clear to you, no doubt the Universe is unfolding as it should"---Desiderata.

So it is a case of --"God is in heaven and all is well on earth!". Just let us "carry on with it" and keep on doing whatever we are doing!!!!!




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AN EXTRACT FROM THE PICKWICK PAPERS
-- CHARLES DICKENS
-- TWO CENTURIES AGO


It was at this moment that Mr. Pickwick made that immortal discovery, which has been the pride and boast of his friends, and the envy of every antiquarian in this or any other country. They had passed the door of their inn, and walked a little way down the village, before they recollected the precise spot in which it stood. As they turned back, Mr. Pickwick's eye fell upon a small broken stone, partially buried in the ground, in front of a cottage door. He paused.
'This is very strange,' said Mr. Pickwick.
'What is strange?' inquired Mr. Tupman, staring eagerly at every object near him, but the right one. 'God bless me, what's the matter?'
This last was an ejaculation of irrepressible astonishment, occasioned by seeing Mr. Pickwick, in his enthusiasm for discovery, fall on his knees before the little stone, and commence wiping the dust off it with his pocket-handkerchief.
'There is an inscription here,' said Mr. Pickwick.
'Is it possible?' said Mr. Tupman.
'I can discern,'continued Mr. Pickwick, rubbing away with all his might, and gazing intently through his spectacles--'I can discern a cross, and a 13, and then a T. This is important,' continued Mr. Pickwick, starting up. 'This is some very old inscription, existing perhaps long before the ancient alms-houses in this place. It must not be lost.'
He tapped at the cottage door. A labouring man opened it.
'Do you know how this stone came here, my friend?' inquired the benevolent Mr. Pickwick.
'No, I doan't, Sir,' replied the man civilly. 'It was here long afore I was born, or any on us.'
Mr. Pickwick glanced triumphantly at his companion.
'You--you--are not particularly attached to it, I dare say,' said Mr. Pickwick, trembling with anxiety. 'You wouldn't mind selling it, now?'
'Ah! but who'd buy it?' inquired the man, with an expression of face which he probably meant to be very cunning.
'I'll give you ten shillings for it, at once,' said Mr. Pickwick, 'if you would take it up for me.'
The astonishment of the village may be easily imagined, when (the little stone having been raised with one wrench of a spade) Mr. Pickwick, by dint of great personal exertion, bore it with his own hands to the inn, and after having carefully washed it, deposited it on the table.
The exultation and joy of the Pickwickians knew no bounds, when their patience and assiduity, their washing and scraping, were crowned with success. The stone was uneven and broken, and the letters were straggling and irregular, but the following fragment of an inscription was clearly to be deciphered:--



Mr. Pickwick's eyes sparkled with delight, as he sat and gloated over the treasure he had discovered. He had attained one of the greatest objects of his ambition. In a county known to abound in the remains of the early ages; in a village in which there still existed some memorials of the olden time, he--he, the chairman of the Pickwick Club--had discovered a strange and curious inscription of unquestionable antiquity, which had wholly escaped the observation of the many learned men who had preceded him. He could hardly trust the evidence of his senses.
'This--this,' said he, 'determines me. We return to town to-morrow.'
'To-morrow!' exclaimed his admiring followers.
'To-morrow,' said Mr. Pickwick. 'This treasure must be at once deposited where it can be thoroughly investigated and properly understood. .....
END OF THE FIRST EXTRACT FROM THE PICKWICK PAPERS



SECOND EXTRACT FROM THE PICKWICK PAPERS
-- CHARLES DICKENS
-- TWO CENTURIES AGO

It appears from the Transactions of the Club, then, that Mr. Pickwick lectured upon the discovery at a General Club Meeting, convened on the night succeeding their return, and entered into a variety of ingenious and erudite speculations on the meaning of the inscription. It also appears that a skilful artist executed a faithful delineation of the curiosity, which was engraven on stone, and presented to the Royal Antiquarian Society, and other learned bodies: that heart-burnings and jealousies without number were created by rival controversies which were penned upon the subject; and that Mr. Pickwick himself wrote a pamphlet, containing ninety-six pages of very small print, and twenty-seven different readings of the inscription: that three old gentlemen cut off their eldest sons with a shilling a-piece for presuming to doubt the antiquity of the fragment; and that one enthusiastic individual cut himself off prematurely, in despair at being unable to fathom its meaning: that Mr. Pickwick was elected an honorary member of seventeen native and foreign societies, for making the discovery: that none of the seventeen could make anything of it; but that all the seventeen agreed it was very extraordinary.
Mr. Blotton, indeed--and the name will be doomed to the undying contempt of those who cultivate the mysterious and the sublime--Mr. Blotton, we say, with the doubt and cavilling peculiar to vulgar minds, presumed to state a view of the case, as degrading as ridiculous. Mr. Blotton, with a mean desire to tarnish the lustre of the immortal name of Pickwick, actually undertook a journey to Cobham in person, and on his return, sarcastically observed in an oration at the club, that he had seen the man from whom the stone was purchased; that the man presumed the stone to be ancient, but solemnly denied the antiquity of the inscription--inasmuch as he represented it to have been rudely carved by himself in an idle mood, and to display letters intended to bear neither more or less than the simple construction of--'BILL STUMPS, HIS MARK'; and that Mr. Stumps, being little in the habit of original composition, and more accustomed to be guided by the sound of words than by the strict rules of orthography, had omitted the concluding 'L' of his Christian name.
The Pickwick Club (as might have been expected from so enlightened an institution) received this statement with the contempt it deserved, expelled the presumptuous and ill-conditioned Blotton from the society, and voted Mr. Pickwick a pair of gold spectacles, in token of their confidence and approbation: in return for which, Mr. Pickwick caused a portrait of himself to be painted, and hung up in the club room.
Mr. Blotton was ejected but not conquered. He also wrote a pamphlet, addressed to the seventeen learned societies, native and foreign, containing a repetition of the statement he had already made, and rather more than half intimating his opinion that the seventeen learned societies were so many 'humbugs.' Hereupon, the virtuous indignation of the seventeen learned societies being roused, several fresh pamphlets appeared; the foreign learned societies corresponded with the native learned societies; the native learned societies translated the pamphlets of the foreign learned societies into English; the foreign learned societies translated the pamphlets of the native learned societies into all sorts of languages; and thus commenced that celebrated scientific discussion so well known to all men, as the Pickwick controversy.
But this base attempt to injure Mr. Pickwick recoiled upon the head of its calumnious author. The seventeen learned societies unanimously voted the presumptuous Blotton an ignorant meddler, and forthwith set to work upon more treatises than ever. And to this day the stone remains, an illegible monument of Mr. Pickwick's greatness, and a lasting trophy to the littleness of his enemies.

