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From: Eddie Edmondson <ed.domain.name.hidden>

Date: Mon, 16 Nov 1998 19:37:46 -0000

Hi Mat

I haven't checked out the archive yet either. Wei - I'm not sure I follow

the instructions, but I'll give it a try.

Mat wrote on 14 November 1998 21:49

*>
*

*>I haven't had time to retrieve the archives, so I hope you don't mind
*

*>putting my two cents in here . . .
*

*>
*

*>On Sat, 14 Nov 1998, Eddie Edmondson wrote:
*

*>
*

*>> snip
*

*>>
*

*>> 1. Mathematics is a continuum, putting it into discretely labelled packages
*

*>> may hinder thought.
*

*>
*

*>I'm not sure what this means . . . certainly our mathematical models of
*

*>the universe represent it as continuous, but I don't know how mathematics
*

*>itself can be a continuum . . . maybe you can fill me in . . .
*

I'm just worrying about the semantics: Max's paper bounds each branch of mathematics by its name. The names imply a hierarchy, and the subsequent inference is that there is some equivalent hierarchy of realities. My use of continuum only means there is a smooth transition from the simplest formal systems to the highest planes of mathematical thought. He even asks the question: Which mathematical structure is isomorphic to our Universe? I just have trouble with the discreteness of the packaging.

*>
*

*> >
*

*>> 2. I believe the total math continuum exists independently of any
*

universe

*>
*

*>Are you are suggesting that mathematical theorems are necessarily existent
*

*>abstracty entities, like some people take propositions and states of
*

*>affairs to be? Or is this something else?
*

Yes. Axioms are existent and therefore so is the entire (infinite) set of theorems, whether proven or not. A line of proof require sentience, and I'm glad we agree anthropicism is a facile cop-out.... Propositions, I think, are not existent naturally: I'm not sure what you mean by states of affairs.

*>
*

*>Also, what's a "universe" on your usage? Is it a spatiotemporally unified
*

*>concrete set of existents? Is it a possible world in some abstract
*

*>representationalist sense?
*

*>
*

Yes to the first, no to the second, but you have made me rethink this. My original thought was that there's a line somewhere which can take you from a dimensionless set of axioms to our 3d+t universe - and to other spatiotemporal theorems or universes. I think I'll stick with it: a universe in my book has to have dimension(s). But that is not a complete definition of universe.

*>> 3. Assuming the total math is consistent (it seems to be so far), then it
*

*>> can never be complete (Godel): there is an infinity of theorems to be
*

*>> discovered.
*

*>>
*

*>There are undoubtedly an infinite number of theorems to be discovered, but
*

*>this isn't a consequence of Godel's incompleteness proof as I understand
*

*>it. Godel's proof merely tells us that for every logical system, some
*

*>statements that are strue in that system will necessarily be unprovable in
*

*>that system. So is you are taking mathematics to be such a system, there
*

*>will be within this sytem unprovable, but true theorems.
*

I thought it was: you cannot have a complete and consistent system, but I guess I made a bad deduction there. And I was just thinking the other day I'd better re-read Hofstadter - it's been ten years, and I'm no mathematician.

*>
*

*>> 4. We should regard theorems as the cause of physical laws, not just the
*

*>> explanations for them.
*

*>
*

*>Cause in what sense? How does one set of abstract entities "cause"
*

*>another set of abstract entities?
*

I agree. I don't mean cause-and-effect. Cause is not really the right word. I'm really trying to say our viewpoint should change a bit. As a very poor physics student of the 60s (there were always better things to do, it seemed), I used to think maths was the tool of the physicist, and a boring evil at that. I now see physics only as a resultant by-product.

*>>
*

*>> 5. It follows from 3 and 4 that there exist mathematical causes for the
*

*>> creation of an infinity of universes and all the physical laws pertinent
*

to

*>> each universe: you can start with a set of axioms and arrive at a set of
*

*>> dimensions, a set of physics and a set of physical phenomena. And in any
*

*>> universe, if a theorem can have a valid physical representation, then the
*

*>> representation will be realised.
*

*>>
*

*>I don't see how this follows. Not unless you are assuming that
*

*>mathematical theorems can somehow be the hylarchic cause of the universe
*

*> (or all universes).
*

Yes. Although I'm ignorant of "hylarchy"!

*>The last statement here strikes me as a very
*

*>questionable maxim. Why assume that all (mathematically consistent?)
*

*>possibilities will be actualized?
*

Um. You're right. If this Universe is finite in space and time then the infinity of actualizable theorems can never be manifest, I guess. That was wishful thinking!

*>On the normal causal model, concrete
*

*>existents must be appealed to in a causal explanation of concrete
*

*>existents. Obviously this won't work in a causal explanation of the
*

*>entire universe (or set of universes). But that, in itself, doesn't
*

*>justify appeal to such an anomalous form of causation.
*

*>
*

Then we shall re-think the model, or our definitions. Does a virtual pair have concrete existence? Is quantum math the "cause" of the particles? I'd like to think so. Perhaps the concept of cause is too hard. Perhaps it's enough to say, something "is", therefore something else "is", or "may be". The only reality in the nothingness or meta-void is mathematics: it may not be concrete, but there's nothing else to "cause " things.

Eddie E

Received on Mon Nov 16 1998 - 12:29:03 PST

Date: Mon, 16 Nov 1998 19:37:46 -0000

Hi Mat

I haven't checked out the archive yet either. Wei - I'm not sure I follow

the instructions, but I'll give it a try.

Mat wrote on 14 November 1998 21:49

I'm just worrying about the semantics: Max's paper bounds each branch of mathematics by its name. The names imply a hierarchy, and the subsequent inference is that there is some equivalent hierarchy of realities. My use of continuum only means there is a smooth transition from the simplest formal systems to the highest planes of mathematical thought. He even asks the question: Which mathematical structure is isomorphic to our Universe? I just have trouble with the discreteness of the packaging.

universe

Yes. Axioms are existent and therefore so is the entire (infinite) set of theorems, whether proven or not. A line of proof require sentience, and I'm glad we agree anthropicism is a facile cop-out.... Propositions, I think, are not existent naturally: I'm not sure what you mean by states of affairs.

Yes to the first, no to the second, but you have made me rethink this. My original thought was that there's a line somewhere which can take you from a dimensionless set of axioms to our 3d+t universe - and to other spatiotemporal theorems or universes. I think I'll stick with it: a universe in my book has to have dimension(s). But that is not a complete definition of universe.

I thought it was: you cannot have a complete and consistent system, but I guess I made a bad deduction there. And I was just thinking the other day I'd better re-read Hofstadter - it's been ten years, and I'm no mathematician.

I agree. I don't mean cause-and-effect. Cause is not really the right word. I'm really trying to say our viewpoint should change a bit. As a very poor physics student of the 60s (there were always better things to do, it seemed), I used to think maths was the tool of the physicist, and a boring evil at that. I now see physics only as a resultant by-product.

to

Yes. Although I'm ignorant of "hylarchy"!

Um. You're right. If this Universe is finite in space and time then the infinity of actualizable theorems can never be manifest, I guess. That was wishful thinking!

Then we shall re-think the model, or our definitions. Does a virtual pair have concrete existence? Is quantum math the "cause" of the particles? I'd like to think so. Perhaps the concept of cause is too hard. Perhaps it's enough to say, something "is", therefore something else "is", or "may be". The only reality in the nothingness or meta-void is mathematics: it may not be concrete, but there's nothing else to "cause " things.

Eddie E

Received on Mon Nov 16 1998 - 12:29:03 PST

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