Henri Poincaré

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Henri Poincaré
Henri Poincaré (photograph published in 1913)
Born	29 April 1854 Nancy, Meurthe-et-Moselle, France
Died	17 July 1912 (aged 58) Paris, France
Nationality	French
Other names	Jules Henri Poincaré
Education	Lycée Nancy (now Lycée Henri-Poincaré [fr]) École Polytechnique École des Mines University of Paris (Dr, 1879)
Known for	Poincaré conjecture Poincaré–Bendixson theorem Poincaré–Lindstedt method Poincaré recurrence theorem Poincaré–Bjerknes circulation theorem Poincaré group Poincaré gauge Poincaré–Hopf theorem Poincaré duality Poincaré–Birkhoff–Witt theorem Poincaré inequality Hilbert–Poincaré series Poincaré series Poincaré metric Automorphic form Coining the term "Betti number" Brouwer fixed-point theorem Bifurcation theory Chaos theory Dynamical system theory French historical epistemology Fundamental group Gravitational wave Hairy ball theorem Homological algebra Limit cycle Phase space Preintuitionism/conventionalism Predicativism Qualitative theory of differential equations Special relativity Sphere-world Rotation number Uniformization theorem Three-body problem Topology
Awards	RAS Gold Medal (1900) Sylvester Medal (1901) Matteucci Medal (1905) Bolyai Prize (1905) Bruce Medal (1911)
Scientific career
Fields	Mathematics physics
Institutions	Corps des Mines Caen University La Sorbonne Bureau des Longitudes
Thesis	Sur les propriétés des fonctions définies par les équations différences (1879)
Doctoral advisor	Charles Hermite
Doctoral students	Louis Bachelier Jean Bosler Dimitrie Pompeiu Mihailo Petrović Alas
Other notable students	Tobias Dantzig Théophile de Donder
Influences	Lazarus Fuchs Immanuel Kant Ernst Mach
Influenced	Louis Rougier George David Birkhoff Albert Einstein
Website	poincare.com
Signature

Jules Henri Poincaré (UK: /ˈpwæ̃kɑːreɪ/, US: stress on last syllable; French: [ɑ̃ʁi pwɛ̃kaʁe] ^ⓘ; 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 Last Universalist", since he excelled in all fields of the discipline as it existed during his lifetime.

As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology.

Poincaré made clear the importance of paying attention to the invariance of laws of physics under different transformations, and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Hendrik Lorentz in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity. In 1905, Poincaré first proposed gravitational waves (ondes gravifiques) emanating from a body and propagating at the speed of light as being required by the Lorentz transformations.

The Poincaré group used in physics and mathematics was named after him.

Early in the 20th century he formulated the Poincaré conjecture that became over time one of the famous unsolved problems in mathematics until it was solved in 2002–2003 by Grigori Perelman.

Life

Poincaré was born on 29 April 1854 in Cité Ducale neighborhood, Nancy, Meurthe-et-Moselle, into an influential French family. His father Léon Poincaré (1828–1892) was a professor of medicine at the University of Nancy. His younger sister Aline married the spiritual philosopher Émile Boutroux. Another notable member of Henri's family was his cousin, Raymond Poincaré, a fellow member of the Académie française, who was President of France from 1913 to 1920, and three-time Prime Minister of France between 1913 and 1929.

Education

Plaque on the birthplace of Henri Poincaré at house number 117 on the Grande Rue in the city of Nancy

During his childhood he was seriously ill for a time with diphtheria and received special instruction from his mother, Eugénie Launois (1830–1897).

In 1862, Henri entered the Lycée in Nancy (now renamed the Lycée Henri-Poincaré [fr] in his honour, along with Henri Poincaré University, also in Nancy). He spent eleven years at the Lycée and during this time he proved to be one of the top students in every topic he studied. He excelled in written composition. His mathematics teacher described him as a "monster of mathematics" and he won first prizes in the concours général, a competition between the top pupils from all the Lycées across France. His poorest subjects were music and physical education, where he was described as "average at best". However, poor eyesight and a tendency towards absentmindedness may explain these difficulties. He graduated from the Lycée in 1871 with a baccalauréat in both letters and sciences.

During the Franco-Prussian War of 1870, he served alongside his father in the Ambulance Corps.

Poincaré entered the École Polytechnique as the top qualifier in 1873 and graduated in 1875. There he studied mathematics as a student of Charles Hermite, continuing to excel and publishing his first paper (Démonstration nouvelle des propriétés de l'indicatrice d'une surface) in 1874. From November 1875 to June 1878 he studied at the École des Mines, while continuing the study of mathematics in addition to the mining engineering syllabus, and received the degree of ordinary mining engineer in March 1879.

As a graduate of the École des Mines, he joined the Corps des Mines as an inspector for the Vesoul region in northeast France. He was on the scene of a mining disaster at Magny in August 1879 in which 18 miners died. He carried out the official investigation into the accident in a characteristically thorough and humane way.

At the same time, Poincaré was preparing for his Doctorate in Science in mathematics under the supervision of Charles Hermite. His doctoral thesis was in the field of differential equations. It was named Sur les propriétés des fonctions définies par les équations aux différences partielles. Poincaré devised a new way of studying the properties of these equations. He not only faced the question of determining the integral of such equations, but also was the first person to study their general geometric properties. He realised that they could be used to model the behaviour of multiple bodies in free motion within the Solar System. Poincaré graduated from the University of Paris in 1879.

The young Henri Poincaré in 1887 at the age of 33

First scientific achievements

After receiving his degree, Poincaré began teaching as junior lecturer in mathematics at the University of Caen in Normandy (in December 1879). At the same time he published his first major article concerning the treatment of a class of automorphic functions.

There, in Caen, he met his future wife, Louise Poulain d'Andecy (1857–1934), granddaughter of Isidore Geoffroy Saint-Hilaire and great-granddaughter of Étienne Geoffroy Saint-Hilaire and on 20 April 1881, they married. Together they had four children: Jeanne (born 1887), Yvonne (born 1889), Henriette (born 1891), and Léon (born 1893).

Poincaré immediately established himself among the greatest mathematicians of Europe, attracting the attention of many prominent mathematicians. In 1881 Poincaré was invited to take a teaching position at the Faculty of Sciences of the University of Paris; he accepted the invitation. During the years 1883 to 1897, he taught mathematical analysis in the École Polytechnique.

In 1881–1882, Poincaré created a new branch of mathematics: qualitative theory of differential equations. He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible). He successfully used this approach to problems in celestial mechanics and mathematical physics.

Career

He never fully abandoned his career in the mining administration to mathematics. He worked at the Ministry of Public Services as an engineer in charge of northern railway development from 1881 to 1885. He eventually became chief engineer of the Corps des Mines in 1893 and inspector general in 1910.

Beginning in 1881 and for the rest of his career, he taught at the University of Paris (the Sorbonne). He was initially appointed as the maître de conférences d'analyse (associate professor of analysis). Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, and Celestial Mechanics and Astronomy.

