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From: Niclas Thisell <niclas.domain.name.hidden>

Date: Wed, 29 Dec 1999 13:15:34 +0100

Here's a half-cooked thought for you to chew on.

One of the initial gripes I had with the turing approach to the

plenitude (vs e.g. the grand ensemble) was that I figured it would favor

a finite resolution lattice and finite resolution calculations. And I

find it very hard to believe that we will ever actually detect an

'absolute' lattice. And it's even harder to believe that we will ever

notice that nature uses a finite number of decimals. This issue has been

discussed before and some of you found that a turing machine won't

properly handle true 'reals'.

The answer is, of course, that the number of computations in the

Schmidhuber plenitude using an insanely high number of decimals is a lot

higher than the ones that use a specific measurable but life-permitting

precision. The measure of a computation using 10^10^10 decimals is

roughly the same as one using 10^10^10^10 decimals. And the computations

themselves will most likely remain virtually identical throughout the

history of the universe and the observer-moments will be identical. The

same goes for grid spacing (and grid extent, for that matter). Therefore

observer-moments in a universe using precision indistinguishable from

'reals' and a lattice indistinguishable from a continuum seem to be

favoured.

Now, in Quantum Field Theory we have this annoying renormalization

problem. One could perhaps state that the equations become

trivial/divergent in the limit of a 4-dimensional continuous spacetime.

There are various tricks to get around this, like doing the complete

calculation in _almost_ 4 dimensions and then look at the result as you

push the dimensionality towards 4. Another trick is to do the

calculations using a finite lattice. This has lead people to believe

that the universe is 'really' using a finite resolution lattice. And it

must have an absolute resolution, mustn't it? (Not really). The

Planck-distance and Planck-time have been suggested.

I guess the Schmidhuber plenitude would predict that any experiment

trying to detect this lattice would fail. Even assuming we could argue

that there must be a finite resolution lattice, all one can conclude

after an experiment is that the resolution apparently must be higher

than was previously thought. And there need not be an absolute coupling

constant etc. - it simply depends on the lattice resolution of the

computation.

This claim is, however, unfortunately fairly vacuous and merely a matter

of retrofitting known theories. Also, the reasoning assumed that there

are no deeper reasons for the necessity of an absolute grid, which there

may be I guess. But still :-).

(Obviously I realise that many of you probably already have come to the

same conclusion. It is a lot more obvious in regard to grid extent. But

I don't recall having seen it on this list so I thought I'd mention it.)

/Niclas

Received on Wed Dec 29 1999 - 04:09:56 PST

Date: Wed, 29 Dec 1999 13:15:34 +0100

Here's a half-cooked thought for you to chew on.

One of the initial gripes I had with the turing approach to the

plenitude (vs e.g. the grand ensemble) was that I figured it would favor

a finite resolution lattice and finite resolution calculations. And I

find it very hard to believe that we will ever actually detect an

'absolute' lattice. And it's even harder to believe that we will ever

notice that nature uses a finite number of decimals. This issue has been

discussed before and some of you found that a turing machine won't

properly handle true 'reals'.

The answer is, of course, that the number of computations in the

Schmidhuber plenitude using an insanely high number of decimals is a lot

higher than the ones that use a specific measurable but life-permitting

precision. The measure of a computation using 10^10^10 decimals is

roughly the same as one using 10^10^10^10 decimals. And the computations

themselves will most likely remain virtually identical throughout the

history of the universe and the observer-moments will be identical. The

same goes for grid spacing (and grid extent, for that matter). Therefore

observer-moments in a universe using precision indistinguishable from

'reals' and a lattice indistinguishable from a continuum seem to be

favoured.

Now, in Quantum Field Theory we have this annoying renormalization

problem. One could perhaps state that the equations become

trivial/divergent in the limit of a 4-dimensional continuous spacetime.

There are various tricks to get around this, like doing the complete

calculation in _almost_ 4 dimensions and then look at the result as you

push the dimensionality towards 4. Another trick is to do the

calculations using a finite lattice. This has lead people to believe

that the universe is 'really' using a finite resolution lattice. And it

must have an absolute resolution, mustn't it? (Not really). The

Planck-distance and Planck-time have been suggested.

I guess the Schmidhuber plenitude would predict that any experiment

trying to detect this lattice would fail. Even assuming we could argue

that there must be a finite resolution lattice, all one can conclude

after an experiment is that the resolution apparently must be higher

than was previously thought. And there need not be an absolute coupling

constant etc. - it simply depends on the lattice resolution of the

computation.

This claim is, however, unfortunately fairly vacuous and merely a matter

of retrofitting known theories. Also, the reasoning assumed that there

are no deeper reasons for the necessity of an absolute grid, which there

may be I guess. But still :-).

(Obviously I realise that many of you probably already have come to the

same conclusion. It is a lot more obvious in regard to grid extent. But

I don't recall having seen it on this list so I thought I'd mention it.)

/Niclas

Received on Wed Dec 29 1999 - 04:09:56 PST

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