Vitalism, Computation, and Mechanism

This continues the line of thinking developed yesterday in Vitalism and Mechanism: Bennett and Bryant.

Let us start with an unassuming passage from Jane Bennett’s Vibrant Matter. This is near the beginning of Chapter 5: Neither Vitalism nor Mechanism (p. 63):

Nature was not, for Bergson and Dreisch, a machine, and matter was not in principle calculable: something always escaped quantification, prediction and control. They named that something élan vital (Bergson) and entelechy (Driesch). Their efforts to remain scientific while acknowledging some incalculability to things is for me exemplary.

I want to look at the notion of calculation and distinguish between analytic predictability and numerical simulation, for they are very different forms of calculation and the latter was, as far as I know, unknown to Bergson, Driesch, and their contemporaries.

Classical Systems

Let us consider a physical system of a type whose laws are well-known in the sense that they are expressed in appropriate equations. What we want to do is to predict the future state of this system. The idea is that we know the current state of the system and want to use the laws to predict its state a some future time.

If the system is analytically predictable, as classical systems are, we can do so directly. We describe its current state in the appropriate form and then we simply solve an equation or equations to determine the positions and velocities of the components at the desired future date. Imagine a ball moving along a flat surface. It’s moving in a straight line at a constant rate of 10 miles per hour. It’s a certain point on, say, 10 PM July 23, 2012, and is moving directly East. Where will it be at 11:33 PM that same day? We simply multiply the speed, 10 mph, by the elapsed time, 1.55 hours, and learn that it will be 15.5 miles further East, wherever that is.

Lots of systems are like that, though the calculations may be considerably more complex. The point is that we can determine the future state through what is basically one calculation.

Deterministic Chaos

But so-called chaotic systems are not like that. These systems are completely deterministic in the sense that “their future behavior is fully determined by their initial conditions, with no random elements involved.” This means that their future state IS NOT analytically predictable. This is where we get the so-called butterfly effect and this is where we see self-organizing systems, such as the chemical clocks that Levi Bryant referenced. We can’t simply a future time into the equations and come up with the future state in one computational step.

Rather, we have to resort to numerical simulation. We start with the state of the system at some known point in time and then evolve it one time-step at a time (t). That is to say, we perform a calculation to determine its state at the next moment (t+1), and then perform the calculation again for the next moment (t+2), and so forth until we’ve calculated the state at the desired t+N. This sort of calculation was all but impossible before the invention of digital computers.

Where does this leave us with respect to the Bennett passage with which we began? Since nowhere that chapter does she distinguish these two kinds of computation, it’s hard to say. But Bergson and Dreisch would only have known the first type, analytically predictable. When they talked of calculation and of mechanism, that’s what they were talking about. They needed élan vital and entelechy, respectively, to get beyond the limitations of that kind of calculation and mechanism.

If they had known of deterministic chaos, would they have invoked those further principles? We cannot say. But Bennett does know of chaos (p. 91) and she feels the need for something more. As far as I know at this point (I’ve not read the book thoroughly) she does not explicitly make the distinction I have made, so I cannot tell what she would think in view of it. Bryant, as far as I can tell, seems to think deterministic chaos and associated notions of self-organization are sufficient.

And Beyond . . .

And perhaps they are. But the point certainly has not been demonstrated, just provocatively argued. It does seem to me, however, that Bennett IS NOT arguing for a vitalism that is outside of matter, outside of the world, some OTHER FORCE intervening in the material realm. If deterministic chaos, with its all but endless calculations and machines, prove inadequate to understand life and mind, then Bennett will have been proved right in insisting on something more.

I for one am not going to take bets on that future. I’m not going to bet on what the outcome will be. Nor am I going to bet on when we’ll know.

I note, however, that the world in which we live is not one big chaotic system. It consists of many interacting systems, some more or less classical, some chaotic. We have worlds within worlds. Our sciences have not yet begun to deal with that.