I use the physicist Faraday to demonstrate that CORRECT CONCEPTS MATTER IN MATH, PHYSICS, ECONOMICS… MORE THAN ANY OTHER LOGICAL INGREDIENT.

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MATH IS AS PRACTICAL AS YOU CAN GET:

The question of the nature of mathematics may sound unduly abstract to those who err in the real world, searching for meaningful employment. But few questions are as practical: economists advise the powers that be, and justify their models, with equations. But even when equations are right, what do they equate? In the real world, they have equated to plutocracy.

It is not because an equation is brandished that a model is right, or relevant, or removed from the basest motives. Verily, mathematical economics looks good, and has been used for oppression, and exploitation, both when it works (for the likes of Goldman Sachs) and when it does not (for the rest of the world).

Before doing good mathematics, or good physics, it is necessary to use good concepts (which then will be equated as equations do equate things, namely in increasingly complicated ways, as civilization advances, and minds become more subtle).

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MATHEMATICS IS FIRST ABOUT CONCEPTS, AND SECONDARILY ABOUT EQUATIONS.

Applications of this observation are all over thinking, physics, economy, politics, etc. I am targeting in particular mindless, equation based economics with no soul to call its own, and little regard to reality…

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GETTING SOME GUIDANCE FROM FARADAY:

The main intellectual adventure of the famous English physicist Michael Faraday embodies how important it is to find the right concepts, even before finding the equations.

By inventing the **concept of FIELD**, Faraday made the

*mathematical*breakthrough that had eluded the likes of Newton with gravitation, and Coulomb (and others) with electricity. So doing he made Maxwell’s

*equations*possible, and thus what became Einstein’s "Electrodynamics of

**Moving**Bodies" ( = "Special Relativity").

Faraday’s method was in blatant contradiction with Newton’s bombastic claim to logical purity. Faraday’s "Hypotheses Fingo" method has deep consequences on mind management. Not just in physics (where it was, could, and ought to be employed to domesticate the Quantum), but also in economics. And, of course, it is the essence of the philosophical method.

In economics the Faraday question becomes: did economists find the fundamental concept to apply their equations to?

Well, no. And the answer comes in two blows:

1) Money cannot be a fundamental concept. Because it was man-made, government made, before it degenerated down to being made by the Gold-Man-Sacks.

2) Physics applies field theory to energy. Ecology and its subset, economy, are therefore about energy. Thus energy is the universal currency and fundamental concept.

So, when Larry Summers talk about "balances", etc, he is knowledgeable, a bit as alchemists were, and all too empty of meaning, as alchemists were all too much (although some of the alchemists’ body of knowledge, going back to the oldest Egypt, was real). Both were mistaken because of primitive concepts getting in the way (besides the conversion of lead into gold).

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NEUROLOGY ABSTRACTED = MATHEMATICS.

What is mathematics? The question has been asked for ever, and there are standard answers, some funny, some bombastic. My answer is that **mathematics are coherent pieces of abstracted display of valuable human neurology**.

Trick questions: what is "neurologically valuable", what is an "abstract"? Well, a way to define complicated things is by telling what they are not. A rictus, or an epileptic crisis are not valuable neurology.

"Abstract" is anything that can be put in a finite set of symbols, or, more generally a drawing or painting, which can also be pictured as a finite set of pixels, and which SIMPLIFIES a body of knowledge .

Now Einstein was "amazed" that the universe was written in mathematics, as Galileo had already professed. But from the point of view here, nothing is more natural: the universe fabricated human neurology (through the process of nanological evolution known as biology). It is no wonder that the Son (human neurology) looks like the Father (the universe; sorry for blaspheming all over Catholic imagery).

Indeed, why did neurology evolve? To make baby universes inside one’s head, so as to be able to predict, more often than not, the behavior of the universe at large. This is done by safely studying at leisure the baby universes inside one’s head (for example when sleeping, which Socrates called his "daemon", and modern US politicians call their "Dimon".)

Hence the brain is made to build theories of whatever comes to the senses, and beyond, from there, to whatever it can make up, as if it had really occurred.

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HYPOTHESES FINGO

This brings us to Michael Faraday. Of modest social extraction, he had not studied the advanced mathematics of his time (which were not as advanced as arrogant mathematicians or physicists thought at the time, this is going to be the main point).

Anxious to understand electromagnetism, the mathematically unsophisticated Faraday did what he could, trying to visualize what really happened. So doing he discovered he could draw it. That was derided, because there were no "mathematics" in these pathetic drawings: no differential equations were involved.

