Science and Hypothesis

by Henri Poincaré

Here is Poincaré's famous discussion of creative psychology as it is revealed in the physical sciences. Explaining how such basic concepts as number and magnitude, space and force were developed, the great French mathematician refutes the skeptical position that modern scientific method and its results are wholly factitious. The places of rigorous logic and intuitive leaps are both established by an analysis of contrasting methods of idea-creation in individuals and in modern scientific traditions. The nature of hypothesis and the role of probability are investigated with all of Poincaré's usual fertility of insight.
Partial On the nature of mathematical reasoning. Magnitude and experiment. non-Euclidean geometrics, space and geometry, experiment and geometry. classical mechanics, relative and absolute motion, energy and thermodynamics. hypotheses in physics, the theories of modern physics, the calculus of probabilities, optics and electricity, electro-dynamics.
"Poincaré's was the last man to take practically all mathematics, both pure and applied as his province. Few mathematicians have had the breadth of philosophic vision that Poincaré's had, and none is his superior in the gift of clear exposition." — Men of Mathematics , Eric Temple Bell, Professor of Mathematics, University of Cambridge

Genres: Science, Philosophy, Nonfiction, Physics, Mathematics, France, Classics

288 pages, Paperback

First published January 1, 1902

About the author

Jules 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.

Reviews

[Genjiro · Rating 5 out of 5]

This book by Poincare was mostly over my head. Still, even though it was a struggle from start to finish, with each turn of the page, forward or backward, it was what I like to call—a beautiful struggle. The title: "Science & Hypothesis" kept me away for a few years until I mustered the courage to get started. In the beginning chapters Poincare (re) examines and overviews fundamental concepts such as: space, motion, energy, position, change, and so forth. The parts I found more intriguing—and no less hard going—were the later chapters on: non-Euclidian geometry, thermodynamics, electrodynamics and the problems of (how we understand) modern physics. It is those areas that I had to force my self to read over and over and over again. Yet it was those areas that I discovered something of value, without actually knowing what that value was in hard quantitative terms. What I feel I can say with some certainty is that Poincare's postulations and formulations, with all its implications in physics, philosophy and politics, leave an impression that the world of physicals systems, the relationship between objects—and the laws that keep everything coherent and whole—are not as immutable as thought, believed, or demonstrated to be, and in need of constant, continuous examination and scrutiny, which is what I found terribly exciting.

[Manuel Alfonseca · Rating 3 out of 5]

FRANÇAIS: Poincaré est l'un des représentants du conventionnalisme, qui soutient que les théories scientifiques sont purement conventionnelles et ne représentent pas fidèlement la réalité. Personnellement, je ne suis pas un conventionnaliste et je me sens plus proche de Popper que de Poincaré.

Dans la première partie, il s'oppose à l'idée que les mathématiques reposent essentiellement sur la méthode déductive. Il soutient que l'induction mathématique est beaucoup plus importante et que cet outil ne peut pas être considéré comme faisant partie de la méthode déductive. Bien entendu, l'induction mathématique apporte une parfaite certitude quant à ses résultats, ce qui n'est pas le cas de la méthode inductive, telle qu'elle est utilisée en sciences expérimentales.

Dans la deuxième partie, l'Espace, il mêle géométrie et anatomie, et vise à expliquer notre sentiment de vivre dans un espace tridimensionnel basé sur les mouvements musculaires de l'œil pour s'assurer que l'image d'un objet en mouvement conserve sa position relative par rapport à nous. Cette explication me semble farfelue. Autant que je sache, je ne bouge généralement pas mes yeux pour que les objets en mouvement conservent leur position relative, je les vois juste bouger. Et pour détecter cet espace à trois dimensions, il suffit de regarder un coin du plafond de ma chambre. Le but de Poincaré est d'affirmer (ce qu'il fait à la fin de cette partie) que la géométrie n'est pas vraie, elle est simplement avantageuse. C'est-à-dire que la géométrie nous serait imposée par la sélection naturelle et ne nous présenterait pas une image fidèle du monde, mais plutôt la plus avantageuse pour notre survie. Cette explication conventionnaliste me semble forcée et élaborée.

La troisième partie est un peu dépassée, car ce livre a été publié en 1902 et est donc antérieur à la théorie de la relativité. Les doutes sur la difficulté de définir la force gravitationnelle, par exemple, disparaissent, car dans la relativité générale, la gravité est une déformation géométrique de l'espace. Mais intéressante est la distinction de Poincaré entre les constantes universelles accidentelles (telles que la constante d'aire, la deuxième constante de la loi de Kepler), dont la valeur aurait pu être différente, du moins pour autant que nous le sachions, et les constantes essentielles, comme l'exposant 2 dans L'équation de Newton, que dans un espace tridimensionnel ne peut pas prendre une autre valeur.

