Escaping Flatland - when determinism falls, it takes reductionism with it


For the reductionist, reality is flat. It may seem to comprise things in some kind of hierarchy of levels – atoms, molecules, cells, organs, organisms, populations, societies, economies, nations, worlds – but actually everything that happens at all those levels really derives from the interactions at the bottom. If you could calculate the outcome of all the low-level interactions in any system, you could predict its behaviour perfectly and there would be nothing left to explain. It’s turtles all the way down.

Reductionism is related to determinism, though not in a straightforward way. There are different types of determinism, which are intertwined with reductionism to varying degrees.

The reductive version of determinism claims that everything derives from the lowest level AND those interactions are completely deterministic with no randomness. There are things that seem random, to us, but that is only a statement about our ignorance, not about the events themselves. The randomness in this scenario is epistemological (relating to our knowledge or lack of it), not ontological (a real thing in the world, that we can observe, but that does not depend on us for its existence).

That’s the clockwork universe – the one where Laplace’s Demon (an omniscient being) could unerringly predict the future of the entire universe from a fully detailed snapshot of the state of all the particles in it at any given instant. It’s pretty boring, that kind of universe.

There is also an ostensibly non-reductive flavour of determinism, which simply affirms that every event has some antecedent physical cause(s). Nothing “just happens”. Under this view, however, causes don’t have to be located solely in the interactions of all the particles or limited to the actions of basic physical forces (which also act at the macroscopic scale, determining the orbits of the planets, for example). The causality, or some of it at least, could inhere in the organisation of a system and the constraints that it places on the interactions of its constituents. In this kind of scheme, there is room for a why as well as a how.

That’s the argument, at least, though it’s a little incoherent, in my view. If there is no real randomness in the system (or in the universe as a whole), then I don’t see how you can escape from pure reductionism. In a deterministic system, whatever its current organisation (or “initial conditions” at time t) you solve Newton’s equations or the Schrodinger equation or compute the wave function or whatever physicists do (which is in fact what the system is doing) and that gives the next state of the system. There’s no why involved. It doesn’t matter what any of the states mean or why they are that way – in fact, there can never be a why because the functionality of the system’s behaviour can never have any influence on anything. I would go even further and say you can never get a system that does things under strict determinism. (Things would happen in it or to it or near it, but you wouldn’t identify the system itself as the cause of any of those things).

But what if determinism is false? Let’s see what happens to reductionism when you introduce some randomness, some indeterminacy in the system. Of course, this is exactly what quantum theory does, at least under one interpretation, though there is deep disagreement among physicists as to whether the randomness observed at quantum levels is epistemological or ontological. But let’s say it’s the latter – that randomness really exists in the universe – that some things, at very small scales at least, do “just happen”.

What effect does that have on things at big scales – the scales of rocks and cats and babies, and other things we care about? Some people argue – rather casually, in my view – that randomness at quantum levels will not have any effect at the level of classical physics, because all that noise will be somehow absorbed or averaged out in the system and will not percolate up to higher levels. This means the behaviour of the system at classical levels can still be considered to be deterministic.  

Is that true? Do quantum effects stay there at the quantum level? I can think of lots of instances where they wouldn’t – like Schrödinger’s famous cat, for example, whose fate was to be determined by the random decay of a radioactive atom. And I would guess that the randomness of quantum phenomena has some important implications for real-world quantum computing. 

But just speaking philosophically, what’s strange about this assertion – as I said, often thrown out very casually – is that it betrays the very idea of reductionism. It relies on the idea that reality is not in fact flat. It claims explicitly that things can be happening at the lowest level of the system that do not percolate up to higher levels. Heresy! How can a good reductionist believe that? Does reductionism only apply at classical levels? Does it stop being true at some scale? Why?

If the properties at the classical level derive from interactions at the quantum level (and we know they do because they can be derived from quantum theory), then why would the subset of such interactions that happen to have arisen randomly not also manifest at higher levels? How would the system know which ones were random and which were determined?

I know that’s a silly way to put it, but it highlights something crucial – the idea that something important is happening at the level of the system. You might say that the reason those quantum fluctuations don’t manifest at the level of the whole system is because they average out. They are random, after all, and if there are many of them and they are independent, then their collective effects should cancel each other out. But that relies on a very non-reductionist mechanism: coarse-graining.