END OF THE SECOND EXTRACT FROM THE PICKWICK PAPERS



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VERY ROUGH DRAFT

THE CHRONICLES OF THE ‘snappy’ iMonsters
A MODEL FOR THE OUTSOURCING PARADIGM
OUTSOURCING AS A REFERENCE TO AN ORACLE
OUTSOURCING RELATED TO THE LETTER OF THE GRAND MASTER OF THE INCOMPLETE
OUTSOURCING PARADIGM RELATED TO THE SOLUTIONS TO THE P=NP PROBLEM USING 'P' TURING MACHINES
THE RELATION BETWEEN OUTSOURCING, SUBCONTRACTING AND REFERENCES TO ORACLES
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THE CHRONICLES OF THE ‘snappy’ iMonsters
SPLITTING TURING MACHINE COMPUTATIONS INTO COMPUTATIONS IN P
SPLITTING TURING MACHINE COMPUTATIONS FOR COMPUATATIONS IN NP
OUTSOURCING RELATED TO THE LETTER OF THE GRAND MASTER OF THE INCOMPLETE
OUTSOURCING PARADIGM RELATED TO THE EXACT COVER PROBLEM WITH 'P' TURING MACHINES
THE RELATION BETWEEN OUTSOURCING, SUBCONTRACTING AND REFERENCES TO ORACLES
THE CHRONICLES OF THE ‘snappy’ iMonsters


THE CHRONICLES OF THE ‘snappy’ iMonsters
A MODEL IMPLEMENTING CONCURRENT TURING MACHINES
COOPERATING, COMMUNICATING AND BROADCASTING COMPUTATIONS IN P
OUTSOURCING RELATED TO THE LETTER OF THE GRAND MASTER OF THE INCOMPLETE
IMPLEMENTING BRANCH AND BOUND AND BACKTRACKING WITH 'P' TURING MACHINES
THE ARCHITECTURES OF P COMPLEXITY TURING MACHINE ORGANISATIONS
THE CHRONICLES OF THE ‘snappy’ iMonsters




CIVILISING THE MONSTERS

The Monsters are a wild, uncivilized lot.
They are like a bunch of Tasmanian Devils at times.
A lot of the keep beating around the bush.
Some of them do whatever they feel like from a set of choices.


NONDETERMINISM IS BANNED

To civilize the monsters we will ban choice.
A Monster is deterministic.
It can only do one thing in any situation.


NONTERMINATING COMPUTATIONS ARE BANNED

Also we will avoid the Superior Monsters and demand they always terminate their computation some time.
So we will deal only with the Inferior Monsters.


THE ROOTS OF THE iMonster

When Adam and Eve were expelled from the Garden of Eden they were allowed to take the Apple with them.
That fruit was a source of inspiration for an Industrialist.


THE CREATION OF THE iMonster

A gifted industrialist had used his Intuition with the famous Apple and created a sleek, cute, artistic iMonster which is a civilized form of the Inferior Monsters.
This has nice User Interface and is a cuddly little affair like a baby Polar Bear or a baby Panda.
However one should keep one’s distance from them.
The intrinsic ferocity is still very much present.


FURTHER CIVILSING THE iMonsters

The iMonsters are a bizarre lot.
Some of them sleep for centuries then start working.
Some rush off like the hare in the story of the Hare and the Tortoise, and in no time at all fall asleep.
Some work by fits and starts.


THE ALGORITHMS CANNOT BE ENUMERATED

No census can be taken for the iMonsters.
Any official taking a census ends up finding that some iMonster has coolly escaped notice.