In 1887, at the young age of 32, Poincaré was elected to the French Academy of Sciences. He became its president in 1906, and was elected to the Académie française on 5 March 1908.

In 1887, he won Oscar II, King of Sweden's mathematical competition for a resolution of the three-body problem concerning the free motion of multiple orbiting bodies. (See three-body problem section below.)

In 1893, Poincaré joined the French Bureau des Longitudes, which engaged him in the synchronisation of time around the world. In 1897 Poincaré backed an unsuccessful proposal for the decimalisation of circular measure, and hence time and longitude. It was this post which led him to consider the question of establishing international time zones and the synchronisation of time between bodies in relative motion. (See work on relativity section below.)

In 1904, he intervened in the trials of Alfred Dreyfus, attacking the spurious scientific claims regarding evidence brought against Dreyfus.

Poincaré was the President of the Société Astronomique de France (SAF), the French astronomical society, from 1901 to 1903.

Students

Poincaré had two notable doctoral students at the University of Paris, Louis Bachelier (1900) and Dimitrie Pompeiu (1905).

Death

In 1912, Poincaré underwent surgery for a prostate problem and subsequently died from an embolism on 17 July 1912, in Paris. He was 58 years of age. He is buried in the Poincaré family vault in the Cemetery of Montparnasse, Paris, in section 16 close to the gate Rue Émile-Richard.

A former French Minister of Education, Claude Allègre, proposed in 2004 that Poincaré be reburied in the Panthéon in Paris, which is reserved for French citizens of the highest honour.

The Poincaré family grave at the Cimetière du Montparnasse

Work

Summary

Poincaré made many contributions to different fields of pure and applied mathematics such as: celestial mechanics, fluid mechanics, optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential theory, quantum theory, theory of relativity and physical cosmology.

He was also a populariser of mathematics and physics and wrote several books for the lay public.

Among the specific topics he contributed to are the following:

• algebraic topology (a field that Poincaré virtually invented)
• the theory of analytic functions of several complex variables
• the theory of abelian functions
• algebraic geometry
• the Poincaré conjecture, proven in 2003 by Grigori Perelman.
• Poincaré recurrence theorem
• hyperbolic geometry
• number theory
• the three-body problem
• the theory of diophantine equations
• electromagnetism
• the special theory of relativity
• the fundamental group
• In the field of differential equations Poincaré has given many results that are critical for the qualitative theory of differential equations, for example the Poincaré sphere and the Poincaré map.
• Poincaré on "everybody's belief" in the Normal Law of Errors (see normal distribution for an account of that "law")
• Published an influential paper providing a novel mathematical argument in support of quantum mechanics.

Three-body problem

The problem of finding the general solution to the motion of more than two orbiting bodies in the Solar System had eluded mathematicians since Newton's time. This was known originally as the three-body problem and later the n-body problem, where n is any number of more than two orbiting bodies. The n-body solution was considered very important and challenging at the close of the 19th century. Indeed, in 1887, in honour of his 60th birthday, Oscar II, King of Sweden, advised by Gösta Mittag-Leffler, established a prize for anyone who could find the solution to the problem. The announcement was quite specific:

Given a system of arbitrarily many mass points that attract each according to Newton's law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly.

In case the problem could not be solved, any other important contribution to classical mechanics would then be considered to be prizeworthy. The prize was finally awarded to Poincaré, even though he did not solve the original problem. One of the judges, the distinguished Karl Weierstrass, said, "This work cannot indeed be considered as furnishing the complete solution of the question proposed, but that it is nevertheless of such importance that its publication will inaugurate a new era in the history of celestial mechanics." (The first version of his contribution even contained a serious error; for details see the article by Diacu and the book by Barrow-Green). The version finally printed contained many important ideas which led to the theory of chaos. The problem as stated originally was finally solved by Karl F. Sundman for n = 3 in 1912 and was generalised to the case of n > 3 bodies by Qiudong Wang in the 1990s. The series solutions have very slow convergence. It would take millions of terms to determine the motion of the particles for even very short intervals of time, so they are unusable in numerical work.

Work on relativity

Main articles: Lorentz ether theory and History of special relativity

Marie Curie and Poincaré talk at the 1911 Solvay Conference.

Local time

Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "luminiferous aether"), could be synchronised. At the same time Dutch theorist Hendrik Lorentz was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" ${\displaystyle t^{\mathrm{\prime }}=t-vx/c^2}$ and introduced the hypothesis of length contraction to explain the failure of optical and electrical experiments to detect motion relative to the aether (see Michelson–Morley experiment). Poincaré was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. Poincaré as a philosopher was interested in the "deeper meaning". Thus he interpreted Lorentz's theory and in so doing he came up with many insights that are now associated with special relativity. In The Measure of Time (1898), Poincaré said, "A little reflection is sufficient to understand that all these affirmations have by themselves no meaning. They can have one only as the result of a convention." He also argued that scientists have to set the constancy of the speed of light as a postulate to give physical theories the simplest form. Based on these assumptions he discussed in 1900 Lorentz's "wonderful invention" of local time and remarked that it arose when moving clocks are synchronised by exchanging light signals assumed to travel with the same speed in both directions in a moving frame.

Principle of relativity and Lorentz transformations

Further information: History of Lorentz transformations

In 1881 Poincaré described hyperbolic geometry in terms of the hyperboloid model, formulating transformations leaving invariant the Lorentz interval ${\displaystyle x^2+y^2-z^2=-1}$, which makes them mathematically equivalent to the Lorentz transformations in 2+1 dimensions. In addition, Poincaré's other models of hyperbolic geometry (Poincaré disk model, Poincaré half-plane model) as well as the Beltrami–Klein model can be related to the relativistic velocity space (see Gyrovector space).

In 1892 Poincaré developed a mathematical theory of light including polarization. His vision of the action of polarizers and retarders, acting on a sphere representing polarized states, is called the Poincaré sphere. It was shown that the Poincaré sphere possesses an underlying Lorentzian symmetry, by which it can be used as a geometrical representation of Lorentz transformations and velocity additions.

He discussed the "principle of relative motion" in two papers in 1900 and named it the principle of relativity in 1904, according to which no physical experiment can discriminate between a state of uniform motion and a state of rest. In 1905 Poincaré wrote to Lorentz about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance". In this letter he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz. In a second letter to Lorentz, Poincaré gave his own reason why Lorentz's time dilation factor was indeed correct after all—it was necessary to make the Lorentz transformation form a group—and he gave what is now known as the relativistic velocity-addition law. Poincaré later delivered a paper at the meeting of the Academy of Sciences in Paris on 5 June 1905 in which these issues were addressed. In the published version of that he wrote:

The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz) of the form:

${\displaystyle x^{\mathrm{\prime }}=k\ell \left(x+\epsilon t\right),t^{\mathrm{\prime }}=k\ell \left(t+\epsilon x\right),y^{\mathrm{\prime }}=\ell y,z^{\mathrm{\prime }}=\ell z,k=1/\sqrt{1-{\epsilon }^2}.}$

and showed that the arbitrary function ${\displaystyle \ell \left(\epsilon \right)}$ must be unity for all ${\displaystyle \epsilon }$ (Lorentz had set ${\displaystyle \ell =1}$ by a different argument) to make the transformations form a group. In an enlarged version of the paper that appeared in 1906 Poincaré pointed out that the combination ${\displaystyle x^2+y^2+z^2-c^2{t}^2}$ is invariant. He noted that a Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing ${\displaystyle ct\sqrt{-1}}$ as a fourth imaginary coordinate, and he used an early form of four-vectors. Poincaré expressed a lack of interest in a four-dimensional reformulation of his new mechanics in 1907, because in his opinion the translation of physics into the language of four-dimensional geometry would entail too much effort for limited profit. So it was Hermann Minkowski who worked out the consequences of this notion in 1907.

