Reductionism and Emergence

OK, time for more armchair philosophy!

Inspired by some Twitter posts by Adam Frank, I’ve been thinking about reductionism and emergence.  Here’s the thread that started me off:

In studying this, I’ve found that there are lots of different meanings of the terms “reductionism” and “emergence”, and a lot of the discussion seems to come from people talking past each other because they’re using different definitions. My thinking on this, I should note, is heavily influenced by Sabine Hossenfelder’s essay here.

In one sense, the terms are polar opposites. If by “reductionism” we mean the general approach to problem solving or studying something of reducing a problem to its component parts and working up from there, then its opposite is “holism” which presumes that a system’s behavior is best considered from the top down.

For instance, if I want to study how water sloshes in a bathtub, then starting from atomic physics or quantum field theory is a foolish approach. The water waves in the bathtub are described by equations of fluid flow that are insensitive to the underlying physics. For simple, low-amplitude waves, one is much better served with linearizing things from the equations for gravity waves, plugging in the measured properties of water, determining the modes in the bathtub, and working from there. For more complex situations you could numerically simulate the water in the tub, maybe with the full set of Navier-Stokes equations plus some corrections for surface tension and stuff. But there’s no need to go working out the van der Waals forces between water molecules or the quark interactions in their nuclei.

We call this an “emergent” property: the combined interactions of all of the water molecules obeying the laws of electromagnetism and quantum mechanics appear, on a sufficiently large scale, to be well described by equations that describe the bulk properties of the matter. One quality of an emergent property is that it is insensitive to the underlying physics: you can’t deduce the molecular structure of water from watching waves because there are lots of potential kinds of microphysics that could (and do!) give rise to the same macroscopic phenomena.

This kind of emergence has many levels: at the bottom we have quantum field theory, special relativity, and the Standard Model which describe how all particles interact. At the next level up we have atomic theory and quantum mechanics, which give us the basis for studying molecules. At this level things like the vacuum states of matter and the strong and weak forces don’t matter: they happen “underneath” at scales too small to matter, and we can summarize their contribution in quantities like an atom’s magnetic moment and rest mass (for instance).

From there, we get physical chemistry, but things quickly get too complicated to calculate, so we begin talking about sigma bonds and valences and electronegativity and now we’re into ordinary chemistry. At larger scales we can talk about the bulk properties of the material like its temperature, which conceals but successfully summarizes even more properties of the aggregate. Again, you can determine some things about atoms from chemistry, like the periodic table, but this can only take you so far. Ultimately if you really want to know the structure of the atom you have to study it directly; you can’t distinguish the plum pudding model of the atom from the Bohr model in a chemistry wet lab. Chemistry is thus an emergent property of atomic physics.

And so on to biology, psychology, sociology, and so on, as xkcd put it:

Purity

In one sense, using chemistry instead of quantum field theory is a “holistic” approach because it uses emergent properties instead of a reductionist approach, but it also reveals a second definition of “reductionism” which I’ll call “physical reductionism” to distinguish it: the scientific approach (axiom?) that all physical behavior arises from more fundamental laws at a smaller scale (or, if you like, at a higher energy).

Now, precisely defining reductionism in this way is the job of philosophers of science and I’m sure one can find holes in the way I’ve put it above, but I think my description above defines things more or less well: emergent behavior at each layer (except, I suppose, the bottom layer, wherever that is) is ultimately the sum of all of underlying microphysics, and not some new physics.

We often write reductionism means that we “could” calculate an emergent phenomenon in principle from a more fundamental theory, but I think that clouds the essence of physical reductionism because it unnecessarily introduces issues like predictability and computability. I’d say reductionism is better simply described as the view that there’s nothing else going on beyond lots small scale interactions. Also, emergence is sometimes defined in terms of “surprising” physics that shows up at large scales, but that’s way too squishy for me.

So from this perspective, there is no contradiction or tension at all between emergence and physical reductionism; indeed, as I’ve defined them the terms don’t even really make sense except with respect to each other, as Sara Walker wisely pointed out:

Now, some philosophers distinguish two kinds of emergence: weak and strong emergence. The precise definitions here seem slippery and I’m not sure I totally grasp them, so to distinguish how I’m going to (improperly?) use the terms I’ll refer to weak physical emergence and strong physical emergence.

The most useful definition of weak (physical) emergence to me as a physicist is basically the emergence that follows from reductionism. If it’s a behavior that arises from the sum of lots of smaller interactions, then that’s weak physical emergence. There is then no tension with reductionism at all because it’s consistent with reductionism by definition.

What, then could strong physical emergence be?

Strong emergence is often invoked to describe the kind of behavior that arises from complex systems that is thought to be more than “just atoms” as Adam put it at the top, and is fundamentally in opposition to physical reductionism.

The usual things people point to when asked for examples of strong emergence are life and consciousness.  To illustrate my point, I’ll use an old example.1

Many cultures have historically taught that animals are distinguished from inanimate objects by their anima, some sort of supernatural quality that imbues their physical bodies with motion. The details vary from culture to culture (for instance, the degree to which these overlap with life, the soul, consciousness, and free will) but the essence is that there is something else in the body beyond its corporeal form that makes it move. When an animal dies, that ineffable something leaves the body, and it stops moving. In this view, the body is just a vessel or puppet for the stuff of animate life.

This is decidedly not physically reductionist. We now know today how it is that living things can generate their motion and maintain their metabolic processes biochemically. We haven’t “solved” life by any means, but we do understand the biomechanical mechanisms for how living things move.

