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The Foundations of Science: Science and Hypothesis, The Value of Science Science and Methods
This is a pre-1923 historical reproduction that was curated for quality. Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide.
568 pages, Hardcover
First published January 1, 1982
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About the author
Henri Poincaré
454 books171 followersJules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime.
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Displaying 1 - 5 of 5 reviews
May 11, 2022
A knowledge-changing book. A life-changing book. Knowledge would not exist in its current form without Henri Poincare.
While absolutely outside of my disciplines, this book was superb. It is brilliantly written, well argued and contextually aware.
As he stated, “I have shown the mind of the mathematician at work." But what we have also seen is the value of theory - with or without the capital T - and how hypotheses are constructed with rigour and clarity.
Published by the Science Press in 1913, this book is fresh and fascinating. For me, I now think differently about 'the general case' and the particulars that challenge it.
While absolutely outside of my disciplines, this book was superb. It is brilliantly written, well argued and contextually aware.
As he stated, “I have shown the mind of the mathematician at work." But what we have also seen is the value of theory - with or without the capital T - and how hypotheses are constructed with rigour and clarity.
Published by the Science Press in 1913, this book is fresh and fascinating. For me, I now think differently about 'the general case' and the particulars that challenge it.
November 13, 2025
WITH HENRI POINCARÉ’S MATHEMATICAL CREATION (THE MONIST (VOLUME 20, ISSUE 3), JUILLET 1910, PARIS)
18 AOÛT 2025.
A latter move to the chair of Sully (1).
Man want a ground to walk on, the foundations of which are rarely questioned. That is, as long as the shake does not bone-rattle. (2) || cf. Henri Poincaré, “The genesis of mathematical creation is a problem which should intensely interest the psychologist. It is the activity in which the human mind seems to take least from the outside world, in which it acts or seems to act only of itself and on itself, so that in studying the procedure of geometric thought we may hope to reach what is most essential in man's mind.”
A woman's vote, I suppose. || cf. Henri Poincaré, “I do not say all, for when the appeal is to universal suffrage unanimity is not to be hoped.”
We enter an opera.
The curtains open and center stage there is a singer.
The singer opens on a threnody.
The singing slips between the sitting audience.
The audience is made up of mechanics and trackers:
- the mechanics hear the threnody pitch to qunta,
- while the trackers hear the threnody pitch to cosmic.
The song is continues, but the slips are of dispute: elegy vs lament.
The threnody is miscast and splinted.
The singer counted counting count—so.
The curtains of the opera close.
A continued opening, fabric encased.
|| cf. Henri Poincaré, “Imagine a long series of syllogisms, and that the conclusions of the first serve as premises of the following: we shall be able to catch each of these syllogisms, and it is not in passing from premises to conclusion that we are in danger of deceiving ourselves. But between the moment in which we first meet a proposition as conclusion of one syllogism, and that in which we reencounter it as premise of another syllogism occasionally some time will elapse, several links of the chain will have unrolled; so it may happen that we have forgotten it, or worse, that we have forgotten its meaning. So it may happen that we replace it by a slightly different proposition, or that, while retaining the same enunciation, we attribute to it a slightly different meaning, and thus it is that we are exposed to error.”
Has any endeavour been as shame-cast as the multiplication table? No cane, but rosey cheeks indeed. No wonder we would rather forget, sore knees and all. (3) || cf. Henri Poincaré, “Thus it is, to take a simple example, that we sometimes make slips in calculation because we have forgotten our multiplication table.”
What were we talking about? I seem to have misplaced my hand on a hot stove. || cf. Henri Poincaré, “I must confess, I am absolutely incapable even of adding without mistakes. In the same way I should be but a poor chess-player; I would perceive that by a certain play I should expose myself to a certain danger ; I would pass in review several other plays rejecting them for other reasons, and then finally I should make the move first examined, having meantime forgotten the danger I had foreseen.”
Pitch be cosmic, pitch be qunta, but the song is a threnody. For the threnody is of consequence, for how the notes are arranged into a movement, and how those movements are arranged into composition. The pitch is a matter of taste. Whereas the arrangement is a matter of gut, not bud. (4) || cf. Henri Poincaré, “A mathematical demonstration is not a simple juxtaposition of syllogisms, it is syllogisms placed in a certain order, and the order in which these elements are placed is much more important than the elements them selves. If I have the feeling, the intuition, so to speak, of this order, so as to perceive at a glance the reasoning as a whole, I need no longer fear lest I forget one of the elements, for each of them will take its allotted place in the array, and that without any effort of memory on my part.”
