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From: GODWIN, William <WGODWIN.domain.name.hidden>

Date: Thu, 21 Sep 2000 12:05:38 +0100

*> --
*

*> From: jmb184.domain.name.hidden[SMTP:jmb184.domain.name.hidden.net]
*

*>
*

* >On Wed, 20 Sep 2000 00:08:15 GMT, davidsmyth
*

* ><davidsmyth6650.domain.name.hidden> wrote:
*

* >>Could there be a universe where the rules concerning number
*

theory

* >>would be different than in this universe?
*

* >Conventional wisdom of course says that logic and hence number
*

theory are independent of physical reality. Suppose you asked in 1822,

whether the rules concerning plane geometry would be different in other

universes. Then the answer would have been that a system of axioms and hence

geometry are independent of physical reality. However in 1823 Bolyai and

Lobachevsky independently realized that entirely self-consistent

"non-Euclidean geometries" could be created in which the parallel postulate

did not hold. Today, the discussion would be quite different. For

geometry, the cosmology of universes with a range of curvatures are now

considered reasonable.

* >In his book, The Structure and Interpretation of Quantum Mechanics,
*

Hughes mentions works which assert that the rules of logic may be empirical.

I find your question stimulating, in that an implication of logic being

empirical is the charming speculation as to whether there could be universes

which operate with different versions of the distributive law.

* >References:
*

*> quant- ph/0001074 An Epistemological Derivation of Quantum Logic. John Foy
*

*>
*

*> math. HO/9911150 Machines, Logic and Quantum Physics. David Deutsch and
*

*> Artur Ekert
*

* >John
*

----------------------------

This seems to be based on a confusion. The Euclidean laws exist in some

universe regardless of any different models of Space-Time used by physicists

in that universe. Just because alternative useful geometries exist (eg

projective finite ones) does not mean that Euclid disappears.

Incidentally, I gather that it is possible for instance to mathematically

rephrase General Relativity in a flat space if that is your preference.

Curvature is in the mind of the modeller.

Maybe what we need to ask is whether there are universes in which physicists

*cannot* see any use for the Euclidean axioms. They are certainly not

complex, so not easy to filter out that way. The same goes for the

distributive law.

BTW, sorry if I am making all sorts of unwarranted assumptions, such as

existence of physicists, minds,...

William Godwin

wgodwin.domain.name.hidden

Received on Thu Sep 21 2000 - 04:15:52 PDT

Date: Thu, 21 Sep 2000 12:05:38 +0100

theory

theory are independent of physical reality. Suppose you asked in 1822,

whether the rules concerning plane geometry would be different in other

universes. Then the answer would have been that a system of axioms and hence

geometry are independent of physical reality. However in 1823 Bolyai and

Lobachevsky independently realized that entirely self-consistent

"non-Euclidean geometries" could be created in which the parallel postulate

did not hold. Today, the discussion would be quite different. For

geometry, the cosmology of universes with a range of curvatures are now

considered reasonable.

Hughes mentions works which assert that the rules of logic may be empirical.

I find your question stimulating, in that an implication of logic being

empirical is the charming speculation as to whether there could be universes

which operate with different versions of the distributive law.

----------------------------

This seems to be based on a confusion. The Euclidean laws exist in some

universe regardless of any different models of Space-Time used by physicists

in that universe. Just because alternative useful geometries exist (eg

projective finite ones) does not mean that Euclid disappears.

Incidentally, I gather that it is possible for instance to mathematically

rephrase General Relativity in a flat space if that is your preference.

Curvature is in the mind of the modeller.

Maybe what we need to ask is whether there are universes in which physicists

*cannot* see any use for the Euclidean axioms. They are certainly not

complex, so not easy to filter out that way. The same goes for the

distributive law.

BTW, sorry if I am making all sorts of unwarranted assumptions, such as

existence of physicists, minds,...

William Godwin

wgodwin.domain.name.hidden

Received on Thu Sep 21 2000 - 04:15:52 PDT

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