Now, it didn’t have to be this way. We could have discovered as we got better at studying living things, for instance, that living animals and dead animals were exactly the same inside physically and biochemically, except living things could move. We might have had to conclude that some things had an extra something that we couldn’t find just by looking inside of them. In fact, some might argue we still might prove that someday, but I’m sure most biologists would say this is not going to happen.

One reason is that we can analyze the biochemistry of life in great detail, and we know that when something dies it’s for a particular reason (like, for instance, lack of blood to the brain, which makes the neurons stop firing), not because its animating force departed. Another reason we can be so confident it’s not going to happen is that it would imply “downward causation”: the electrons in the animal would have to be moving due to some force other than electromagnetism caused by that supernatural anima. The animal’s leg moves because of its muscles, which are triggered by neurons, which are part of an enormously complex central nervous system. But at some point, if the anima2 were responsible and not just lots of individual electrons and ions doing their thing, then somewhere in that chain some electron or ion in some neuron had to pushed by the anima, and not just by its neighbors. If not, then there would be no difference between the inanimate and the animate versions, and clearly something is!

So that would have been an example of strong physical emergence. Another candidate, often brought up, is consciousness and free will. Lots of ink has been spilled over the Hard Problem of consciousness and qualia and so on, and I’m not going to dive into it here. Ultimately, it has the same problem of downward causation: if my consciousness and free will is due to a strongly emergent phenomenon (whether a supernatural soul or something less metaphysical) then at some point the neurons in my brain are responding to that new phenomenon and not just each other (“just atoms”) when they tell me to type these words.

But this is testable! That something firing that neuron could, in principle, be studied scientifically (for instance, by finding a neuron firing for no physically reductionist reason). If there’s more than “just atoms,” then at some point atoms need to respond to something other than “just atoms.”

There are other examples I can think of too (and ones less laden with religious implications). For instance, what if gravity has a smallest scale?  By this I mean, what if gravity only works above some threshold, when enough mass gets together in one place? The exact equation near this threshold might not be expressible in terms the sum of the gravitational forces of individual masses—that is, Newton’s formula could be correct when m and r are above some level, but incorrect below that.

Now this would be very surprising because Newton showed that his formula held even if you summed up the individual actions of all of the underlying atoms—in other words, that it is consistent with being a weakly physically emergent phenomenon.  Also, there are theories of gravity that are strictly physically reductionist that do predict gravity will behave differently or even go away on small scales, so it’s more complex than I’ve described.

Or, more straightforwardly, perhaps the dark energy of the universe or the dark matter works as a physical force that only manifests on large scales and simply can’t be described as an underlying field or sum of interactions of smaller pieces. I think that would be another example of strong physical emergence as I’ve defined it, though I admit this might be inconsistent with how the term is used by others.

One way that Adam has teased that he’s going to look at the problem of strong emergence is in terms of life as a processor of information. I’m looking forward to it, but ultimately information is a statistic or other description we assign to the arrangement of matter and energy in time and space. We have rules for how matter and energy react to each other in time and space, so ultimately any information-based description of life is, once again, physically reductionist. In order for information processing to generate strong physical emergence, there would have to be something else, some definition of information that went beyond a Shannon entropy or something, and I can’t imagine what that would be. If it’s not based on matter and energy’s distribution in time and space, then what is it based on?

One way I’ve seen people try to get around the downward causation problem is with various aspects of quantum mechanics. One avenue is by working with the concept of an “observer” (which is an unfortunate jargon term in physics whose conventional meaning invites us to give consciousness a privileged role in physical phenomena, leading to all sorts of popular misconceptions about quantum physics.)  The other is the apparently random and irreversible phenomenon of wavefunction collapse, which is the source of lots of debate about the meaning and nature of quantum mechanics.  These issues are tricky and still unsettled in quantum mechanics (indeed, they are at the heart of the Measurement Problem, which has capital letters, so you know it’s important) so this could be a way in for a strongly physical emergent phenomenon to push electrons around. Maybe! That seems at least plausible to me, though others have thought about it a lot more than I have. Indeed, Sabine Hossenfelder has gone so far as to define exactly what it would mean for there to be free will without metaphysics and shown that it’s at least possible in principle.

Anyway, that’s where I am on the topic! Again, I’m not a philosopher, so I’m sure I’ve gotten a lot wrong. My purpose was to be clear about my definitions, and hopefully clarify my “physicist’s perspective”.


And now two philosophers have written up their perspective on these ideas! You can read their take here.

Because I don’t want to change things out from under them, I’m making annotations to the above instead of edits and corrections:

1 I did not have the word ready at the time I wrote the post, but this long-discredited view is called vitalism.

2 I should have written vital spark, referring to whatever the extra thing is that vitalism is about. “Anima” is a term from Jungian psychology and refers to a property of the mind.

One thought on “Reductionism and Emergence

  1. Noah Groth

    I like your thoughts on emergence, but you failed to say anything about large system organization and complexity. Iin order to exhibit strong emergence the underlying physical structure requires a certain type of organization that cannot be defined with physics, and irreducible from a physics point of view. Robert Laughlin – Nobel Laureate in Physics 1997 – advocates replacing reduction with a holism, i.e. emergence, Study from the top down rather than bottom because in practiice reductionism cannot alone describe large complex systems. You can also study Nobel Laureate Philip Anderson who popularize emergence in the 1970 and wrote a paper titled More is Different. Anderson and Laughlin are in agreement on emergence.

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