4 ms·

I'll leave this here “I believe that the clue to his mind is to be found in his unusual powers of continuous concentrated introspection. A case can be made out

I'll leave this here “I believe that the clue to his mind is to be found in his unusual powers of continuous concentrated introspection. A case can be made out, as it also can with Descartes, for regarding him as an accomplished experimentalist. Nothing can be more charming than the tales of his mechanical contrivances when he was a boy. 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. I fancy his pre-eminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted. Anyone who has ever attempted pure scientific or philosophical thought knows how one can hold a problem momentarily in one's mind and apply all one's powers of concentration to piercing through it, and how it will dissolve and escape and you find that what you are surveying is a blank. 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.” ― John Maynard Keynes

Wistar 8y ago
Not nearly so grand but I once read a quote describing the fragility of holding state in one's head as "juggling priceless eggs in variable gravity."
- ColinWright 8y ago
  That quotation is actually from Jerry Pournelle and is uttered by one of the Moties in the book "The Mote in God's Eye". In full: “We juggle priceless eggs in variable gravity. I am afraid. I will taste fear until I die.” The book is well-known to many programmers and the quotation is very likely to have been lifted and re-purposed.
icc97 8y ago
This reminds me of G. Polya's book "How to Solve It" [0], there he talks about the process that teachers can go through to get students to think through problems. But more than that it's trying to build in a habit, so that you tackle problems in the same way each time and can train your brain pathways to hold more of the process in your head. [0]: https://www.math.utah.edu/~alfeld/math/polya.html https://www.math.utah.edu/~alfeld/math/polya.html
- vram22 8y ago
  That's a very good book. I first read it while in college or high school, IIRC. Should buy a copy again, it's worth it. BTW, for others who might not know, it is not applicable just to math (although Polya was a mathematician). It's good for general problem solving. And there is a book that was inspired by it, called How to Solve it by Computer. I had and read that one too. It is very good too. See descriptions of both books below. https://en.wikipedia.org/wiki/How_to_Solve_It https://en.wikipedia.org/wiki/How_to_Solve_It https://en.wikipedia.org/wiki/How_to_Solve_It#Influence https://en.wikipedia.org/wiki/How_to_Solve_It#Influence https://en.wikipedia.org/wiki/How_to_Solve_it_by_Computer https://en.wikipedia.org/wiki/How_to_Solve_it_by_Computer
espeed 8y ago
This ability to see -- an ability honed by the product of relentless determination combined with a mind possessed with an almost singular desire to seek and see true -- is a master key found among many of the most penetrating insights. Feynman said it this way: You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, “How did he do it? He must be a genius!" [1] [1] http://alumni.media.mit.edu/~cahn/life/gian-carlo-rota-10-lessons.html http://alumni.media.mit.edu/~cahn/life/gian-carlo-rota-10-le... [1] http://wiki.c2.com/?FeynmanAlgorithm http://wiki.c2.com/?FeynmanAlgorithm
teddyh 8y ago
That is a lot like what Nikola Tesla describes himself doing in his autobiography when inventing the alternating current electric motor – he could, in his mind’s eye, see the motor, turn it off and on and make it go backwards and forwards, and even momentarily forgot that the other people who were with him could not also see it. EDIT: Quote: I started by first picturing in my mind a direct-current machine, running it and following the changing flow of the currents in the armature. Then I would imagine an alternator and investigate the processes taking place in a similar manner. Next I would visualize systems comprising motors and generators and operate them in various ways. The images I saw were to me perfectly real and tangible. […] The images I saw were wonderfully sharp and clear and had the solidity of metal and stone, so much so that I told him: “See my motor here; watch me reverse it.” […] The pieces of apparatus I conceived were to me absolutely real and tangible in every detail, even to the minute marks and signs of wear. I delighted in imagining the motors constantly running, for in this way they presented to mind’s eye a more fascinating sight.
- hef19898 8y ago
  I achieved this state once so far in my life, scary and just great at the same time. Back then I basically had the supply chain I was working on running in my head almost 24/7. Not quantitiv but qualitiv, computers are there for the exact numbers. I can just assume I drove most of my colleagues crazy. Still it made work relativly easy and fun, also exhausting.

Wistar 8y ago

Not nearly so grand but I once read a quote describing the fragility of holding state in one's head as "juggling priceless eggs in variable gravity."

ColinWright 8y ago
That quotation is actually from Jerry Pournelle and is uttered by one of the Moties in the book "The Mote in God's Eye". In full: “We juggle priceless eggs in variable gravity. I am afraid. I will taste fear until I die.” The book is well-known to many programmers and the quotation is very likely to have been lifted and re-purposed.

icc97 8y ago

This reminds me of G. Polya's book "How to Solve It" [0], there he talks about the process that teachers can go through to get students to think through problems. But more than that it's trying to build in a habit, so that you tackle problems in the same way each time and can train your brain pathways to hold more of the process in your head. [0]: https://www.math.utah.edu/~alfeld/math/polya.html https://www.math.utah.edu/~alfeld/math/polya.html

vram22 8y ago
That's a very good book. I first read it while in college or high school, IIRC. Should buy a copy again, it's worth it. BTW, for others who might not know, it is not applicable just to math (although Polya was a mathematician). It's good for general problem solving. And there is a book that was inspired by it, called How to Solve it by Computer. I had and read that one too. It is very good too. See descriptions of both books below. https://en.wikipedia.org/wiki/How_to_Solve_It https://en.wikipedia.org/wiki/How_to_Solve_It https://en.wikipedia.org/wiki/How_to_Solve_It#Influence https://en.wikipedia.org/wiki/How_to_Solve_It#Influence https://en.wikipedia.org/wiki/How_to_Solve_it_by_Computer https://en.wikipedia.org/wiki/How_to_Solve_it_by_Computer

espeed 8y ago

This ability to see -- an ability honed by the product of relentless determination combined with a mind possessed with an almost singular desire to seek and see true -- is a master key found among many of the most penetrating insights. Feynman said it this way: You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, “How did he do it? He must be a genius!" [1] [1] http://alumni.media.mit.edu/~cahn/life/gian-carlo-rota-10-lessons.html http://alumni.media.mit.edu/~cahn/life/gian-carlo-rota-10-le... [1] http://wiki.c2.com/?FeynmanAlgorithm http://wiki.c2.com/?FeynmanAlgorithm

teddyh 8y ago

That is a lot like what Nikola Tesla describes himself doing in his autobiography when inventing the alternating current electric motor – he could, in his mind’s eye, see the motor, turn it off and on and make it go backwards and forwards, and even momentarily forgot that the other people who were with him could not also see it. EDIT: Quote: I started by first picturing in my mind a direct-current machine, running it and following the changing flow of the currents in the armature. Then I would imagine an alternator and investigate the processes taking place in a similar manner. Next I would visualize systems comprising motors and generators and operate them in various ways. The images I saw were to me perfectly real and tangible. […] The images I saw were wonderfully sharp and clear and had the solidity of metal and stone, so much so that I told him: “See my motor here; watch me reverse it.” […] The pieces of apparatus I conceived were to me absolutely real and tangible in every detail, even to the minute marks and signs of wear. I delighted in imagining the motors constantly running, for in this way they presented to mind’s eye a more fascinating sight.

hef19898 8y ago
I achieved this state once so far in my life, scary and just great at the same time. Back then I basically had the supply chain I was working on running in my head almost 24/7. Not quantitiv but qualitiv, computers are there for the exact numbers. I can just assume I drove most of my colleagues crazy. Still it made work relativly easy and fun, also exhausting.