La quatrième partie, consacrée aux hypothèses scientifiques, a été dépassée par les travaux de Karl Popper, Thomas Kuhn et d'autres auteurs, bien qu'elle présente quelques idées intéressantes, telles que la citation suivante, qui exprime graphiquement la différence entre l'histoire et la science expérimentale: Carlyle a écrit quelque part quelque chose comme ceci: "Le fait seul importe; Jean sans Terre a passé par ici... voilà une réalité pour laquelle je donnerais toutes les théories du monde." Carlyle était un compatriote de Bacon; mais Bacon n’aurait pas dit cela. C’est là le langage de l’historien. Le physicien dirait plutôt: "Jean sans Terre a passé par ici; cela m’est bien égal, puisqu’il n’y repassera plus."

Ou cette citation, qui exprime assez bien la différence entre la physique théorique et expérimentale: Qu’on me permette de comparer la Science à une bibliothèque qui doit s’accroître sans cesse; le bibliothécaire ne dispose pour ses achats que de crédits insuffisants; il doit s’efforcer de ne pas les gaspiller. C’est la physique expérimentale qui est chargée des achats; elle seule peut donc enrichir la bibliothèque. Quant à la physique mathématique, elle aura pour mission de dresser le catalogue. Si ce catalogue est bien fait, la bibliothèque n’en sera pas plus riche. Mais il pourra aider le lecteur à se servir de ces richesses. Et même en montrant au bibliothécaire les lacunes de ses collections, il lui permettra de faire de ses crédits un emploi judicieux; ce qui est d’autant plus important que ces crédits sont tout à fait insuffisants.

ENGLISH: Poincaré is one of the representatives of conventionalism, which holds that scientific theories are purely conventional and don't faithfully represent reality. Personally I'm not a conventionalist, and feel closer to Popper than Poincaré.

In the first part, he speaks against the widespread idea that mathematics relies essentially on the deductive method. He argues that mathematical induction is much more important, and that this tool cannot be considered part of the deductive method. Of course, mathematical induction provides perfect certainty regarding its results, which is not the case with the inductive method, as used in the experimental sciences.

In the second part, Space, he mixes geometry with anatomy, and aims to explain our feeling of living in a three-dimensional space based on the muscular movements of the eye to ensure that the image of a moving object maintains its relative position with respect to us. I find this explanation far-fetched. As far as I know, I don't usually move my eyes so that moving objects maintain their relative position, I just see them move. And to see that space has three dimensions, I can just look at a corner of the ceiling of my room. Poincaré's goal is to assert (which he does at the end of this part) that geometry is not true, but simply advantageous. That is to say: geometry has been forced on us by natural selection and does not provide us with a faithful image of the world, rather with the most advantageous for our survival. This conventionalist explanation seems to me forced and elaborate.

The third part is a little outdated, as this book was published in 1902 and therefore predates the theory of Relativity. Disquisitions about the difficulty in defining the gravitational force, for example, are not necessary, for in General Relativity gravity is a geometric deformation of space. But an interesting distinction Poincaré makes is that between accidental universal constants (such as the area constant, in Kepler's second law), the value of which could have been different, at least as far as we know, and essential constants, such as exponent 2 in Newton's equation, than in a space three-dimensional cannot take another value.

The fourth part, dedicated to scientific hypotheses, has been surpassed by the work of Karl Popper, Thomas Kuhn and other authors, although it introduces a few interesting ideas, such as the following quote, which graphically expresses the difference between history and experimental science: Carlyle has somewhere said something like this: "Nothing but facts are of importance. John Lackland passed by here... Here is a reality for which I would give all the theories in the world." Carlyle was a fellow countryman of Bacon; but Bacon would not have said that. That is the language of the historian. The physicist would say rather: "John Lackland passed by here; that makes no difference to me, for he never will pass this way again."

Or this quote, that expresses quite well the difference between theoretical and experimental physics: The librarian has at his disposal insufficient funds for his purchases. He ought to make an effort not to waste them. Experimental physics is entrusted with the purchases. It alone can enrich the library. As for mathematical physics, its task will be to make out the catalogue. If the catalogue is well made, the library will not be any richer, but the reader will be helped to use its riches. And by showing the librarian the gaps in his collections, it will enable him to make a judicious use of his funds; which is all the more important because these funds are entirely inadequate.

ESPAÑOL: Poincaré es uno de los representantes del convencionalismo o instrumentalismo, que sostiene que las teorías científicas son puramente convencionales y no representan fielmente la realidad, pero son útiles si sirven para hacer predicciones correctas. Personalmente no soy convencionalista, y me siento más cerca de Popper que de Poincaré.

En la primera parte, se opone a la idea de que las matemáticas se apoyan esencialmente en el método deductivo. Sostiene que la inducción matemática es mucho más importante, y que esta herramienta no puede considerarse parte del método deductivo. Pero hay que tener en cuenta que la inducción matemática proporciona certidumbre absoluta respecto a sus resultados, cosa que no ocurre con el método inductivo, tal y como se utiliza en las ciencias experimentales.

