p56
Keynes’ ``Newton, the Man’’ (1946)
III-971 Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago. Isaac Newton, a posthumous child born with no father on Christmas Day, 1642, was the last wonder child to whom the Magi could do sincere and appropriate homage. [J. M. Keynes, “Newton, the Man” 1946)]
III-972 There are his telescopes and his optical experiments, These were essential accomplishments, part of his unequalled all-round technique, but not, I am sure, his peculiar gift, especially amongst his contemporaries. His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it. [J. M. Keynes, “Newton, the Man” (1946)]
III-973 I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret. Then being a supreme mathematical technician he could dress it up, how you will, for purposes of exposition, but it was his intuition which was pre-eminently extraordinary - ’so happy in his conjectures’, said De Morgan, ’as to seem to know more than he could possibly have any means of proving’. The proofs, for what they are worth, were, as I have said, dressed up afterwards - they were not the instrument of discovery. There is the story of how he informed Halley of one of his most fundamental discoveries of planetary motion. ’Yes,’ replied Halley, ’but how do you know that? Have you proved it?’ Newton was taken aback - ’Why, I’ve known it for years’, he replied. ’If you’ll give me a few days, I’ll certainly find you a proof of it’ - as in due course he did. [J. M. Keynes, “Newton, the Man” (1946)]
III-974 Certainly there can be no doubt that the peculiar geometrical form in which the exposition of the Principia is dressed up bears no resemblance at all to the mental processes by which Newton actually arrived at his conclusions.
His experiments were always, I suspect, a means, not of discovery, but always of verifying what he knew already. [J. M. Keynes, “Newton, the Man” (1946)]
III-975 He regarded the universe as a cryptogram set by the Almighty - just as he himself wrapt the discovery of the calculus in a cryptogram when he communicated with Leibniz. By pure thought, by concentration of mind, the riddle, he believed, would be revealed to the initiate. [J. M. Keynes, “Newton, the Man” (1946)]
III-976 All would be revealed to him if only he could persevere to the end, uninterrupted, by himself, no one coming into the room, reading, copying, testing-all by himself, no interruption for God’s sake, no disclosure, no discordant breakings in or criticism, with fear and shrinking as he assailed these half-ordained, half forbidden things, creeping back into the bosom of the Godhead as into his mother’s womb.
...
And so he continued for some twenty-five years. In 1687, when he was forty-five years old, the Principia was published.
....
During these twenty-five years of intense study mathematics and astronomy were only a part, and perhaps not the most absorbing, of his occupations. Our record of these is almost wholly confined to the papers which he kept and put in his box when he left Trinity for London. [J. M. Keynes, “Newton, the Man” (1946)]
III-977 All his unpublished works on esoteric and theological matters are marked by careful learning, accurate method and extreme sobriety of statement. They are just as sane as the Principia, if their whole matter and purpose were not magical. [J. M. Keynes, “Newton, the Man” (1946)]
III-978 Very early in life Newton abandoned orthodox belief in the Trinity. He arrived at this conclusion, not on so-to-speak rational or sceptical grounds, but entirely on the interpretation of ancient authority. He was persuaded that the revealed documents give no support to the Trinitarian doctrines which were due to late falsifications. The revealed God was one God.
....
But this was a dreadful secret which Newton was at desperate pains to conceal all his life. It was the reason why he refused Holy Orders, and therefore had to obtain a special dispensation to hold his Fellowship and Lucasian Chair and could not be Master of Trinity. Even the Toleration Act of 1689 excepted anti-Trinitarians. After his death Bishop Horsley was asked to inspect the box with a view to publication. He saw the contents with horror and slammed the lid. A hundred years later Sir David Brewster looked into the box. He covered up the traces with carefully selected extracts and some straight fibbing. His latest biographer, Mr More, has been more candid. Newton’s extensive anti-Trinitarian pamphlets are, in my judgement, the most interesting of his unpublished papers . [J. M. Keynes, “Newton, the Man” (1946)]
On superstition
Superstition is to believe something that does not exhibits any reason to believe. For example, it is impossible to distinguish believing in the miracles in the Bible from the ordinary superstitions. It may be sensible to discriminate such obviously nonsensical superstitions just mentioned and the superstition due to mistaking correlation as causality.
