LOGIC IS MATERIAL

Logic doesn’t just matter, it is matter.

FUNDAMENTAL PROCESSES, INCLUDING COMPUTATIONS, LOGIC, ARE MATERIAL OBJECTS:

Is there something besides matter? No. What is matter? Ah, two types of things, corresponding to wave-particle duality… Or, as I put it often, process-quanta duality.

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We should have come a long way in 24 centuries, yet some keep repeating ideas of Plato, an Athenian plutocrat. Plato (and his teacher Socrates and student Aristotle) had an extreme right wing agenda, much of it pursued later as the “Hellenistic” regimes (dictatorships), imperial fascist Roman Principate, and the rage against innovation. Plato’s metaphysics has much in common, if not everything, with Christianism (this explains its survival…)

And now for a word from this essay’s sponsor, the gentleman contradicting me. Robin Herbert replied to me: …”many don’t seem to grasp that the classical logics are not tied to any physical assumptions… the classical logics are not tied to any physical assumptions. I think the problem is that we have this term “classical physics” and another term “classical logic” and people think they are related. They aren’t.”

Are we that stupid? I guess, our enemies wish we were…

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Only those who have never heard of Platonism would not be familiar with the notion that logic is not “material”: it is at the core of Plato’s view of the universe. And also at the core of Christianism, so help me not god!

I beg to oppose the dematerialization of logic. Differently from Plato, I have a careful observation of nature, Quantum theory, the mechanics of atomic theory, to back me up. Frankly, relative to what we know now, Plato is an ignorant twerp. So why the reverence for his antique antics? My unforgiving mood is driven in part by the observation that the Ancient Greeks had plenty of holes in their axiomatics… Especially in mathematics (where they made several ludicrous mistakes, such as forgetting non-Euclidean geometry, generations after discovering it).

If logic is not tied to “physics”, or what’s material, we want to know what that is. But, as I am going to show, all we do is go back to the Gospel of John as the ultimate authority (itself straight out of Plato!)

Twentieth Century physics has revealed that physics is made of “Fundamental Processes” (see the very nice, pre-QCD book by that title from Feynman)… And Quanta. The former, the processes, are described by waves, the second, those lumps of energy, by particles.

Thus, saying that “logic is not physics” is tantamount to saying that logic is neither a fundamental process (or set thereof), nor quanta (or set thereof).

Orbitals to an electron around a proton (the Hydrogen atom), visualized in 2013 (Phys. Review). What you are looking at is one electron, when it is delocalized. The electron is the cloud. The cloud is a process. The process is what an atom of hydrogen is, 99.9999999% of the time… At least…

There are several problems with such a claim: far from being immaterial, any logic shows up as quanta (aka “symbols”), and is itself a process (classical logic rests on implication, the simplest process:”if A then B”, and chains therefrom). Logic shows up as nothing else, so that’s what it is: a bunch of fundamental processes and quanta. This is the modern philosophy of physics, in action! (It originated with Newton and Laplace, and was then amplified by Jules Henri Poincaré)

There was a famous exchange between Heisenberg and Einstein; the latter, at the peak of his glory, accused the young Quantum physicist to have only put observables in his matrix quantum theory. Heisenberg coolly smirked back that it was Einstein who taught him to do so! (Constructively infuriated, ten years later Einstein rolled out the EPR thought experiment, alleging a contradiction between Quantum Mechanics and LOCAL “elements of reality“. The effect was relabeled “entanglement” by Schrödinger, now the central notion in Quantum theory… Einstein should have realized that it was this very delocalization which made atoms wholes…)    

So what’s “material”? What’s observable! And what is observable? (Delocalized) fundamental processes and (localized, yet ephemeral) quanta. Claiming that the logos is neither is (implicitly) done in the first sentence of the Gospel of John, and John adds that its name is god. We of the natural school shall excommunicate those evoking god. Those who claim “logic”, the logos, escapes nature (= physis) are just followers of whom John followed, namely Plato. They are Platocrats, a particular prototype of plutocrats…

Fundamental processes are described by equations, but that doesn’t mean the equations are “real”, beyond symbols (“quanta”) of a medium. First of all, equations are approximations: a classical computer can only make a finite number of operations (differently from a full Quantum computer, which works with a continuum, the circle S1). Instead what is really real is the fundamental process(es) the equations approximate.

Indeed, consider atoms: they are real, “indivisible” (sort of)… and yet mostly made of delocalized processes known as electronic orbitals.  It is the delocalization which creates the substance: see the picture above… 

So is a classical computation a real object, in the aforementioned sense? Yes, because it is a FINITE set of fundamental processes (moving electrons and photons around). However, if the proposed computation, or logical deduction, takes an infinite amount of time, it becomes something that never comes to exist. (That’s an allusion to a classical computer trying to duplicate Quantum computers; in the case of the chlorophyll molecule, no classical computer could do what the molecule, viewed as a Quantum computer, does!)

In this view, call it material logic, time, whether we want it or not, whether logicians realize it, or not, is an essential part of logic: the time-energy principle de facto granulates time (we need infinite energy for infinitely small time intervals, hence for would be infinite logical computations). To say time is not part of logic is another of these oversights (as Archimedes did, implicitly using what non-standard analysts, Robinson and Al. called “Archimedes Axiom”, which excludes infinitely small (or large) integral numbers). Any piece of logic comes with its own duration, namely how many steps it needs in its simplest form.   

Quantum computing uses one (hypothesized) infinity: the assumed instantaneity of what I call the Quantum Interaction (aka Quantum Collapse). That enables to delocalize Quantum logic (no distributive law of propositional logic!), as delocalized Quantum processes, and this is why it can’t be classically duplicated (aka “Quantum supremacy”).

Happy processes!

Patrice Aymé