En la segunda parte, el Espacio, mezcla la geometría con la anatomía y pretende explicar que tengamos la sensación de vivir en un espacio tridimensional en función de los movimientos musculares del ojo que aseguran que la imagen de un objeto móvil mantenga su posición relativa respecto a nosotros. Esta explicación me parece rebuscada. Que yo sepa, no suelo mover los ojos para que los objetos móviles mantengan su posición relativa, simplemente los veo moverse. Y para ver que el espacio tiene tres dimensiones, me basta mirar a una esquina del techo de mi habitación. El objetivo de Poincaré es afirmar (lo que hace al final de esta parte) que la geometría no es verdadera, simplemente es ventajosa. Es decir: la geometría nos vendría forzada por la selección natural y no nos presenta una imagen fiel del mundo, sino la más ventajosa para nuestra supervivencia. Esta explicación convencionalista me parece forzada y rebuscada.

La tercera parte está un poco atrasada, pues este libro se publicó en 1902 y por tanto es anterior a la teoría de la Relatividad. Las disquisiciones sobre lo difícil que es definir la fuerza de la gravedad se vuelven innecesarias, pues en la Relatividad General la gravedad es una deformación geométrica del espacio. Pero es interesante la distinción que hace Poincaré entre constantes universales accidentales (como la constante del área, la de la segunda ley de Kepler), cuyo valor podría haber sido diferente, al menos que sepamos, y las constantes esenciales, como el exponente 2 en la ecuación de Newton, que en un espacio de tres dimensiones no puede tomar otro valor.

La cuarta parte, dedicada a las hipótesis científicas, ha sido sobrepasada por el trabajo de Karl Popper, Thomas Kuhn y otros autores, aunque introduce algunas ideas interesantes, como la cita siguiente, que expresa gráficamente la diferencia entre la historia y la ciencia experimental: Carlyle escribió algo parecido a esto en algún sitio: “Solo los hechos importan; Juan sin Tierra pasó por aquí... y por esta realidad yo cambiaría todas las teorías del mundo". Carlyle era compatriota de Bacon; pero Bacon no habría dicho eso. Este es el lenguaje del historiador. Un físico diría: “Juan sin Tierra pasó por aquí; no me importa, porque no volverá a pasar por aquí."

O esta cita, que expresa bastante bien la diferencia entre física teórica y experimental: Permítaseme comparar la ciencia con una biblioteca que debe estar en constante crecimiento; el bibliotecario tiene un presupuesto insuficiente para hacer las compras; debe tratar de no desperdiciarlo. La física experimental es responsable de la compra; solo ella, por tanto, puede enriquecer la biblioteca. En cuanto a la física matemática, su misión será elaborar el catálogo. Si este catálogo está bien hecho, la biblioteca no se enriquecerá, pero ayudará al lector a usar estas riquezas. Y al mostrarle al bibliotecario las deficiencias de sus colecciones, le permitirá hacer un uso juicioso de su presupuesto; lo cual es tanto más importante, cuanto que este presupuesto es completamente insuficiente.

[mohab samir · Rating 5 out of 5]

فى ظل التغيرات العلمية الثورية التى شهدها النصف الثانى من القرن التاسع عشر ، سادت نزعة شكٍّية تجاه بنية العلم وإمكانية تأسيسها بشكل جذرى . تعددت التوجهات المتعارضة فى هذه المسألة التى سادت طوال تلك الفترة ، فمن العلماء المفكرين من قال بإمكان قيام بنية علمية موحدة ومنهم من نفى ذلك إطلاقاً . ومن الأوائل من كانوا ماديين فى تصورهم لتلك البنية ، ومنهم من بناها على دعامة من المفاهيم المثالية ، ومنهم من نادى ببنية وصفية ترابطية بين مختلف مواضيع المعرفة . وكان تصور هوسرل الفينومينولوجى - الذى جاء فى نهاية تلك الحقبة - هو الأكثر قبولاً نظراً لمنطقه العتيد ولتلاؤمه مع كافة ما إستجد من الإكتشافات العلمية طوال تلك الفترة . وكان الهدف النهائى لهوسرل والذى لم ينجح فيه بالضرورة إلا جزئياً هو تأسيس العلم بشكل نهائى على الفلسفة أى إيجاد نظرية نهائية فى المعرفة تحسم كل جدل وهى نظرية مثالية بالضرورة ولكنها فى المقابل تتطلب أولاً وقبل كل شئ تأسيس الفلسفة ذاتها كعلم .
يعاصر هذا الكتاب كتابات هوسرل الأولى فى المنطق ولكنه يسبق مرحلة الفينومينولوجيا ولكنه يبقى متأثراً بمنابع هذه الفلسفة بدايةً من كانط ومروراً ببرجسون وبرنتانو .
تظل قضية إمكان��ة بناء العلم فى ظل التبدلات المتلاحقة للنظريات وكثرة الفرضيات الجديدة التى تواجه بعضها بعضاً فى كافة أفرع العلم بشكل مستمر ومتجدد نظراً للثورة العلمية المصحوبة بتطور سريع فى المعرفة مدعوم ومصحوب بتط��ر مستمر فى دقة آلات القياس . وهى الثورة التى لاقت مداها الأوسع فى مجال الفيزياء وصراع نموذج الفيزياء الكلاسيكية مع الفرضيات الفيزيائية الجديدة التى فرضت نفسها عليه نتيجة لإكتشافات الكهرومغناطيسية والإشعاع وإرهاصات إستكشاف الجسيمات ما دون الذرية التى لا تتوافق مع نماذج الفيزياء والميكانيكا الكلاسيكية النيوتونية . بالإضافة إلى إكتشافات أخرى لا تقل عنها اهمية فى الديناميكا الحرارية وتحولات الطاقة .
كان من الصعب إيجاد نموذج علمى يشمل كل هذه المكتشفات وفروع المعرفة العلمية الجديدة والتى تتطلب لحساب المستقبل البحث عن نموذج معرفى مرن يقود آلية البحث العلمى من جانب ويساعد من جانب آخر على إدراج المعارف الجديدة لهذا البحث ضمن بنية علمية مُطَّرِدة التضخم .


