Monday, 17 September 2012

On Determinism

After my last blog on free will, I said I’d write one on Determinism – which may be quite prudent, as I think Determinism is a word that people mostly misuse.  Determinism, in the sense implied by some kind of universal destiny, means information regarding the laws of physics suffices to determine the entirety of the universe from start to finish. Given the laws the universe has - it seems its entire story from start to finish followed (and will continue to follow) a path that would be entirely predictable and mappable to a series of deterministic computations if we had complete knowledge of it.  This is Steven Wolfram's conjecture. What Stephen Wolfram is basically saying, is that if given enough execution time the majority of relatively small algorithms can compute everything that can be computed.

If Wolfram is correct in his assumption (and I believe he is) then this means that any given (finite) physical pattern or structure can be described by a physical theory - and by 'theory' we mean it is defined as an algorithm or function.  Admittedly Wolfram’s ideas are conjectural at present, but if they are right it means that there aren't any finite objects out there that cannot be described using a theory. With enough computation time a theory has the scope to reach a point at which it will describe any stated physical system.

In theory, determinism is an even trickier subject than free will, because to most people ‘determinism’ means something like ‘The way things will be is a result of how things are and the work of natural laws’. In other words, if we know exactly how things are at the present moment and the laws that govern how the universe works, then we can derive how things will be at some future time.  This kind of definition is something you would do well to forget about when you’re considering free will and determinism, because you’re left with a determinism contingent on human knowledge.  That is, you can know X+1 only if X contrives to fit a mental pattern.  I’m going to show you how I think this topic is best dealt with, but before I do, it is worth bringing up an important distinction regarding how our minds work. 

The way we describe the universe is through the construction of terms and ideas based on our physical perceptions of the world (the macroscopic world).  What we don't have is an adequate way to describe the universe in terms that would give a proper definition to determinism.  We don't even have a proper method of describing the quantum world - even then we resort to using terms implicitly related to the macroscopic world (particles, waves, position, locality, state, spin, collision, energy, etc). 

Imagine the problem in trying to define a universe in terms other than our spatio-temporal terms used.  We find all we have is a reality that’s apprehended from the first person perspective of the physical world.  That's why I think determinism is opaque – words limit us to terms related to the physical.  The best way I've found to circumvent this is to describe the universe in a completely different way.  Every physical system can in principle be described in terms of computation - so what we have to do is imagine the entire universe in terms of pattern, not physical structure.  This is no problem, because it requires a hypothetical description of the universe in terms of pattern storage* (a very large pattern - but small compared with the whole system of mathematics).  So what we can do is define the pattern of the entire universe in binary 1s and 0s.  No doubt this is a far too complex task for any human – it would require execution times that beggar belief - so the easiest thing to do is imagine you are a being who can traverse the entire pattern from outside of the universe (let's call the entire pattern P).  Now determinism becomes clearer, because with the required execution time (it's not literally time, of course) to search the pattern we can observe its determinism. 

Absolute and Relative Determinism
I’ve said that determinism is hard to define.  One of the reasons is that we only get to grips with what absolute determinism is (as per my above definition of an overall determinism) if we can conceive of relative determinism too.  This, as you’ll see, is the key to understanding the universe in terms of an overall determinism – and it is an understanding that is desperately needed, because many believe that modern knowledge of quantum randomness, the Aspect experiments or any of Bell's theorems has led to the conclusion that determinism has been given its redundancy notice, because of the random agitations.  But as we’ll see, this is a misunderstanding.  I will also show why both freedom and determinism are not single qualities that can be put up against each other – they are, in fact, both scaled in a spectrum. 

On first showing, whatever the mind is, it seems to bring about a mechanism that belies its real deterministic nature.   The first way to correct the mistakes is to frame the word ‘determinism’ in its proper context – as a spectrum, not as a fixed quality.  To do this we have to identity the fact that determinism can be thought of in terms of the relative and the absolute.  At the human level indeterminism-determinism is a spectrum related to knowledge.  Here’s a simple way to look at it; if I drop an apple the algorithm that calculates the motion is deterministic because we know what will happen - the apple will head towards the centre of the earth.  If I attempt to track a particle in fluid subjected to Brownian motion then the algorithm that calculates the motion is indeterministic because it cannot predict the pattern it will take.  That is what I mean by relative determinism.  If you know a pattern it can be said to be relatively deterministic, if you do not it can be said to be relatively indeterministic.  This, of course, changes over time (or it can do).  If one day we work out the random patterns in Brownian motion (I doubt we will) then we could call it relatively deterministic because its patterns could then be mapped to a deterministic algorithm.