To trim the fat on some meat, or remove the dirt on a vegetable, or to remove the plastic of a wrapped sweet; least we eat the harmful and die of a clogged lung. || cf. Henri Poincaré, “To create consists precisely in not making useless combinations and in making those which are useful and which are only a small minority. Invention is discernment, choice.”
And then perhaps, our audience will be well fed and their disputed pitch harmonised; for the singer must wish to move past the opening. || cf. Henri Poincaré, “Among chosen combinations the most fertile will often be those formed of elements drawn from domains which are far apart.”
But, dear Sir, I am a woman. I was born frightened. And like all women, I cried from womb to life, and so I cry as I write. This tear soaked keyboard, too, begs your pardon for what is a woman of suffrage reading such a paper? I am un-obliged to understand. (5) || cf. Henri Poincaré, “I beg the reader's pardon; I am about to use some technical expressions, but they need not frighten him, for he is not obliged to understand them.”
Let us leave this opera house, and enter my office. For this chair is Freudian stitched, but Oedipus it is not. (6) || cf. Henri Poincaré, “This theorem will have a barbarous name, unfamiliar to many, but that is unimportant; what is of interest for the psychologist is not the theorem but the circumstances.”
An artist may sit at their desk and be incapable of drawing a nose. After much frustration they may leave, for they too are disgusted by the incapability of their hands. Upon return, an attempt is made and the consequent nose is not just drawn adequate, but drawn in so that rivals the devil of liberty.
This is experience exists amongst those who game too. For one may rival a boss only to fail every time, and with deep frustration they unplug and sleep. After such a nap, the game is replugged and docked, and with a tense breath the boss is faced and defeated on the first attempt therein. That is to say, art and maths are not unalike. Perhaps they are the very same machinery from which life itself ticks. We may then propose that it is within this ticking that invention is propagated by the subconscious.
|| cf. Henri Poincaré, “Often when one works at a hard question, nothing good is accomplished at the first attack. Then one takes a rest, longer or shorter, and sits down anew to the work. During the first half hour, as before, nothing is found, and then all of a sudden the decisive idea presents itself to the mind. It might be said that the conscious work has been more fruitful be cause it has been interrupted and the rest has given back to the mind its force and freshness. But it is more probable that this rest has been filled out with unconscious work and that the result of this work has afterward revealed itself to the geometer”
Would one have not known that a hot stove is only to be touched once cool, least one is to blister? To err is to learn, and to err into disgust or frustration is to reel subconscious and return conscious with resolve. || cf. Henri Poincaré, “These efforts then have not been as sterile as one thinks; they have set agoing the unconscious machine, and without them it would not have moved and would have produced nothing.”
For the subconscious is not err immune. || cf. Henri Poincaré, “But do not think this a rule without exception; often this feeling deceives us without being any the less vivid, and we only find it out when we seek to put on foot the demonstration. I have especially noticed this fact in regard to ideas coming to me in the morning or evening in bed while in a semi hypnagogic state.”
A question for the modern age: can that which we program part-take in mathematical creation? For how does one code a subconscious? stepwise? (7) || cf. Henri Poincaré, “But usually the subliminal self is considered as purely automatic. Now we have seen that mathematical work is not simply mechanical, that it could not be done by a machine however perfect.”
And with such an insight should one not question the arbitrary split of that which is objective and that which is subjective? For are they not that which holds the other up—a wall for the other, when the other aches from tire? || cf. Henri Poincaré, “A first hypothesis now presents itself: the subliminal self is in no way inferior to the conscious self; it is not purely automatic ; it is capable of discernment; it has tact, delicacy; it knows how to choose, to divine. What do I say? It knows better how to divine than the conscious self, since it succeeds where that has failed. In a word, is not the subliminal self superior to the conscious self? You recognize the full importance of this question.”