ويمكن ملاحظة أن الإكتشافات الفيزيائية الجديدة الخاصة بالجسيمات ما دون الذرية والإشعاع تردم هوة كبيرة بين معرفة الأجسام فى المقياس الكبير ( الماكروى ) للعالم ثلاثى الأبعاد والأجسام الموجودة فى أبعاد أخرى لا يمكننا ملاحظتها مباشرة أو بالأدوات العلمية البسيطة المعتادة كالمجهر أو التليسكوب مثلاً لكونها شديدة الضآلة ولا يمكن قياسها الا بمقاييس شديدة الضآلة والدقة بالضرورة . وهو ما أدى فيما بعد إلى ظهور النظرية النسبية التى تمكنت من جمع هذا الشتات والربط بين الفيزياء القديمة والإبقاء عليها فى مجال عملها الذى تتمتع فيه بالبساطة مع الفيزياء الحديثة وهى فيزياء الكم الخاصة بالجسيمات ما دون الذرية .
وبالتوازى مع ذلك نلاحظ ردومات أخرى لهوىً كثيرة تقع عند الحدود القائمة بين مختلف العلوم الطبيعية من خلال نشأة فروع علمية جديدة تحتم ظهورها نتيجة لتطور البحث كالفيزياء الرياضية ، أو الكيمياء الفيزيائية التى ربطت بين دراسة المواد الكيميائية وخصائصها الفيزيائية المحتملة ، كما ظهرت الكيمياء الحيوية والديناميكا الحرارية والفيزياء الفلكية وغيرها العديد من فروع العلم الثانوية التى ربطت بين مجالات العلوم الرئيسية . ساد نتيجة لذلك شك متزايد فى أن تتمكن بنية العلم من التأكيد على حدود فاصلة بشكل متواصل بين مختلف الظواهر التى تلزمها نظرياتها الخاصة والتى لا تنفصل عن الأسس المعرفية للظواهر الكبرى ، كونها فروع ثانوية منها تقلص بشكل متصل من عمق كل هوة قائمة بين العلوم الكبرى بحيث لا يمكن أن تظل هذه العلوم واضحة المعالم بذاتها من جانب ولا يمكن أن يتم ردم أى هوة بشكل نهائى من جانب آخر ، فكل علومنا هى علوم تجريبية لابد وأن تتأسس على فرضيات نظراً لكون هذه التجريبية لا تتعامل إلا مع كل ذى حد وكل ما يمكن قياسه بالنسبه إلى آخر ولذلك فإن هذه النسبية الحاضرة فى كل الظواهر التى يتناولها العلم بالدراسة تخفى عنا إمكان التعرف على أى حقيقة مطلقة من آية نوع .