Differential equations had been used, in the two centuries prior, to go from forces (say) to the effect of the forces, through the computation known as integration. For example, describing the forces of gravity and the pull of a chain on a small element of chain (the differential equation), one could "integrate" it (a symbolic mathematical manipulation) to get to the description of the entire chain hanging (a so called catenary curve well known by suspension bridges and overhead electric trains).

The problem Faraday confronted was more basic: describing the force. No forces described, no differential equation, so the usual approach of going from an infinitesimal element to the big picture failed.

On the surface, the electric force had been solved: Coulomb had found that it was proportional to the electric charges involved (with likes repelling and opposites attracting), and inversely proportional to the square of the distance (like gravitation). But Faraday did not feel that everything that could be seen had been said.

Maybe he thought about Newton’s perplexity about what gravitation did between bodies. Faraday saw that there was something there, that there was a lot to be said about what was going on between bodies, that Newton had not bothered making theses about.

Faraday was familiar with the strange patterns of magnetic fields, and weird orientations of compass needles. He drew them down, visualized them, helped by materials that responded to them, like metallic, or magnetic powders.

With a number of application of common sense, he thus invented the concept of field. Where the lines were densest, the field was greatest, Faraday said. Bringing two opposite electric charges close together, there was a characteristic pattern, a "dipole". If the charges came in contact, they annihilated each other. Naturally Faraday ASSUMED ("hypothese fingo") that the field would then die in the center, and the death of field would propagate. If the charges oscillated, the field would oscillate as it propagated out.

By pure mind work, Faraday had legislated that interactions propagated at a finite speed (at least in magnetism and electricity; it was only natural to suppose it would be the same for gravitation; Newton had been bothered by gravitation as an instantaneous interaction, but, since he "did not find hypotheses", that is the way his equations looked at it … which, by itself was nevertheless an hypothesis of his, however he felt about it.)

This is of course the big picture behind radio and gravitational wave effects. None of the illustrious predecessors of Faraday, and there were many, including Laplace, Newton and Leibnitz, had thought about that picture. Retrospectively, some will say it was not much. But it was everything. Mathematically it just associated to a charge a *smooth* function: f(x,y, z, t).

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FARADAY WAS DOING MATHEMATICS THAT NO ONE HAD DONE BEFORE!

What was Faraday doing as he invented his field concept and drew the lines? New mathematics, and new physics, because he had discovered a new entity. This is highly ironical: Faraday was cordially despised in his lifetime for his lack of mathematical knowledge. His recourse to drawing fields, instead of beautiful equations, was called spitefully "Faraday’s crutch".

As it turned out, Coulomb’s law, just as the gravitational law Newton had been using so well, did not contain all what could said about the electric and gravitational interactions. Newton had been highly mystified by the nature of the gravitational force, that he could not visualize as propagating through empty space. He grumbled: "Hypotheses non fingo." So Newton did not find "theses" that lay "below" what he observed. But Faraday proceeded to do just that.

(Though, although more modestly, so did Newton when, sitting on his farm below a tree, he hypothesized that the apple and the moon were both submitted to Earth’s gravitation, although one of the two, the moon, had an important perpendicular inertial momentum, as first explained by the physicist Buridan in Paris, 350 years before… Another one with "hypotheses fingo".)

Lesser mathematicians confuse proving theorems and solving well known problems with the entirety of mathematics. But actually theorems are not its hardest part (although they, or their proofs, often motivate one to invent new concepts).

The hardest part is finding out new concepts with which to construct new mathematics (examples: the zero, negative numbers, and other sorts of new numbers, algebraic notation, infinitesimals, curved geometry, etc…).

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BAFFLED & BLINDED BY SCIENCE:

Greek mathematicians were stopped in their tracks when they met curved geometry and irrational numbers, and thereafter they shrunk their field of study to whatever they could understand without asking themselves too many deep questions.

They left the study of weird numbers to business men, and concentrated on Euclid’s simple, flat geometry. The knowledge was left to percolate to India and central Eurasia. It was a near miss, and Rome can be guessed to have something to do with it: Archimedes had invented a piece of infinitesimal calculus all by himself, but he was killed by a Roman soldier, and that was Rome’s rare contribution to mathematics. A strictly negative one, for sure, but Romans did not understand negative numbers, so they were all right, and free to pursue their anti-intellectual drive, for many centuries to come. (Infinitesimal calculus had to wait 19 centuries after Archimedes’ assassination until Fermat resurrected it, using Descartes’ just invented concept of algebraic notation).