The beauty of mathematics is that it is a brush held by an artisan, but without some intuition how would one see the beauty of a perfectly balance equation, or notice where a formula leans too far left, so much so that a slight nudge would result in the notational tip-over? (8) || cf. Henri Poincaré, “This would be to forget the feeling of mathematical beauty, of the harmony of numbers and forms, of geometric elegance. This is a true esthetic feeling that all real mathematicians know, and surely it belongs to emotional sensibility.”
Cast my parasol aside, for there is plenty of a shade here. || cf. Henri Poincaré, “The useful combinations are precisely the most beautiful, I mean those best able to charm this special sensibility that all mathematicians know, but of which the profane are so ignorant as often to be tempted to smile at it.”
The sun is aglow, yet my age is safe. || cf. Henri Poincaré, “Thus it is this special esthetic sensibility, which plays the role of the delicate sieve of which I spoke, and that sufficiently explains why the one lacking it will never be a real creator.”
The Freudian chair squeaks, for it resides in a house, on a hill. (9) || cf. Henri Poincaré, “The conscious self is narrowly limited, and as for the subliminal self we know not its limitations, and this is why we are not too reluctant in supposing that it has been able in a short time to make more different combinations than the whole life of a conscious being could encompass. Yet these limitations exist. Is it likely that it is able to form all the possible combinations, whose number would frighten the imagination?”
I choose the gnats, for I ought to avoid the stove. || cf. Henri Poincaré, “where they are enclosed, as would, for example, a swarm of gnats or, if you prefer a more learned comparison, like the mole cules of gas in the kinematic theory of gases. Then their mutual impacts may produce new combinations.”
A thought laid to rest does not die, it bone-timers and reanimates once the conscious mind is ready (but we must remember not to fighten our selves). || cf. Henri Poincaré, We think we have done no good, because we have moved these elements a thousand different ways in seeking to assemble them and have found no satisfactory aggregate. But, after this shaking up imposed upon them by our will, these atoms do not return to their primitive rest. They freely continue their dance.”
To take this rough proclamation and move it into chemistry, we might say these atoms bonds just so. After nary an attempt water fits a glass in perceived smoothness only after the bonds between molecules are settled and re-arranged after a few turbulent swings. (10) || cf. Henri Poincaré, “Then the mobilized atoms undergo impacts which make them enter into combination among themselves or with other atoms at rest which they struck against in their course.”
The wall of prior note. || cf. Henri Poincaré, ”It seems that thinking in the evening upon the factors of a multiplication, we might hope to find the product ready made upon our awakening, or again that an algebraic calculation, for example a verification, would be made unconsciously. Nothing of the sort, as observation proves. All one may hope from these inspirations, fruits of unconscious work, is a point of departure for such calculations. As for the calculations themselves, they must be made in the second period of conscious work, that which follows the inspiration, that in which one verifies the results of this inspiration, and deduces their consequences. The rules of these calculations are strict and complicated. They require discipline, attention, will, and therefore consciousness.”
Ah, this is where I must present a question: must disorder be born of chance? One does not learn to draw the perfect nose, or beat a boss, because of a dice rolled? Is it luck? Or is it a combination that what is deformed into being, and informed by that which was once erred? For if we had not erred as we did, the combination would not hold the same geometric edges as it now does. For an atom or a module (as in the example of present) is not just an abstract thing with no body? They must have some shape, and so there must be some type of edges? And would such edges not have been shaped by prior conscious work? || cf. Henri Poincaré, “In the subliminal self, on the contrary, reigns what I should call liberty, if we might give this name to the simple absence of discipline and to the disorder born of chance. Only, this disorder itself permits unexpected combinations.”
Nor do I repent having read such interests; such tears are not hypothesis hinged. || cf. Henri Poincaré, “Surely they have need of it, for they are and remain in spite of all very hypothetical: the interest of the question is so great that I do not repent of having submitted them to the reader.”
———
REFERENCES.
0. H. Poincaré, Mathematical Creation, The Monist, Volume 20, Issue 3, 1909, public domain.
1. Institut de France Académie Française, Discours prononcé dans la séance publique tenue par l’Académie Française pour la réception de M. Henri Poincaré, le jeudi 28 janvier 1909 (Paris: Institut de France, 1909), public domain.