إلا أن بوانكاريه لا تمثل له هذه الفكرة آية إشكالية حيث يعتمد نزعة منظورية تجعله لا ينسى على أى أرض يقف . فما دام يمدنا التفكير العلمى بشكل مستمر بناء على معطياتنا المستجدة رؤىً موحدة جديدة نختار من بينها أبسطها وأكثرها شمولاً ، يظل العلم بذلك يوفر لنفسه بنفسه صورة بنيته الملائمة لما ظهر لنا من معرفة بظواهر العالم . فى عملية تشبه تصورنا لما يظهر لنا من نجوم فى السماء على أنها صورة كاملة منتظمة قد تختلف من شخص لآخر مثل تصور مجموعة نجوم فى صورة عذراء أو دب قطبى أو كرسى عند قبيلة ما ، أو تصور أى منهم على نحو مختلف نتيجة لاختلاف فى التصور والمخيلة أو لإختلاف فى منظور الرؤية لدى قبيلة أخرى فى مكان وزمان آخرين . إلا أن كلا الرؤيتين تؤدى غرضها النهائى كأن تحدد لأفراد كل قبيلة إتجاه الشمال ، فلا يكون لأى الفرضيتين صحة أكثر مما لصحة الأخرى .
أما فى العلم فتتزايد المعرفة وتتزايد بها النجوم المتلألأة فى سماء المعرفة عموماً كما فى سماء كل فرع من فروعها ، ما يسمح برسم تصورات ( فرضيات ) جديدة يتم التأكد من صحتها وشموليتها ودقتها تجريبياً - وهو مالا يختلف فى تصوره بين البشر - وعملياً من خلال التقنية والمنفعة التى تعود بها على الإنسان . مما يرقى بالفرضية إلى درجة النظرية والتى تظل فى إنتظار نظرية أوسع منها تشملها فى جوفها كأحد مقدماتها أو عناصرها وهذا ما يحدث عندما نتطرق إلى ظاهرة جديدة لا يمكن تفسيرها من خلال النظرية القديمة كما لم تستطع الفيزياء الكلاسيكية تفسير حركة الجسيمات ما دون الذرية .
ومادام العلم يؤدى عمله بهذه الطريقة فهو لا يختلف عن أى كيان متطور فهو فى تطوره يرتبط بتطور كيانات ما أخرى ولكن هذا التطور وهذه الإرتباطات لا تنفى كيانه أو أثره الملحوظ . بل تدعو لتأمل آلية عمله والتعرف عليها خلال هذا العمل وهنا تبقى حتى أهمية وقيمة للفرضيات الخاطئة أو حتى الزائفة فى تاريخ العلم .

إن التأملات الفلسفية المحمولة داخل النص هى من مستوى رفيع وهى ليست مجرد تجريدات فهى على الدوام مرتبطة بالظواهر سواء من خلال التجربة الذهنية او الرياضية - والتى لا تتوانى عن نقد نفسها - أو ربط مكوناتها بالظواهر الطبيعية . وهى مرتبطة من جانب آخر بتاريخ العلم وبسيرورة تطوره كتجربه فى حد ذاتها . وقد تمتعت تلك الفترة من الزمن بعقول كثيرة عظيمة من أمثال هنرى بوانكاريه وإرنست ماخ وفيلهلم اوستفالد وغيرهم الكثيرين ممن مزجوا الخبرة العلمية التجريبية بالمعارف الفلسفية النقدية - من دون خلط - من أجل البحث عن الأساس الأعمق للعلم وتأكيد إمكانيته كوحدة واحدة أو على الأقل البحث عن صورة العلم المنطقية كونها نظرية للمعرفة .

[Matt · Rating 5 out of 5]

Henri Poincare was no purist. Described as a polymath, his writing reflects the same wide-ranging view as his skills. He used everything available to him overcome walls. Observations were his lumber and hypotheses filled his tool box. If he needed a ladder, he built that; if a pulley lift, then that; he would use everything… and build a catapult if necessary.

By not shackling himself to a particular theory, he could explore the utility of all those available and disregard what didn’t work. A good example of this approach is found in his discussion of Euclidean geometry. For those of us less brilliant, we can follow along as he describes how its axioms fail when moving into third and fourth dimensions, but its imperfections do not mean it lacks utility:

What, then, are we to think of the question: Is Euclidean geometry true? It has no meaning. We might as well ask if the metric system is true, and if the old weights and measures are false; if Cartesian co-ordinates are true and polar co-ordinates false. One geometry cannot be more true than another; it can only be more convenient. Pg. 22

Similarly be compares and contrasts the competing theories of relativity, energy and thermodynamics, optics and electricity, among others. Surprisingly, it is all fairly digestible as he summarizes main points using plain language instead of mathematical language. I’m sure the mathematicians would take exception, but even if it is not providing the deeper and nuanced understanding that formulas can convey, it helps us more fuzzy liberally-art'ed trained readers.

In the end, Poincare wants to impress the reader with the “standing on the shoulder of giants” approach to appreciating math and science. It works within its own limitations to provide a chance to build a better understanding of tomorrow.

The ephemeral nature of scientific theories takes by surprise the man of the world. Their brief period of prosperity ended, he sees them abandoned one after another; he sees ruins piled upon ruins; he predicts that the theories in fashion to-day will in a short time succumb in their turn, and he concludes that they are absolutely in vain. This is what he calls the bankruptcy of science.