WELL BEHAVED FUNCTIONS AND WELL BEHAVED MONSTERS

The iMonsters are further divided into well-behaved iMonsters.
These well-behaved iMonsters compute for a time that depends on their input.
Larger the input the more they compute.
Also the ‘function’ that tells us how long they compute is said to be well-behaved by the mathematicians.
These are a rich class.


COMPLEXITY CLASSES

All the iMonsters whose computations can be described by some well-behaved function, belong to some Complexity Class.


THE BEHAVIOUR OF THE ‘well-behaved’ iMonsters

Only well-behaved iMonsters are considered to be worthy of notice.
So any reference an iMonster is a reference to a well-behaved iMonster.


A COMPLEXITY CLASS CAN BE ENUMERATED

The iMonsters now being well-behaved are amenable to the census officials.
A census can be taken and they can be enumerated.


THE DIAGONALISATION ARGUMENT APPLIED TO A COMPLEXITY CLASS

From any enumeration an iMonster who is a foreigner to the class can be created.
He differs from each member of the class in at least one thing.


THE CREATION OF A HIERARCHY OF COMPLEXITY CLASSES

Thus the concept of a Complexity Class imposes a class hierarchy on the well-behaved iMonsters.


THE SIMPLE LINEAR iMonster

A simple linear iMonster is a Inferior Monster which does the job of computation efficiently.
It reads each element in its input a fixed number of times.
Then it terminates its computation.


ALGORITHMS OF LINEAR TIME COMPLEXITY

Examples of problems for which simple linear iMonsters exist can be given.


THE MAXIMUM AND MINIMUM DETERMINATION

One simple linear iMonster exists for determining the tallest Dwarf in the Land of Dwarfs.
One simple linear iMonster exists for determining the shortest Giant in the Land of Giants.


THE SIMPLE iMonster DEFINED

A simple iMonster, not necessarily linear does its job ‘ easily’.


EXAMPLES OF SIMPLE iMonsters

Examples of problems for which simple iMonsters exist can easily be given.


THE GREEDY STRATEGY

One strategy suggested for creating decent simple iMonsters is called the Greedy Method.
It turn out in life that in many situation being as greedy as possible, as lazy as possible or as stingy as possible pays.


THE SINGLE SOURCE SHORTEST PATH ALGORITHM

A Great Sage from the Land of Dikes had used a Greedy Strategy and created a simple iMonster to determine the shortest path one should take when traveling from one’s home to any other place.


USE OF THE SINGLE SOURCE SHORTEST PATH ALGORITHM

This simple iMonster can be regularly employed to travel from one’s house to all the pubs in the world.


THE DIVIDE AND CONQUER STRATEGY

Another strategy suggested for creating decent simple iMonsters is called the Divide and Conquer strategy.
It comes from an old fable.
A rich but very old landlord had seven sons who always used to quarrel.
The father was worried.
If he died then the unpopular neighbor would see his sons quarreling and take away all the money.
He made a bundle of seven sticks and asked each one of his sons to break the bundle.
None of them could.
Then he untied the bundle and asked each son to break a single stick.
They could do it easily.
He told them the moral of the story, that United they stand and Divided they fall.
The sons stopped quarrelling and the greedy neighbor ran away.


THE QUICKSORT ALGORTIHM

A Great Sage while a student in Russia had used the Method of Divide and Conquer and created a famous, clever, simple iMonster to sort elements in a collection.
He called it the QuickSort iMonster.


THE USE OF THE QUICKSORT ALGORITYM

This simple iMonster could be usefully employed by Drill Masters all over the world to make a bunch of students fall in line in ascending order of height.


THE MINIMISATION OF FINITE STATE MACHINES

A Great Sage had used the Greedy Method and created a clever, simple iMonster to minimize the number of states a starved person is in when gobbling up a variety of dishes at a lavish birthday party.
He used the breakup to the joint family system in India as an example.
A family splits when two members disagree on some count, and stays together if they agree on all counts.


MULTIPLICATION OF TWO NUMBERS

A Great Sage from the Land of Beethoven had created a very clever simple iMonster to multiply two numbers.
This simple iMonster was a great improvement over the traditional simple iMonster to multiply two numbers.
It is not known if a still cleverer simple iMonster exists for the problem.


MULTIPLYING TWO MATRICES

Two Great Sages from the Land of Wagner had created by Divide and Conquer a clever simple iMonster to multiply two sudoko type arrangements of numbers.
This can be extended to create clever simple iMonsters for various Metamorphoses of Sudoku type arrangements of numbers.


LOWER BOUNDS FOR MATRIX OPERATIONS

For half a century it was a fashion to find faster and faster, cleverer and cleverer simple iMonsters to multiply two Sudoku type arrangements of numbers.
The end is not in sight as of yet.
It is suspected that ultimately a simple linear iMonster will emerge for the problem, though it will never be actually reached.


MODULO ARITHMETIC

Operating with very large numbers can be simplified.
One can consider the primes as the Big Chiefs of the world of integers.
An ordinary number is a plebian.
It can be described as a combination of short relations it has with the Big Chiefs.
By combining these short relations for various integers we can obtain short relations with the Big Chiefs and hence the description and manipulation of large integers.
This is used regularly by various ‘good guys’ and ‘bad guys’ to encode and decode messages.
This can all be done by simple iMonsters.


