Abstract: The greatest discovery of our civilization maybe that, when the thinking gets tough, the tough goes "meta". Meta is the very symbol of our civilization, as Charles Quint pointed out five centuries ago. More: MIND IS FROM META. Thus, in contradistinction with Mr. Safire, we hold that "meta" deserves to be a nominative of its own, and we celebrate its glory with a profusion of examples of the mightiest type.

Mr. Safire:

In your editorial "Mind over meta: a narcissistic prefix" you crack down on the uppity prefix "meta" for acquiring a life of its own (International Herald Tribune, December 26, 2005). You sneer that "we are marching into meta", as "meta is part of the unearned irony of the improperly educated postmodern crowd".

Perhaps unearned by the uneducated, but, as you may see below, maximal creativity is synonymous with going meta. Besides, "meta" used to be free standing in Greek, where it meant later, and beyond, or in Latin, where it meant unknown. "Meta" was also a deity.

"Meta" got explicitly at the forefront of thinking with the liar paradox of Eubulides (~400 BCE: "A man says he is lying. Is he telling the truth?"). That logical quandary is alive and well 26 centuries later; the way it seems to have been solved (by B. Russel and K. Godel), as we will show, illustrates how erroneous the old picture of what it meant to be logical was.

Meta was used as a prefix in Aristotle's "Metaphysics". Beyond physics, the real world out there, there was more, one had to admit, and Aristotle, following all his prestigious philosophical predecessors, tried to understand what. He started by what should not have been said. Aristotle demolished (his teacher) Plato's (metaphysical) theory of forms; he rejected the substance-less Platonic mumbo-jumbo, for very good reasons, and claimed that the key to metaphysics was in the "senses". That was an amazingly modern conclusion by the founder of biology. Interestingly, many modern mathematicians are still worshipping Plato's metaphysics, never having heard that Aristotle corrected some of Plato's mistakes, right away.

It is becoming increasingly likely that Aristotle's reflection was cogent, and hinted at what we would call now neurological processes. In other words, "meta", as in "metaphysics" is at the heart of where the mind turns physics into sentience. Aristotle's hint points in a direction so profound, it is still beyond (meta) our scientific explorations. We will try to be a bit more precise below.

The concept of meta is mostly employed within the world of understanding. An example: Aristotle was affronted by a body of "knowledge" in zoology where even serious authors described incredible monsters (some half human chimeras). Aristotle went meta in a very practical fashion here too. Instead of hypocritically reclining on a couch like the older prudish Socrates, saying he knew nothing, Aristotle did something about it. He decided that the very way in which biological information had been gathered so far was erroneous. Thus, he sent some of his students to describe and classify, in a rigorous fashion, all living species they could find.

The Americans have an expression for drastically creative thinking: "thinking outside of the box". We prefer the expression "going meta", because going outside of the box does not add topologies, dimensions, or landscapes of possibilities to thinking, whereas full meta can, and does. Technically, going meta consists in adding a proposition, the veracity, or provability, of which is now asserted, although it was not part of the preceding logical universe (see Godel incompleteness of logic theorem below, and also the theory of types, all related to what Middle Ages thinkers tellingly labeled the "unsolvables").

Going "meta" is the mental act of considering a totality, and going beyond it, in space, or time, or by undergoing metamorphosis (the evolution of a shape), or making the preceding logical universe into a detail which has been overcome (in mathematics it is often found that the greater power of a very general approach is much easier to handle than the morass of details one started from; for example "Arabic" numerals are easier than the Roman ones: the morass of Roman numerical symbols, and variable, lousy ordering, is replaced by a much neater ordering which, besides going just one way, works with only 10 symbols; the effort towards extreme generalization is more alive than ever in modern mathematics, as the case of category theory shows).

A succession of renaissances during the millennium of the Middle Ages allowed civilization to go beyond the Greco-Roman errors (of slavery, military fascism and religious totalitarianism). Those metamorphoses were in ethics first, thus constraining civilization far beyond (meta). Time and time again, during that millennium, renaissance after renaissance, civilization went beyond itself. In one word, civilization went meta again and again. Western civilization came to dominate, because it is a meta machine.

Going meta is much more than any principle of relativity, however generalized. It reflects a general attitude of psychological creativity, which got progressively unleashed in Europe as the Middle Ages metamorphized into the Thermonuclear Age.