His skepticism is superficial; he does not take into account the object of scientific theories and the part they play, or he would understand that the ruins may still be good for something. Pg. 63.

[Michael Greer · Rating 5 out of 5]

I will confine myself to a discussion of Part 1, Number and Magnitude. Under this title, the author develops some concepts that will be useful as we proceed through the book. The first is the term "syllogism." The received account is that Aristotle was the first to systematize the study of the syllogism. The syllogism is a formal 'proof' of a proposition from two propositions already known to be true. "All men enjoy pursuing pleasure" and "Socrates is a man" therefore "Socrates enjoys the pursuit of pleasure." If we grant the first two propositions, then the last one is derived from them. So, as our author states, "the syllogism teaches us nothing new." It's not new because the last statement is contained within the two provided. All of this is possible only if we grant the principle of identity.

Now, Poincare makes another move to axioms. In my understanding an axiom is an unchallenged statement used to provide leverage for further proof-making. And, keeping with this interest, the author mentions "synthetic a priori statements" (this seems to be the language of Kant). Those were truths which can be arrived at ("synthetically") prior to any experience. Most writers will model them on mathematical statements used in arithmetic.

Now, we are coming to the important work Poincare achieved in this first section: you must distinguish mathematical reasoning from syllogistic reasoning. They are not the same. Furthermore, we must refine our understanding of proof by distinguishing a demonstration from a verification. When we use conventionally defined terms, then we verify them in operation. Verification is of itself analytical and hence nothing new is offered. This is what is troubling to our author: how to understand the creative nature of mathematics without reducing it to syllogism, tautology, or derivations.

[Marie Martin · Rating 2 out of 5]

Why, oh, why did I want to read this book? No, seriously? This book was entirely too deep for me, very technical. The only thing I will take away from this book, other then I am not a math and science person, is that there are no absolutes. That's it.

[Abdaljbbar Dawod · Rating 2 out of 5]

الكتاب مترجم من اللغه الانجليزيه لذلك تظهر هناك صعوبه فى ربط الافكار بالعبارات فى اللغه العربيه و يؤدي ذلك الى عدم التركيز

[Gérard Doux · Rating 4 out of 5]

La première partie, plus mathématique, est très intéressante et encore très actuelle. La deuxième, plus physique, est hélas assez "vieillie" : de l'ether partout, des électrons assez méconnus,... Cela donne toutefois envie de se plonger dans l'histoire de la physique.

[Jonathan Morrow · Rating 5 out of 5]

This book kind of blew my mind. I absolutely love this style of writing. Precise, dense and deep. It's like this guy doesn't know how to write frivolous words. You have to pay attention to every sentence because he'll say something profound and in the very next sentence say something even more profound without giving you any time to digest or unpack the previous sentence. He has an appreciation for the essence of science that I think is lost on most scientists, past and present, let alone laypersons. I wish everyone could be introduced to the concepts he explores here, but I think it takes more effort than most are willing to expend.

I also found it fascinating to read his description of the physics of his day. When I learned about Einstein's "year of miracles" in school it was always presented as if it came out of nowhere. However, I can see in this book that all the elements were there, and Poincare at least had identified all the major gaps that needed to be filled and the concepts that needed to be connected. This was written just a few years before Einstein's famous year, so he must have read it. It didn't come out of thin air; Einstein came up with the solutions to problems that other smart people knew were important and were within reach.

Ok, I don't want the review to be longer than the book but suffice to say I highly recommend this book to the philosophically inclined. I would skip the last couple of chapters, though. They are pretty technical, outdated, and not very generalizable.

[Alex · Rating 5 out of 5]

Cette oeuvre propose au lecteur de faire un travail essentiel de mise en perspective de la science (et probablement de comment la science met le monde en perpective, via l'expérience et l'intuition).
Contient des expériences de pensée lumineuses, mises dans leur contexte historique.
Contient également un point de vue fort sur ce qu'est la science et en particulier la mathématique.

[Craig · Rating 3 out of 5]

I would give this book a perfect 2.5 if I good. Poincaré is expectedly rigorous and well spoken (even after translation). However the philosophy of science in the book is often presented in a matter of fact way such as to convince the reader the obvious view is Poincaré's own. While I disagree with him on few of his conclusion, I believe there are better ways to get there. All in all the book can still be thought provoking, if occasionally a slog.

[Ahmed Atef · Rating 4 out of 5]

الكتاب لم يكن يعرض تاريخ العلم فقط.الكتاب به شق فلسفي وهو يتحدث عن الفرض وما هو وما هي شروطه وخصائصه ويعرض كيف كانت تتجلي خصائص الفرض العلمي من خلا ل التجربة؟ ...الشق العلمي في الكتاب دسم جدا فهو يحكي كيف كانت توضع فروض ظاهره علمية ما؟ وكيف كان يدور النقاش حولها وما دور التجربة والاثبات الرياضي في حسمها؟...الكتب يحتاج لشخص درس رياضيات وفزياء مستوى جامعي وليس بمستوي الثانوية العامة .

