Science and Life, N4 1979 г.

Mnemonic - Articles Science and Life, N4 1979 г.

GENIALITY OR METHOD?

A. Leonovich

A poster which notify of
competition between R. S. Arrago
and D. N. Goldshtein.

10 december 1929. In the Communist auditorium to the MGU (Moscow Government University) must occur an event, interesting exceedingly: competition of two music-hall calculators. One of them - a famous master of mental calculatings Arrago, other - little known before that times David Goldshtein.

Name Аrrаго, unusual nature of competition, effective advertisment and cheapest of tickets have done its deal - an auditorium ate contained wanting. Newcomer felt nervous: not easy fought with such opponent! But this caused internal resistance - do not lose self-controls!

So, meeting has begin. Аrrаго asks, agree and can his adversary to do in the mind such task: add five 6-digit numbers, add five 5-digit numbers, from the first sum subtract the second and to the received difference add two squares of 4-digit numbers.

The newcomer take bravery, brings forth a counter requirement: add to the result else product of two 4-digit numbers. Auditorium has meet this offer of boers of applause, Arrago - a discontent, because it is out of his standard scheme.

But any case competitors go out of the scene and on two desks draw an same task. Again calculators on the scene. They stand halfreverse one another and on the signal begin a count.

In the absolute silence pass several minutes, and... the first result draws a newcommer! He turns around, but on the Arrago's desk still no answer, and he still in calculations. Using minute, Goldshtein checks itself, finds a mistake, corrects it, and in this moment in auditoriums begins something indescribable - Arrago received that wrong result, which in the beginning has draw a newcommer! Mistake learned a famous calculator and at the extraction of cube root from the multibillionth number...

- I am firmly convince that loss Arrago in this "duel", - recalls further David Naumovich,- is explained by the unbalanced psychic condition, which I promoted in some measure, but not quality of his work. He, certainly, calculated much better me, and do not be psychological premiseses - hardly I can to leave successfully thereof competitions.

Interest to experiences of actors-calculators come to me when I was teenager, when in Poltava first time I has see on the scene of boy-calculator of eight-nine years old. His name was Volodya Zubritsky. His show was so unbelieveble, that to say truth I can not think anything except it. Several years after in the Kharkov, being already student, I come to Arrago's show. I was devastated and definitively has lost a quietness.

I begin training in the fast mental calculations, snout in the special literature. Love for the deal, work ability, knowledge mathematicians in necessary limits and own developments have allow me in the end to emerge at the beginning of 1929 with the special report on the fast calculating.

In same year I hear, that in the MGU on 12 August is nominated competition Arrago with the certain student Melentyev (in the future professor one of the Kharkov's Institute). I hope you understand an impatience and interest, what I have to this meeting. However it was not consist, because Arrago on unknown reasons did not come. Melentyev prefix this that Arrgo awe of possible defeat. I has ask the word. I spoke of that Melentyev no grounds so interprete Arrago's not comings, that on the strength of his skill already, regardless of possibilities Melentyev, does not deserve such relations to itself. End all absolutely unexpectedly: Melentiev nervoused, and here realize that I too on something pretend in the field of fast mental calculations, and he suggest me compete, defining weekdays on assign dates. "Buttle", to the great pleasure of auditorium, was consist, but nobody get advantages: answers come literally synchronous.

After the competition with Melentyev I get angazhement in the Bauman's Garden. Not become confirm that my first steps on the scene were brilliant: absence of the experience, nervous on the unaccustomed situation - to say short I have not something required for the number. I can get my right on the scene, but appear a question: how to value my work? In Posredrabis I have declare: "Needed Arrago, we will compare his and your work, and then will define a shutter".

Necessary to say, Arrago not immediately has agree compete with me, long "checking" me before meeting, try to understand how strong adversary. Why hide, I bluffed, not demonstrating before him all my possibilities. But think, what can I do - otherwise meeting could not be! And here is when Arrago has feel that I am not so terrible, he present me his review of such contents: "I think, that comrad Goldshtein D. N. - a calculator of high marks... His work is based on incredible memory and innate abilities solely. I am much complacent that my deal has found in him sufficiently well-earned successor.

R. S, Arrago, Moscow, 05.11.1929.".

Competition with Arrago become a first successful step in my musik-hall activity, which I has finish at 1956, emerging already under the Darayev (Gifted rus.) pseudonym.

- What was "flavor" your appearances? That distinguished them from numbers other scene calculators?

- A most important difference was that at the end of each appearance I gave a theoretical explanation of my results, showed: idea not only and not in some exclusive, "phenomenal" abilities (how wrote Arrago in his review), but in the knowledge of some mathematical laws, allowing quickly produce calculations. Master their possible by drills, which under the known system brings brilliant results! After all drill muscles of peoples under the rational atheletics became better. And our brian device will too yield an atheletics. Question was reduce to the rational system only.

When somebody ask me about known today calculators, such, as Shelushkov, Prikhodko, what I think about, answer: envy unbeleiveble! People without the training, on native, "from the god" produce that work, for the sake of which I consumed days and nights through, nosing rational method.

- Could you show readers, as you showed it to spectators, at least several methods of fast calculatings?