PATTERN MATCHING

Simple iMonsters have been found to find patterns.
This can be in texts to isolate plagiarism, it can be simple in pictures to locate some particular simple image or simple outline of the same.


THE USE OF TRANSFORMATIONS

Sometimes it happens that difficult problems in one part of the world are easy to solve in another part of the world.
Sometimes simple iMonsters do not seem to exist for some problems.
If we apply Metamorphoses to the environment by transformations then simple iMonsters can solve the problem in the new environment.
Then we transform back to the new environment.


CLASSIFICATION AND ARCHIVING THE simple iMonsters

A vast number of simple iMonsters have been found and defined.
The memex has archived and recorded many of them.


THE iMonster ELABORATED UPON

The cute, sleek, user friendly iMonster not necessarily simple or linear is a model for any Inferior Monster.
It is basically very lazy, and comes from the Leisure Class.
If a problem cannot be done by a simple iMonster then the iMonster will sub-contract, or outsource parts of the ‘job’.
This outsourcing is what is called referring to a simple oracle.
Consulting a simple oracle, or outsourcing basically costs a pittance.
So its cost and effort can be ignored.
It is basically free.
An iMonster will outsource to a iMonster, which in turn can outsource to another iMonster and so on.
It is like having levels of sub-contracters, or levels of simple oracles.


THE DEFINITION OF THE iMonster

In short an iMonster is a ’ good old’ simple iMonster that can optionally use at any step of its computation an iMonster as a simple oracle or sub-contractor who works for a pittance.


THE simple iMonster DEFINED

The simple, tractable iMonster belongs to an environment where outsourcing is banned, but the jobs can be done ‘easily’.


ALTERNATIVE DEFINITON OF THE iMonster WITH OUTSOURCING

Alteratively the simple, tractable iMonster belongs to an environment where the number of levels of outsourcing, subcontracting, or simple oracle instances is fixed.
They do not depend on the input size.
The results of the outsourcing are combined together in all possible ways.
Some people prefer to call simple iMonsters as ipMonsters.
They are basically a very tractable lot.


THE ARRANGEMENT OF THE iMonsters

The iMonster is a very modular structure.
The modules are all uniformly simple iMonsters.
These can be arranged as an organization tree.
The root of the tree is the Main iMonster.
The others are oracles to it.
The oracles may have oracles.
The organization tree may be static or dynamic.
It could be a Sudoku type structure where the numbers represent simple iMonsters.
A number can represent an iMonster.
In this case the number is a short form for another Sudoko type structure which serves as an oracle to the simple iMonster representing the number.
Various Geometric arrangements of the simple iMonsters can also be considered.


THE BASIC PROTOCOLS

The iMonsters compute by arranging for harmoniously “Cooperating iMonsters”, “Communicating iMonsters”, or “Broadcasting iMonsters”.
An iMonster basically communicates with another iMonster which is its oracle.


THE HARD INTRACTABLE(?) ihMonster DEFINED

The incorrigible, seemingly intractable ihMonster is a Monster that deals with hard computations.
When converted to iMonsters it has a requirement that the number of instances of levels of outsourcing, subcontracting, or simple oracle references are dependent on the input size.
The results of the outsourcing are combined in all possible ways.


THE EFFECT OF THE EXPONENTIAL

In practice it turns out that in no time at all, as soon as the input size starts exceeding 40 elements, the instances of outsourcing, subcontracting or simple oracle references soon equals and rapidly exceeds the number of stars in the visible Universe.


THE SUPERIOR MONSTER RELATED TO iMonsters AND OUTSOURCING

A Superior Monster requires an equivalent iMonster that in general has the instances of outsourcing, subcontracting, simple oracle references be at times be infinite.
Also the instances may not be easy to elaborate.


THE INFERIOR MONSTER RELATED TO iMonsters AND OUTSOURCING

An Inferior Monster requires an equivalent iMonster that in general has the instances of outsourcing, subcontracting, simple oracle references be finite at most.


THE ‘snappy’ iMonster AND THE IP=PSPACE SITUATION

A special class of iMonsters is the ‘snappy’ iMonsters.
These are simple iMonsters that can outsource, subcontract or refer to simple oracles.
The number of levels of such references must be determinined by a simple iMonster.


THE CLASS OF npiMonsters RELATED TO THE P=NP SITUATION

A special class of Monsters, known as the inpMonsters, can be reduced to equivalent iMonsters that have the number of instances of levels of outsourcing, subcontracting, simple oracle instances be at most equivalent to the number of PRIMES in the input size, or perhaps half of this number.
This class is of special interest and will be elaborated upon by the Visitor from the Land of the Redwood Trees using his famous Can.


THE TRACTABLE ihMonsters AND DYNAMIC PROGRAMMING-I

Some ihMonsters are seemingly intractable.
Actually they represent problems where the equivalent iMonsters are overdoing their outsourcing, subcontracting and referring to simple oracles.
They keep on doing it over and over again for the same problems.
This leads to astronomical bills for outsourcing though each outsourcing contract should cost only a pittance.
It is like a search engine calmly making a billion dollars a nickel at a time.


THE TRACTABLE ihMonsters AND DYNAMIC PROGRAMMING-II

The method of Dynamic Programming was invented to avoid this wasteful repetition of outsourcing, sub-contracting and simple oracle references.
The outsourcing orders are ordered so that no repetition takes place.


