“Just Physics”
Abstractions are constantly on trial for their own existence—they border too close to teleology, to the non-physical realm of ideas. As far as I can tell, no one has a satisfying account of how they might square with our modern understanding of physics, how it might be that they actually exist despite running on the same laws that underlie everything else.
The central tension here is that physics, as we currently understand it, operates like so: there was an initial set of conditions and laws which operate on those conditions. That’s it. That framework explains everything quantum, which explains everything atomic, which explains everything chemical, so on and so forth. Hence, anything “big” can be reduced to its parts and in fact everything “big” is just its parts. Abstractions are just illusions, then, maps we project onto reality. They aren’t real, can’t cause anything, do not exist.
Cognitive scientists, for instance, say such abstract things like “minds are computations which run on representations,” but they use this conceptualization almost metaphysically: no one knows how things like “beliefs” connect up to “brains.” Hence, there’s all this philosophical debate about whether or not something intangible like a ‘belief’ could cause something physical like an action (e.g., Fodor’s work).
According to Hofstadter, “Minds can’t push material stuff around because physical law alone would suffice to determine its behavior,” and, referencing abstractions such as primality, “... has the curious property of not talking about anything physical at all… These properties somehow transcend the physical and have to do with pure abstractions.”
Minds, as opposed to brains, are these metaphysical spaces of ideas; intangible, non-physical, abstract. Abstractions then, as the brain sciences seem to think about them, are these floofy, imaginary things that sort of ride on top of brains. We can talk about them—god knows it’s easier to predict behavior if we assume things like beliefs power our actions—but these are mere projections. Abstractions are useful, sure, but they’re not real.
Likewise, biology, according to most biologists, is “just chemistry,” which of course is “just physics.” Despite this you often find them using cognitively loaded words to describe their subject matter, phrases like “regulatory networks,” “protein committees,” even “cellular memory,” and “intelligence.” Don’t worry though—it’s all metaphor—it’s not what’s actually happening. Just convenient language we overlay onto base reality (physics!).
Let’s take Hofstadter, again, from the example that spawned the above quotes. He asks us to imagine a computer we constructed out of dominoes (spring loaded so they stand up again after they fall). Say we designed said computer to tell us whether a number is prime. Now we input 641 (which is prime) into our domino machine and the last domino never falls. What happened?
Here, we’re tempted to offer two types of explanation. The first, the sort of mechanical and physical explanation, is that the last domino didn’t fall because the one before it didn’t, and so on and so forth. The second explanation, one that appeals to a more abstract understanding of the situation, is that the last domino didn’t fall because 641 is prime.
Or take an even more run of the mill example: if we see the cookies we want at the store we grab them. We can talk about it like this in “abstract land,” where things like cookies and stores and arms exist, or we can talk about it in “physics land” wherein all that really happened was some quantum bubbling. And we are so tempted to ask—well, which one is right??
These two types of explanation, the ones composed of “just physics” versus the “abstracted ones” are often pitted against each other, as if they could not reside in the same universe. Like Hofstadter, many philosophers conclude that there is no room in our world for “abstractions,” those can’t cause anything, it’s all “just physics” at the end of the day. Any abstraction is just a way for us to understand something, it doesn’t actually exist.
This seems like a mistake to me. It seems as though scientists and philosophers have looked hard at this problem, wherein life, the most interesting phenomena in existence, lives and breathes on abstractions, this incredible, perplexing feat, and they have thrown up their hands and said “It’s all just physics! Abstractions are useful illusions!”—reducing one of the most beautiful and puzzling processes in the universe into a framework that cannot do it justice.
Well, I do think our world is physical—I just don’t think that means abstractions don’t exist. They do, they are real, and I think if we could figure out precisely what we mean by this, we’d gain a whole lot of clarity in a field that is struggling to reduce away the very thing that makes it all so interesting in the first place.
I have many things to say about abstractions, most of them not fully formed, certainly not ready for a blog post. Here I only aim to sketch out why I think abstractions do exist, why top-down causality is a coherent thing to talk about, and why “641 is prime” does in fact cause the last domino to fall.
Small Things and Big Things
When I say that abstractions exist, I am trying to say something like “small things ‘know about’ big things” and “those small things can ‘affect’ big things.”
