Sam's blog

Day 005 - Quantum, chance and free will

Submitted by Sam on 25 May, 2011 - 22:59

Extrapolating the principles of a game of chess to produce the super-abundance of possibilities necessary to fuel an illusion of free will works neatly in a fully determined universe, where nothing whatsoever is left to chance. This rule-described model produces chance-like properties through the chaotic (yet ultimately determinable) interaction of a vast number of variables, a condition which is critically distinct from the pure chance which would exist in a non-determined universe. By definition, a non-determined universe must contain truly random elements which decouple cause from certain (i.e. infallibly predictable) effect.

The last point is worth some attention, so here it is again: a system which cannot be determined completely by rules must have components which are utterly, utterly random. If it didn't, then in principle it would be predictable, and therefore fully-determinable. “Rules” in such a system are affected on a fundamental level by chance, and all such “rules” can therefore only be considered probabilistic.

Our current understanding of quantum physics requires chance. For instance, as far as we know there is absolutely no way to predict how a quantum particle will behave when it strikes a surface – it seems to us in 2011 to be a genuinely random event as to whether it will be transmitted or reflected. Chance is crucial.

The corollary to this is bad news for free-will. If our mentation is predicated on by fundamentally chance events, then the choices we make must have a fundamentally random element to them. Choices tempered by chance, however infinitesimally, are not true choices at all.

Day 004 - Free will in a deterministic system

Submitted by Sam on 25 May, 2011 - 00:04

As hinted at earlier, an essential ingredient of the human condition – free will – violently resists deterministic theories of our own universe, which throws a bit of a dampener on the whole thing. How can Stephen Wolfram, a well-regarded physicist, software developer, mathematician, author and businessman even begin to consider the existence of a rule for the universe when such a rule would utterly preclude true free will, which is presumably as integral to his own humanity as it is to ours? After all, a rule for the universe would render Wolfram himself as functionally no different from one of his own cellular automata, and would simultaneously reduce all of human endeavour to nothing more than a procedural inevitability.

So how might a man with free will be explained by a deterministic universe? In a nutshell, it can't be done. Not if we're talking about one particular flavour of free will we might find in the OED, which is as follows:

The power of an individual to make free choices, not determined by divine predestination, the laws of physical causality, fate, etc. Also: the doctrine that human beings possess this power and are hence able to direct and bear responsibility for their own actions. Freq. opposed to determinism n. 2, predestination n. 1b.1

A deterministic universe can't satisfy this OED definition, but it is able to specify programmatic thinking machines who happen to be constructed in such a way that they offer themselves a healthily compelling illusion of free-will. Ooh-er!

These thinking machines would experience the sensation of free will as a result of the practically unpredictable emergent interactions of a finite set of rules. This is the butterfly effect once again, and this is chess on a very, very, very big level. Here's the chess analogy: chess has very rigid rules, but yet produces very unpredictable games – so unpredictable that there are probably more board positions than there are atoms in the universe. With many orders of magnitude more rules than chess, the 'brain' of a thinking machine in a deterministic universe would have a near-infinite number of possible configurations, which are to all intents and purposes unpredictable. If the brain's configuration (read: thoughts) cannot be predicted in any practical sense, then the experience of free will can emerge.

Day 003 - Complexity from simplicity

Submitted by Sam on 23 May, 2011 - 21:24

The height of excitement in a deterministic universe is the truth that hiding somewhere in the space of all possible equations is an expression that describes everything – a rule-set that perfectly recreates the whole of reality, from beginning to end.

An equation that produces general relativity, the miracle of life, and the works of Pelham Grenville Wodehouse sounds as though it must be impenetrably complex. Counter-intuitively, this is not necessarily the case. Very simple programs (so simple that they can be completely described by a graphical illustration) can be made to generate extremely complex patterns from just a few basic rules. Sometimes the results that these well-defined rules produce are so complex that they can be used as random number generators, as is the case with Stephen Wolfram's Rule 30.