To finish the Faraday story: Faraday viewed fields as physical objects. Using another imaginary device, the ether, Maxwell succeeded to gather all known electromagnetic law into four equations (now, with differential form theory, we are down to just two tiny equations!) Then he proved that the field was a wave, and that wave travelled at a finite speed, which happened to be the speed of light. But light was known to be a wave, so Maxwell declared he "could hardly avoid to deduct that light was an electromagnetic wave" (or words very close to this).

Later the ether as conceived by Maxwell turned out to be incoherent, and so did the Galilean addition of speeds. Einstein turned around the former, and Lorentz found the correct speed addition law (also involving the speed of light).

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Morality: CLEAN AND MODERNIZE YOUR CONCEPTS, THEN THINK: Some people will quibble that Faraday did not do mathematics, but just invented a new concept on which to use mathematics. But that is an objection that could be addressed to a lot of mathematical objects (negative numbers are just there to use addition on them, etc.).

Mathematical playground and, or just physical concept, the field changed physics, and even mathematics into completely different … fields. Actually the mathematician Riemann in 1866, thinking of forces in general, noticed they could be described as a curvature field (that is the fundamental idea of "Einstein’s" theory of gravitation).

Are there consequences for the economy ( = house management) and politics (~philosophy applied practically to civilian society)? Sure. It’s important to start with the right concepts. Correct fundamental axioms from which to proceed.

Faraday observed that a force was not just about exerting force, it was about creating a field, and this field behaved as a physical concept of its own. Faraday had found a correct concept underlying physics.

A pollution with erroneous fundamental concepts was the problem with Alchemy for a very long time (because the occult mixed with secular experiments). Pollution with erroneous, or irrelevant, concepts is the problem with many other fields of activity.

In the war in Afghanistan, for example, the right concept is not fundamentally used. When applying war, namely ultimate violence, on, or in, a country, it is necessary to have a clear idea of what one is fighting for. That is the fundamental right concept for war. As I explained in other essays, this condition is not met in Afghanistan. Dying for Karzai, or for the Islamist constitution, are, de facto, the underlying aims, and they are not clearly expressed, because, if they were, the war would be found inadmissible in an instant.

In economy the proper fundamental concepts are not used. That is why the theory is like a castle in the air, instead of being grounded in physics (hence energy). Although there are some valuable parts hanging up there magically, this has major negative consequences for most people and the fate of the biosphere. Being grounded in the air is most useful to the plutocracy, though, so it perdures…

Patrice Ayme

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P/S 1: There is a strict definition of abstraction in mathematical logic (from Alonso Church, 1930s). It has turned out very difficult to use, even to prove the simplest arithmetic. Thus we may as well stick to the vaguer definition of abstraction used above.

P/S 2: I used the word “neurology” above, but what I truly meant is neuroglialogy, a neologism describing what is really going on: 90% of the brain tissue is made of glial cells. Glial cells make networks, and interact so closely with neurons they direct their growth and geometry, when they do not turn into them outright.

P/S 3: QUANTUM FIELD ANYBODY? By this I do not mean the Quantum Theory of Fields ("QFT") but whether the Quantum itself can create a field. Bohm, expanding his way on ideas of De Broglie, has such a field in his hidden variable version of Quantum Mechanics.

It is my observation that there is something as a Quantum field (but more general than Bohm’s) and that Faraday’s basic reasoning can be extended to that field.

P/S 4: From the news wire, July 30, 2009: In 2008, Merrill Lynch and Citi got 55 billion dollars in TARP funds from taxpayers, because they were broke, and then distributed 8 billion dollars to their employees, the very same ones who had broken the banks. The New York State Attorney General is enquiring.

Economically and politically, though, it is clear that something is as wrong as possible there. Indeed, searching quickly through history, all the way back to Egypt’s Old Kingdom and the Sumerian Cities, 5,000 years ago, I do not know of a single, more brazen theft… except, of course for Gold Man Sacks’s promised and still to come, conversion of 13 billion dollars of TARP funds into its own bonuses…

Grand larceny to this extend is tolerated because the breakdown of economic and political theories, from incompetent concepts at their foundations, leaves people so incapable of mentally processing the situation, that enough of them are incapable of even feeling indignation. Reminding us of a tuna on a beach, trying to breathe, Obama gulped that "we saved the financial system". By the skin of the back of the People, and on this raw flesh the plutocrats shall keep on riding…

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