Friday, 20 September 2013

Random Will

I want to approach the idea of “free will” from a slightly different direction.

If the universe is entirely deterministic, there is no free will because our actions are merely the consequence of our interactions with our environment.  Presented again with precisely the same environment, our brains would go through exactly the same processes and we would make the same decisions, take the same actions and think the same thoughts.

If the universe is entirely random (and therefore entirely indeterminate), then there is no free will either.  There would be little, if any, causal relationship between action and reaction in a random universe.  Presented again with precisely the same environment, our brains would likely react in a vastly different way.  However, integral to the concept of free will is the idea that there is some degree of constancy in our thoughts and behaviour.

Could a partly random, partly deterministic universe lead to a sense of free will?

Consider a variation of an old style pin-board game as illustrated below.

In a world of perfection, with the balls lined up perfectly above the outputs and the pins aligned perfectly, we would see a ball released through an input slot fall perfectly into the corresponding output slot.

This would be a simple deterministic system, from which the end state could be confidently predicted by the rather simple initial conditions.

However, this presumes that there are no additional factors involved – no unequal friction conferred by the input slot, no spin on the ball, no imperfections on the board – that would result in the balls touching any of the pins.

If we allow these sorts of imperfections, we would have a much more rich and complex sort of deterministic system – one in which the end state can be confidently predicted, so long as one took into account all factors.  Perhaps we were to release a ball through the Input One slot, knowing that there is a slight imperfection in the weight of the ball, that the original orientation of the ball and the resultant friction will cause a spin that would cause the ball to hit the left most pin with the right force to cause it to bounce into the gap between the second and third pins.  We might calculate that the ball will bounce between these two pins in such a way as to pass relatively cleanly into Output Two.

So long as the full range of initial conditions remains the same, we will get the same result every time.

But what happens if we don’t assume unchanging initial conditions?  Continually dropping balls onto pins will lead to them bending to some extent and the surface of the balls will be affected by repeated interaction with the pins.  The board will wear and friction will act on the input slot.

Even if we allow for these effects, we still have a deterministic system – we can at least conceptually work out the effect of the interactions between balls and pins, pins and balls, balls and slots and balls and boards, so on and so forth.  Once we have factored these in we can still calculate, from our initial conditions, the result from each drop of the ball.  The calculation has not become impossible – it has just become more complex.

We could add yet another layer of complexity by incorporating some logic into the system.  See the illustration below.

Now all the pins are attached to rods which can be moved by the control boxes on the right hand side.  The movement will be in response to indications from sensors on each pin (with the signals conveniently sent to the control boxes via wiring within the rods).  Basically, when hit, each pin will send a message which the control box will interpret as “Pin X got hit” and the control box will active a response based on command statement like “When Pin X gets hit, perform Action Y”.

Again, if we know the full range of these command statements along with the full range of initial conditions and the effects of each component on all other components (ie deformation of the ball and pins, wear and so on), we can calculate the result from each drop of the ball.  Our system remains deterministic, complex but nevertheless deterministic.

We could add more levels of complexity having more inputs, more outputs, more pins, more levels, more control boxes, more complex command statements and so on.  But we still don’t get away from a deterministic system.

However, if we zoomed in and looked at all the components at subatomic level, we would start encountering the Heisenberg uncertainty principle.  Occasionally, a ball will pass so close to a pin that sometimes it will hit and sometimes it won’t – even if the path is precisely the same – because of the configuration of electrons in the outer layer of the pin.

Or does it?

If you’ve agreed that the system as described is entirely deterministic, then you’ve been thinking classically (or you had in mind what can be referred to as a "manifest image").  To you, the ball was solid like one indivisible particle.  The pins were solid like indivisible, strangely shaped particles.  But we know that’s not the case.  Not even atoms are indivisible particles.  We won’t, however, go beyond the standard subatomic particles (electrons, protons and neutrons) because it starts getting really strange.

The system as illustrated seems rather simple but there is another implicit assumption – that the ball is sized somewhere between a pea and a grapefruit.  I doubt that anyone had thought that it could be a Buckyball (but bonus points to you if you did) or representative of a molecule of water.  At these scales, the movement and location of individual sub-atomic particles could have considerable impact on the outcomes.  Putting Heisenberg aside for a moment, we could still conceptually collect all the data and still work out the outcome, if we could just have all the starting conditions (and a sufficiently good understand of how all the subcomponents interact).

Now, everything we’ve discussed explicitly so far has been inside the system.  But in the real world things outside the system can effect what goes on inside the system.  We’ve totally ignored it up until now, but the force pulling the balls down does not originate in the system.  We’ve assumed gravity.  We’ve also assumed that the effect of gravity is constant within the system and that there are no other effects at play (such as barometric pressure, the coriolis effect or uneven thermal heating effects on the system).

If we no longer make these assumptions then, to understand the system, we need to include data about the outside world in our calculations.

Now, let’s say our illustration is a vast simplification of the real system, which has many thousands of pins, hundreds of possible input slots and hundreds of possible output slots.  There are also hundreds of control boxes.  Add in a history keeping system and say that the control boxes are pre-programmed with the intent of guiding a ball that enters via a specific input slot exits via the “correct” output slot.

Now if we watch the board when a ball is entered, the control boxes will do their thing, responding to each cry of “ouch, I got hit” by various pins by moving the rods around and gently shepherding the ball towards the correct slot.

Imagine that a few minutes ago, a high-energy particle burst out of the sun and hurtled along a path towards this pin-ball system.  When it enters the system, it interacts with a single pin which, despite not being hit by a ball, yells “ouch, I got hit”.

The control boxes react as they must (remember they are pre-programmed) to that cry and the rods are rearranged accordingly.

Now, unless we included the sun (and every other potential source of high-energy particles) into our calculations, the path of the ball through the system is no longer entirely predictable.  The system will continue to act as it always did, deterministically, responding to pins being hit (or at least saying that they were hit) with the balls and the pins reacting in an entirely deterministic way – but from time to time, the system will appear to have made a decision, to have an output which is not strictly related to the (apparent) input, to have expressed “free will”.

Now, replace the pin-ball system with something far less simple to model, the human brain, which consists of billions of neurons interacting with each other.

Anyone for godless free will?

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