2. R. Descartes, Meditations on First Philosophy: with Selections from the Objections and Replies (originally published 1641; 2008 edition translated by Michael Moriarty, Oxford University Press, 2008) (copyright © Oxford University Press, all rights reserved)
3. When schooling becomes a place of shame, our slips become a place of shame rather than the inviable misstep in order to allow correction. The instructions of today may no longer invoke the cane but the act of shaming a child is widespread and suffocating, yet we wonder why the children of today can no longer breathe? This is not a problem of cramping hands and a habit born of swiping tablets but of a broken institution. (I)
4. C. Saint-Saëns, The Carnival of the Animals (1886), public domain.
5. Such a trail of tears find such a way in a list of such references. Such pardons are mine, to such an objective place as this.
6. S. Freud, Interpreting Dreams (Die Traumdeutung, 1899; English translation 1913) (copyright © Vintage International, all rights reserved).
7. A. Vaswani, et al., “Attention is All You Need,” NeurIPS, 2017 (copyright © NeurIPS, all rights reserved). (II)
8. P. A. M. Dirac, “The Evolution of the Physicist’s Picture of Nature,” Scientific American, Vol. 208, No. 5, May 1963, pp. 45–53 (contains the phrase “It is more important to have beauty in one’s equations than to have them fit experiment”) (copyright © Scientific American, all rights reserved).
9. S. Jackson, The Haunting of Hill House (1959) (copyright © The Estate of Shirley Jackson, all rights reserved).
10. L. D. Landau, Collected Papers of L. D. Landau, ed. D. ter Haar (Oxford: Pergamon Press Ltd. and Gordon and Breach Science Publishers, Inc., 1965), pp. 193–216 (“On the Theory of Phase Transitions”) (copyright © Pergamon Press Ltd. and Gordon and Breach Science Publishers, all rights reserved).
———
CITE-REFERENCES.
I. Is a citation needed, or, , are you the citation?
II. But is it? (1)
18 AOÛT 2025.
A latter move to the chair of Sully (1).
Man want a ground to walk on, the foundations of which are rarely questioned. That is, as long as the shake does not bone-rattle. (2) || cf. Henri Poincaré, “The genesis of mathematical creation is a problem which should intensely interest the psychologist. It is the activity in which the human mind seems to take least from the outside world, in which it acts or seems to act only of itself and on itself, so that in studying the procedure of geometric thought we may hope to reach what is most essential in man's mind.”
A woman's vote, I suppose. || cf. Henri Poincaré, “I do not say all, for when the appeal is to universal suffrage unanimity is not to be hoped.”
We enter an opera.
The curtains open and center stage there is a singer.
The singer opens on a threnody.
The singing slips between the sitting audience.
The audience is made up of mechanics and trackers:
- the mechanics hear the threnody pitch to qunta,
- while the trackers hear the threnody pitch to cosmic.
The song is continues, but the slips are of dispute: elegy vs lament.
The threnody is miscast and splinted.
The singer counted counting count—so.
The curtains of the opera close.
A continued opening, fabric encased.
|| cf. Henri Poincaré, “Imagine a long series of syllogisms, and that the conclusions of the first serve as premises of the following: we shall be able to catch each of these syllogisms, and it is not in passing from premises to conclusion that we are in danger of deceiving ourselves. But between the moment in which we first meet a proposition as conclusion of one syllogism, and that in which we reencounter it as premise of another syllogism occasionally some time will elapse, several links of the chain will have unrolled; so it may happen that we have forgotten it, or worse, that we have forgotten its meaning. So it may happen that we replace it by a slightly different proposition, or that, while retaining the same enunciation, we attribute to it a slightly different meaning, and thus it is that we are exposed to error.”
Has any endeavour been as shame-cast as the multiplication table? No cane, but rosey cheeks indeed. No wonder we would rather forget, sore knees and all. (3) || cf. Henri Poincaré, “Thus it is, to take a simple example, that we sometimes make slips in calculation because we have forgotten our multiplication table.”
What were we talking about? I seem to have misplaced my hand on a hot stove. || cf. Henri Poincaré, “I must confess, I am absolutely incapable even of adding without mistakes. In the same way I should be but a poor chess-player; I would perceive that by a certain play I should expose myself to a certain danger ; I would pass in review several other plays rejecting them for other reasons, and then finally I should make the move first examined, having meantime forgotten the danger I had foreseen.”