A USE OFDYNAMIC PROGRAMMING-THE SHORTEST PATHS PROBLEM

Using this method it is possible to find the shortest path from any pub in the world to any other pub in the world using a simple iMonster.


A USE OF DYNAMIC PROGRAMMING-OPTIMAL BINARY SEARCH TREES

A Great Sage had created using Dynamic Programming an optimal tree structure like a hierarchy or organization chart for housing the animals in a Zoo such that the popular animals are nearer the entrance to the Zoo and the less popular animals deep down in the Zoo.
The amount of walking the children must do on the average is minimized.
The computation is done by a simple iMonster.


THE USE OF DYNAMIC PROGRAMMING

The net result is that a large class of problems ends up having simple iMonsters solving them.


THE HARD PROBLEMS OF HISTORICAL INTEREST

From time immemorial a large class of problems had mathematicians ‘stumped’.
There seemed to be no simple iMonster solving the problem.
The iMonster for the problem was actually a inpMonster.


THE HAMILTONIAN CIRCUIT PROBLEM

One classic problem of this type was the problem of the Curse of the Grand Slave of the Celtic Monsters.


THE BIN PACKING PROBLEM

Another classic problem was that of determining the minimum number of sacks of fixed size the Romans needed to loot the treasuries of Carthage.
Later on the same problem was faced by Attila the Hun in determining the minimum number of sacks of fixed size needed to loot the treasuries of Rome.
The story goes on.
The problem requires a inpMonster i.e. an iMonster with the number of outsourcing contracts depending on the input size.
No simple iMonster has been found for the problem.


THE TRAVELING SALESMAN PROBLEM

Another classic problem was that of determining the minimum distance the milkman should walk everyday from his house, deliver the milk to all the customers in huts in the forest, without visiting the same hut twice and return to his house.
The problem requires an inpMonster i.e. an iMonster with the number of simple oracle references depending on the input size.
No simple iMonster has been found for the problem.


THE REGISTER OPTIMISATION PROBLEM

Another problem of interest deals with the perks of Ministers.
In some country no work can get done unless it is of the Ministers, for the Ministers, by the Ministers.
In some Public Sector and Government organizations the story repeats.
The Ministerial berths or the high Management and beauracratic posts are limited in number.
Also they are expensive to maintain as it involves a lot of perks to be built into the post.
The minimum number of Ministerial berths in a Cabinet to get all the work done without some Minister being ‘bounced’ or ‘spilled back to a plebian’ is the Minister Optimization Problem.
It turns out that this is a inpMonster solvable problem for which no simple iMonster is known as of yet to solve the problem.


THE JOB SEQUENCING WITH DEADLINES PROBLEM

Another problem deals with a group consisting of more than one Washer man.
They are a very popular group and thousands of people want their services.
They are booked for years on end.
The Washer men maintain a register to consult and record for orders booked.
An order from a customer can be executed in a day’s time.
It has a profit associated with it and a deadline date by which the customer wants his clothes.
The Washer men must select the customers so that they maintain the deadlines and maximize their profit.
This problem is called a scheduling problem and no simple iMonster can solve it.
It requires a inpMonster and it is not known if a simple iMonster exists to solve the problem.


THE NP-complete PROBLEMS

For all such problems there exists a simple iMonster which can convert an iMonster for one problem to an iMonster to any other problem of the club.
Thus these problems form a Club.


THE RELATION OF THE CLASS NP AND OUTSOURCING AND PRIME NUMBERS

All these ihMonsters or more specifically the inpMonsters require subcontracting, outsourcing or simple oracle references to be dependent and bounded by the number of PRIMES in the input size.


THE CAN OF WORMS HOUSES NP-complete PROBLEMS

It is these ihMonsters that are housed in the Can of Worms.


THE PROBLEM RELATED TO THE PROBLEM POSED BY THE GRAND MASTER OF THE INCOMPLETE-I

The problem posed by the Grand Master of the Incomplete is as to whether the inpMonsters have an equivalent simple iMonster i.e. an iMonster that will not use subcontracting, outsourcing or refering to a simple oracle.


THE PROBLEM RELATED TO THE PROBLEM POSED BY THE GRAND MASTER OF THE INCOMPLETE-II

A view of the inpMonsters Brer Fox wants to find the way to Brer Rabbits house.
He is too proud to ask for directions.
He tries all possible paths.
This requires an ihMonster to simulate the problem.
If Brer Fox takes the advice of Brer Bear for guiding him he is better off---
1) Brer Fox is very lazy.
He asks Brer Bear to find out the path.
He gives him a map.
Brer Bear now has an outsourcing job.
He determines the path and dictates the steps to Brer Fox.
Brer Fox is now an iMonster.
So is Brer Bear an iMonster.
2) He can take a fixed number of steps and consult Brer Bear as to which one is right step.
Then he proceeds to the next step.
Here Brer Bear is the oracle who answers in a jiffy.
He is an iMonster and so is Brer Fox.
3) He can give a map to Brer Bear and consult him for each step.
Brer Bear studies the map at each step.
Here Brer Bear has the outsourcing job and consults the map and advices the step based on the past history of the journey and the existence of a path to Brer Rabbits’s house.
Here Brer Bear doubles up as a simple iMonster.
4) In all the above Brer Bear can look up the MEMEX or he can use a simple iMonster to find the path from the map.
A simple iMonster is known to exist to solve the problem.
In either case Brer Bear is a simple iMonster and hence so is Brer Fox.
5) This is the eternal problem which predates the Ages of Man.


