Friday, 1 March 2013

Chaos 2

What broad conclusions do we draw from chaos theory I wonder? It seems to me that the discovery of such enormous complexity arising from simple iterative processes must tell us something about how we describe the real world.

There are all manner of threads to follow, but where do they lead? Is it anywhere significant and how much credence do we give to the experts?

It’s hard to say. As with much modern science, a huge amount of work is shrouded in its own vastness and complexity. Who benefits from the scope and complexity of arcane research isn’t always clear, but there are enough examples to suggest it may often be the experts.

Strongly mathematical experiments are limited in number and range of applicability. Huge areas of science are not strongly mathematical, if at all. Yet somehow we have been fed a notion that they should be at some fundamental level we can’t quite define, but it generates a vast amount of literature and discussion.

 Some scientists have claimed and still do claim that the universe is mathematical, a notion impossible to prove by experiment which strictly speaking makes it unscientific.

Even worse, it seems incoherent. If our contact with reality is mediated by symbols, then beyond the symbols there is a logical void. No symbols, no logic. Identifying reality with the symbols seems both anthropocentric and incoherent to me.  

Standing back, I tend to wonder if chaos theory may be another hint that the universe is not mathematical even if bits of it are well described by mathematical symbolism. Maybe that should be no surprise because mathematics is probably best seen as a kind of language - a symbolism which may or may not be a useful way to describe some aspects of reality. 

If the universe is not wholly mathematical, it may not be wholly scientific either. That would imply that we need non-scientific language to describe it more fully, a conclusion not at all unfamiliar to those of a religious or artistic persuasion.

In the end, I think chaos theory begs an important question. An assumption seems to be implied in the word theory – an implication that we have resolved something merely by naming it. As if we have cleared a path to new discoveries, albeit a difficult path.

Maybe it isn’t so. Maybe chaos theory marks a boundary across which we cannot carry the exact sciences without some genius of a philosophical bent to show us how to adapt our symbolism. Or maybe that putative genius will show us why it can’t be done. Maybe we already know but don’t like the implications.


Sackerson said...

I think Kurt Gödel showed that mathematics cannot fully describe reality as any mathematical system capable of generating the series of natural numbers is logically incomplete.

Also, even without introducing the possibility of randomness, we cannot describe an initial state of reality with sufficient precision to make subsequent events fully determinable.

I think.

James Higham said...

I'm not so sure unprovable means unscientific. There are many things there is a high probability of without definitive final proof.

A K Haart said...

Sackers - even if we leave Gödel out of it, I think Laplace's demon is blown away by chaos theory, even for systems much smaller than the whole universe.

As you say, there is no way to know initial conditions with sufficient accuracy. It may well be that the required mathematical accuracy is physically meaningless such as lengths less than the Planck length.

James - there are, and in these cases personal judgement comes into it, but many seem to prefer consensus.

Sackerson said...

Is Planck length the same as two short Plancks?

A K Haart said...

Sackers - or maybe it was how he referred to his children.