Mass–energy relation

Like others before, Poincaré (1900) discovered a relation between mass and electromagnetic energy. While studying the conflict between the action/reaction principle and Lorentz ether theory, he tried to determine whether the center of gravity still moves with a uniform velocity when electromagnetic fields are included. He noticed that the action/reaction principle does not hold for matter alone, but that the electromagnetic field has its own momentum. Poincaré concluded that the electromagnetic field energy of an electromagnetic wave behaves like a fictitious fluid (fluide fictif) with a mass density of E/c². If the center of mass frame is defined by both the mass of matter and the mass of the fictitious fluid, and if the fictitious fluid is indestructible—it's neither created or destroyed—then the motion of the center of mass frame remains uniform. But electromagnetic energy can be converted into other forms of energy. So Poincaré assumed that there exists a non-electric energy fluid at each point of space, into which electromagnetic energy can be transformed and which also carries a mass proportional to the energy. In this way, the motion of the center of mass remains uniform. Poincaré said that one should not be too surprised by these assumptions, since they are only mathematical fictions.

However, Poincaré's resolution led to a paradox when changing frames: if a Hertzian oscillator radiates in a certain direction, it will suffer a recoil from the inertia of the fictitious fluid. Poincaré performed a Lorentz boost (to order v/c) to the frame of the moving source. He noted that energy conservation holds in both frames, but that the law of conservation of momentum is violated. This would allow perpetual motion, a notion which he abhorred. The laws of nature would have to be different in the frames of reference, and the relativity principle would not hold. Therefore, he argued that also in this case there has to be another compensating mechanism in the ether.

Poincaré himself came back to this topic in his St. Louis lecture (1904). He rejected the possibility that energy carries mass and criticized his own solution to compensate the above-mentioned problems:

The apparatus will recoil as if it were a cannon and the projected energy a ball, and that contradicts the principle of Newton, since our present projectile has no mass; it is not matter, it is energy. [..] Shall we say that the space which separates the oscillator from the receiver and which the disturbance must traverse in passing from one to the other, is not empty, but is filled not only with ether, but with air, or even in inter-planetary space with some subtile, yet ponderable fluid; that this matter receives the shock, as does the receiver, at the moment the energy reaches it, and recoils, when the disturbance leaves it? That would save Newton's principle, but it is not true. If the energy during its propagation remained always attached to some material substratum, this matter would carry the light along with it and Fizeau has shown, at least for the air, that there is nothing of the kind. Michelson and Morley have since confirmed this. We might also suppose that the motions of matter proper were exactly compensated by those of the ether; but that would lead us to the same considerations as those made a moment ago. The principle, if thus interpreted, could explain anything, since whatever the visible motions we could imagine hypothetical motions to compensate them. But if it can explain anything, it will allow us to foretell nothing; it will not allow us to choose between the various possible hypotheses, since it explains everything in advance. It therefore becomes useless.

In the above quote he refers to the Hertz assumption of total aether entrainment that was falsified by the Fizeau experiment but that experiment does indeed show that that light is partially "carried along" with a substance. Finally in 1908 he revisits the problem and ends with abandoning the principle of reaction altogether in favor of supporting a solution based in the inertia of aether itself.

But we have seen above that Fizeau's experiment does not permit of our retaining the theory of Hertz; it is necessary therefore to adopt the theory of Lorentz, and consequently to renounce the principle of reaction.

He also discussed two other unexplained effects: (1) non-conservation of mass implied by Lorentz's variable mass ${\displaystyle \gamma m}$, Abraham's theory of variable mass and Kaufmann's experiments on the mass of fast moving electrons and (2) the non-conservation of energy in the radium experiments of Marie Curie.

It was Albert Einstein's concept of mass–energy equivalence (1905) that a body losing energy as radiation or heat was losing mass of amount m = E/c² that resolved Poincaré's paradox, without using any compensating mechanism within the ether. The Hertzian oscillator loses mass in the emission process, and momentum is conserved in any frame. However, concerning Poincaré's solution of the Center of Gravity problem, Einstein noted that Poincaré's formulation and his own from 1906 were mathematically equivalent.

Gravitational waves

In 1905 Poincaré first proposed gravitational waves (ondes gravifiques) emanating from a body and propagating at the speed of light. He wrote:

It has become important to examine this hypothesis more closely and in particular to ask in what ways it would require us to modify the laws of gravitation. That is what I have tried to determine; at first I was led to assume that the propagation of gravitation is not instantaneous, but happens with the speed of light.

Poincaré and Einstein

Einstein's first paper on relativity was published three months after Poincaré's short paper, but before Poincaré's longer version. Einstein relied on the principle of relativity to derive the Lorentz transformations and used a similar clock synchronisation procedure (Einstein synchronisation) to the one that Poincaré (1900) had described, but Einstein's paper was remarkable in that it contained no references at all. Poincaré never acknowledged Einstein's work on special relativity. However, Einstein expressed sympathy with Poincaré's outlook obliquely in a letter to Hans Vaihinger on 3 May 1919, when Einstein considered Vaihinger's general outlook to be close to his own and Poincaré's to be close to Vaihinger's. In public, Einstein acknowledged Poincaré posthumously in the text of a lecture in 1921 titled "Geometrie und Erfahrung (Geometry and Experience)" in connection with non-Euclidean geometry, but not in connection with special relativity. A few years before his death, Einstein commented on Poincaré as being one of the pioneers of relativity, saying "Lorentz had already recognized that the transformation named after him is essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further ....".

Assessments on Poincaré and relativity

Further information: History of special relativity and Relativity priority dispute

Poincaré's work in the development of special relativity is well recognised, though most historians stress that despite many similarities with Einstein's work, the two had very different research agendas and interpretations of the work. Poincaré developed a similar physical interpretation of local time and noticed the connection to signal velocity, but contrary to Einstein he continued to use the ether-concept in his papers and argued that clocks at rest in the ether show the "true" time, and moving clocks show the local time. So Poincaré tried to keep the relativity principle in accordance with classical concepts, while Einstein developed a mathematically equivalent kinematics based on the new physical concepts of the relativity of space and time.

While this is the view of most historians, a minority go much further, such as E. T. Whittaker, who held that Poincaré and Lorentz were the true discoverers of relativity.

Algebra and number theory

Poincaré introduced group theory to physics, and was the first to study the group of Lorentz transformations. He also made major contributions to the theory of discrete groups and their representations.