[Matt · Rating 4 out of 5]

Extremely dense, Poincare's work is full of mathematics and physics. The reader must bring some knowledge to the table in order to appreciate anything. I certainly did not know enough to fully grasp everything, but Poincare's skepticism and clarity of thought can be treasured by any critical mind.

[Jens · Rating 5 out of 5]

The work of an exceptionally penetrating mind. Poincaré saw the problems and possibilities of the physics of his day clearly and in their full philosophical context. Fascinating to read with the benefit of 100+ years of hindsight.

[Juke · Rating 5 out of 5]

Un classique, à relire éventuellement plus tard

[Ouden · Rating 3 out of 5]

N.N. Taleb descrive Poincaré come un paladino della "vera" scienza: matematico e fisico-matematico, si guarda bene dal teorizzare ciecamente vagando nella metafisica e nell'astratto. Forse più di tutti Poincaré tratta la matematica come una scienza: dal canto mio, non credo che la matematica sia una scienza, ma leggendo questo libro credo che chiunque concluderà che Poincaré fu uno scienziato. Spaziando molto e trattando tematiche di ampio respiro, questo libro ruota però tutto intorno ad una questione: che ruolo hanno le ipotesi nella scienza? La risposta di Poincaré (che direi a cavallo tra Platonismo e Costruttivismo, almeno dal punto di vista matematico) sorprende per la sua coerenza e la sua sensatezza, ma soprattutto sbalordisce per il fatto di essere formulata all'inizio del secolo scorso. Si comprende che l'autore (benché anziano) già percepiva la rivoluzione scientifica imminente, quando egli discute il ruolo dell'osservatore e della misura (la geniale intuizione della relatività speciale di Einstein) o il senso dell'elettromagnetismo o dell'ipotesi atomica.
Il voto non troppo alto è dovuto sostanzialmente a due ragioni:
1) il libro è accessibile praticamente solo a chi è del campo, troppo specifico e con troppi riferimenti
2) molte tematiche trattate sono ormati obsolete e si fanno continui riferimenti a teorie e discussione che il moderno insegnamento della fisica elide, il che rende molti passaggi di semplice interesse storico.

[Emmanuel Gil Torres · Rating 3 out of 5]

I enjoyed this book because it shows you how to think. Moreover, how we use mathematics as convenient conventions in attempts to approximate what we see in nature which in the end seems to be universally connected. This is definitely the type of book in which you learn more from it the more times you read it. The last few chapters on electromagnetism were a bit over my head since I do not have much experience this area. A word of caution is that this book is purely text, with no figures and no formulas which can make it hard to understand some topics unless you have previous knowledge and know what he is talking about. I found some parts of the book difficult to read and weirdly worded, no doubt due to the translation from french to english. Overall, while at times difficult to read and capture all the ideas by merely reading it once, the I think the main ideas in this book will give a new perspective on science for anyone who is interested and familiar in the area.

[John Workman · Rating 3 out of 5]

This book, printed in English in 1905, is another one of the science classics that has, within it, a rather dense but insightful documentation of the methods by which "Science" and "Hypothesis" have evolved and how to better wrap one's head around the burgeoning discoveries in physics at the time. Even though Poincaré is more interested in talking about physics I think, even at the time, there is much need to discuss these kinds of philosophical novelties within areas like biology, chemistry, and the vast assortment of social sciences. For those who have read Bertrand Russel before, I would say that Poincaré seems to mimic his method of analysis aimed at physics which seems to be easier to understand than Russels lectures on pure math. The conversations within this book related to semantics and meaning, especially that of geometry and it's relation to space, are extremely valuable insures into the epistemological complexities while discussing any science.

[Ari · Rating 4 out of 5]

This is a wonderful little book. I unfortunately read it in the wiki source translation, which is not wonderful, but I was able to catch most of the meaning I think.

Poincaré was one of the great mathematical physicists of the late 19th century. He wrote this book at the start of the 20th century, as the tensions within classical physics were becoming increasingly dire. Different corners of physical science had made different and contradictory assumptions about things like whether they were absolute velocities and whether atoms move in deterministic trajectories under the influence of non-dissipative forces.

Poincaré is interested in the interplay between definition and experiment. He articulates many of the themes which Kuhn would later emphasize concerning the resistance of mature theories to experimental disproof. We write F equals MA but we only can detect the existence of a force by watching a mass accelerate. So in some sense, this is definition.

[Antoine JEAN · Rating 3 out of 5]

Pas si simple à lire : ressemble à une thèse/ réflexion très théorique, sur la nature fondamentale des sciences physiques et mathématiques. Le but semble être de pouvoir distinguer dans les paradigmes scientifiques actuels (théories globales + ensembles des lois et exceptions) ce qui est issu de la théorie pure, et ce qui a une origine dans l'expérience/ l'hypothèse.