Pitch be cosmic, pitch be qunta, but the song is a threnody. For the threnody is of consequence, for how the notes are arranged into a movement, and how those movements are arranged into composition. The pitch is a matter of taste. Whereas the arrangement is a matter of gut, not bud. (4) || cf. Henri Poincaré, “A mathematical demonstration is not a simple juxtaposition of syllogisms, it is syllogisms placed in a certain order, and the order in which these elements are placed is much more important than the elements them selves. If I have the feeling, the intuition, so to speak, of this order, so as to perceive at a glance the reasoning as a whole, I need no longer fear lest I forget one of the elements, for each of them will take its allotted place in the array, and that without any effort of memory on my part.”
To trim the fat on some meat, or remove the dirt on a vegetable, or to remove the plastic of a wrapped sweet; least we eat the harmful and die of a clogged lung. || cf. Henri Poincaré, “To create consists precisely in not making useless combinations and in making those which are useful and which are only a small minority. Invention is discernment, choice.”
And then perhaps, our audience will be well fed and their disputed pitch harmonised; for the singer must wish to move past the opening. || cf. Henri Poincaré, “Among chosen combinations the most fertile will often be those formed of elements drawn from domains which are far apart.”
But, dear Sir, I am a woman. I was born frightened. And like all women, I cried from womb to life, and so I cry as I write. This tear soaked keyboard, too, begs your pardon for what is a woman of suffrage reading such a paper? I am un-obliged to understand. (5) || cf. Henri Poincaré, “I beg the reader's pardon; I am about to use some technical expressions, but they need not frighten him, for he is not obliged to understand them.”
Let us leave this opera house, and enter my office. For this chair is Freudian stitched, but Oedipus it is not. (6) || cf. Henri Poincaré, “This theorem will have a barbarous name, unfamiliar to many, but that is unimportant; what is of interest for the psychologist is not the theorem but the circumstances.”
An artist may sit at their desk and be incapable of drawing a nose. After much frustration they may leave, for they too are disgusted by the incapability of their hands. Upon return, an attempt is made and the consequent nose is not just drawn adequate, but drawn in so that rivals the devil of liberty.
This is experience exists amongst those who game too. For one may rival a boss only to fail every time, and with deep frustration they unplug and sleep. After such a nap, the game is replugged and docked, and with a tense breath the boss is faced and defeated on the first attempt therein. That is to say, art and maths are not unalike. Perhaps they are the very same machinery from which life itself ticks. We may then propose that it is within this ticking that invention is propagated by the subconscious.
|| cf. Henri Poincaré, “Often when one works at a hard question, nothing good is accomplished at the first attack. Then one takes a rest, longer or shorter, and sits down anew to the work. During the first half hour, as before, nothing is found, and then all of a sudden the decisive idea presents itself to the mind. It might be said that the conscious work has been more fruitful be cause it has been interrupted and the rest has given back to the mind its force and freshness. But it is more probable that this rest has been filled out with unconscious work and that the result of this work has afterward revealed itself to the geometer”
Would one have not known that a hot stove is only to be touched once cool, least one is to blister? To err is to learn, and to err into disgust or frustration is to reel subconscious and return conscious with resolve. || cf. Henri Poincaré, “These efforts then have not been as sterile as one thinks; they have set agoing the unconscious machine, and without them it would not have moved and would have produced nothing.”
For the subconscious is not err immune. || cf. Henri Poincaré, “But do not think this a rule without exception; often this feeling deceives us without being any the less vivid, and we only find it out when we seek to put on foot the demonstration. I have especially noticed this fact in regard to ideas coming to me in the morning or evening in bed while in a semi hypnagogic state.”
A question for the modern age: can that which we program part-take in mathematical creation? For how does one code a subconscious? stepwise? (7) || cf. Henri Poincaré, “But usually the subliminal self is considered as purely automatic. Now we have seen that mathematical work is not simply mechanical, that it could not be done by a machine however perfect.”