Topological transformation of a mug into a torus

Title page to volume I of Les Méthodes Nouvelles de la Mécanique Céleste (1892)

Topology

The subject is clearly defined by Felix Klein in his "Erlangen Program" (1872): the geometry invariants of arbitrary continuous transformation, a kind of geometry. The term "topology" was introduced, as suggested by Johann Benedict Listing, instead of previously used "Analysis situs". Some important concepts were introduced by Enrico Betti and Bernhard Riemann. But the foundation of this science, for a space of any dimension, was created by Poincaré. His first article on this topic appeared in 1894.

His research in geometry led to the abstract topological definition of homotopy and homology. He also first introduced the basic concepts and invariants of combinatorial topology, such as Betti numbers and the fundamental group. Poincaré proved a formula relating the number of edges, vertices and faces of n-dimensional polyhedron (the Euler–Poincaré theorem) and gave the first precise formulation of the intuitive notion of dimension.

Astronomy and celestial mechanics

Chaotic motion in three-body problem (computer simulation)

Poincaré published two now classical monographs, "New Methods of Celestial Mechanics" (1892–1899) and "Lectures on Celestial Mechanics" (1905–1910). In them, he successfully applied the results of their research to the problem of the motion of three bodies and studied in detail the behavior of solutions (frequency, stability, asymptotic, and so on). They introduced the small parameter method, fixed points, integral invariants, variational equations, the convergence of the asymptotic expansions. Generalizing a theory of Bruns (1887), Poincaré showed that the three-body problem is not integrable. In other words, the general solution of the three-body problem can not be expressed in terms of algebraic and transcendental functions through unambiguous coordinates and velocities of the bodies. His work in this area was the first major achievement in celestial mechanics since Isaac Newton.

These monographs include an idea of Poincaré, which later became the basis for mathematical "chaos theory" (see, in particular, the Poincaré recurrence theorem) and the general theory of dynamical systems. Poincaré authored important works on astronomy for the equilibrium figures of a gravitating rotating fluid. He introduced the important concept of bifurcation points and proved the existence of equilibrium figures such as the non-ellipsoids, including ring-shaped and pear-shaped figures, and their stability. For this discovery, Poincaré received the Gold Medal of the Royal Astronomical Society (1900).

Differential equations and mathematical physics

After defending his doctoral thesis on the study of singular points of the system of differential equations, Poincaré wrote a series of memoirs under the title "On curves defined by differential equations" (1881–1882). In these articles, he built a new branch of mathematics, called "qualitative theory of differential equations". Poincaré showed that even if the differential equation can not be solved in terms of known functions, yet from the very form of the equation, a wealth of information about the properties and behavior of the solutions can be found. In particular, Poincaré investigated the nature of the trajectories of the integral curves in the plane, gave a classification of singular points (saddle, focus, center, node), introduced the concept of a limit cycle and the loop index, and showed that the number of limit cycles is always finite, except for some special cases. Poincaré also developed a general theory of integral invariants and solutions of the variational equations. For the finite-difference equations, he created a new direction – the asymptotic analysis of the solutions. He applied all these achievements to study practical problems of mathematical physics and celestial mechanics, and the methods used were the basis of its topological works.

• The singular points of the integral curves
• 

  Saddle

• 

  Focus

• 

  Center

• 

  Node

Character

Photographic portrait of H. Poincaré by Henri Manuel

Poincaré's work habits have been compared to a bee flying from flower to flower. Poincaré was interested in the way his mind worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris. He linked his way of thinking to how he made several discoveries.

The mathematician Darboux claimed he was un intuitif (an intuitive), arguing that this is demonstrated by the fact that he worked so often by visual representation. Jacques Hadamard wrote that Poincaré's research demonstrated marvelous clarity and Poincaré himself wrote that he believed that logic was not a way to invent but a way to structure ideas and that logic limits ideas.

Toulouse's characterisation

Poincaré's mental organisation was interesting not only to Poincaré himself but also to Édouard Toulouse, a psychologist of the Psychology Laboratory of the School of Higher Studies in Paris. Toulouse wrote a book entitled Henri Poincaré (1910). In it, he discussed Poincaré's regular schedule:

• He worked during the same times each day in short periods of time. He undertook mathematical research for four hours a day, between 10 a.m. and noon then again from 5 p.m. to 7 p.m.. He would read articles in journals later in the evening.
• His normal work habit was to solve a problem completely in his head, then commit the completed problem to paper.
• He was ambidextrous and nearsighted.
• His ability to visualise what he heard proved particularly useful when he attended lectures, since his eyesight was so poor that he could not see properly what the lecturer wrote on the blackboard.

These abilities were offset to some extent by his shortcomings:

• He was physically clumsy and artistically inept.
• He was always in a rush and disliked going back for changes or corrections.
• He never spent a long time on a problem since he believed that the subconscious would continue working on the problem while he consciously worked on another problem.

In addition, Toulouse stated that most mathematicians worked from principles already established while Poincaré started from basic principles each time (O'Connor et al., 2002).

His method of thinking is well summarised as:

Habitué à négliger les détails et à ne regarder que les cimes, il passait de l'une à l'autre avec une promptitude surprenante et les faits qu'il découvrait se groupant d'eux-mêmes autour de leur centre étaient instantanément et automatiquement classés dans sa mémoire (accustomed to neglecting details and to looking only at mountain tops, he went from one peak to another with surprising rapidity, and the facts he discovered, clustering around their center, were instantly and automatically pigeonholed in his memory).

— Belliver (1956)

Publications

• Leçons sur la théorie mathématique de la lumière (in French). Paris: Carrè. 1889.
• Solutions periodiques, non-existence des integrales uniformes, solutions asymptotiques (in French). Vol. 1. Paris: Gauthier-Villars. 1892.
• Methodes de mm. Newcomb, Gylden, Lindstedt et Bohlin (in French). Vol. 2. Paris: Gauthier-Villars. 1893.
• Oscillations électriques (in French). Paris: Carrè. 1894.
• Invariants integraux, solutions periodiques du deuxieme genre, solutions doublement asymptotiques (in French). Vol. 3. Paris: Gauthier-Villars. 1899.
• Valeur de la science (in French). Paris: Flammarion. 1900.
• Electricité et optique (in French). Paris: Carrè & Naud. 1901.
• Science et l'hypothèse (in French). Paris: Flammarion. 1905.
• Thermodynamique (in French). Paris: Gauthier-Villars. 1908.
• Dernières pensées (in French). Paris: Flammarion. 1913.
• Science et méthode. London: Nelson and Sons. 1914.