That was relative determinism.  Absolute determinism is different.  For quick shorthand, the truth about absolute determinism can be summarised thus: “The universe will do what the universe will do” – meaning, there is an inevitability about nature’s laws that shows it will run its course.  Everything within the universe, every thought, every dream, every stone rolling down the hill, every burst of wind, every formation of a planet, every nucleosythesis, every galaxy, every cosmic expansion is all nature running its course, and that course is entirely deterministic.  There is no way to affect change on nature’s plan - she is our sister, and everything we do to believe we have changed the course of nature was really only part of the deterministic inevitability.  In other words, nature has a script already written – and your conceptions of randomness, unpredictability, surprise, and cause and effect alterations are not in any way an alteration of that script – they are simply pages of that script being revealed to us.  That is what I mean by absolute determinism.  Nature’s story is being turned page by page – and this story is underpinned by forces beyond our control.  To say we could affect nature’s overall determinism is about as silly as saying that a drop of water in a waterfall could stop the power of gravity. 

The difference between our normal conceptions of nature and this conception of determinism is that now, instead of viewing those things in terms of the spatio-temporal, we are now considering the script in terms of a pattern of 1s and 0s.  We think we are uncertain about determinism because we deal with nature in terms of its smaller constituent parts, not as a whole.  With mathematics and computation nature tells us something very relevant here; providing that the search space is linked together in a nexus, with indefinite amounts of execution time, we can map anything into a descriptive algorithm or function, giving us a pattern.  We could do this with nature if we had access to it from outside, and could observe the entire pattern.  

But here’s what the objectors are missing; it is because we have incomplete knowledge from inside that we have radically unpredictable events, and it is because we have radically unpredictable events that the indeterminism and determinism spectrum comes in from the inside.  If we had complete knowledge of the universe then its absolute deterministic path would be deterministic to us in the second (the relative) sense too, as well as in the absolute sense described above.  If we define indeterminism as a physical system that cannot be described with an algorithm or function, then there are no (finite) systems that are indeterminate – because all systems can potentially be calculated from a basic equation if we have access to the search space and allow the necessary execution time.  This is where the practical and the theoretical cross swords.  In terms of being a large mathematical object, the universe is a closed system, and as such there is no theoretical reason why anything in the universe cannot be mapped into a descriptive algorithm or function. 

But once we get into the realms of practicability, things change, for we know that systems within nature are too intractable for us human beings to map.  As well as Brownian motion, a good example is the randomness of quantum mechanics – it is almost certain that the randomness of quantum mechanics will always be indeterministic to us.  In wave mechanics, quantum physics suggests that because the wave packet of a particular particle has non-zero amplitude the position of that particle is uncertain to us.  Increasing the number of sine waves gives a ‘compression’ effect which enables us to detect the position of a particle, because the momentum of the particle requires wave number probability.  But increasing waves inhibits the ability to measure momentum.  A wave with a precise position has an indefinite momentum, and a wave with a definite wavelength has no precise position, so for humans uncertainty looms large because we cannot know both the precise position and precise momentum of a particle.

Couple that with the fact that wave packets (like clouds) don’t have single velocities and positions and we soon know that we are observers of limited cognitive and experimental resource, where a kernel of uncertainty must loom large.  Quantum mechanics doesn’t undermine determinism, it merely offers formal tokens that explain why in a universe of overall determinism we are stuck somewhere in the spectrum of relative indeterminism and relative determinism.  That is why quantum randomness, the Aspect experiments or any of Bell's theorems do not impinge on whether the universe is deterministic. 

Some objectors ask; How can we be sure the universe is deterministic?  Here’s what the objectors are not understanding. We know the universe is absolutely deterministic because what we theorise about determinism at an absolute level is based on our practical perceptions of determinism and indeterminism at a relative level.  We generate and map deterministic paths all the time, just at a much smaller scale, and with observations of uniformity at the classical level.  Once we think of nature in terms of mathematical patterns, all we need to do is inductively stretch out the conceptual logic trail to the furthest contingency barrier and we would eventually arrive at a final point of determinism - just as in smaller terms we can generate more simplistic forms in a relatively short computation time.  You see, to reiterate, in the determinism/indeterminism spectrum, the description is subjective because it is a model that recognises that some systems are less humanly manageable than others.  That is why we are always on the pursuit of more knowledge – it is this indicator that tells us we haven’t yet arrived at a full understanding of nature*. 

In summary, unfortunately the problem with this debate has been that many people are quick to change the definition of determinism to apply overly simplistic theories of cause and effect or as a rival theory to the perennially fuzzily defined ‘free will’.  The indeterminism-determinism spectrum comes into play because with our limited capacity some systems are “more deterministic” than others - and that is why ‘fully indeterministic’ and ‘fully deterministic’ are expressions of extreme ends of a vast cosmological and mathematical spectrum, and why, with complete knowledge of the universe it would be, by definition, mappable to a complete deterministic algorithm.

* Footnote: Make sure you're clear of one thing though - this concept of pattern storage is only one way (of many) to describe nature - but it's the best way to describe it to show it is deterministic.  We needed to find this way because nature cannot be described deterministically in those macroscopic terms.  With the above terms, it can.