86

x 3

258

+ 16 = 8x2

274

+ 12 = 6x2

2752

- OK, lets begin... with multiplication tables,- Goldshtein smiles, seen my misunderstanding.- No-no, my "table" - a certain code of rules, graceful ways of multiplying. Understand their uncomplicated. Lets, you want to multiply 86 on 32. Keep a check as I write process of calculation, and all will become clear.

Main idea, as you see, in that, to first multiply groups of ten, and afterwards to the result to add a making the last digits. This the most simple example. In following will be used some correlations between used numbers. Recommended by me for these events acceptance can will be show elaborated, however, if understand, they have a table ask and strict explanation.

Well, for example: you are offerred multiple 48 on 36. Write additions these numbers before fifty: 2 and 14. Now notice that difference of first number and second addition is same as differences of second number and first addition: 34. Really, in such event to the half of this difference (17) presents a beginning of result, but multiple additions (28) - an end. So, write: 48 X 36=1728.

X 96 100-96= 4

87 100-87=13

8352

96-13=83 4x13=52

For small additions to hundred works same rule, only at the end a difference no need to divide on two:

X 984 1000-984=16

973 1000-973=27

957432

984-27=957 16x27=432

Same for small additions to thousand and so on:

X 989 11

992 8

981088

If multiple of additions will give two or one sign, necessary signs change zeroes:

- But if numbers very distant from "round"?

- All numbers have their own curious combinations, which nonbad fix in memories of calculator. In most cases this combinations more or less typical. Each of them, presenting known dependency of one number from another, allows quickly to find a result.

Here is example. I hope you can raise in the square number under 25? So, we must multiply 187 on 173. Dependency between both numbers that the ten of first on one more than another. Between last digits dependency that the sum of they give ten (7 + 3). From the square of number of groups of ten of greater number deprive an beginning (182 - 1 = 324 - 1 = 323) and to the received number prefix on the right addition before one hundred squares of greater number (100 - 49 = 51). Result is 32351.

- Not too much acceptance will come remember? How justified such voltage of memory?

- On my glance, is wholly justify. Practice, drill, will bring finally such advantage during, that all initial costs will payed. After all while we spoke of most simplest actions. But how much spare will be when handling by greater numbers, at the extraction a cortex! Additionally quick calculations - in known degrees an atheletics of brain.

- With this it is impossible not to agree. Say, in what books are stated acceptance fast calculating?

- Regrettably, this subject of mathematicians have little literature. Naturally, that I much interest all, that is publish on this subjects. Here is brochure A. S. Sorokin "Technology of calculating" - that all what was at last timer. I find interesting this book, apropos, in introduction an author writes: "Worship before the mathematics as the most exact science quite often moves over to the faith in truth and optimality that methods, which we get in the secondary school. Any interference in stale, but well master by us methods most often causes a protest (sometimes native), which is first of all show in respect of to new methods".

In XV centiry, to maltiply 7 on 8, was offerred to do six intermediate operations of adding, subtractions and multiplyings! Say, as today we made same? Naturally expect, as today, standard methods not limit of possible, their can and needed to change, and new methods - broadly spread, carry in program of schools. This, I think, big and important task our populators and teachers.

- David Naumovich, did you try propagandize your strategy, except as on music-hall?

D. N. Goldshtein emberges before
workmans of Moscow radiouniversity,
explaining his methids of fast calculatings
(picture from the magazine "Radiolistener" N1, 1930).

- As far back as begin 1930 a Radiocentre has organizine a cycle of lectures by radio, in which I introduced listeners with methods of handling by huge numbers. That lectures at 1931 was published on book, but the number only 4000 copies. Flow of orders on it did not stop for a long time, that, I think, speaks of popularity and usefulity lectures. At 1948 Uchpedgiz has release one more my book "Technology of fast calculations", where was collected and systematize ensemble of acceptance and ways, part from which - my own developments.

After leaving music-hall, I has show two times before the juvenile auditorium. At 1971 years - in special school by academician A. N. Kolmogorov, and, must say, emerged successfully. Afterwards has get an invitation from 52-nd Moscow school - a base school of Computing center Akademy of Science of USSR. I give consent, wanted to check myself - is save else little gunpowder in my weepon? As judged by reviews, session was ingenious. Folk is collect much: students, teachers, employees from the institute of psychology. Was present and emerged an academician A. R. Luria, say several words on dug memories in the training. As a psychologist he note "amazing (though and professional) memories and skills in such old age", but me then already knocked eighty...

But I was discontented - even so not that! Presently public appearances for me are labored. However hopes, this conversation newly to come into notice and interest in the fast calculatings. In this deal I has put all my own power, abilities, spirit - the whole life! And wants, to it continued be useful, fascinating for many and many, for juniors in the first place.

LITERATURE

Берман Г. Н. Приемы счета, изд. 6-е, М., Физматгиз, 1959.

Гольдштейн Д. Н. Курс упрощенных вычислений. М., Гос. учебно-пед. изд., 1931.

Гольдштейн Д. Н. Техника быстрых вычислений. М., Учпедгиз, 1948.

Катлер. Э., Мак - Шеин Р. Система быстрого счета по Трахтенбергу. Пер. с англ. М., "Просвещение", 1967.

Перельман Я. И. Быстрый счет. Л.; Союзпечать, 1945.

Сорокин А. С. Техника счета. М., "Знание", 1976.