Re: what relation do mathematical models have with reality?

From: <chales1.domain.name.hidden>
Date: Sat, 23 Jul 2005 18:09:39 +1000

"Hal Finney" writes:
>
> : Paper in white the floor of the room, and rule it off in one-foot
> : squares. Down on one's hands and knees, write in the first square
> : a set of equations conceived as able to govern the physics of the
> : universe. Think more overnight. Next day put a better set of equations
> : into square two. Invite one's most respected colleagues to contribute
> : to other squares. At the end of these labors, one has worked oneself
> : out into the door way. Stand up, look back on all those equations,
> : some perhaps more hopeful than others, raise one's finger commandingly,
> : and give the order `Fly!' Not one of those equations will put on wings,
> : take off, or fly. Yet the universe 'flies'.
>
> My current view is a little different, which is that all of the equations
> "fly". Each one does come to life but each is in its own universe,
> so we can't see the result. But they are all just as real as our own.
> In fact one of the equations might even be our own universe but we can't
> easily tell just by looking at it.
>
> Hal Finney

Hi Hal,
Your 'flying equations' sound a bit like the idealist 'a-priori'... interesting but different topic for another day. :-) Thanks for the wheeler link....

On that note I'm not sure Wheeler's description is the same. In my idea of the calculus all there is is the sheets of paper. There are no symbols (no intrinsic representation). There are intrinsic rules of formation and transformation that relate and associate the bits of paper. If the bits of paper were jigsaw pieces with implicit connective rules then it is more like my idea.

If you try an build a universe as a monism from an enormous quantity of only one thing (a primitive sign - piles of little bits of paper :) ) then you can construct space and the leftovers become the stuff we call matter. Deep down it's all the one thing, however. It's been a fascinating mental exercise for me.

The problem is to let go of all the maths in a symbolic sense. We have this huge and very historically justified tendency to think the linear maths is the 'real stuff' of the natural world. I have been able to think of ways in which that is not the case, but that look 'as if' it was. It doesn't invalidate our maths, it just makes it look like it's not justified to ascribe anything more to the existence of our maths than that of a useful limited description.

The main thing is to get used to the idea of ridding your preconceptions of symbolic 'aboutness'. There is no intrinsically meaningful sign. However an intrinsic event: the expression of the sign (any sign), can literally be a truth in itself. The fact of the utterance of the sign itself is a truth. From that all other truths can be expressed through meaningless signs combining through intrinsic properties (affinities) for other signs.

It's more like a reified mega-dimensional cellular automata, actually. Not a traditional computational one. It took me a long time to be able to let go of my symbolic mathematical tendencies when I needed to.

You can make our universe out of hierarchically structured noise starting from nothing. The 'sign' in the calculus is basically the elemental noise event of the entropy calculus I have played with. Stuff that looks like the rules of quantum mechanics appears well up the hirearchy. Waaaaaay up the hierarchy it looks ontological but with structure all the way down to the elemental signs. The one that makes us is somewhere between 15? and 40? organisational layers deep. Very busy, these Leibniz's !!

Lots of fun! Don't know what to make of it but at least it has enabled me to post to this thread with a little bit of novelty!

cheers

colin
Received on Sat Jul 23 2005 - 04:11:42 PDT