And with such an insight should one not question the arbitrary split of that which is objective and that which is subjective? For are they not that which holds the other up—a wall for the other, when the other aches from tire? || cf. Henri Poincaré, “A first hypothesis now presents itself: the subliminal self is in no way inferior to the conscious self; it is not purely automatic ; it is capable of discernment; it has tact, delicacy; it knows how to choose, to divine. What do I say? It knows better how to divine than the conscious self, since it succeeds where that has failed. In a word, is not the subliminal self superior to the conscious self? You recognize the full importance of this question.”
The beauty of mathematics is that it is a brush held by an artisan, but without some intuition how would one see the beauty of a perfectly balance equation, or notice where a formula leans too far left, so much so that a slight nudge would result in the notational tip-over? (8) || cf. Henri Poincaré, “This would be to forget the feeling of mathematical beauty, of the harmony of numbers and forms, of geometric elegance. This is a true esthetic feeling that all real mathematicians know, and surely it belongs to emotional sensibility.”
Cast my parasol aside, for there is plenty of a shade here. || cf. Henri Poincaré, “The useful combinations are precisely the most beautiful, I mean those best able to charm this special sensibility that all mathematicians know, but of which the profane are so ignorant as often to be tempted to smile at it.”
The sun is aglow, yet my age is safe. || cf. Henri Poincaré, “Thus it is this special esthetic sensibility, which plays the role of the delicate sieve of which I spoke, and that sufficiently explains why the one lacking it will never be a real creator.”
The Freudian chair squeaks, for it resides in a house, on a hill. (9) || cf. Henri Poincaré, “The conscious self is narrowly limited, and as for the subliminal self we know not its limitations, and this is why we are not too reluctant in supposing that it has been able in a short time to make more different combinations than the whole life of a conscious being could encompass. Yet these limitations exist. Is it likely that it is able to form all the possible combinations, whose number would frighten the imagination?”
I choose the gnats, for I ought to avoid the stove. || cf. Henri Poincaré, “where they are enclosed, as would, for example, a swarm of gnats or, if you prefer a more learned comparison, like the mole cules of gas in the kinematic theory of gases. Then their mutual impacts may produce new combinations.”
A thought laid to rest does not die, it bone-timers and reanimates once the conscious mind is ready (but we must remember not to fighten our selves). || cf. Henri Poincaré, We think we have done no good, because we have moved these elements a thousand different ways in seeking to assemble them and have found no satisfactory aggregate. But, after this shaking up imposed upon them by our will, these atoms do not return to their primitive rest. They freely continue their dance.”
To take this rough proclamation and move it into chemistry, we might say these atoms bonds just so. After nary an attempt water fits a glass in perceived smoothness only after the bonds between molecules are settled and re-arranged after a few turbulent swings. (10) || cf. Henri Poincaré, “Then the mobilized atoms undergo impacts which make them enter into combination among themselves or with other atoms at rest which they struck against in their course.”
The wall of prior note. || cf. Henri Poincaré, ”It seems that thinking in the evening upon the factors of a multiplication, we might hope to find the product ready made upon our awakening, or again that an algebraic calculation, for example a verification, would be made unconsciously. Nothing of the sort, as observation proves. All one may hope from these inspirations, fruits of unconscious work, is a point of departure for such calculations. As for the calculations themselves, they must be made in the second period of conscious work, that which follows the inspiration, that in which one verifies the results of this inspiration, and deduces their consequences. The rules of these calculations are strict and complicated. They require discipline, attention, will, and therefore consciousness.”
Ah, this is where I must present a question: must disorder be born of chance? One does not learn to draw the perfect nose, or beat a boss, because of a dice rolled? Is it luck? Or is it a combination that what is deformed into being, and informed by that which was once erred? For if we had not erred as we did, the combination would not hold the same geometric edges as it now does. For an atom or a module (as in the example of present) is not just an abstract thing with no body? They must have some shape, and so there must be some type of edges? And would such edges not have been shaped by prior conscious work? || cf. Henri Poincaré, “In the subliminal self, on the contrary, reigns what I should call liberty, if we might give this name to the simple absence of discipline and to the disorder born of chance. Only, this disorder itself permits unexpected combinations.”
Nor do I repent having read such interests; such tears are not hypothesis hinged. || cf. Henri Poincaré, “Surely they have need of it, for they are and remain in spite of all very hypothetical: the interest of the question is so great that I do not repent of having submitted them to the reader.”
———
REFERENCES.