Let’s start small. Take two atoms which are bumping around in a box, unbonded. If I take a measurement of atom A, I get no information about atom B (or at least, very little). When they form a bond, though, knowing about atom A tells me a lot about atom B. In other words, I get information about B “for free” just by “knowing about A.” This is a tiny example of a small thing knowing about a big thing, which is basically saying “you can know about more of the space than you actually represent.” If I know A, I automatically know about B. A “small thing,” atom A, “knows about” a “big thing,” atoms A and B.
The flip side of this, the one I think people neglect in talking about abstractions, is that I can do more in the bonded system (given that I can do anything at all with this system). In the unbonded world, knowing about atom A only really lets me interact with atom A, but if A is bonded to B, then knowing about A lets me affect both atom A and B for the price of one! I.e., I can push atom A around and B will follow (for the most part). In other words, a “small thing,” atom A, can affect a “big thing,” atoms A and B.
So far I’ve basically just said that abstractions are tracking correlations (across space and time). But correlations are interesting in what they allow for. I can represent a correlation via a compression, because of this 2 for the price of 1 thing. The compression is smaller than the whole thing, so abstractions, which are small, can come to represent things which are big. But also, the actions you take with correlated things in the territory are “smaller” than the events that unfold in the territory—your abstraction of a situation enables you to impinge on a single variable (one atom, or one little chunk of them), and the rest follows.
Another way to think about it is that abstractions need order to survive. Without it—without any bonds, without any macroscopic structure, without correlations—you cannot “know” about anything distal from you. You cannot predict anything. Looking at any one thing only tells you about that one thing. You don’t get anything for free, you can’t infer distal information. Small things can only ever tell you about small things. “Big things” don’t exist.
Order is a necessary condition for abstractions to exist, to make sense. They cannot happen in a maximum entropy world.
E. coli, and Neurons, and Bears, oh my!
Let’s go up some levels and look at E. coli, a tiny single-celled bacteria. E. coli can perform chemotaxis which just means it can reliably follow chemical gradients (which it eats). How does it do this? Basically, it has a few receptors for the chemical, a protein called CheY which, upon a certain ratio of these receptors being active, changes state (by, e.g., methylation), which then causes certain genes to upregulate proteins which cause flagella movement.
I’m skipping a bunch of steps here, but this is the basic idea. I want to say that CheY is an abstraction. It represents a ton of information—i.e., the chemical concentration many millions of molecules away from it. It “knows” about that concentration, not everything about it, but there is information conserved, by a series of reliable protein transformations. It is a “small thing,” relative to the receptors and the concentration outside, but it “knows” about these “big things.” This is possible because chemical trails are correlated—i.e., they tend to clump together. So E. coli can build sensing strategies which reliably correspond to this phenomena. Those sensors can reliably couple to CheY, and so on and so forth.
So abstractions have this nice property, in living systems, where reality sort of “fans in” to the smaller representation (e.g., CheY), and then small actions “fan out” into the world, with large effects (e.g., moving E. coli). In other words, both representations and actions benefit from abstractions: this 2 for the price of 1 property applies in both (although of course you can get huge bang for your buck, too, as in when “apple” stands in for trillions of atoms).
These examples feel very intuitive, physical, and grounded to me, which is why I like them so much. There is a small object, an atom, or a protein, which is connected up, which “knows about,” other, bigger objects, by way of being physically coupled to them. This can happen because a “big object” is one that is correlated (like the blob below)—one where “knowing about X” tells you a lot about A and B. X can then reliably connect up to a far away C (via molecular bonds, via a series of transformations, via electromagnetic radiation? I don’t know I’m not a physicist) to “tell it” about the whole object.
This is all I mean by an abstraction, as I’m using it here. It seems quite mundane when spelled out this way. But that’s sort of a blessing, too: abstractions are not mysterious metaphysical intangibles, they are concrete, physical objects.
This mundane, straightforward sense of abstraction is lost on the life sciences, I think. Biologists are of course the ones that charted out these pathways in E. coli, but I don’t think they would ever call CheY an “abstraction.” CheY is a protein, which is just a bunch of molecules, which is just a bunch of atoms, so on and so forth. It’s all just a convenient description of lower-level phenomena. But abstractions are real. CheY is just a bunch of atoms, that’s true, and it is informationally connected to many more atoms very far away.
And I think that once you’re looking at a human brain without this physical, grounded sense of abstraction, it’s easy to start saying things like “abstractions are non-physical.” Because what the hell is a belief? Well presumably it’s just some neurons firing at the end of the day. Oh but what were neurons firing, again? That was just some proteins responding to some atoms, which are themselves quantum fluctuations and… we’re back. Beliefs aren’t real, abstractions don’t “power” anything, they’re just useful descriptions of base reality.
