Not THAT again
The dreaded words of “emergent phenomena” were uttered today in class. Yes, I know that I (and kleinschmidt, sort of) have been beating the subject to death for the past couple of months. Alas, since it’s the first day of the semester I was still awake enough to notice when the professor (i.e. biology-rockstar/Discovery channel host) Rob Lue went on to mumble about multimodular tensegrity in cells.
You don’t really need to know what that is — except that tensegrity = tension + integrity (ludicrous, but I kid you not) — and I doubt I can really convey the feeling of understanding I got at that moment, which I’ve lost anyway after a spirit-crushing session of physical and organic chemistry in the afternoon. What I thought interesting was a question Lue posed at the beginning of class: can understanding the details of how all individual cellular components work allow us to derive an understanding of the whole of the cell’s function?
The example used was an actin monomer, a relatively small protein molecule that binds to itself in long chains to provide structure inside cells. The changes in size and number of the actin chains, or polymers, leads to all sorts of interesting behavior and is actually the basis for how cells move. At the turn of the 20th century, had we known the exact structure of an actin monomer (which we now do) and the physical rules by which it abides, many scientists would have assumed that that was enough information to characterize, indeed predict, the behavior of the entire skeleton of actin filaments in the cell. In fact, as modern biology has found, it is excruciatingly difficult to predict such behavior from first principles, precisely because of the way that it “emerges” from the complex, multi-leveled interactions of many small components.
Analogous examples abound in physics, chemistry, and the social sciences. These various manifestations of the “unpredictability of everything” take on names like dynamical systems, chaos, sensitive dependence on initial conditions, and obviously, emergent phenomena. The fallibility of reductionist science has even become an object of popular (mis)understanding, as Michael Pollan’s piece in this Sunday’s NYTimes magazine shows (The essay has been insightfully but untactfully subtitled “Are scientists ruining the way we eat?” on the cover.) I think my professor’s intended point, and that of Pollan’s, in fact, was that on a practical level, modern science has made it meaningless to consider specific, single mechanisms in understanding biological systems. Implicitly, however, I got the sense that he was trying to describe some sort of metaphysical disconnect between the low-order “mechanistic” phenomena and the higher-order “emergent” ones. As if somewhere between the study of an actin monomer and the study of actin-based cell motility, an impenetrable wall frustrates all our theoretical, analytical, and perceptual means of breaching it.
The shallow scientific understanding — i.e. my understanding — is that this is a moot point. Suppose that the properties of actin molecules imply a set of natural “equations” that predict what happens when they polymerize. These equations would take as their arguments the physical properties of each individual actin molecule, and, as no cellular process is truly independent of another, every single other parameter of the cell. The solution to these equations is provided by nature in the very simple fact of cell movement.
Thus, given what we know on the one hand about individual molecules and Newton’s laws, our observations on the other hand of macroscopic events serve as a sort of “proof” of the solubility of nature’s equations. Just because mathematical constructs are incapable of analyzing what has happened in between mechanism and the observe emergence, doesn’t mean that a rational link doesn’t exist. After all, sensitive dependence on initial conditions is just that — DEPENDENCE. If there were reason to believe that natural phenomena should be studied with an appeal to “completely random fluctuations from initial conditions,” or equally to “black magic,” then that’s what it would be called.
That’s why I wanted to say to my professor, well it only seems like we can’t understand cell motility from studying actin monomers — in fact, the futility of our approach stems from the fact that we can’t know EVERYTHING about individual actin molecules, and it is simply more efficient to observe them in the aggregate, in order to learn about them in the aggregate. Our inability to bridge levels of complexity is a practical failure, not a fundamental conceptual one.
Does this mean that in principle, some sort of deterministic link, in the manner of the soundly discredited 19th century scientific worldview, still exists between actin monomers and their network behavior? I understand just enough of 20th century physics to suspect that the “practical failure” I pithily dismiss above is actually something much deeper and crippling, but not enough to finish the connection. Guess I’d better take quantum mechanics. Ugh.
Okay, lemme at it. First of all, the relationship between amount of information know about a system and how predictable it is has been studied pretty well in mathematics, under the guise of entropy. I’ve only looked at it in discrete (dynamical) systems, and not in continuous (differentiable) ones, but at least in dynamical systems there’s an interesting relationship between the entropy of a transformation (i.e. rule describing how the system changes over time) and other important properties (like, does it “mix” the space up? is it “fundamental,” that is, ergodic?) It turns out that the interesting ones, ones with ergodicity/mixing, all have positive entropy, which means that, as we extend our knowledge of the past further and further, the amount of new information about the present continues to grow at a positive rate that does not approach zero (I can send you the paper I wrote on this for my final last semester if you’d like).
What this means, though, is that for all but the silliest, simplest processes, to predict the future with any real accuracy we’d need knowledge of the infinite past of the system, which essentially translates into perfect knowledge of the present state of the system and the rules governing its change over time. This is where the reductionistic program breaks down, because at the lowest levels (which you will ultimately have to go to, if you’re a serious reductionist) knowledge is governed by the Heisenberg uncertainty principle, which basically says we can’t have perfect knowledge of the position and momentum of a particle at the same time.
So there’s always a little bit of uncertainty in the state of the system, and that means that any predictions we make at the reductionistic level are basically moot, because of the positive entropy of, well, everything…is that thermodynamics? I don’t know…
Anyway, I don’t know how this relates to the whole issue of the small reductionistic step that you’re talking about here, although I do think that it shows that the general principle of reductionism is deeply flawed. I also think that the whole question of why, at higher levels of conceptual organization, systems suddenly become well-behaved, and that sensitive dependence on initial conditions can be sort of stepped around if we only look at the right, sufficiently abstract set of “initial conditions.”
hmm, that’s long, I think I’ll post it on mine, too…
oh, and good luck with classes, we start tomorrow!
Okay, I think I get it a little more now…I was trying to say “We can IN PRINCIPLE derive macroscopic behavior from molecular/atomistic understanding, BUT we can’t know enough about molecular/atomistic properties.” As Heisenberg (or Sir Mix-a-lot) might tell us, that is one huge “BUT,” in fact so big that it renders the “IN PRINCIPLE” more or less meaningless. It doesn’t matter that the derivation can hold, since you can’t satisfy the assumptions you need.
[...] 31Jan07 Jue’s got a neat post today about an experience in a bio lecture that got him thinking about emergence again, and what he [...]
Yeah, and that’s what did in reductionistic science! Apparently the 20th century was all about shattering massive intellectual projects: Heisenburg, Gödel, Derrida, errrrr…anyone else?