Jean Buridan (priest, physicist and Rector of the university of Paris) discovered the law of inertia (~ 1330 CE; Buridan's concept was to become, through Descartes, Newton's first law of motion (~ 1680 CE)). Buridans's impetus theory massively contradicted Aristotle's erroneous considerations on motion. Thus equipped, Buridan destroyed the false argument that a moving earth would have left things behind. It was a meta jump. Buridan and his student (bishop) Oresme (Paris ~1350 CE) then described the (now so called "Galilean") principle of the relativity of motion (Galileo flourished three centuries later). Thus incited, the two Parisian philosopher-physicists found plenty of arguments in favor of why gravity would make the earth go around and the heliocentric theory (generally attributed to Copernicus (~ 1543 CE) who plagiarized the idea from Aristarchus, Buridan, Oresme, and al.). At this point Buridan and Oresme seem to have been paralyzed by the enormity of embarking on an earth moving through space at incredible speed, leaving all of the church and all of tradition behind. Maybe they had too much invested in the old universe. Maybe they feared ostracism. Or bodily harm (several philosophers were burned alive in the next 3 centuries, some on flaming piles of their own books). At the last logical instant, Buridan and Oresme concluded that, after all, although it looked way simpler and way better if the earth rotated on itself and moved around the sun, it did not, according to "scripture".

In general, scholastic science had a psychological problem with going meta: time and time again, crack thinkers shrank from the enormous consequences they had nearly drawn. For example, gravity clocks contained the essentials of Galilean-Newtonian physics, but it took four centuries to make those explicit on paper, because civilization was bewitched and besieged by God and tradition (less so than in more fascist Islam, but still bewitched and besieged by fascists). Going meta was too scary. The tensions with the Church were maximal; for example, the French government of Philippe Le Bel, not satisfied with burning alive the Templar monks, and with winning a ferocious tax war with the Church, issued an international warrant of arrest against the Pope in Rome (as an afterthought, for meddling with affairs of the French state), and sent special forces headed by a lawyer to go get him, resulting in the death of the Holy Father. Those were horrible times: an overpopulated Europe collided with the Little Ice Age, the Black Death and the "100" year war. At the times, intellectuals were not just cheating in the little ways they do nowadays. A posthumous campaign by Okhamists succeeded to put ALL of Buridan's writings in the Index of Prohibited Books (1474 CE), silencing his name to this day (Buridan's shattering meta jumps are still attributed by the commons to Galileo, who lived a dozen generations later). No wonder Buridan, a student of the liar paradox, was careful! His children, the meta jumps of inertia and relativity, lived on.

Going meta is the opposite of going totalitarian. Totalitarianization decreases the dimensionality of the mind, going meta does the opposite. Going meta makes the ex-totality into a subset, a subspace, a hypersurface, something which has been overtaken, simplified, lower dimensionalized. Indeed, the act of going beyond can be viewed as adding a dimension where there was none. It's this crucial moment when the conquering spirit takes command of what used to be overwhelming preexisting logic and reduces it to simplified data, so that the details of that tree stop masking the proverbial forest. Going meta is at the core of the process of abstraction: details disappear, but a lesson is left behind. An example is the modern definition of number in set theory. "Two" is the set of all sets in bijection with the set whose only elements are the empty set, together with the set whose only element is the empty set. In other words from "two bananas", "two stars", "two whatever", the "whatever" have been cut out, and only what's left has been made into one concept which is viewed as finite (although it's truly infinite, being the total number of all pairs).

The psychological difference between thinkers of the Middle Ages and those of "the" Renaissance was that the latter WANTED to go meta. Even Francois Premier, sponsor of French and Da Vinci ("his father") wanted to go meta. So did Charles Quint, who, as he became emperor of most of Europe, took "Meta" as his motto (in his native French: "Plus Oultre"). Thus Charles Quint acknowledged that GOING META HAD BECOME THE MAIN DRIVE OF WESTERN CIVILIZATION (1520; after centuries of discoveries and creations, which had left all other civilizations, and all of the preceding world of thinking, including Aristotle, behind).

A bit later, a European mathematician, going meta on his own, solved the general third degree equation by deciding it was OK to do as if negative numbers had square roots. Nobody could point out to a number whose square was negative, but that did not stop Cardanus, for whom no proof of existence was not proof of inexistence, whereas need for existence, without SELF contradiction resulting, was good enough. This is typical of the logic inherent in all meta points of view, and is closely related to the Godel theorem setup (see below).

