''The Value of Science'' (french: La Valeur de la Science) is a book by the French mathematician,
physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.
Physicists generally are interested in the root or ultimate caus ...
, and philosopher
Henri Poincaré
Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
. It was published in 1905. The book deals with questions in the
philosophy of science
Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ultim ...
and adds detail to the topics addressed by Poincaré's previous book, ''
Science and Hypothesis
''Science and Hypothesis'' (french: La Science et l'Hypothèse) is a book by French mathematician Henri Poincaré, first published in 1902. Aimed at a non-specialist readership, it deals with mathematics, space, physics and nature. It puts forwar ...
'' (1902).
Intuition and logic
The first part of the book deals exclusively with the mathematical sciences, and particularly, the relationship between
intuition
Intuition is the ability to acquire knowledge without recourse to conscious reasoning. Different fields use the word "intuition" in very different ways, including but not limited to: direct access to unconscious knowledge; unconscious cognition; ...
and
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
in mathematics. It first examines which parts of science correspond to each of these two categories of scientific thought, and outlines a few principles:
* What we define as intuition changes with the course of time (
Classical philosophers were seen as
logician
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
s in their time, but today we might think of them as using intuition) – it is therefore the ideas that change, in the evolution of scientific thought;
* This evolution began with the
arithmetization of analysis
The arithmetization of analysis was a research program in the foundations of mathematics carried out in the second half of the 19th century.
History
Kronecker originally introduced the term ''arithmetization of analysis'', by which he meant its c ...
, and ended with the revival of intuitive ideas in an axiomatic system, by the first (true) logicians.
This ''historic'' intuition is therefore mathematical intuition. For Poincaré, it is a result of the
principle of least effort
The principle of least effort is a broad theory that covers diverse fields from evolutionary biology to webpage design. It postulates that animals, people, and even well-designed machines will naturally choose the path of least resistance or "effo ...
, that is, of a link to scientific
convention based on
experimentation
An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when ...
. Convention, thus given a context, permits one to consider different theories of the same problem, and subsequently make a choice based on the degree of simplicity and usefulness of explanations advanced by each of these theories (see also
Occam's razor
Occam's razor, Ockham's razor, or Ocham's razor ( la, novacula Occami), also known as the principle of parsimony or the law of parsimony ( la, lex parsimoniae), is the problem-solving principle that "entities should not be multiplied beyond neces ...
). The example chosen by Poincaré is that of
three-dimensional space
Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position (geometry), position of an element (i.e., Point (m ...
. He shows how the representation of this space is only one possibility, chosen for its usefulness among many models that the mind could create. His demonstration rests on the theory of ''
The Mathematical Continuum'' (1893), one of Poincaré's earlier publications.
Finally, Poincaré advances the idea of a fundamental relationship between the sciences of ''
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
'' and ''
analysis
Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
''. According to him, intuition has two major roles: to permit one to choose which route to follow in search of scientific truth, and to allow one to comprehend logical developments: Moreover, this relation seems to him inseparable from scientific advancement, which he presents as an enlargement of the framework of science – new theories incorporating previous ones, even while breaking old patterns of thought.
Mathematical physics
In the second part of his book, Poincaré studies the links between physics and mathematics. His approach, at once historical and technical, illustrates the preceding general ideas.
Even though he was rarely an experimenter, Poincaré recognizes and defends the importance of experimentation, which must remain a pillar of the
scientific method
The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article history of scientific m ...
. According to him, it is not necessary that mathematics incorporate physics into itself, but must develop as an asset unto itself. This asset would be above all a tool: in the words of Poincaré, mathematics is "the only language in which
hysicistscould speak" to understand each other and to make themselves heard. This language of numbers seems elsewhere to reveal a unity hidden in the natural world, when there may well be only one part of mathematics that applies to theoretical physics. The primary objective of
mathematical physics
Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...
is not invention or discovery, but reformulation. It is an activity of synthesis, which permits one to assure the coherence of theories current at a given time. Poincaré recognized that it is impossible to systematize all of physics of a specific time period into one axiomatic theory. His ideas of a three dimensional space are given significance in this context.
Poincaré states that mathematics (analysis) and physics are in the same spirit, that the two disciplines share a common aesthetic goal and that both can liberate humanity from its simple state. In a more pragmatic way, the interdependence of physics and mathematics is similar to his proposed relationship between intuition and analysis. The language of mathematics not only permits one to express scientific advancements, but also to take a step back to comprehend the broader world of
nature
Nature, in the broadest sense, is the physics, physical world or universe. "Nature" can refer to the phenomenon, phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. ...
. Mathematics demonstrates the extent of the specific and limited discoveries made by physicists. On the other hand, physics has a key role for the mathematician - a creative role since it presents atypical problems ingrained in reality. In addition, physics offers solutions and reasoning - thus the development of
infinitesimal calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
by
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
within the framework of
Newtonian mechanics
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
# A body remains at rest, or in motion ...
.
