Cantor's proof of uncountability of continuum, likely, divided all thinkers into two parts. Those believed in discrete world (reductionists) learned from it that if the world is continuous, they will never get it. Correspondingly, others (holists) saw that it is pointless to explain reductionists anything, because they are unable to get. The earlier did not forgive him this and his end was very sad. But the nearest future was very happy for them, then they only prepared themselves to rule the world.
I know P. Ehrenfest to be convinced reductionist which worked strictly by manipulating symbols.
Unlike him, H. Bateman was a holist and probably the first to consider curved space-time three years before H. Minkowski presented his report in which he claimed that space and time should be considered as an integral whole. Bateman proved form-invariance of Maxwell equations under arbitrary conformal transformations of the space-time. In 20s P. Ehrenfest worked in Berkley and gave the following characteristic to Bateman: "He... can calculate wonderfully, but... has no physical intuition" (Judith Goodstein and Donald Babbitt. E.T Bell and Mathematics at Caltech between the Wars. Notices of the AMS, Vol 60, Number 6, p. 686). So, according to P. Ehrenfest, a person deprived of physical intuition was nevertheless able to understand that space by itself and time by itself are meaningless notions and discover conformal invariance of the Maxwell equations. And Ehrenfest himself, a habitant of his discrete world, had rich physical intuition. Very strange. Reductionists were just coming to power. However, Ehrenfest's end came soon and was even more sad than that of Cantor.
Reductionists came to the power ultimately soon after the WWII. Their ideology became obligatory to everyone, particularly, in exact science. All the people should know that formal logic is the only kind of reasoning, that chess players are much more clever than others, that one can understand what he cannot imagine and many other things of this kind. After all, everyone should come to strong belief that the world is discrete and hence is nothing but the set of natural numbers. Once I have shocked people answering the question "Why do you dislike chess?" I said: "Because my brain contains more than 64 cells." However, I was not alone. Surprisingly, the world champion B. Spasskiy said once that one day computer will kill this game. Maybe, he was careful only about chess, but computer was to bring much greater disasters. I was happy to hear this. But afterwards more messages were coming which made me happy.
I have read somewhere that some Japanese mathematician have composed a program which proved all theorems from 20-volumes Bourbaki Opera Mathematica. I understood that one needs no intellectual abilities to become a prominent mathematician, but did not see how to prove this. Then, B. Spasskiy's prediction almost came true, a program defeated some world champion in chess. So, no brains were needed to do this. That is what I meant. Programmers are smarter that chess players, but they use computer. The game was not killed, but the next step was again made by Japaneses, they have demonstrated a monkey which is much more successful in some numerical test than a human. Hardly they will make a chimpanzee a professor of mathematics in a university, but they can well teach one to play chess quite good. I hope, they will do it soon.
The last message which made me happy came from news: a Russian program passed A. Turing's test of intelligent behavior. That is enough. Intelligent behavior cannot be tested by a computer just because it is discrete and intelligent behavior belongs to continuous world. If reductionists possess any elements of intelligent behavior, they are not of reductionist origin. There is a chasm between their beliefs and intelligence, the same as between them and holists. Still, they hold power in some areas, particularly, they control universities and promote censorship in scientifis journals, but the end of their rule is on the way.
I know P. Ehrenfest to be convinced reductionist which worked strictly by manipulating symbols.
Unlike him, H. Bateman was a holist and probably the first to consider curved space-time three years before H. Minkowski presented his report in which he claimed that space and time should be considered as an integral whole. Bateman proved form-invariance of Maxwell equations under arbitrary conformal transformations of the space-time. In 20s P. Ehrenfest worked in Berkley and gave the following characteristic to Bateman: "He... can calculate wonderfully, but... has no physical intuition" (Judith Goodstein and Donald Babbitt. E.T Bell and Mathematics at Caltech between the Wars. Notices of the AMS, Vol 60, Number 6, p. 686). So, according to P. Ehrenfest, a person deprived of physical intuition was nevertheless able to understand that space by itself and time by itself are meaningless notions and discover conformal invariance of the Maxwell equations. And Ehrenfest himself, a habitant of his discrete world, had rich physical intuition. Very strange. Reductionists were just coming to power. However, Ehrenfest's end came soon and was even more sad than that of Cantor.
Reductionists came to the power ultimately soon after the WWII. Their ideology became obligatory to everyone, particularly, in exact science. All the people should know that formal logic is the only kind of reasoning, that chess players are much more clever than others, that one can understand what he cannot imagine and many other things of this kind. After all, everyone should come to strong belief that the world is discrete and hence is nothing but the set of natural numbers. Once I have shocked people answering the question "Why do you dislike chess?" I said: "Because my brain contains more than 64 cells." However, I was not alone. Surprisingly, the world champion B. Spasskiy said once that one day computer will kill this game. Maybe, he was careful only about chess, but computer was to bring much greater disasters. I was happy to hear this. But afterwards more messages were coming which made me happy.
I have read somewhere that some Japanese mathematician have composed a program which proved all theorems from 20-volumes Bourbaki Opera Mathematica. I understood that one needs no intellectual abilities to become a prominent mathematician, but did not see how to prove this. Then, B. Spasskiy's prediction almost came true, a program defeated some world champion in chess. So, no brains were needed to do this. That is what I meant. Programmers are smarter that chess players, but they use computer. The game was not killed, but the next step was again made by Japaneses, they have demonstrated a monkey which is much more successful in some numerical test than a human. Hardly they will make a chimpanzee a professor of mathematics in a university, but they can well teach one to play chess quite good. I hope, they will do it soon.
The last message which made me happy came from news: a Russian program passed A. Turing's test of intelligent behavior. That is enough. Intelligent behavior cannot be tested by a computer just because it is discrete and intelligent behavior belongs to continuous world. If reductionists possess any elements of intelligent behavior, they are not of reductionist origin. There is a chasm between their beliefs and intelligence, the same as between them and holists. Still, they hold power in some areas, particularly, they control universities and promote censorship in scientifis journals, but the end of their rule is on the way.
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