Rule 30 is an arresting example of how rapidly complexity can arise even in a fully determined system. Cellular automata that exhibit the complexity of Rule 30 give a practical insight into chaos theory, visually illustrating how the slightest change in initial conditions can produce highly unpredictable changes in a system's behaviour. This is the idea behind the butterfly effect, which shows how great differences can arise from the smallest changes in past states of a system. The butterfly effect explains neatly why the weather forecast is such a compelling work of fiction.

In a deterministic universe, it is possible to short-circuit chaos theory altogether and find out with utter certainty whether it will rain or not tomorrow evening1 . Stephen Wolfram is obviously very partial to this idea, and believes that there might just be a chance that we ourselves are lucky enough to live in a deterministic universe. The very possibility of holding a rule for the universe in our hands, as he puts it, is enough motivation to commit serious research and resources into finding it. Watch him say so himself in the TED talk below.

  • 1. Some poetic license is operational here. There is the small matter of computational irreducibility that might get in the way of predictions about tomorrow's weather, as a full simulation of the entire universe might be rather slow to run.

Day 002 - A universe determined by rules

Submitted by Sam on 22 May, 2011 - 16:24

Let's take a hypothetical jump and imagine that our universe is indeed described by rules. This may hardly feel like a jump at all as we're very chummy with the standard model of Newtonian physics and the deterministic systems it gives us. We're very happy that everything that happens has a cause and an effect, and we're very familiar with various chains of causation, whether or not we understand the rules that govern them.

In our rule-described universe, absolutely everything is deterministic. Physicists (who spend their lives studying causes and effects) are particularly happy here. Quantum physicists are over the metaphorical moon as they can rest assured that the aspects of quantum mechanics that seem inexplicably random on May 22nd 2011 are in fact governed precisely by a nice set of rules, and perhaps one day they will find them. This is all very well for the physicists, but anyone who happened to glance at the OED's definition of 'determinism' in this rule-described universe might feel somewhat less cheerful. Here's what the OED says about determinism:

  1. The philosophical doctrine that human action is not free but necessarily determined by motives, which are regarded as external forces acting upon the will.
  2. The doctrine that everything that happens is determined by a necessary chain of causation. 1

In this universe, hard determinism is the plat du jour and both of these doctrines are facts of life. The second definition validates the first through the following logic: human action is determined by thoughts in the brain, the brain is made from atoms, atoms behave deterministically, therefore all human thought and action are fully determined. This is rather rotten news for fans of free-will and human society as a whole (ethics and morality are sticky topics when everything is pre-determined), but a deterministic universe might just make possible the following:

  • True artificial intelligence. Here's one devastatingly inefficient but plausible method: reverse-engineer the rules that animate atoms in a brain, and re-apply these rules to an atomic-level replica of a brain. 2
  • Prediction of the future. The more rules that are decoded, the greater the ability to predict future events. Whilst laplace's demon might be too much to hope for, versions which generalize and work with macro-scale events rather than individual particles could definitely find a home in a rule-described universe.
  • A computational theory of everything. Find the one rule to describe them all.

Day 001 - First principles

Submitted by Sam on 21 May, 2011 - 15:13

We've got some pretty good physical rules that describe how and why apples fall from trees, and we're having a stab at finding some more that might just describe the other bits of the universe. There is a general agreement that all of the order and pattern we see strewn about the place is the product of some rather marvellous physical laws, however myriad, subtle and hopelessly opaque they may seem at the moment. Science is the business of ferreting out and describing these rules, with the ultimate aim of finding a theory for everything, unified or otherwise.

But are all domains wholly describable through rules? Are there perhaps states, processes and interactions in our universe that operate outside of any ultimately authoritative rule-set? There are certainly phenomena that are hugely resistant to both explanation and observation, and they will probably remain so for a very long time. A quick springboard for the rest of this blog presents itself: do truly anomalous phenomena exist, utterly beyond the reach of all laws? Is everything in our universe describable by rules?

Here are two possible answers:

  1. No; some phenomena exist in our universe with behaviour that cannot be modelled by universal rules.
  2. Yes; our universe is built from elementary particles that obey fundamental universal rules.

Option one is a universe that contains irreducible complexity and is ultimately beyond full comprehension. Option two is much more fun, and gives rise to some very interesting hypothetical consequences, which I'll be teasing out over the next few days.

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