I’m not really blaming anyone, I was confused for a long time about this too, on how abstractions could fit into the Laplacian world. On the one hand it really seems like gliders (a la the Game of Life) are just expressions of the lower-level dynamics, not ontologically distinct from the the rules they ride on top of, and on the other hand it really seems like they take on a whole life of their own, like they are “things,” separate, and powerful, and causal. I puzzled for a long time over how both of these things could be true.
Well, I do think abstractions are causal. I do think that, e.g., seeing a bear will cause you to run. It’s the same story as E. coli, just a bit more zoomed out. There is the collection of trillions and trillions of atoms, all bumping around in their correlated trajectories, making up the fuzzy mass of “bear.” You see that churning mass, your neurons, cells, proteins, atoms, which are specialized to detect light and build up circuits with that light, to detect edges, and the like.
You don’t not have as many neurons as there are atoms in the bear, but that’s okay because when you live in a correlated world, coarse graining makes sense: neurons can average over sections of space because sections of space will tend to be related to each other. And if one piece of space can tell you a lot about the pieces of space around it, then you need only represent one bit of information there, i.e., you can compress it, by averaging, by max-pooling, by only paying attention to X, whatever.
And the complex series of physical couplings that ensues from your retina to “higher order brain regions” results in an abstraction: a neuron, or a cluster of them, that represents “bear”—represents in the sense that the relatively few atoms in those neurons are tightly correlated to the many, many more atoms in the bear. A small thing sees a big thing.
And that small thing, that cluster of neurons can then spark this big subroutine—running. Those neurons will influence the atoms around it, serially, causing them to rush into axons all along the leg, and those impulses will cause actin and myosin to begin their work in the muscles; all of this is part of one “thing,” a temporally correlated series of physical states. In other words, most of the atoms in the leg “know” about the bear, from the neurons that connected up to them—the abstraction fans in and out. A small thing causes a big thing.
In some sense this has to be true. Living things cannot exist without order—we need it to make any sense of the world, to predict it, but we also need it to be able to do anything with it. We take advantage of subroutines, these series of couplings which we have developed within ourselves, but which also exist outside of us. Entropy always increases. We must, therefore, rely on order pre-made, in the food we eat, in correlations we take advantage of, in the “buttons” we can press in reality—those couplings that fan out into the world.
Drawing Lines
Could we undraw any of these lines, though? Could we undraw them around E. coli and neurons and bears and just look at base reality (whatever that is), and say anything interesting? I think we both can and can’t. Any analysis of an abstraction is going to rest on the ability to say that a bunch of things are relevantly the “same,” which means we’re looking at how groups of things act, and this story of physics where individual particles move around seems a bit antithetical to that. But I also feel like I can say “when you look at these two particles, they’re always coupled to these other four” without breaking any ontological commitments.
I don’t know what “base reality” looks like, but say it’s sort of like this picture below with some particle-like things and some trajectories of those things. Under this ontology, I don’t see why it’s inconsistent to say that there are some parts of reality that we can carve out as A, and others as B, and we can talk coherently about A causing B in the sense that A is coupled to B—knowing A type things reliably tell you about type B things, and you don’t need to know about anything in the middle for A to be informative of B.
Perhaps the line drawing is still unsatisfying. I don’t think it should be. It simply is the case, that some bits of reality have more “power” so to speak, that when you look at them as a group, you see that they have greater rippling effects, they enable you to “say more” about things far away, without having to follow those trajectories in their entirety.
And I feel that, once you have this picture about how “base reality” connects up to orderliness, correlations, and abstractions, that the scale stops mattering. I can talk about A as being atoms, or molecules, or proteins, or cells, or mountains, or humans, and likewise for B. It’s all the same sort of thing—correlations over space and time, persistent patterns, rippling through the universe.
Or is it?
Obviously cells and humans and computers and the like are much more “interesting” than rocks, even though they’re all abstractions under my characterization. There’s something special about the way abstractions are “hooked up” in living things, in computers, that differs in degree and perhaps kind than a rock. I’m not sure exactly what these differences are, but I want to figure it out. This is not the focus of this post, though.
“641 is prime” is a Powerful Force
The focus of this post is to see if we can coherently say that “641 is prime” caused the last domino to fall. What could that mean? Well, the story is going to be a bit more convoluted, but essentially it’s the same explanation of how the bear caused me to run.