Honours

Awards

• Oscar II, King of Sweden's mathematical competition (1887)
• Foreign member of the Royal Netherlands Academy of Arts and Sciences (1897)
• American Philosophical Society (1899)
• Gold Medal of the Royal Astronomical Society of London (1900)
• Bolyai Prize (1905)
• Matteucci Medal (1905)
• French Academy of Sciences (1906)
• Académie française (1909)
• Bruce Medal (1911)

Named after him

• Institut Henri Poincaré (mathematics and theoretical physics center)
• Poincaré Prize (Mathematical Physics International Prize)
• Annales Henri Poincaré (Scientific Journal)
• Poincaré Seminar (nicknamed "Bourbaphy")
• The crater Poincaré on the Moon
• Asteroid 2021 Poincaré
• List of things named after Henri Poincaré

Henri Poincaré did not receive the Nobel Prize in Physics, but he had influential advocates like Henri Becquerel or committee member Gösta Mittag-Leffler. The nomination archive reveals that Poincaré received a total of 51 nominations between 1904 and 1912, the year of his death. Of the 58 nominations for the 1910 Nobel Prize, 34 named Poincaré. Nominators included Nobel laureates Hendrik Lorentz and Pieter Zeeman (both of 1902), Marie Curie (of 1903), Albert Michelson (of 1907), Gabriel Lippmann (of 1908) and Guglielmo Marconi (of 1909).

The fact that renowned theoretical physicists like Poincaré, Boltzmann or Gibbs were not awarded the Nobel Prize is seen as evidence that the Nobel committee had more regard for experimentation than theory. In Poincaré's case, several of those who nominated him pointed out that the greatest problem was to name a specific discovery, invention, or technique.

Philosophy

First page of Science and hypothesis (1905)

Poincaré had philosophical views opposite to those of Bertrand Russell and Gottlob Frege, who believed that mathematics was a branch of logic. Poincaré strongly disagreed, claiming that intuition was the life of mathematics. Poincaré gives an interesting point of view in his 1902 book Science and Hypothesis:

For a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if the scientists are sometimes mistaken, this is only from their mistaking its rule.

Poincaré believed that arithmetic is synthetic. He argued that Peano's axioms cannot be proven non-circularly with the principle of induction (Murzi, 1998), therefore concluding that arithmetic is a priori synthetic and not analytic. Poincaré then went on to say that mathematics cannot be deduced from logic since it is not analytic. His views were similar to those of Immanuel Kant (Kolak, 2001, Folina 1992). He strongly opposed Cantorian set theory, objecting to its use of impredicative definitions.

However, Poincaré did not share Kantian views in all branches of philosophy and mathematics. For example, in geometry, Poincaré believed that the structure of non-Euclidean space can be known analytically. Poincaré held that convention plays an important role in physics. His view (and some later, more extreme versions of it) came to be known as "conventionalism". Poincaré believed that Newton's first law was not empirical but is a conventional framework assumption for mechanics (Gargani, 2012). He also believed that the geometry of physical space is conventional. He considered examples in which either the geometry of the physical fields or gradients of temperature can be changed, either describing a space as non-Euclidean measured by rigid rulers, or as a Euclidean space where the rulers are expanded or shrunk by a variable heat distribution. However, Poincaré thought that we were so accustomed to Euclidean geometry that we would prefer to change the physical laws to save Euclidean geometry rather than shift to a non-Euclidean physical geometry.

Free will

Poincaré's famous lectures before the Société de Psychologie in Paris (published as Science and Hypothesis, The Value of Science, and Science and Method) were cited by Jacques Hadamard as the source for the idea that creativity and invention consist of two mental stages, first random combinations of possible solutions to a problem, followed by a critical evaluation.

Although he most often spoke of a deterministic universe, Poincaré said that the subconscious generation of new possibilities involves chance.

It is certain that the combinations which present themselves to the mind in a kind of sudden illumination after a somewhat prolonged period of unconscious work are generally useful and fruitful combinations... all the combinations are formed as a result of the automatic action of the subliminal ego, but those only which are interesting find their way into the field of consciousness... A few only are harmonious, and consequently at once useful and beautiful, and they will be capable of affecting the geometrician's special sensibility I have been speaking of; which, once aroused, will direct our attention upon them, and will thus give them the opportunity of becoming conscious... In the subliminal ego, on the contrary, there reigns what I would call liberty, if one could give this name to the mere absence of discipline and to disorder born of chance.

Poincaré's two stages—random combinations followed by selection—became the basis for Daniel Dennett's two-stage model of free will.

Bibliography

Poincaré's writings in English translation

Popular writings on the philosophy of science:

• Poincaré, Henri (1902–1908), The Foundations of Science, New York: Science Press; reprinted in 1921; this book includes the English translations of Science and Hypothesis (1902), The Value of Science (1905), Science and Method (1908).
• 1905. "Science and Hypothesis", The Walter Scott Publishing Co.
• 1906. "The End of Matter", Athenæum
• 1913. "The New Mechanics", The Monist, Vol. XXIII.
• 1913. "The Relativity of Space", The Monist, Vol. XXIII.
• 1913. Last Essays., New York: Dover reprint, 1963
• 1956. Chance. In James R. Newman, ed., The World of Mathematics (4 Vols).
• 1958. The Value of Science, New York: Dover.

On algebraic topology:

• 1895. Analysis Situs (PDF), archived (PDF) from the original on 27 March 2012. The first systematic study of topology.

On celestial mechanics:

• 1890. Poincaré, Henri (2017). The three-body problem and the equations of dynamics: Poincaré's foundational work on dynamical systems theory. Translated by Popp, Bruce D. Cham, Switzerland: Springer International Publishing. ISBN 978-3-319-52898-4.
• 1892–99. New Methods of Celestial Mechanics, 3 vols. English trans., 1967. ISBN 1-56396-117-2.
• 1905. "The Capture Hypothesis of J. J. See", The Monist, Vol. XV.
• 1905–10. Lessons of Celestial Mechanics.

On the philosophy of mathematics:

• Ewald, William B., ed., 1996. From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols. Oxford Univ. Press. Contains the following works by Poincaré:
  • 1894, "On the Nature of Mathematical Reasoning", 972–81.
  • 1898, "On the Foundations of Geometry", 982–1011.
  • 1900, "Intuition and Logic in Mathematics", 1012–20.
  • 1905–06, "Mathematics and Logic, I–III", 1021–70.
  • 1910, "On Transfinite Numbers", 1071–74.
• 1905. "The Principles of Mathematical Physics", The Monist, Vol. XV.
• 1910. "The Future of Mathematics", The Monist, Vol. XX.
• 1910. "Mathematical Creation", The Monist, Vol. XX.

Other:

• 1904. Maxwell's Theory and Wireless Telegraphy, New York, McGraw Publishing Company.
• 1905. "The New Logics", The Monist, Vol. XV.
• 1905. "The Latest Efforts of the Logisticians", The Monist, Vol. XV.

Exhaustive bibliography of English translations:

• 1892–2017. Henri Poincaré Papers, archived from the original on 1 August 2020.