It can be argued that mathematics was always all about going meta in a very organized manner. For example inventing the zero, or negative numbers, was already a way of going meta: it was convenient, not self contradictory, contradicted only all the minds and all the cultures which had existed before... i.e., it was insufferable to old minds, because it required new mental circuitry, which never had been before. If one thinks about it, inventing these new mathematics involved probably the construction of new circuitry in the brain. So meta = new geometry (in the brain!).

Going meta was at the core of the extension of infinitesimal calculus in the 17C beyond Archimedes' initial effort. Mathematics went meta, by treating infinite processes or quantities as if they were finite (that is why calculus is called "infinitesimal"; it's a rather unobvious trick the brain had been doing all along, but not consciously). The logic of infinitesimal calculus was often murky (Fermat, Newton) or outright scandalous (Leibnitz). Still the end, "meta", justified the means (said means, model theory, real analysis, integration and measure theories, were sorted out in the next three centuries). When one goes meta, abstraction makes previous obstacles into yesterday's irrelevant details. Being capable of "Going Meta" is the key. This is why some intelligent people do not understand mathematics. They do not conceive that going meta without contradiction is most of the proof and motivation that mathematicians need to proceed. The rest are details. Mathematicians often proceed top down, by trying to prove conjectures they have, i.e. use meta even in their daily activity.

Going meta was used in physics. Descartes had gone overboard. Newton was more delicate: his meta jumps consisted in equating the behavior of the moon with that of the apple, and a geometrical form of infinitesimal calculus. Later on, Maxwell decided that electromagnetism should be pretty on paper, with nice balanced equations. In other words, he had gone meta, from an esthetics motive. That made him correct Ampere's law (with the displacement current). Dirac followed a similar meta procedure when he invented QED, also with an esthetic impulse (1927 CE). Dirac wanted to write the simplest relativistic wave equation which could be imagined for the electron. The simplest wave equation is first order, but that made no sense in normal space. So Dirac, imposing his meta esthetic rule, invented spinors, and predicted what turned out to be anti matter. Well, it was just what was going on. Not all physics is invented that way, though: Young, Faraday, Hertz, Becquerel, Rutherford and many others made striking new observations, not meta jumps (Galileo did both).

Back to the 19C. Inspired by sound and water, most physicists decided that light waves could only wave inside something, that they called the ether (a mini meta jump, because they had taken for granted something they had no real reason for, so they had gone meta, without knowing it). Thus invigorated, they confidently searched for a manifestation of this metavision of theirs. This proved experimentally discombulating: light was waving, indeed, but, weirdly, the Americans Michelson and Morley found that it was not waving inside a medium (1877). This is a mystery to this day, but it led the famous mathematician and philosopher Henri Poincare' to invent and advertise the (so called "Einstein's") Relativity Principle (before 1904). So the impulse to go meta can lead to instructive mistakes which end up leading us much beyond the erroneous meta we started with. Indeed, if we did not have again and again an impulse to go meta to start with, we would have stayed fishes, happily munching fields of algae in a lower dimensional daze instead of metamorphosing ourselves into higher thinkers.

The paradox of the liar is self referential, and therein the problem. It ignores meta, hence the pain. The logician and philosopher B. Russell solved it by his theory of types, which is the establishment of a hierarchy of meta. Confronted to the same difficulty, K. Godel massaged the statement "is not provable" in a similar self referential way to show that any theory naturally is incomplete, and NECESSITATES META TO GROW. Godel showed that any theory boils down to a succession of meta jumps. One jumps around from axiomatics to axiomatics, until one finds a place one wants to study. Not exactly what people used to understand as reason in earlier, more naive centuries. Hence EMOTION WAS MADE FRONT AND CENTRAL IN SYSTEMS OF THOUGHT, ARTICULATED BY META.

Let's notice in passing that the causal loops of the Einstein's naive theory of gravitation (GR, "General Relativity"), are also self referential... because GR is not articulated by meta (its Achilles' heel; meaning there is nothing really new in GR: it is basically a giant tautology, leading to, well, causal loops, i.e., "unsolvables" as the Middle Age semantics had it).