APPROXIMATE SOLUTIONS FOR THE PROBLEMS IN THE CAN

It has been shown that one cannot approximate the computation represented by a worm in the can by a simple iMonster.
Any approximation is also a worm in the can.
No worm can claim to be almost a worm in the can.
Either a worm belongs to the can or it does not.


APPROXIMATE SOLUTIONS THAT ALMOST WORK

If the iMonster organizes the outsourcing by an hierarchy chart then techniques called Branch and Bound and Backtracking can be used at times to obtain solutions in many instances.
They will not always work efficiently.
The simple iMonsters in the outsourcing scheme can be determined at the start of the project in a static hierarchy chart.
Alternatively the simple iMonsters can be added in a modular fashion dynamically as the computation proceeds in a dynamic hierarchy chart.
Another method is to use the oracle with backtracking techniques.















NOTES & COMMENTS

(Computation in all Environments predating all Ages, all Revolutions, all Civilizations)

During his Visit to India in the mid-seventies Prof, C A R hoare,FRS had suggested and directed that the concepts in Computer Science were basically very simple. The had been made unnecessarily complex and complicated. Common Sense explanations had to be found. The Goedel Turing Society of India has been attempting the implementation of the directive.

Mass IT literacy for a couple of million school children has been attempted for two decades by ECIL, India. This particular study is an updating & adaptaion of studies made during 1996-2006.

Earlier 'hobbyist' studies were from 1975-1995, at ECIL, India. This was the classical period in the environment when industrial strength software had to be developed without a reliable computer. Barring the isolated islands of a few higher tier institutions, education and training in Computer Science and Software in the vast mass of the environment had to be done without a computer, with very limited literature, with at times only traces of the industrial and information technology revolutions. At times the environment could be pre-agrarian and feudal.

The main reliable computational tool for education, training and development of software was the RASP, a variant of the Monsters considered above. The RASP (along with other models of universal computation) was the tool used successfully for mass instruction during the Y2K period. This shows perhaps the 'power' of metamathematics.

The dry subject of Metamathematics is considered. For decades in the environment it has been found that all attempts to teach, study or force feed the subject have been avoided and/or evaded by most students.

To make it palatable it is converted to an attempted user friendly fairy tale.

The treatment is however superficial. Today a motivated person has the MEMEX at his/her disposal. The tale is written so that it can be adapted and translated easily to any culture and language. This localization is essential to cater to local cultural sensitivities, prejudices and beliefs.

Common sense depends on the environment, language, history, geography, economic situation, and way of life and culture of the audience. So examples have to be tailored by localization. Sometimes it is Universal like animal stories, provided the animals are acceptable. Some cultures ban animal stories. Some consider astrologers and oracles a farce. This goes on and on.

The core of the present exposition is however based on the accepted standard fare in the curriculum of Metamathematics and The Theory of Computation. The spice can be dispensed with. Search engines and pointers to the MEMEX can be used for formal studies.

The yardstick used to measure the success of the exposition matters. Here it is a simple requirement that the students should 'clear' their standard examinations and get over the long lasting 'terror' and 'hate' of the areas involved.

They should be able to appreciate the humorous side of the concepts, which results from the limitations of the human race in putting comprehensible order and purpose into what Lincoln in one of his famous letters termed the 'eternal mystery'.

The blind vociferous extrapolations from the finite and bounded to the infinite and unbounded always lead to humorous situations. This is like the naive software programmer assuming his methods can be indefinitely scaled up to colossal software and beyond.

It is like a Software Engineering Environment dedicated to small Organic software or just lower level Software Service activities extrapolating itself to all the activities of industrial strength Semi-detached and Embedded Software Engineering Environments.

It is like a villager or tribal from pre-agrarian societies extrapolating his environment to that of a modern advanced Mega polis.

It is like a child extrapolating the power of the contents of its Piggy Bank with the power of the 'kiddy banks' of Croesus or Kubera.

It is very, very difficult to comprehend meaning and effects of the explosive power of the exponential or Ackermann’s function. One normally deals with a small limited size environment.

For most people it is very, very difficult to appreciate the complexity that can be there behind a simple very user friendly naive user interface. This refers to the first acquaintance one makes with a Turing Machine, any model capable of Universal Computation, a Google-type search engine, or any very user-friendly naive looking GUI of a software package.

If one wants to be 'scientific' one can remove most of the references to epics, myths and legends from this study.

The mapping to various myths, legends and cultures shows some of the crudeness of metamathematics. The 'beliefs' of the former and the 'axioms' of the latter are equally 'humorous'. Both have resulted in all the 'good' activities and 'bad' activities of the human race. Both 'miraculously' explain a lot of things. What they cannot express or explain are either 'open problems' which are conveniently left for future study or just declared or made 'taboo'.

It appears now that as expected both have suspiciously met each other at the same dead end.