 

Food system

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Food_system

The term food system describes the interconnected systems and processes that influence nutrition, food, health, community development, and agriculture. A food system includes all processes and infrastructure involved in feeding a population: growing, harvesting, processing, packaging, transporting, marketing, consumption, distribution, and disposal of food and food-related items. It also includes the inputs needed and outputs generated at each of these steps. Food systems fall within agri-food systems, which encompass the entire range of actors and their interlinked value-adding activities in the primary production of food and non-food agricultural products, as well as in food storage, aggregation, post-harvest handling, transportation, processing, distribution, marketing, disposal, and consumption. A food system operates within and is influenced by social, political, economic, technological and environmental contexts. It also requires human resources that provide labor, research and education. Food systems are either conventional or alternative according to their model of food lifespan from origin to plate. Food systems are dependent on a multitude of ecosystem services. For example, natural pest regulations, microorganisms providing nitrogen-fixation, and pollinators. 

According to the IPCC, the global food system, including all of the various industries involved in sustainable and conventional food systems, provide employment for 1 billion people. This global food system is facing a number of challenges created by impeding global food security issues created by climate change and non-climate change stresses on the system. About 34% of total greenhouse gas emissions are attributable to the global food system. In 2020 an EU evidence review found that food system gas emissions are on course to increase by 30–40% by 2050 due to population growth and dietary change. According to FAO, it is crucial to build the resilience of agrifood systems so that they have the capacity over time, in the face of any disruption, to sustainably ensure availability of and access to sufficient, safe and nutritious food for all, and sustain the livelihoods of agrifood systems' actors.

Transitioning to sustainable food systems is critical for addressing global challenges such as climate change, hunger, biodiversity loss, and deforestation. Addressing issues at each stage in the system, can have system-wide effects for 30-40 percent of food produced is lost from post-harvest up to retail and the consumer. Reducing food waste then reduces the environmental impacts of agriculture, such as land use impacts, and reducing food prices or preventing shortages. International policy has increasingly approached policy from a food systems perspective: Sustainable Development Goal 2: Zero Hunger and Sustainable Development Goal 12: "responsible consumption and production" focus on sustainable food systems and Sustainable and in September 2021 the United Nations hosted the first Food Systems Summit.

Conventional food systems

Conventional food systems operate on economies of scale. These food systems are geared towards a production model that requires maximizing efficiency in order to lower consumer costs and increase overall production, and they utilize economic models such as vertical integration, economic specialization, and global trade. The growing soil quality degradation, climate change, and growing world population put pressure on agricultural land, leading to innovations to increase agricultural productivity on the limited available land and urban space. Though conventional farming practices have increased crop yield through the use of climate-smart agriculture (CSA), smallholder farming systems and limited knowledge of CSA remain constraints for enjoying economies of scale and sustainable crop production and food security.

The term “conventional” when describing food systems is largely due to comparisons made to it by proponents of other food systems, collectively known as alternative food systems.

History of conventional food systems

See also: Timeline of agriculture and food technology

The development of food systems can be traced back to the origins of in-situ agriculture and the production of food surpluses. These surpluses enabled the development of settled areas and contributed to the development of ancient civilizations, particularly those in the Fertile Crescent. The system of trade associated with the exchange of foodstuffs also emerged in East Asia, North America, South America, and Subsaharan Africa with common commodities of exchange such as salt, spices, fish, grains, etc. Through events in world history such as the conquests of Alexander the Great, the Crusades, the expansion of Islam, the journeys of Marco Polo, and the exploration and colonization of the Americas by Europeans led to the introduction and redistribution of new foods to the world at large, and food systems began to intermingle on a global scale. After World War II, the advent of industrialized agriculture and more robust global trade mechanisms have evolved into the models of food production, presentation, delivery, and disposal that characterize conventional food systems today.

Impacts of conventional food systems

See also: § Effects on climate change

The development of conventional food systems is directly responsible for decreased food prices and increased food variety. Agronomic efficiency is driven by the necessity to constantly lower production expenses, and those savings can then be passed on to the consumer. Also, the advent of industrial agriculture and the infrastructure built around conventional food systems has enabled the world population to expand beyond the "Malthusian catastrophe" limitations. According to the IPCC, food supply per capita has increased by more than 30% since 1961.

However, conventional food systems are largely based on the availability of inexpensive fossil fuels, which is necessary for mechanized agriculture, the manufacture or collection of chemical fertilizers, the processing of food products, and the packaging of the foods. The increase in the availability of food since 1961 has primarily been driven by an 800% increase in the use of nitrogen fertilizers (which are fossil fuel dependent) and high water usage (an increase of over 100% since 1961).

The impacts of these intense resource processes are many a varied: food processing began when the number of consumers started proliferating. The demand for cheap and efficient calories climbed, resulting in nutrition decline; and industrialized agriculture, due to its reliance on economies of scale to reduce production costs, often leads to the compromising of local, regional, or even global ecosystems through fertilizer runoff, nonpoint source pollution, and greenhouse gas emission.

The need to reduce production costs in an increasingly global market can cause the production of foods to be moved to areas where economic costs (labor, taxes, etc.) are lower or environmental regulations are laxer, which are usually further from consumer markets. For example, the majority of salmon sold in the United States is raised off the coast of Chile, due in large part to less stringent Chilean standards regarding fish feed and regardless of the fact that salmon are not indigenous in Chilean coastal waters. The globalization of food production can result in the loss of traditional food systems in less developed countries, and have negative impacts on the population health, ecosystems, and cultures in those countries. As a result of these forces, 2018 estimates suggest that 821 million people are currently undernourished, and 2 billion adults are overweight and obese.

The issue of having minimal access to food, or access to primarily unhealthy food, is often described in terms of food security. The 1996 World Food Summit defined food security as a state in which "all people, at all times, have physical and economic access to sufficient, safe and nutritious food to meet their dietary needs and food preferences for an active and healthy life. " Many groups argue that food security is largely determined by a given person's socioeconomic status, race, ethnicity, or other socially defined categories, making food access a social justice issue. This has given rise to numerous social movements whose goal is to increase access to healthy and culturally appropriate foods, among a wide variety of groups. These movements are often described as belonging to a more significant food justice movement.

Scientists estimated the extensive pesticide pollution risks worldwide with a new environmental model and found that a third of global agricultural land is at high risk for such pollution, of which a third are high-biodiversity regions.

Sustainable food systems

A sustainable food system is a type of food system that provides healthy food to people and creates sustainable environmental, economic, and social systems that surround food. Sustainable food systems start with the development of sustainable agricultural practices, development of more sustainable food distribution systems, creation of sustainable diets, and reduction of food waste throughout the system. Sustainable food systems have been argued to be central to many or all 17 Sustainable Development Goals.

Moving to sustainable food systems, including via shifting consumption to sustainable diets, is an important component of addressing the causes of climate change and adapting to it. A 2020 review conducted for the European Union found that up to 37% of global greenhouse gas emissions could be attributed to the food system, including crop and livestock production, transportation, changing land use (including deforestation), and food loss and waste. Reduction of meat production, which accounts for ~60% of greenhouse gas emissions and ~75% of agriculturally used land, is one major component of this change.

The global food system is facing major interconnected challenges, including mitigating food insecurity, effects from climate change, biodiversity loss, malnutrition, inequity, soil degradation, pest outbreaks, water and energy scarcity, economic and political crises, natural resource depletion, and preventable ill-health.