The Quantum picture of the world suffers from the opposite problem to GR: meta is everywhere. The Quantum makes meta into a gigantic (universe sized, actually) interrogation, because of the non local entanglements which are the essence of the Quantum. It is not clear where those non local entanglements stop. Do they respect "black holes"? Actually do they stay inside anything? The Quantum theory we have says: no. Hence what does local mean? Is local a statistical notion? It appears to be. In other words, the Quantum puts into question not only the notion of point (clearly hopeless) or of old fashion space, but even the notion of meta (where does "beyond" start, and where does it end?)

Nietzsche pointed out that the most important philosophical problem was the hierarchy of all values (following ... Aristotle, and common sense, he proposed to base it in physiology). Friedrich proposed a "genealogical" approach to establish said hierarchy, in other words, to find which values were meta relative to others. More recent authors (Foucault, etc...) have generalized this evolutionary approach a bit. We propose to generalize that hierarchy of meta to all thinking processes, be they logical or emotional or in between. This is not surprising: as exposed above, pure logic (also tellingly called metamathematics) require the notion of meta as its organizing principle.

We believe that a whole ordered structure of principles, methods, habits, mantras, metastructures inside the mind are reflected in metastructures inside the brain and it's this meta order which differentiate the values of both individuals and civilizations. Said structures do not come from genetics, or epigenetics alone, but from a co-computation between those and the environment, history, and the ... will to meta (a generalization of the will to power, which incorporates the will to wisdom, because there is no wisdom without it).

All of this to tell you, Mr. Safire, that meta, being everything, deserves to be its own nominative. You meant to be ironical when you said that "we are marching into meta", but, as the preceding should have showed you, so have we been doing for centuries. All we are, and call modern, came from meta. "The" renaissance (of the 15C) happened when going meta became THE way. META DESERVES TO STAND ALONE, AS THE SYMBOL AND NEW RELIGION OF THE MENTAL PROCESSING WE NEED FOR OUR METACIVILIZATION. So let there be that word, proud, free, unattached and dominant. Let there be that thought: when the going gets tough, the tough goes meta. When all hope is lost, and the darkness is infinite, all you need is meta. Metamorphize yourself, and you may survive!

Patrice Ayme',
7 January 2006,

P/S 1: How mathematics fits the world has long been viewed as a deep mystery. The explanation maybe different from what has been suggested before. What may happen is that going meta forces the brain into building mental structures (which are, literally geometrical constructions) which are forced top down by the intuition of that particular "meta" (remember, going meta decomposes into steps that can be reduced to just one proposition, such as Dirac's proposition of making it so that the electron would fit into a first order PDE). If the top down process can be done, if the castle in the air can be constructed without any blatant contradiction to preexisting logical ground, then that structure has been demonstrated to exist as a real object somewhere in the universe (namely in one's brain, by building it explicitly as a new piece of brain geometry). Having thus built it up in that piece of nature known as one's brain, now alert to what it looks like, the physicist finds out that nature seems to have been using it somewhere else too. So mathematics is not about what is "true", but about what can be MADE to look "true" as structures in one's brain. Hence Plato's theory of forms gets geometrically incarnated along Aristotle's lines! It goes without saying that this is the essence of what makes the brain USEFUL: creating mini geometries in the brain which seem to fit the geometrodynamics of possibilities apparently observed in the real world. So the essence of the brain is mathematical, according to the definition of mathematics we just proposed. A mathematical demonstration consists into building a (non contradictory!) geometry in the mind/brain.

P/S 2: The geometry we have in the brain is maximally powerful, because it's Quantum. It's Quantum, because fine brain structures are much smaller than the nano scale, where Quantum can't be ignored anymore. This Quantum geometry is all the more powerful, because we don't know much about what the Quantum means (we know a few things, though, namely that, for example that various approaches to Non Commutative Geometry are part of it). The Quantum relates to all: time, space, fundamental processes, probabilities... Nobody understands even the simplest form of Quantum geometry, as Richard Feynman pointed out in the introduction to his lectures on Quantum mechanics. What Feynman did not say explicitly was that the non local nature of Quantum processes is one of the factors which makes the Quantum mysterious -in other words, what "meta" means in the realm of physics, in the real world, remains a mystery. And an omnipresent one, because Quantum mechanics is the mechanics of the universe. The Quantum meta transcends all the classical understanding of space and time. Not only meta can't be ignored, but it's everywhere, and mocks (classical) time! Meta is even perhaps inside the "isolated" elementary particle, which, come to think of it, may not be isolated, however hard we try... All completely metapsychic, so we will have to change our psyche, if we want to progress further beyond....