Having arrived home, Gardner immediately showed to Conway more than 20 articles devoted to calculation of a day of the week for any date. Lewis Carroll's rule looked better than the others. Gardner turned to Conway and told: "John, you need to develop simpler rule which I will be able to share with readers". And, as Conway, long winter nights when Mr. and Mrs. Gardner went to sleep at home (though on a visit he came to them only in the summer) tells, Conway reflected how to make such calculation rather simple that it could be explained to the average any passer-by.
He thought over it all way home, and in the general room of university, and at last guessed "the rule of the Doomsday". For work only addition, subtraction and storing were required for algorithm. Also Conway thought up the mnemonic rule helping to store intermediate calculations on hand fingers. And for the best storing of information on date, Conway bites the thumb.
Traces from teeth have to be visible! Only this way it is possible to remember it. When I tell students about this method, I always ask someone from the first row to confirm existence of marks from teeth in a finger. Serious people so you will not force to do – they will decide that it is kindergarten. But sense that all this business usually is not delayed at you in a brain and you forget the date of birthday designated to you by the person. But the thumb is capable to remember for you how far this date will be spaced from next "Doomsday".
Over the years Conway taught this algorithm thousands of people. Sometimes in a conference room the person on 600, calculating birthdays of each other and biting the thumbs is taken. And Conway, as always, tries to be unreasonable – he is not satisfied with the simple algorithm any more. Since the moment of development he tries to improve it.
Except the periodic trips to Gardner, Conway wrote that long letters in which summed up the researches. It was in the habit to insert into the typewriter a paper roll (similar to that in which wrap meat) and printed letters, measuring them longwise. Usually there was enough letter a little more than a meter long though the record, according to the estimates of Gardner, was equivalent to 11 normal pages.
Usually it began letters with a preamble:
Received the first sending with books directly before Christmas, and so was delighted that several days read them and re-read, especially "Alice" with comments (my wife is not excited about you!).
Then it went deep into news on the researches, having begun, let us assume, with the solution concerning separation of pie, passing to a new riddle with a wire and a thread, and then devoting the most part of the letter:
Escapes. We thought up this game two weeks ago, in the afternoon on Tuesday. To the environment all mathematical department was infected with it, even secretaries gave in. We begin with n of points on a sheet of paper. The course consists in consolidation of two points (it is possible to integrate a point with itself) by means of a curve, and then in designation on this curve new point. The curve should not pass through old points, should not cross old curves, and one point should not leave more than three curves. The one who cannot make the course loses in normal Escapes. In Escapes miserable amount loses the last, made course.
"Escapes" were invented jointly with the student Mike Paterson and lit in the column Scientific American in July, 1967. In response to the letter Gardner sent the list of questions beginning with a question "What designates H in the name John H. Conway?". After each question Gardner left a lot of place on a leaf to enter the answer.
Horton. And why a lot of place left? You thought, it will be something like Hog-ginthebottomtofflinghame-Frobisher-Williamss-Jenkinson?
Gardner was also interested in game origin parts. "I foretell that this game will become so commonly accepted and known that parts of its creation will be interesting to history, - Gardner wrote. – You could not tell about them in more detail? You drew a scribble at lecture (if yes, that what?) Or behind a glass of beer?"
We drew a scribble after tea drinking in the general room of department, trying to invent game for a pencil and paper. It was how I carried out the complete analysis of one old game in which there were points, but there was no adding new – so it had no "escapes". It came from one quite difficult game with folding of brands which Mike Paterson turned into game for a pencil and paper, and we tried to modify its rules. And Mike told – why not to add a point in the middle? And at once all other rules were discarded, the initial position is simplified to n of points (initially – 3), and escapes began to grow …
Next day it was played, appear, by all. Behind coffee or tea of a small group of people drew silly or very difficult pictures from escapes. Some were already engaged in it on Klein's bottles, etc., and one mathematician reflected on multidimensional option of game. Leaflets with batches could be found in absolutely unexpected places.
As soon as I try to acquaint somebody with it, it turns out that he already somewhere heard about it. Even my daughters play 3 and 4 years it – though I usually win against them.
And Conway did not stop. The following letter was entitled:
IMPORTANT! BREAK IN POBEGOLOGIYA!