The concept of sustainable food systems is frequently at the center of sustainability-focused policy programs, such as proposed Green New Deal programs.

Local food systems

See also: International trade § International trade versus local production

A map of wheat production (average percentage of land used for its production times average yield in each grid cell) across the world.

Local food systems are networks of food production and consumption that aim to be geographically and economically accessible and direct. They contrast to industrial food systems by operating with reduced food transportation and more direct marketing, leading to fewer people between the farmer and the consumer. As a result, relationships that are developed in local food systems emerge from face-to-face interactions, potentially leading to a stronger sense of trust and social connectedness between actors. In addition to this, consumers can also encourage farmers to be environmentally friendly by teaching them about practices such as organic farming. As a result, some scholars suggest that local food systems are a good way to revitalize a community. The decreased distance of food transportation has also been promoted for its environmental benefits. Also, farmers can enjoy a better quality of life because producing healthier food will allow them to be paid more, and not live under the poverty line.

Both proponents and critics of local food systems warn that they can lead to narrow inward-looking attitudes or ‘local food patriotism’, and that price premiums and local food cultures can be elitist and exclusive. In contrast, many food sovereignty activists argue that local production of food is essential to achieving food security, especially among indigenous communities, and thus are crucial to the public health of those communities.

Examples of local food systems include community-supported agriculture, farmers markets and farm to school programs. They have been associated with the 100 Mile Diet and Low Carbon Diet, as well as the slow food movement. The food sovereignty movement is also related to local food production. Food sovereignty activists argue that local communities should not only have access to nutritious and culturally appropriate foods, but that those communities should also be able to define the means by which their food is produced. Various forms of urban agriculture locate food production in densely populated areas not traditionally associated with farming. Garden sharing, where urban and suburban homeowners offer land access to food growers in exchange for a share of the harvest, is a relatively new trend, at the extreme end of direct local food production.

An FAO study on food transport networks of 90 countries finds that where food is transported more locally and where the network is denser – such as in high-income countries and densely populated countries like China, India, Nigeria and Pakistan –, systematic disturbances (i.e., adverse events), have a much lower impact on increases in travel time and food costs than where food is transported further distances.

Organic food systems

An organic certification

Organic food systems are characterized by a reduced dependence on chemical inputs and an increased concern for transparency and information. Organic produce is grown without the chemical pesticides and fertilizers of industrial food systems, and livestock is reared without the use of antibiotics or growth hormones. The reduced inputs of organic agriculture can also lead to a greater reliance on local knowledge, creating a stronger knowledge community amongst farmers. The transparency of food information is vital for organic food systems as a means through which consumers are able to identify organic food. As a result, a variety of certification bodies have emerged in organic food systems that set the standards for organic identification. Organic agriculture is promoted for the ecological benefits of reduced chemical application, the health benefits of lower chemical consumption, the economic benefits that accrue to farmers through a price premium, and the social benefits of increased transparency in the food system.

Organic food systems have been criticized for being elitist and inaccessible like local food systems. Critics have also suggested that organic agriculture has been conventionalized such that it mimics industrial food systems using pesticides and fertilizers that are organically derived.

Cooperatives in food systems

A greenhouse with salad of a cooperative

An organic food box of a organic food delivery service

A farmers' market offering food produced by community-supported agriculture that is also delivering online orders

Cooperatives can exist both at the farmer end of food production and the consumer end. Farming cooperatives refer to arrangements where farmers pool resources, either to cultivate their crops or get their crops to market. Consumer cooperatives often refer to food cooperatives where members buy a share in the store. Cooperative grocery stores, unlike corporate grocery stores, are socially owned, and thus surpluses cannot be taken from the store as profit. As a result, food co-ops do not work for profit, potentially keeping prices more cost representative. Other forms of cooperatives that have developed more recently include community-supported agriculture, where community members buy a share in a farm's harvest, and may also be engaged in farm labor, operating at both the consumer and producer end of food systems. Garden sharing pairs individual landowners and food growers, while variations on this approach organize groups of food gardeners for mutual assistance.

Producer associations and cooperatives reinforce small-scale agricultural producers’ livelihoods by allowing the pooling of resources to achieve scale, facilitating access to productive resources, and enhancing  marketing power. Coordination with other actors is also key to managing market risks. Mutual benefits can be achieved, for example, through forwarding contracts: farmers receive guaranteed prices for their outputs regardless of market conditions, while processors and distributors receive products of a desired quality. For farming cooperatives that share resources, the burden of investment is disbursed to all members rather than being concentrated in a single individual. A criticism of cooperatives is that reduced competition can reduce efficiency.

Alternative food systems

Alternative food systems refer to resilient foods or emergency foods, which can be defined as those foods, food production methods or interventions that would allow for significant food availability in the face of a global catastrophic food shock (GCFS). An expected 345.2 million people projected to be food insecure in 2023 – more than double the number in 2020, but a global catastrophe such as nuclear winter could threaten billions with mass starvation. Several studies have argued resilient food could provide the calories to support the global population even without agriculture. According to the book Feeding Everyone No Matter What and peer-reviewed study paths to a full solution include: global-scale conversion including natural gas-digesting bacteria (single cell protein), extracting food from leaves, and conversion of fiber by enzymes, mushroom or bacteria growth, or a two-step process involving partial decomposition of fiber by fungi and/or bacteria and feeding them to animals such as beetles, ruminants (cattle, sheep, etc.), rats and chickens. Most alternative food work covers carbohydrates and protein, but there are also ways to make synthetic fat. By mixing many alternative foods micro-nutrient balance is possible. Substantially more research is needed in this area to realize resilient food systems for the globe and even wealthy nations.

Fair trade

Main article: Fair trade

See also: Global supply chain management

Fair trade may require decisions that lead to relevant supply-chain management.

Fair trade has emerged in global food systems to create a more excellent balance between food price and the cost of producing it. It is mainly defined by more direct trading and communication systems whereby producers have greater control over the conditions of trade and garner a greater fraction of the sale price. The main goal of Fair Trade is to "change international commercial relations in such a way that disadvantaged producers can increase their control over their own future, have a fair and just return for their work, continuity of income and decent working and living conditions through sustainable development"  Like organic food systems, fair trade relies on transparency and the flow of information. Well-known examples of fair trade commodities are coffee and cocoa.

Climate change

Main article: Effects of climate change on agriculture

Effects of climate change

The IPCC Special Report on Climate Change and Land describes the current global food system as potentially having major food security risks due to changes created by climate change, including changing local weather conditions, socioeconomic effects of climate change, vulnerability of certain types of agriculture (such as pastoral) and changes in diets due to availability.

Effects on climate change

The heavy industrialization of USA, Europe and China is responsible for 90% of the world's pollution.

Deforestation in Indonesia is mainly driven by nonintervention in processes related to the production and consumption of palm oil and has a large impact on climate change.

Deforestation in Europe, 2020. The continent reduced its original vegetation cover to less than 30% in order to carry out its agriculture and livestock.