First of all, to assume a correlation is to make a hypothesis. If something occurs twice or three times, or if something occurs once in three times, we have a tendency to assume there is some regularity. This is the basis of superstition. If the regularity is coupled to the time ordering, we easily promote correlation to causality. Since a salient feature of Homo sapiens in order to compete successfully with other creatures is the cognitive power of causality, it is all too natural that we are superstitious. It is understandable even if one becomes to rely excessively on the inference scheme that is fairly often successful. That is, without consciously or unconsciously executing skeptical checking, it is our human fundamental characteristic that we are trapped by superstitions. It is a consequence of natural selection.
Gell-Man wrote in Quark and Jaguar p276 as follows about superstition:
Is the prevalence of superstition alongside science a phenomenon peculiar to human beings or should intelligent complex adaptive systems elsewhere in the universe be expected to have similar proclivities?
and
In more anthropomorphic terms, we can expect intelligent complex adaptive systems everywhere to be liable to a mixture of superstition and denial.
The following paper is somewhat related (at least as to the rule extraction):
Feher da Silva C, Baldo MVC, A Simple Artificial Life Model Explains Irrational Behavior in Human Decision-Making. PLoS ONE 7 e34371 (2012)
Suppose there are two lamps L and R; L lights with P=2/3 and R with 1/3 (Bernoulli). If you can correctly guess which light will light next you win. The best strategy is to perseverate on L. However, human adults perform the probability matching. The produce their own Bernoulli process with the same law. This is suboptimal.
* We found that, whereas animats with smaller neural capacity kept perseverating with the best alternative as before, animats with larger neural capacity, which had previously been able to learn the pattern of repeating strings, adopted probability matching, being outperformed by the perseverating animats.
Isn’t ``Don’t be bound by dogmas’’ a dogma?
The author always recall Ratnakuta ( 宝積経 ). Regrettably, this sutra has no electronic version yet (no English translation; in German, F. Weller, Zum Kasyapaparivarta; the following is a rough English translation of the Japanese translation by M. Nagao and N. Aramaki (Chuo-koron 1965):
829 Kasyapa, if you say Self exists, it is one extreme opinion. If there is no Self, this is again another extreme opinion. The correct middle of Self and no-Self is something without shape, that is invisible, that cannot be revealed, that cannot be recognized, that does not have the foundation, and that cannot be named. Kasyapa, this is the Middle Way and is the truthful observation about existence. [宝積経（57)]
830 Kasyapa, to say something exists is an extreme opinion; to say something does not exist is also another extreme opinion. [宝積経（60)]
831 Kasyapa, the state of enlightenment and the state of spiritual darkness are not two different things and not to be distinguished. [宝積経（61)]
832 Indeed, Kasyapa, if some people make the idea of Emptiness, and believe in it, Kasyapa, I will call them apostates and destroyers of the Teaching. [宝積経（64)]
833 Buddha told ― Kasyapa, it is Emptiness that makes everyone who clings to various ideas transcend them (and leads him to the Free state). However, Kasyapa, if there is a person who clings to the idea of Emptiness, I will call him the unredeemable. [宝積経（65)]
Addition to Footnote 46 On paradigm and the viewpoint to emphasize discontinuity
I. Asimov’s essay, The Relativity of Wrong (Isaac Asimov - The Skeptical Inquirer, Vol. 14 No. 1, Fall 1989) explains in detail that
`` The basic trouble is that people think that "right" and "wrong" are absolute ’’
It is worth serious reading.
Additional comment on paradigm
Notice that the Aristotelian mechanics is wrong, because it cannot justify why geocentrism is natural.