The named positions: wood louse, bug, cockroach, ear ring, scorpion
Today there is already "The international association of game in escapes" [The World Game of Sprouts Association] which "is devoted to studying of reality of escapes" and to "serious research of game". She holds the annual online championships. Only people as the computer analysis of game for these years inspired some can participate in them to write bots for game. Conway learned about this association recently, but he knew of existence of the computer programs playing game for a long time.
It was sad news. Computers were used for a solution of a number of open problems. They could solve the problems existing for 100 years. We wanted to invent game which it would be difficult for computer to play.
At the beginning of the 90th three scientists from Laboratory Bella and Universiteta Karnegi-Mellon wrote work "The computer analysis of game in escapes" in which advantageous strategy up to n=11 were analyzed. "After 11 points their program could not cope with complexity of game", - Gardner for the readers wrote. In a couple of decades two French students who decided to break a record wrote the GLOP program (in honor of the French character of comics Pif le chien telling glop every time when he tested satisfaction). They protected doctor's on this subject, and claim that they found advantageous strategy up to n = 44. Conway was very interested and surprised with it:
Strongly I doubt. They claim that they made impossible. If somebody claimed that he invented the machine issuing plays it is not worse than Shakespeare – you would believe them? It is very difficult, and all here. It how to teach pigs to fly. But it would be interesting to me to look at their work.
One more example of genius of Conway – the game "Traffic jams" in which the invented country has the triangular card and the cities are provided by letters. All letters are the first letters of names of the real cities — Aberystwyth, Oswestry and Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch.
I suspect that Conway invented game only once again to have an opportunity to say the name of the city Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch. He saw it on the plate at railway station and on a city square. It is interesting that these signs differed on single letters. And as for game, her question was – what first step the player has to take?
In the game "Stoppers" four players begin with Aberystwyth (A), Dolgellau (D), Ffestiniog (F) and Merioneth (M). They in turn move on one-sided streets between the cities. Game comes to an end when all players get stuck in Conwy from which there is no output. That whose course had to be the following loses.
All these games delivered data for the theory of syurrealny numbers of Conway. His own daughters, Suzy and Rosi, 7 and 8 years were the best experimental players.
By a lucky chance, during this period (about 1970), the champion of Britain according to Guo, John Daymond, studied in Cambridge. It founded Guo's society and constantly played this game in the general room. Daymond who now is the president of the British association go does not remember that he at least once played with Conway. Conway usually stood nearby, looked at a board and reflected over the courses of players.
They discussed the courses behind game, and uninvited advisers made a din around: "Why you so silly descended?". And these bad courses for me looked the same as good. I never understood go. But I understood that by the end it breaks into several games – in one big game there were small games in different parts of a board. And it roused me to development of the theory of the sums of guerrilla games.
And it, in turn, roused it to a bigger addiction to games. It with itself always had all necessary accessories that it was possible to fall upon the rival unexpectedly. In its leather case there were always cubes, checkers, a board, paper, pencils, a rope, and several packs. It were successful gamblings and tricks. Its analysis of games evolved from simple before compound games, to cases when the player at the same time played several games at once (sometimes, for example, chess, go and the game "Domineering") – and the player selected in what of games to him to descend. And it filled paper rolls with the analysis of these games. As he told the reporter of the Discover log:
I was waited by a surprising surprise – I understood that there is an analogy between my records and the theory of real numbers. And then I understood that it is not analogy – it really there were real numbers.
And all this developed as a result to become syurrealny numbers – the biggest expansion of a set of real numbers. The name to them was given by the computer specialist from Stanford Donald Cnut. And since then Conway did not worry about the workaholic professor Frank Adams and about pleasing him and his colleagues any more. He understood that this opening which came from "silly games" belonged already to serious mathematics. After for one period in 12 months it thought up syurrealny numbers, invented the game "Life" and opened Conway's groups, it accepted "oath": "And yes you will stop worrying and feeling guilty, and yes you will do that, anything to you". He gave up to the natural curiosity, went there where it led it — though to entertainments though to researches though in general to some nonmathematical place.
Gardner summed up the theory of syurrealny numbers as "Vintage Conway: deep, the innovation, concerning, original, brilliant, witty and different the Kerrollovsky word play. And on the trivial base Conway builds the huge and fantastic building. But to what it is devoted?