Mathematical physics finds its scientific origins in the study of
celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
. Initially, it was a consolidation of several fields of physics that dominated the 18th century and which had allowed advancements in both the theoretical and experimental fields. However, in conjunction with the development of
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
(at the time disputed), physicists began developing an energy-based physics. In both its mathematics and its fundamental ideas, this new physics seemed to contradict the
Newtonian concept of particle interactions. Poincaré terms this the ''first crisis of mathematical physics''.
Second crisis
Throughout the 19th century, important discoveries were being made in laboratories and elsewhere. Many of these discoveries gave substance to important theories. Other discoveries could not be explained satisfactorily - either they had only been occasionally observed, or they were inconsistent with the new and emerging theories.
At the beginning of the 20th century, the unifying principles were thrown into question. Poincaré explains some of the most important principles and their difficulties:
* The principle of
conservation of energy
In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means th ...
(which he called ''
Mayer's principle'') - the discovery of
radium
Radium is a chemical element with the symbol Ra and atomic number 88. It is the sixth element in group 2 of the periodic table, also known as the alkaline earth metals. Pure radium is silvery-white, but it readily reacts with nitrogen (rather t ...
and
radioactivity posed the problem of the continuous (and seemingly inexhaustible) energy emission of radioactive substances.
* The principle of
entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
(which he called ''
Carnot's principle'') -
Brownian motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas).
This pattern of motion typically consists of random fluctuations in a particle's position insi ...
seemed to be in opposition to the
second law of thermodynamics
The second law of thermodynamics is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...
.
*
Newton's Third Law
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
# A body remains at rest, or in motion ...
(which he called ''
Newton's principle'') — This law seemed to conflict with the laws of
electrodynamics
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
proposed by
Maxwell, and with the
ether
In organic chemistry, ethers are a class of compounds that contain an ether group—an oxygen atom connected to two alkyl or aryl groups. They have the general formula , where R and R′ represent the alkyl or aryl groups. Ethers can again be c ...
theory he had proposed to explain them.
* The principle of
conservation of mass
In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass can ...
(which he called ''
Lavoisier's principle'') — the consideration of movements at a speed close to that of light posed a problem for this principle; this is again an electrodynamic problem : the mass of a body in such a state of motion is not constant.
* the
principle of relativity
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.
For example, in the framework of special relativity the Maxwell equations have ...
.
* Finally, he added the
principle of least action
The stationary-action principle – also known as the principle of least action – is a variational principle that, when applied to the '' action'' of a mechanical system, yields the equations of motion for that system. The principle states tha ...
.
At the beginning of the twentieth century, the majority of scientists spoke of Poincaré's "diagnosis" concerning the crisis of the ''physical principles''. In fact, it was difficult to do otherwise: they had discovered experimental facts which the principles could not account for, and which they evidently could not ignore. Poincaré himself remained relatively optimistic regarding the evolution of physics with respect to these severe experimental difficulties. He had little confidence in the nature of principles: they were constructed by physicists because they accommodate and take into account a large number of laws. Their objective value consists in forming a scientific convention, in other words in providing a firm foundation to the basis on which truth and falsehood (in the scientific meaning of the words) are separated.
But if these principles are conventions, they are not therefore totally dissociated from experimental fact. On the contrary, if the principles can no longer sustain laws adequately, in accordance with experimental observation, they lose their utility and are rejected, without even having been contradicted. The failure of the laws entails the failure of the principles, because they must account for the results of experiment. To abolish these principles, products of the scientific thought of several centuries, without finding a new explanation that encompasses them (in the same manner that the "Physics of principles" encompasses the "Physics of
central force
In classical mechanics, a central force on an object is a force that is directed towards or away from a point called center of force.
: \vec = \mathbf(\mathbf) = \left\vert F( \mathbf ) \right\vert \hat
where \vec F is the force, F is a vecto ...
s"), is to claim that all of past physics has no intellectual value. Consequently, Poincaré had great confidence that the principles were salvageable. He said that it was the responsibility of mathematical physics to reconstitute those principles, or to find a replacement for them (the greater goal being to return the field to unity), given that it had played the main role in questioning them only after consolidating them to begin with. Moreover, it was the value of mathematical physics (in terms of the scientific method) which itself saw criticism, due to the implosion of certain theories. Two physics thus existed at the same time: the physics of
Galileo
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
and Newton, and the physics of Maxwell; but neither one was able to explain all the experimental observations that technical advances had produced.
Electrodynamics of moving bodies
The array of problems encountered concentrated on the electrodynamics of moving bodies. Poincaré swiftly proposed the idea that it is the ether modifying itself, and not the bodies acquiring mass, which came to contradict the older theories (based on a perfectly immovable ether). Overall, Poincaré shed light on the
Zeeman effect
The Zeeman effect (; ) is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel prize ...