Lourd car essaye de retracer la construction des theories d'ensemble de plusieurs domaines en repartant de 0 (reconstruire l'algèbre, la géométrie, la mécanique, l'optique, ...), avec certains raisonnements et tentatives de nouvelles hypothèses fondamentales assez complexes.
Amusant qd même de voir cette démarche + une vision sur plusieurs domaines et l'ensemble des lois de la physique datant d'avant Einstein (physique quantique, atomes, électricité etc.). Ce sont des considérations très générales sur la nature de la science, qui restent vraies avec une grille de lecture actuelle. Peut aider à mettre en perspective les réflexions sur le modèle physique actuel (théorie du tout, éléments inconnus ajd)

- Paradoxe des maths : pourquoi les présenter comme une science purement déductive (et pq une telle rigueur en conséquence) si ce n'est pas le cas ? A l'inverse, si les maths étaient uniquement déductives, est-ce que ce ne serait pas juste une tautologie géante ?

=> "Distinguer nettement ce qui est expérience, ce qui est raisonnement mathématique, ce qui est convention, ce qui est hypothèse"

- "La géométrie n'est pas vraie, elle est avantageuse" : elle n'est pas prouvable, c'est un modèle mathématique basé sur des prémisses théoriques qu'on n'a pas su réfuter. D'autres géométries que celle qu'on utilise (basées sur d'autres axiomes, tout aussi acceptables) pourraient aussi bien exister, et on ne pourrait pas les réfuter non plus. On a simplement choisi le modèle le plus pratique pour décrire le monde que nous percevons : malgré les apparences, la géométrie n'est pas basée sur l'expérience.

- But de la physique expérimentale : généralisation des expériences pr déduire des lois. But de la physique mathématique : guider cette généralisation en aidant à identifier les forces et les lacunes du système connu.

[François Jacob · Rating 3 out of 5]

Poincaré était un scientifique surdoué et précurseur. Malheureusement il faut un très haut niveau scientifique pour le comprendre ce qui n'est pas mon cas. Quelques réflexions intéressantes ressortent de ma lecture: "pourquoi ne parle-t-on plus d'éther?" et "le mouvement absolu est-il détectable ?"

[Tom · Rating 4 out of 5]

Delayed review.


I particularly enjoyed the first part (motivating science and the problem of inductive inference from the (presumably) unquestionable rigor of geometry). Poincaré does a phenomenal job of getting the reader to think about the difference between reality, model (in the broadest sense), and convention. I also liked the chapter on statistics and his objective vs subjective statistics idea (great framing of frequenting vs Bayesian). The more contemporary science sections were tough because of how particularly focused they were on current theories and intrigued and the translation I don’t think was the best. Overall, very insightful and interesting.

[Hassaan Naeem · Rating 3 out of 5]

Obviously a brilliant book by a brilliant man, covering a multitude of topics, but I didn’t quite enjoy reading as much as I thought I would, maybe was the translation. Will give this a reread some day.

[Adrien Mogenet · Rating 3 out of 5]

Incredible open scientific mind, who suggested that the Ether theory could be dismissed in the future, and able to explain the past and future successes and failures of science. A great lesson.

[Lin · Rating 4 out of 5]

Welp this dude was wrong about set theory. Still a genius tho

[Audiobook Heaven · Rating 5 out of 5]

Great book, I listened to the audiobook version. I will leave the link below so that everyone can enjoy it! https://www.youtube.com/watch?v=9H2yd...

[Alex · Rating 5 out of 5]

If you are interested in hearing a discussion of this book on my podcast, you can check it out here:

https://www.buzzsprout.com/2132180/14...

[Konstantina-Dimitra]

Important work to understand Poincaré s views of conventionalism
Though , his way of expressing his thoughts is a bit too vague sometimes

[frances]

Poincare, not the best reader of Kant.

[Jonathan Hockey · Rating 4 out of 5]

Makes a good argument for operational/conventional approach, and how it is not arbitrary conventions that we are left with, just the best and most simple hypotheses remain after much debate and study of the phenomena. A kind of principle of least action applies to the hypotheses we adopt in the long run.

Also an interesting historical document soon before Einstein's relativity discoveries, in the midst of there still being a belief in the ether. Poincare defended its convenience at the time, for where could light be but in some medium between the time it leaves a distant star and the time it gets to earth as light for us to see. This notion can remain perhaps with some kind of luminiferous ether and Poincare does document the various failed attempts to find a mechanical ether, and yet the need for some type of ether at that time to account for electrodynamic phenomena to avoid the ability to detect absolute motion based on them.

It may perhaps have been soon after this that Lorentz discovered his transformation equations for length contraction, and Poincare suggested his form of the relativity principle.