Conway in work under the name "All Numbers, Big and Small", raises a question more simply: whether this structure has an advantage?
" It is on border of entertainments and serious mathematics, - the American mathematician of the Hungarian origin Paul Halmos says. – Conway understands that it will not call great, but can try to convince you that it such". On the contrary, Conway believes that syurrealny numbers – the great thing, without everyones "can". He is simply disappointed that they did not lead to greater things yet.
And on what place they put it on the way of ancient intellectual travel to beauty and the truth? Conway sees himself the member of the orchestra on parade marching on streets of time. In top-10 Observer newspapers Conway will be mentioned among mathematicians whose opening changed the world. But try to discuss with it this list, or other list in which it found itself(himself) recently – in Clifford Pikover's book "Miracles of numbers", under the name "ten most influential mathematicians of our time" … He will at once object:
On the one hand, pleasantly. I can be one of the most famous mathematicians of our time – but it not the same as to be the best. And it, most likely, because of "Life". But it confuses me. People can think that I lag behind the best. But it not so. And in general, that else confuses me that Archimedes or Newton are not in these lists.
Conway considers Archimedes as the father of mathematics. He understood real numbers, and was the first, calculated number π and limited it on top 3 1⁄7, and from below — 3 10⁄71. But in Observer rating on the first place there is Pythagoras. If it and not the best, then known more others, generally thanks to the theorem of his name. And usually at these lists there are Euler, Gauss, the Cantor, Erdos. Conway goes at the end, he is followed by Perelman and Tao.
The youth age of Conway had on sexual the 70th and unlimited the 80th. In the 80th he got divorced from the first wife and married the mathematician Larisa Quinn, having begun a new family. Became the member of Royal society and professor of Cambridge. And then it was transferred to Princeton in the 1987th. For the present we too close are to Perelman, Tao and Conway correctly to evaluate their contribution to science – especially how their abstract theories will be able to be useful in practice. This analysis will take a lot of time.
Interesting exception was John Nash, Conway's colleague in Princeton about whom the book is written and the movie "Beautiful Mind" is shot. Nash made the contribution to games theory which was instantly useful in evolutionary biology, an accounting, policy, the military theory and market economy as led to receipt of the Nobel Prize by it on economy. From the point of view of Conway, the work which deserved to Nash the Nobel Prize was less interesting, than Nash's Theorem of regular attachments (any Riemannian manifold can be included isometrically in the Euclidean space). Conway aimed at receipt of an award of Abel ("Nobel for mathematicians"). He won a heap of other prizes, but with Abel's award so far nothing leaves.
And the practical application of its work still should be opened. The few doubt that at least something from its creations will be able to find application. For example, syurrealny numbers. "Syurrealny numbers will find application, - the colleague, Peter Sarnak says it. – A question only in what and when". Sarnak in general eulogizes Conway. "Conway is the temper", - Sarnak says, meaning Conway's talent as teacher and interpreter, whether it be occupation with students, mathematical camp, lecture at a private party or its alcove in the general room of Princeton.
It can always be found in this alcove where it is not busy. And though he hopes to come across other "hot" subjects like syurrealny numbers, more often he is played with favourite trivialities. It never hesitates of to catch the stranger and to begin to fill up it with the interests. One of recent – "the theorem of a free will" in which, in his opinion, each person is interested. It is developed in ten years together with the colleague Simon Kochen, and is formulated through geometry, quantum mechanics and philosophy. The simple formulation sounds so: if physicists have a free will when carrying out experiments, then particles have it also. And it, in their opinion, explains why people in general have a free will. It is not a vicious circle, but the spiral more closed which supports itself, but is untwisted and becomes more and more.
But usually it is most of all keen on numbers. It turns them, overturns, turns out and watches how they behave. And most of all he appreciates knowledge and wants to learn everything about the Universe. Conway's charm goes from his desire to share the thirst for knowledge, to extend this hobby and the related romanticism. It it is stubborn, persistently aims to explain inexplicable, and even when it remains not explained, it manages to inspire the audience fastened with unfortunate attempt, feeling part of one command satisfied with what they could poflirtovat with an understanding gleam.
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