“641 is prime” is not a non-physical idea, non-physical things don’t exist, after all! “641 is prime” is a belief, which is instantiated in some neurons somewhere, perhaps yours, as you read this. But it was also instantiated in the programmers mind when she made the domino computer (or rather, “primality” was).
What does it mean for primality to be instantiated in someone's mind? It’s just going to look like a more confusing, complicated version of CheY—there’s a set of stimuli, prime numbers, which themselves are just ink on a page, which are coupled to some neurons. That’s the basic story. Of course here there’s all this weird stuff like primality being more about features of the numbers than the numbers themselves, but the bottom line is the same.
Yes, it’s true, after all this time I spent grappling with metaphysics and abstractions and minds and I went round and round into these eccentric corners of meme-space, I ended up with pretty party-line beliefs. I guess that’s usually how it goes when you try to figure things out for yourself!
Anyways, once we think that primality is some physical piece of matter (like neurons) that are coupled to prime-number-things (like ink on a page), then we can say that the programmer relied on this abstraction to construct the domino computer, that this abstraction ‘fanned out’ into reality. She did this by representing prime numbers (and all the operations on them) in the dominos, by making a mapping between them, these abstractions she has stored in her head, and the domino layout. They were, hence, physically coupled.
After she makes the computer, her neurons may not always be physically coupled to the machine (e.g., when she’s not looking at it), but she’s constructed it such that some of the stimuli that were physically coupled to her abstraction of “prime,” are now physically coupled to her domino instantiation of it. She’s transferred her abstraction into another piece of physical reality. Whatever number she might have seen, in ink, and done some mental operations with, has now been converted to the domino world, where isomorphic computations can take place.
And now, when the last domino doesn’t fall, I do think it is coherent to say that it didn’t because 641 is prime. “641 is prime” is an abstraction, yes, a complicated and convoluted one, but one that exists in physical reality nonetheless—one that you can draw lines around and predict (find is informationally coupled to) the state of the last domino.
This is the sense in which I think that abstractions and top-down causality exist. It feels like a small part of the story, to me. What I really want to know is why computers and brains are so much more interesting than rocks. But it feels like an important piece, nonetheless, especially as I explore biology more (which at present suffers a great deal from not understanding this, I think). I think Michael Levin does understand this, and I expect it’s why he’s one the few people exploring the consequences of it in the science of life.
Life Runs on Abstractions
I do worry that I have said nothing new or interesting. That after all of my thought on this, I have just come round to very party-line views. I’m not sure. On the one hand it seems like many people in the life sciences are pretty confused about this. On the other hand it seems very obvious when I look at it now, and I’m remembering people saying things like “abstractions are statistical regularities.” But I always had this sense of hand-waviness whenever I read these accounts. At least I never felt satisfied with them, in the way I do when I now look at E. coli or bears or neurons and can say, “yes there is a physical abstraction here.”
Because abstractions are real, tangible, physical things. They are clumps of matter which connect up over space and time to things “bigger than themselves,”—big things being possible because we live in an ordered world. “Connecting up” in the sense that there are little clumps whose activity precedes big clumps, in correlated ways, and vice versa. This property, the fanning in and out of abstractions, feels central to me in explaining living things—that they take advantage of correlations not just in their compressed representations, but in the sorts of things they can do in the world. When viewed this way it seems obvious that clumps could cause other clumps to do things. “Top down causality” as some people could call it, seems incredibly non-spooky from this point of view.
And sure, you could undraw all of these lines and stop looking at clumps and instead at particles and trajectories, but why would you? It simply is the case that drawing these lines can tell you more for less—that once we’re in “abstract land” where things like arms and stores exist, that you get to say more about more parts of “just physics” land without needing to consider each base-reality-unit individually. Atom A tells you about atom B, without needing to inspect it yourself. Two for the price of one. And, I think, it simply is the case that this is what life is doing—finding inventive ways to compress and hence affect their surroundings. Living and breathing and running on abstractions that they find within and all around themselves.
That’s the fantastic, beautiful, and ultimate nature of abstractions—the one that allows us to exist at all, collections of atoms that have grown up out of the mud and into all this complexity—clumps of organized matter, feeding off of that orderliness while we can.
Abstractions are real, do exist, can exert their influence. It’s what life’s all about, after all, and we’d be mistaken to neglect it, to treat it as illusory—to forget what makes it all so wonderful, powerful, and beautiful to be alive in the first place.