0. H. Poincaré, Mathematical Creation, The Monist, Volume 20, Issue 3, 1909, public domain.
1. Institut de France Académie Française, Discours prononcé dans la séance publique tenue par l’Académie Française pour la réception de M. Henri Poincaré, le jeudi 28 janvier 1909 (Paris: Institut de France, 1909), public domain.
2. R. Descartes, Meditations on First Philosophy: with Selections from the Objections and Replies (originally published 1641; 2008 edition translated by Michael Moriarty, Oxford University Press, 2008) (copyright © Oxford University Press, all rights reserved)
3. When schooling becomes a place of shame, our slips become a place of shame rather than the inviable misstep in order to allow correction. The instructions of today may no longer invoke the cane but the act of shaming a child is widespread and suffocating, yet we wonder why the children of today can no longer breathe? This is not a problem of cramping hands and a habit born of swiping tablets but of a broken institution. (I)
4. C. Saint-Saëns, The Carnival of the Animals (1886), public domain.
5. Such a trail of tears find such a way in a list of such references. Such pardons are mine, to such an objective place as this.
6. S. Freud, Interpreting Dreams (Die Traumdeutung, 1899; English translation 1913) (copyright © Vintage International, all rights reserved).
7. A. Vaswani, et al., “Attention is All You Need,” NeurIPS, 2017 (copyright © NeurIPS, all rights reserved). (II)
8. P. A. M. Dirac, “The Evolution of the Physicist’s Picture of Nature,” Scientific American, Vol. 208, No. 5, May 1963, pp. 45–53 (contains the phrase “It is more important to have beauty in one’s equations than to have them fit experiment”) (copyright © Scientific American, all rights reserved).
9. S. Jackson, The Haunting of Hill House (1959) (copyright © The Estate of Shirley Jackson, all rights reserved).
10. L. D. Landau, Collected Papers of L. D. Landau, ed. D. ter Haar (Oxford: Pergamon Press Ltd. and Gordon and Breach Science Publishers, Inc., 1965), pp. 193–216 (“On the Theory of Phase Transitions”) (copyright © Pergamon Press Ltd. and Gordon and Breach Science Publishers, all rights reserved).
———
CITE-REFERENCES.
I. Is a citation needed, or, , are you the citation?
II. But is it? (1)
July 9, 2018
The five stars are for treating philosophy of science. I am currently not interested in philosophy or psychology of mathematics - so I skimmed through those sections.
Poincare is a very dense writer(because of his genius?). But still, he makes a remarkable presentation of science upto his days. Even in his days, mechanics(physics) was in crisis - no one knew how radium produced energy. He repeats many ideas and eventually tries to make sense of what radium means for future of science.
After this book was published, entire subatomic world would open. Relativity and quantum mechanics would take their place in the fabric of scientific thought. Therefore, this book acts as a great standard for the foundations of science of pre-relativity days. Nonetheless, it still gives a great view of what science is and how scientists approach their work.
Poincare is a very dense writer(because of his genius?). But still, he makes a remarkable presentation of science upto his days. Even in his days, mechanics(physics) was in crisis - no one knew how radium produced energy. He repeats many ideas and eventually tries to make sense of what radium means for future of science.
After this book was published, entire subatomic world would open. Relativity and quantum mechanics would take their place in the fabric of scientific thought. Therefore, this book acts as a great standard for the foundations of science of pre-relativity days. Nonetheless, it still gives a great view of what science is and how scientists approach their work.
December 6, 2016
Interesting and a very smooth read. He hits upon so many truths about science that are often forgotten. One quote is an example of the clarity with which this book is written. "It is often said experiments must be made without a preconceived idea. That is impossible. Not only would it make all experiment barren, but that would be attempted which could not be done. Every one carries in his mind his own conception of the world, of which he can not so easily rid himself. We must, for instance, use language; and our language is made up only of preconceived ideas and can not be otherwise. Only these are unconscious preconceived ideas, a thousand times more dangerous than the others." This author, one of the 19th century's most brilliant men, is very important to read if you are interested in the philosophy of science.
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March 10, 2009nach: James Webb Young: A Technique for Producing Ideas.
eigentlich: Science and Method. transl. by F. Maitland
eigentlich: Science and Method. transl. by F. Maitland
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