2022-10-07 #3 what the degrees of freedom is responding to in the universe

12:49PM Jan 23, 2023

Speakers:

Forrest

Keywords:

reductionism

universe

chemistry

case

degrees

inorganic chemistry

freedom

field

molecule

physics

structure

topology

number

substrate

systems

molecular structures

molecular

microscopic

model

exemplar

In your foregoing notes, there was one explicit question which has to do with degrees of freedom. This is actually a very interesting question for a number of fairly subtle reasons. I wanted to just detail that for you in this in this audio note. On the face of it, on first blush, people might say "There's just not that many degrees of freedom at the scale of the microscopic because basically there's only four forces in the universe. For the most part, we're only really going to be working with one of them, i.e. electromagnetism, because we can't really do that much shaping things gravitationally and or by the strong or weak nuclear forces." You might say "The microscopic structure of the universe is really simple. and the standard model covers things pretty well. Maybe there's amendments to it, and so on, and so forth. But this isn't infinitely complex and therefore there's going to be not that many degrees of freedom in which you represent things."

I would just basically say "This is not the right level at which to be making this consideration." We're actually looking at levels above this. The first exemplar of this would be chemistry, actually, which is to say that when we're looking at degrees of freedom, we're basically saying "What are the different kinds of molecular arrangements that can be made?" I'm only mentioning this as an exemplar of the kinds of things that might be surprising. The amounts of chemicals themselves represent a networked combinatoric structure of selected atoms that can be in relationships as defined by the combinatoric, by that network. Every molecule is a topology in the space of all possible molecules. When we say all possible molecules, it turns out that that number is truly vast. Just looking at inorganic chemistry, for example, I think it's the case that if you were to just make one instance of each possible molecule, you would tell the entire universe.

It might be that that's inorganic chemistry, it does that many, many, many times larger than the universe. Literally, every single atom, if used to make each molecule only once, would be consumed in the entire visible universe. In other words, the sheer variety of possible molecular structures is far far far beyond anything that can be reasonably implemented. All of these represent weird possible things that can happen from a protein dynamics point of view or stuff like that. Just from the sheer number of microstructures that can be created, of course, if you're looking at engineering, metamaterials, and stuff like that, or the field of metamaterials in particular is starting to give some indication as to the sheer number of things that can happen. Once you get even just a little bit beyond just the single molecule phase of looking at things, the number of degrees of freedom in that space is truly enormous.

When I was thinking about degrees of freedom, I wasn't actually thinking about that. I was thinking about that as not so much being something that was the degrees of freedom that were important from the artificial intelligence general infrastructure point of view, but more in a sense of what it is responding to in the universe, i.e. that the universe itself. If I take the topology of all of chemistry down and I just call that physics, that physics is actually quite complex. It has all sorts of corners and underlying fields of selecting one thing over another just because they have advantages molecularly or chemically or something like that. The underlying topology of the potentiality field of the universe, the Hilbert space of all kinds of interactions between molecular structures, it's not only not homogenous, but it's also fantastically detailed in a sense of having what would otherwise just be like random structure. Hills and valleys, and again, the dynamics fields of the relationships.

That's not the degrees of freedom that we're interested in, that's the degrees of freedom that we're interested is in response to. The simulated universes in which we do our modeling of AI systems is tremendously simpler than the actual physical universe in which the substrate itself in a practical sense is actually going to be living. Anything that I make out of atoms is going to affect the subject to the physics, the particularly nuanced physics of just general chemistry. General chemistry in areas which are largely unexplored, i.e. molecular relationships primarily involving things like silicone, or at least elementals outside of the classic eight or nine or so that are used in carbon-based molecular systems. The modeling universe is just very, very, very simple with respect to the actual practical universe when we're talking about feedback effects potentially interacting with things at the substrate level.

This is the important bit. That there is a data channel there that no amount of simulation is ever going to come near to actually emulating. In fact, this is this is one of the areas where there was a general breakdown in what has been called reductive thinking or the idea that you could reduce the complete understanding of the totality of chemistry to potentially say "A complete understanding of quantum mechanics, i.e. that by understanding the Schrodinger equation or its variance, the Dirac equation, or chromodynamics, quantum chromodynamics basically, that you would have some way of being able to model and to describe the complete interactions of what's happening at a chemical level, i.e. the intermolecular forces in Van der Waals forces and things like that. It turns out that there's no computer on Earth which is powerful enough to do even modeling a very simple quantum mechanical system, i.e. we can model the hydrogen atom pretty well and helium to some extent. We might be able to get all the way to carbon but after that, it just gets ridiculous.

What happens is that there's this just not very much mentioned fact that there's a lot of stuff going on in chemistry that we just don't actually even know how to use quantum mechanics to describe it all. There is a failure to reduce chemistry to physics, even though again, physicists are going to say that "In principle, at least it's possible to do that," where it turns out that in practice, it is never possible to do that. Except for the simplest possible systems. I'm thinking that as soon as you hear me say "Except for the simplest possible systems," that ends up becoming the kind of exception that everybody points to to justify the idea of reductionism. But on the other hand, really, what we're saying is that there is a rejection of reduction even for the most classical case for which the notion of reductionism is normally posited. i.e. There is no simpler case of reductionism, aside from chemistry to physics, that literally every other form of reductionism is going to be less visible and or less likely.

When the basic case fails, then of course, you have to wonder whether or not all of the rest of the cases are going to fail with it. In philosophy in general, I reject reductionism, largely. I'm not saying it's not a useful concept in some cases, but the number of cases for which it's useful ends up being far, far, far smaller than the number of cases that we're actually concerned with. That has implications. I'm going to continue in the next note.