For that averaging out to happen, it means that the low-level details of every particle in a system are not all-important – what is important is the average of all their states. That describes an inherently statistical mechanism. It is, of course, the basis of the laws of thermodynamics and explains the statistical basis of macroscopic properties, like temperature. But its use here implies something deeper. It’s not just a convenient mechanism that we can use – it implies that that’s what the system is doing, from one level to the next.

Once you admit that, you’ve left Flatland. You’re allowing, first, that levels of reality exist. And second, that what happens at one level is only a coarse-grained, statistical reflection of what is happening at the level below.

In my view, that’s almost but not quite right. Any hierarchical system is averaging, or integrating over, or in some way coarse-graining the low-level details, but not just the random ones (how could it be?) – it’s coarse-graining ALL of them. And not just from the lowest, quantum level, to the next one up. This happens at EVERY level. It may be turtles all the way down, but it’s not turtles all the way up.

The macroscopic state as a whole does depend on some particular microstate, of course, but there may be a set of such microstates that corresponds to the same macrostate. And a different set of microstates that corresponds to a different macrostate. If the evolution of the system depends on those coarse-grained macrostates (rather than on the precise details at the lower level), then this raises something truly interesting – the idea that information can have causal power in a hierarchical system, and, more generally, in the universe.

The low level details alone are not sufficient to predict the next state of the system. Because of random events, many next states are possible. What determines the next state (in the types of complex, hierarchical systems we’re interested in) is what macrostate the particular microstate corresponds to. The system does not just evolve from its current state by solving classical or quantum equations over all its constituent particles. It evolves based on whether the current arrangement of those particles corresponds to macrostate A or macrostate B.

Some criteria embodied in the structure of the system itself drive a different response to these two macrostates. Simple versions could involve a threshold effect, such as a thermostat triggering a heater if the temperature drops below its set point, or a neuron firing an action potential if the voltage across its membrane is high enough. That kind of control is inherently informational. In philosophical terms, it relies on counterfactuals being ontologically real – that is, the current state can only carry causally effective information if in fact it was actually possible that it could have been different.

That little bit of indeterminacy is thus key – otherwise it doesn’t matter what the microstate corresponds to as the system is simply going to follow a deterministic trajectory. But I’ve just been talking about those random events being coarse-grained, along with all the non-random events, so how could they lead to different macrostates? The answer is they’re averaged but not always averaged out. Sometimes those random events will make a crucial difference, especially for a system poised at the boundary between two macrostates. In fact, such a scenario actually amplifies small random fluctuations, by causing a qualitative change in macrostate.

In complex, dynamical systems that are far from equilibrium, some small differences due to random fluctuations may thus indeed percolate up to the macroscopic level, creating multiple trajectories along which the system could evolve. This brings into existence something necessary (but not by itself sufficient) for things like agency and free will: possibilities.

What this means is that causation does not reside simply at the lowest levels and the basic laws of physics, nor is it completely instantaneous. The system will not evolve along a single pre-determined line, nor will its evolution simply follow a random path in a tree of possibilities. Instead, in some types of systems – like living organisms – how the system evolves will depend on what those various macrostates mean. What do they correspond to or reflect in the environment, what consequences are they linked to in terms of action, what feedback does the organism get on the outcomes of those actions, and how does that feedback alter the configuration of the system to set criteria for processing that information in the future?

By building up, not out, creating a functional hierarchy of levels within their own structure, and incorporating meaning in feedback loops that extend through action and consequence into the environment and over time, evolution has created organisms that use the wiggle room provided by stochasticity to exert “top-down” causal power to do things for reasons. The organism itself can choose among those branching possibilities. (More on that here and much more to come).

To come back to where we started, while they are often presented as independent, I argue that if strict determinism falls, it takes reductionism down with it. Turns out a little bit of randomness is the key to escaping Flatland.




Further reading:

Mitchell KJ. Does Neuroscience Leave Room for Free Will?. Trends Neurosci. 2018;41(9):573-576. doi:10.1016/j.tins.2018.05.008 


Erik P. Hoel, Larissa Albantakis, Giulio Tononi. Quantifying causal emergence.

Krakauer D, Bertschinger N, Olbrich E, Flack JC, Ay N. The information theory of individuality. Theory Biosci. 2020;139(2):209-223. doi:10.1007/s12064-020-00313-7

Noble R, Noble D. Harnessing stochasticity: How do organisms make choices?. Chaos. 2018;28(10):106309. doi:10.1063/1.5039668
 

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