, caused by discontinuous emissions of electrons. The problem of discontinuous matter forced the formulation of a minimally-destabilizing model of the atom. In 1913,
Niels Bohr
Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922. B ...
presented his
atomic model
Atomic theory is the scientific theory that matter is composed of particles called atoms. Atomic theory traces its origins to an ancient philosophical tradition known as atomism. According to this idea, if one were to take a lump of matter an ...
which was based on the concept of electron orbits, and which explained
spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
as well as the stability of the atom. But, in 1905, the problem with all attempts to define the behavior of the microscopic world was that no one then knew if they needed to consider a similar model to the one known for the macroscopic objects (the model of classical mechanics), or if they should try to develop an entirely new model to give account of new facts. The latter idea, which was followed with the quantum theory, also implied definitively abandoning the unity already found in prior theories of mechanics.
Future of mathematical physics
Poincaré argued that the advancement of the physical sciences would have to consider a new kind of
determinism
Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and consi ...
, giving a new place to chance. And in effect, the history of twentieth century physics is marked by a paradigm where
probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...
reigns. In The Value of Science, Poincaré writes and repeats his enthusiasm for two lines of research : statistical laws (taking the place of differential laws), and relativistic mechanics (taking the place of Newtonian mechanics). Nevertheless, he did not take into account the ideas of
Planck
Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918.
Planck made many substantial contributions to theoretical p ...
. This latter had in 1900 published the spectral laws governing
blackbody radiation
Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spect ...
, which were the foundation of
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
. In 1905, the same year as the publication of The Value of Science,
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
published a decisive article on the photoelectric effect, which he based on the work of Planck. Despite the doubts of Poincaré, which were no doubt related to his vision of physics as an approximation of reality (in contrast to the exactness of mathematics), the probabilistic rules of quantum mechanics were clearly the response to the second crisis of mathematical physics, at the end of the nineteenth century. (One can point out that in 1902, Poincaré envisaged a relativistic physics which closely matched, in its theoretical development, the one developed and propounded by Einstein several years later.)
Objective value of science
"What is the purpose of science?" is the question repeatedly asked in Poincaré's book. To this
teleological
Teleology (from and )Partridge, Eric. 1977''Origins: A Short Etymological Dictionary of Modern English'' London: Routledge, p. 4187. or finalityDubray, Charles. 2020 912Teleology" In ''The Catholic Encyclopedia'' 14. New York: Robert Appleton ...
problem, Poincaré responds by taking the opposite position from that of
Édouard Le Roy
Édouard Louis Emmanuel Julien Le Roy (; 18 June 1870 in Paris – 10 November 1954 in Paris) was a French philosopher and mathematician.
Life
Le Roy entered the ''École Normale Supérieure'' in 1892, and received the '' agrégation'' in mathe ...
, philosopher and mathematician, who argued in a 1905 article (''Sur la logique de l'invention'', "On the logic of invention") that science is intrinsically anti-intellectual (in the sense of
Henri Bergson
Henri-Louis Bergson (; 18 October 1859 – 4 January 1941) was a French philosopherHenri Bergson. 2014. Encyclopædia Britannica Online. Retrieved 13 August 2014, from https://www.britannica.com/EBchecked/topic/61856/Henri-Bergson ) and nominalistic. In contrast to Le Roy, Poincaré follows the thought of
Pierre Duhem
Pierre Maurice Marie Duhem (; 9 June 1861 – 14 September 1916) was a French theoretical physicist who worked on thermodynamics, hydrodynamics, and the theory of elasticity. Duhem was also a historian of science, noted for his work on the Euro ...
. He explains that the notion that science is anti-intellectual is self-contradictory, and that the accusation of
nominalism
In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels. There are at least two main versions of nominalism. One version denies the existence of universalsthings t ...
can be strongly criticized, because it rests on confusions of thoughts and definitions. He defends the idea of ''conventional principles'', and the idea that scientific activity is not merely a set of conventions arranged arbitrarily around the raw observations of experiment. He wishes rather to demonstrate that objectivity in science comes precisely from the fact that the scientist does no more than translate raw facts into a particular language: "''(...) tout ce que crée le savant dans un fait, c'est le langage dans lequel il l'énonce''". The only contribution of science would be the development of a more and more mathematized language, a coherent language because it offers predictions which are useful – but not certain, as they remain forever subject to comparisons with real observations, and are always fallible.
Other contributions
Prof Richard Feynman contributed in a 1955 paper to the question of ''What is the Value of Science''.
References
*
*
*
Further reading
* ''Mind'', New Series, Vol. 2, No. 6. (Apr., 1893), pp. 271–272.
External links
*
{{DEFAULTSORT:Value of Science
1905 non-fiction books
Works about philosophy of physics
History of mathematics