The yardstick used to measure the success of the exposition and related instruction has shown that quite a few students like to study the areas further. Clearing the standard examinations is easy. The irrational fear reduces or vanishes. It is a case where the end justifies the means.

Samuel Johnson had commented on the dog standing on its hind legs. "It is not done well; but you are surprised to find it done at all." This applies to the present exposition and in general to most solutions to problems using Interactive Verifiers to replicate the solution of a Solver.

This attempted Common Sense exposition is for a target group of K-12 schools and beginning undergraduates in any area.

The target groups do not easily accept two valued logic, rationalism and decidability as the norm. They are at times hostile or not able to comprehend the treatment of the infinite in the metamathematics of the current times. For some cultural backgrounds the treatment of infinities is naive and common place.

The concept of proof does not exist in some environments. The reliance on intuition is common. One guesses the result and verifies it. Alternatively one reuses the solution 'someone' has found. One waits patiently like a Turing Machine till the 'guesser' arrives.

The normal traditional tendency is to wait for decades for the gifted person to turn up to do the job. The Interactive Verifier is used to replace the gifted person for a low cost 'if possible'. The Verifier competes with the gifted using procedures for finding faults, and normally wins. The prized secure government jobs cater to Verifiers.

The person with Vision or any normal person suddenly getting inspired and finding a solution to a problem parallels the ancient legend of Prometheus bringing Fire. Thus we have a hypothetical model of Prometheus making never ending but asynchronous, unpredictable trips bringing "fire" and training Interactive Verifiers. The Solver vanishes and only Interactive Verifiers and Verifiers exist.

Some persons have a Vision that cannot be reduced to procedures. They cannot articulate the steps involved. In this case we do not consider them to be Solvers. They are possessed. Either we put them on a pedestal or consign them to the stake. The 'pedestal' and the 'stake' have equivalents in all cultures and environments. Actually there are 'pedestals' of varying heights and a large variety of 'stakes'.


Every human being has both types of Visions many times during their life. Some have it more often and more intensively.

In the environment undecidability and hierarchies of undecidability are a usual accepted way of life.

However the target groups are very much interested in the opportunities the Global Village creates. Thus they are amenable to experiments in "Leapfrogging Technologies and Cultures".

The discussion here tries to use only traces of the agrarian, industrial and information technology revolutions. This is the common situation.

Outsourcing in the Global Village demands a broad knowledge and tolerance of multifarious cultures and appreciation of their buried past.

The discussion here is to be supplemented by adding a base of (slightly Procrustean) general knowledge from History, Geography, Mathematics, comic characters, Folk wisdom, folklore, epics, myths and legends as required. This can be in the form of stories or can be obtained by surfing the MEMEX (i.e. Net).

The story starts from 1800 AD. This was the time Gauss posed the problem of primality, and articulated his views on the same. He also talked about Geometries with a curvature in space.

The great contributions of Germany from 1800-1900 AD are just not known in India. They have been effectively blanked out in educational systems in India for over a century, even after the end of Imperialism. This explains why metamathematics as it is defined today finds a vacuum in the local environment.

The comic characters used are Tom and Jerry, Popeye & Co., Winnie the Pooh, Tigger & Co, Asterix & Co., and in due course others like Bluto. The Beagle Boys are referred to so the concept of 'goon' becomes user-friendly. They really are not essential and can be replaced by local cultural equivalents, as they are used as stereotypes. The block of Marble is an adaptation from the Menhirs of Obelix in the comics Asterix the Gaul. The Druids and magic potion is motivated by the same source.

The aim is to fit the fairy(?) tale in a setting of general knowledge. This is to stimulate the use of the MEMEX for the same. The MEMEX is seen to take the role of the Solver for Interactive Verifiers.

An attempt has been made to refer to all the continents including the mythical lost continent of Atlantis, the Island Continents of Antarctica, Australia and Madagascar. Some other facts from Geography is thrown in.

Use has been made of Greek Mythology as per ancient renderings for children like Charles Kingsley, Bullfinch's Mythology, or the (Procrustean?) movie The Clash of the Titans. From Norse mythology Odin has been used both as a warrior and as a seeker of knowledge. He also models an oracle machines as per mythology. Thor from Norse mythology is just used using the story of his visit to the Giants. The Midgard Serpent is used for spice. The references to Hindu mythology or the High Priest and his activities are only for spice and not essential. The Christmas Carol is accommodated. The Virgin Goddess Isis and her son Horus are from Egyptian mythology. The Jinn are from the mythology of the Middle East and the Rakshsas from Hindu mythology. They are used for the concept of 'nondeterminism' by multiple copies.

Nostradamus is referred to by using the prediction relating to the man made mountains. He is used as the living example of an oracle. Joan of Arc and Michelangelo are used as living examples of The Gifted Ones. The Atheist is both accommodated and not accommodated.

The concept of immortality is mapped to a machine computing forever, or an entity living for ever. The concept of mortality is mapped to two types. The machine chooses when to terminate the computation, the Bheeshma concept. It is not preempted by an external agency. The other type is that it is preempted like a normal living thing. It appears only the first type leads to the current open problems, and it is only this which had been considered.

