All feedback appreciated - An introduction to Algebraic Physics

[Brian Tenneson]

I will be updating this as time progresses.  All versions including
the current and only version, 00-00-04 can be found here:
http://www.universalsight.org/conference_abstract/

The current and only version is 00-00-04 which can be downloaded
directly in pdf format here:
http://www.universalsight.org/conference_abstract/00-00-04.pdf
The file size is 47 kb.

The document itself is an abstract in an attempt to provide a talk at
the following conference in September:
http://www.mat.unisi.it/~latd2008/

Connections are made between Tegmark's MUH, a plausibility argument is
made for the CRH (if not a proof altogether), MV-algebra (part of
Fuzzy Logic), and l-groups with distinguished order units.  Also, a
structure is proposed to be isomorphic to the universe.
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[Brian Tenneson]

There was a flaw in version 00-00-04.  Version 00-00-05 is now up at
http://www.universalsight.org/conference_abstract/ and version 5 can
be downloaded directly here:
http://www.universalsight.org/conference_abstract/00-00-05.pdf
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[Bruno Marchal]

Le 28-avr.-08, à 21:46, Brian Tenneson wrote :

>
> I will be updating this as time progresses.  All versions including
> the current and only version, 00-00-04 can be found here:
> http://www.universalsight.org/conference_abstract/
>
> The current and only version is 00-00-04 which can be downloaded
> directly in pdf format here:
> http://www.universalsight.org/conference_abstract/00-00-04.pdf
> The file size is 47 kb.



There, you write:

<<Conjecture 1. The completeness of gamma_l will provide either
plausibility
argument for or proof of the computable reality hypothesis (CRH).
Conjecture 1. The completeness of gamma_l will provide either
plausibility
argument for or proof of the computable reality hypothesis (CRH).>>


  I have already presented an argument (an easy consequence of the
Universal Dovetailer Argument, which is less easy probably) showing
that:

-  CRH implies COMP
-  COMP implies the negation of CRH
-  Thus, with or without COMP (and with or without the MUH) the CRH
does not hold.

-  Unless "I" am the whole reality. (which I doubt).


Brian wrote also:


> I was skimming though a book by Roberto Cignoli, Itala D'Ottaviano, and
> Daniele Mundici called Algebraic Foundations of Many-Valued Reasoning.



"What I tell you three times is true"
"What I tell you three times is true"
"What I tell you three times is true"

This is how, if I remember well, Mundici begun a talk I assisted on
Many Values Logic in Brussels years ago. A very interesting talk. I am
not sure how it bears on our topics though. (Mundici was alluding to
Lewis Carroll's Hunting of the Snark" of course).

Reichenbach has been the first logician to try to use MV logic for
solving the conceptual problem raised by Quantum Mechanic, without not
much success (description and critics can be found in the book by Max
Jammer, ref in one my thesis). yet I do agree that Mundici works has
some formal bearing on the possible quantum logic, and I don't want to
discourage you to dig on that issue. Algebraïc physics can be a very
interesting topic per se, but unless you give some reason to use such
approach I'm afraid it can easily be used to hide conceptual problems.

Your abstract is indeed very ... abstract. It uses elaborate
mathematics without providing much motivation, and it put the mind body
problem under the rug. OK, I know it is a tradition (in science) since
more than 1500 years .... Perhaps you take the identity thesis as
granted? In that case you have to consider a *very* strong non-comp
hypothesis. Why not indeed.

Bruno



http://iridia.ulb.ac.be/~marchal/

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[Brian Tenneson]

Thanks, Bruno.  Feedback from you is quite valuable.
I vaguely recall mentioning somewhere online that I am attempting to give a contributed talk at this conference:
http://www.mat.unisi.it/~latd2008/

I mainly need something to get my foot in the door.  Now since April 30th is my deadline, I'd rather simply drop conjecture 1 than investigate it between now and the deadline.

So, if I remove conjecture 1 and all mentions of the CRH....would that help improve this abstract's "acceptability" in your opinion as far as that conference is concerned?

Here is a version with conjecture 1 gone, to be investigated later.
http://www.universalsight.org/conference_abstract/00-00-06.pdf


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[Bruno Marchal]

Le 29-avr.-08, à 13:40, Brian Tenneson a écrit :

> Thanks, Bruno.  Feedback from you is quite valuable.
> I vaguely recall mentioning somewhere online that I am attempting to
> give a contributed talk at this conference:
> http://www.mat.unisi.it/~latd2008/
>
> I mainly need something to get my foot in the door.  Now since April
> 30th is my deadline, I'd rather simply drop conjecture 1 than
> investigate it between now and the deadline.
>
> So, if I remove conjecture 1 and all mentions of the CRH....would that
> help improve this abstract's "acceptability" in your opinion as far as
> that conference is concerned?
>
> Here is a version with conjecture 1 gone, to be investigated later.
> http://www.universalsight.org/conference_abstract/00-00-06.pdf

In my opinion it is far better. (Hope you will see the CRH point one
day). If you would have more time, I would have suggested some attempt
to relate shortly the intuition which makes you relating Tegmark's MUH
and your algebraïcal hypotheses (insisting perhaps on Mundici's work).
The conference being quite open on Algebra and technics/philosophy, you
could raise some interest. In any case it is worth to try. It's also a
good idea to add some references notably on Tegmark and Mundici.