The food system is one of the largest sources of greenhouse gas emissions, attributable for between 21 and 37% of global emissions. In 2020, an evidence review for the European Union's Scientific Advice Mechanism found that, without significant change, emissions would increase by 30–40% by 2050 due to population growth and changing consumption patterns, and concluded that "the combined environmental cost of food production is estimated to amount to some $12 trillion per year, increasing to $16 trillion by 2050". Another 2020 study concluded that reducing emissions from the global food system to be essential for achieving the Paris Agreement's climate goals.

The IPCC's and the EU's reports concluded that adapting the food system to reduce greenhouse gas emissions impacts and food security concerns, while shifting towards a sustainable diet, is feasible.

Public policy

See also: Economic policy, Education policy, Science policy, and Eco-tariff

European Union

The European Union's Scientific Advice Mechanism has published a systematic review of all European policies related to sustainable food systems, and their analyses in the academic literature.

In September 2019, the EU's Chief Scientific Advisors stated that adapting the European food system for the future should be a high priority for the EU:

Although availability of food is not perceived as an immediate, major concern in Europe, the challenge to ensure a long-term, safe, nutritious and affordable supply of food, from both land and the oceans, remains. A portfolio of coordinated strategies is called for to address this challenge.

In January 2020, the EU put improvements to the food system at the core of the European Green Deal. The European Commission's 'Farm to Fork strategy for a sustainable food system' was published in May 2020, which laid out how European countries will reduce greenhouse gas emissions, protect biodiversity, reduce food waste and chemical pesticide use, and contribute to a circular economy.

In April 2020, the EU's Scientific Advice Mechanism delivered to European Commissioners a Scientific Opinion on how to transition to a sustainable food system, informed by an evidence review report undertaken by European academies.

In June 2023, the Scientific Advice Mechanism delivered a second piece of advice, this time on the role of consumers in a sustainable food system, again based on an evidence review report by SAPEA. The main conclusion of this advice was:

Until now, the main policy focus in the EU has been on providing consumers with more information. But this is not enough. People choose food not just through rational reflection, but also based on many other factors: food availability, habits and routines, emotional and impulsive reactions, and their financial and social situation. So we should consider ways to unburden the consumer and make sustainable, healthy food an easy and affordable choice. That will require a mix of incentives, information and binding policies governing all aspects of food production and distribution.

Public–Private Partnerships

Private sector corporations have been successful in building partnerships with governments which allows discussion and collaboration for how food systems work and are governed. Public–private partnerships and private sector led multistakeholder governance have positioned corporations as a leading voice on decisions where public governance authorities have become dependent on private sector funding. Lobbying influences trade agreements for food systems which led to creating barriers to competition and technical barriers to trade. Concerns around corporate governance within food systems as a substitute for regulation were raised by the Institute for Multi-Stakeholder Initiative Integrity. In April 2023, United States Agency for International Development (USAID) and the Global Food Safety Initiative (GFSI) announced a Memorandum of Understanding (MOU) to improve food safety and sustainable food systems in Africa.

Transparency

Transparency within food systems refers to the full disclosure of information about rules, procedures, and practices at all levels within a food production and supply chain. Transparency ensures that consumers have detailed information about the production of a given food item. Traceability, by contrast, is the ability to trace to their origins all components in a food production and marketing chain, whether processed or unprocessed (e.g., meat, vegetables) foods. Concerns about transparency and traceability have been heightened with food safety scares such as bovine spongiform encephalopathy (BSE) and Escherichia coli (E. coli), but do not exclusively refer to food safety. Transparency is also important in identifying foods that possess extrinsic qualities that do not affect the nature of the food per se, but affect its production, such as animal welfare, social justice issues, and environmental concerns.

One of the primary ways transparency is achieved is through certification and/or the use of food labels. In the United States, some certification originates in the public sector, such as the United States Department of Agriculture (USDA) Organic label. Others have their origin in private sector certification (e.g., Humanely Raised, Certified Humane). Some labels do not rely on certification, such as the USDA's Country of Origin Label (COOL).

Participation in local food systems such as Community Supported Agriculture (CSA), Farmers Markets, food cooperatives, and farmer cooperatives also enhances transparency. Diverse program are promoting purchase of locally grown and marketed foods.

In June 2023, the Scientific Advice Mechanism to the European Commission concluded that "Evidence generally supports a moderate impact of nutrition labelling on (un)healthy consumption in different contexts (retail, out-of-home). Sustainability-oriented labels tend to reach those who are already motivated and interested, and they strongly depend on the trustworthiness of labels, given that sustainability cannot be directly observed by consumers. However, there is much less research devoted to sustainability labelling in comparison to nutritional labelling. To conclude, shaping the information environment through labelling is necessary but not sufficient to advance healthy and sustainable diets".

Labeling

USDA Organic Label	Organic (USA) – The USDA Organic label indicates that the product has been produced in accordance with the USDA's Federal Organic Standard, part of the National Organic Program federal regulatory framework. This label is applied to fruits, vegetables, meat, eggs and dairy products. Some states, such as California, have their own organic label. Organic labelling is prominent internationally as well.
Fair Trade Show in UK	Fair Trade – Indicates that the product has been grown and marketed in accordance with Fair Trade standards. This is an independent certification, awarded by FLO-CERT and overseen by FLO International. Major food items that are marketed under Fair Trade are coffee, tea and chocolate. Many items other than food are sold with a Fair Trade label.
	Food Alliance Certified – Food Alliance is a nonprofit organization that certifies farms, ranches, and food processors and distributors for safe and fair working conditions, humane treatment of animals, and good environmental stewardship. Food Alliance Certified products come from farms, ranches and food processors that have met meaningful standards for social and environmental responsibility, as determined through an independent third-party audit. Food Alliance does not certify genetically modified crops or livestock. Meat or dairy products come from animals that are not treated with antibiotics or growth hormones. Food Alliance Certified foods never contain artificial colors, flavors, or preservatives.
Examples of COOL Labeling	Country of Origin – This label was created by enactment of the 2002 Farm Bill. The US Department of Agriculture is responsible for its implementation, which began 30 September 2008. The bill mandates country of origin labeling for several products, including beef, lamb, pork, fish, chicken, perishable agricultural commodities and some nuts. USDA rules provide specifics as to documentation, timetables and definitions. There is not one specific label to indicate the country of origin; they will vary by country.
	American Humane Certified – This certification is provided by the American Humane Association, and ensures that farm animals are raised according to welfare standards that provide for adequate housing, feed, healthcare and behavior expression. Antibiotics are not used except for therapeutic reasons; growth promoters are not used. Other issues including transport, processing and biosecurity are addressed as well. Species covered are poultry, cattle and swine.
	Certified Humane Raised & Handled – This label ensures that production meets the Humane Farm Animal Care Program standards, which addresses housing, diet (excluding routine use of hormones or antibiotics) and natural behavior. Additionally, producers must comply with food safety and environmental protection regulations. They must meet standards set by the American Meat Institute, that are more stringent than those laid out in the Federal Humane Slaughter Act. Certification has been applied to beef, poultry and eggs, pork, lamb, goat, turkey, veal, dairy products and wool.