A novel of interest is Dr. Jekyll and Mr. Hyde to show that appearances are deceptive, and that two valued logic is limited. The other novel of interest is Oliver Twist adapted so that Oliver gets more so long as he asks for more. This models Growing Automata. The Pit and the Pendulum is from Poe. It has been diluted to make it palatable for small children.

Formalization of mathematics is restricted to stating two formulas: P=NP & IP=PSPACE. No 'learned' explanations of them are attempted. The overuse of symbolism and abstraction in all methamathematics has led many persons with the feeling of encountering unspeakable horrors.

To interestingly state a NP-complete problem without mathematical notation the Hamiltonian circuit problem is recast with Celtic Monsters. It is still not clear as of yet how to reduce the Satisfiability Problem to a common sense, easily comprehendible problem involving Monsters. The vandalism of the Sphinx and pyramids during the French invasion of Egypt is historically recast and pushed into antiquity.

The legend of Beowulf is added for just spice, to illustrate in a light way how motivation comes to a gifted person. The pre-agrarian, agrarian, industrial, information technology revolutions are bypassed to leapfrog from "the mythical times of Beowulf" to the invention of the Turing machine. The actual history can always be read up on the "MEMEX" in all the gory details of the environment of the World Wars.

The surface knowledge about ancient Rome only assumes one has seen some classical popular Hollywood movies. Rome is used for spice. Napoleon is used for his reference to China as the sleeping giant.

The Mandarin is used as the stereotype of a high IQ Verifier who only follows procedures. He represents the steel frame of effective high IQ beauracracy.

The Verifiers form a pyramid and the upper end Verifiers are expected to be of the highest IQ. This was pointed out by Prof. C A R Hoare, FRS as being essential for the development of high quality large industrial strength software.

The Grand Master of the Incomplete is Goedel. The reference to Redwood Trees is an allegorical reference to the collective wisdom of Computer Scientists on Intractability from Western USA. The reference to Man Made Mountains is an allegorical reference to the collective wisdom of Computer Scientists on Intractability from Eastern USA. The reference to the Wanderers is an allegorical reference to the collective wisdom of Computer Scientists on Intractability from the International Community. The reference to Great Lakes is an allegorical reference to the collective wisdom of Computer Scientists on the creation and use of the MEMEX. The Land of The Five Rivers is the Indian subcontinent. The Land of Leo Tolstoy is Russia.

The references to Software Engineering are an adaptation from Software Engineering Economics, by Capers Jones. The references to Google are an adaptation from The Google Story by Vise.

The Universal fables used are those of The Fox and the Crow, The Fox and the Grapes, The Ass in the Lion's skin, The Frog and the Ox & The Emperor's New clothes.

In an unkind cut, perhaps because they have made their subject unnecessarily difficult, the metamatheticians have been held responsible for the bloodshed of the French Revolution, the Communist Revolution and the horrors of the World Wars, and perhaps current wars also.

The Liar's Paradox, the Barber's paradox, Zeno's paradox, the Cannibals paradox are standard fare along with Archimedes and finite numbers.

The Proclamation of Commandments for Sets are the ZF, ZFC and similar finite collections of axioms.

Relating them to example involving the Aztecs and Incas is to kindle a historical study of the Voyagers, the discovery of the New World, the Pirates of the Caribbean, etc. etc., to the current outsourcing scenario. The tortoise holding up the Earth is from Hindu mythology and using it as a Beast of Burden is from the Windows 7 desktop.

Decades ago the poor allosaurus was accused of having a brain of a few grams in its tail. This was later refuted. However it seems to be an interesting concept and is used here as a model for most Managers, Administrators, feudal Aristocrats, Bosses and hence most (Interactive) Verifiers.

Informal words which speak volumes are 'dumb', 'jiffy', 'soften', 'easily’, ‘goon', 'gang' and 'stumped'. They are freely used for communicating concepts succinctly and effectively.

The concept of reducibility has been illustrated by using Ovid's Metamorphoses. This can be culturally mapped to the local folklore or legends.

The Piggy Bank mentioned can be replaced by Kiddy Bank or the local equivalent time immemorial pot. The use of the word 'Pig' is offensive in some cultures.

To cater to the sensibilities of some cultures the words 'High Priest' and 'excommunicated' will have to be replaced by terms like 'medicine man'.


SCROLL UP A WEE BIT FOR THE FAIRY TALE!!!!!








THE GLOBAL VILL AGE HAS TAKE N OFF!!!
THE GLOBAL VILL AGE HAS TAKE N OFF!!!
THE GLOBAL VILL AGE HAS TAKE N OFF!!!
THE GLOBAL VILL AGE HAS TAKE N OFF!!!
THE GLOBAL VILL AGE HAS TAKE N OFF!!!
THE GLOBAL VILL AGE HAS TAKE N OFF!!!
THE GLOBAL VILL AGE HAS TAKE N OFF!!!
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS

THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSP ACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE MEMEX + THE DUMM Y AND IP=PSPACE! OOPS !
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!

COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS

COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS
COMPUTATIONAL COMPLEXITY AND CHAOS

THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!
THE GLO B AL V ILLA G E ==> VERIFIERS RU LE!!


SOLVER!!! SOLVER!!! SOLVER!!! SOLVER!!! SOLVER!!! SOLVER!!! SOLVER!!! SOLVER!!! SOLVER!!!