Best wishes,

Bruno


http://iridia.ulb.ac.be/~marchal/


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[Brian Tenneson]

Your feedback is valuable and most appreciated.


I'd like to continue learning about the CRH after this gets sent off.

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[Brian Tenneson]

I believe I found some upgrades.  I was going to write all my ideas down but with a deadline, I just wanted to get the basic kernel down by April 30.


Here is the latest version:
http://www.universalsight.org/conference_abstract/00-01-00.pdf

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[Günther Greindl]

Hi List,

I found this:

S. A. Terwijn, Computability and measure, PhD thesis, University of
Amsterdam, 1998.

Downloadable here:
http://www.logic.at/people/terwijn/publications/thesis.pdf

(I am currently attending his course, he is a very good teacher :-)

Maybe of interest to the OM-measure/White Rabbit question?

It is quite technical and still over my head I must admit, but maybe
Bruno or some others can glean some interesting stuff from this work?

Cheers,
Günther

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[Günther Greindl]

Dear Bruno,

> I have already presented an argument (an easy consequence of the
> Universal Dovetailer Argument, which is less easy probably) showing that:
>
> - CRH implies COMP
> - COMP implies the negation of CRH
> - Thus, with or without COMP (and with or without the MUH) the CRH does
> not hold.



Regarding:

COMP implies the negation of CRH

Is this also in your Sane 2004 paper? (then I missed that point) - if
not, where did you argue this?

Cheers,
Günther

--
Günther Greindl
Department of Philosophy of Science
University of Vienna
guenther.greindl@...
http://www.univie.ac.at/Wissenschaftstheorie/

Blog: http://dao.complexitystudies.org/
Site: http://www.complexitystudies.org

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[Brian Tenneson]

At the very least, I could register and start wiki-ing -my- posts here before they get anywhere near massive in number, right?  OR is it frozen?  I think I'm confused on that point.

I'd like to have a hyperlinked version of the explanation of Bruno's argument against the CRH.  I think the "physical universe" -might- be (or is) computable but I think the "entire" universe, at least in algebraic physics, can -not possibly- be computable except perhaps by a computer of a sort not known in mathematics to me as of yet.  Even with hyperlinks, it would take me a while to digest Bruno's arguments and everyone's counterarguments.  This should be something I should examine in the "algebraic physics" theory.




Well, I've been working on my "algebraic physics" theory some more, not to be confused with prior notions or other notions of algebraic physics.  I really don't know what to call this multi-mathematical-disciplinary approach...

And I've been focusing on dimensions.  I see, from my point of view, that I am creating the paradigm that I live in but the last thing I want to do is trap anyone into someone else's paradigm.  I will try to type up what I have so far about my set of dimensions which seems to have a vector space structure with a natural operator I call the "transition operator," to be broadcast when I am done proving my dimension set is a vector space, if it is.

The set of dimensions is Q* in the theory of algebraic physics with only some of these being "special" in the sense that they are relevant to conjecture 1 of my paper, which is that the multiverse studied in physics is isomorphic to the "universe generated by Q*," with more precision in the type-up posted in version 00-02-00 above.

There are concrete dimensions, the positive integers, the transition dimensions, which end up being more natural if they are the positive integers greater than 1 (including 4 and higher for transition on the first three dimensions--to be compatible with Einstein's paradigm), and other classifications:
The microscopic dimensions are those positive infinitesimal elements of Q*
The macroscopic dimensions are those positive unlimited elements of Q*
The abstract dimensions are those not given in any other scheme, the complement of the union of every other "natural" class of dimension, with respect to Q* (the complement is with respect to Q*).

Now if |D is the set of all subsets of Q*, this is the main carrier for my thought-to-be vector space, the set of all concrete and abstract dimensions.  (I prefer that nonmenclature to something like "real and imaginary.")

The addition of two elements of |D, call them D_1 and D_2, is defined to be the set of all sums of elements of D_1 and D_2.

The set of scalars is Q* and note that Q* is a field.  Scalar multiplication kD, where k is in Q* and D is in |D is defined thusly:
kD := D + k, by which, I mean { d+k : d is in D}.

The zero element of the (proposed) vector space is {0} which is an element of |D.  Denote this with a capital O.  (In my write-up, to be posted later, this is blackboard capital O.)

I hope V := < |D, F, +, ., O > is a vector space.  I am attempting to find it's basis; I think it is simply {0,1}, which would make V a two-dimensional vector space over F.  If that is the case, all the tools of finite dimensional linear algebra would then be at my disposal for analyzing my set of dimensions, with the concrete dimensions being of most interest to physicists.

Ah, so the transition operator is defined so that it maps |D to itself and for all D in |D, ie for all subsets D of Q*,
T(D) := D + 1 := {d + 1 : d is in D}.  This is nothing more than translation along the hyper-rational axis.

In this event, and if D_c is the set of concrete dimensions and D_t is the set of transition dimensions, then
T(D_c) = D_t, which is why I call T the transition operator.




I am observing that I used the word event instead of definition.  But maybe interesting blurt there if I can grasp what I meant by event.  Is defining something an event in the theory of paradigm creation?
  I would think so....

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