Justifying the Theory of Everything
Jason
ensemble, the first comes from information theory which says the
information content of everything is zero (or close to zero). The
other is mathematicalism/arithmatical realism which suggests
mathematical truth exists independandly of everything else and is the
basis for everything.
My question to the everything list is: which explaination do you
prefer and why? Are these two accounts compatible, incompatible, or
complimentary? Additionally, if you subscribe to or know of other
justifications I would be interesting in hearing it.
Thanks,
Jason
Torgny Tholerus
exist. (Game of Life is one possibility...) But this theory doesn't
say anything about our universe. So the information content is zero.
--
Torgny Tholerus
Russell Standish
I take the view that mathematics is all about data
compression. Certain mathematical structures are chosen as the laws of
physics because they have a utility in accurately reprsenting reality
in as minimal a fashion as possible. Note that the most accurate
description of the real worl is just the raw data, and the most
minimal mathematical model has poor predictive ability. As in
everything, useful physical models are a tradeoff.
So if all possible "descriptions" exist (ie all possible forms of raw
data), with overall zero information complexity, then all forms of
mathematical compression will be useful in one context or another,
subject to any anthropic constraints (how can something be useful, if
nobody finds it useful?)
Cheers
--
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A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 hpc...@hpcoders.com.au
Australia http://www.hpcoders.com.au
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George Levy
I have not contributed to the list for a while but your question interests me.
I do not accept as primitive an independent mathematicalism/arithmetical realism. I think that math and logic are co-emergent with the consciousness of the observer. In addition physics is also co-emergent with the observer. So in a sense the "I" or first person is primitive-emergent. "I", math and physics are all anthropically linked.
The information of the plenitude being zero is the simplest case that requires the least explanation. Any other information content would have to be justified, and that would force us an endless causal chain. Now let me qualify that the "perceived" information of the plenitude is definitely not zero because it is contingent on the observer. Here the causal chain can begin at the observer.
The simplest theory of everyting is that everything exists. But this is hardly satisfying. A useful theory of everything should bring in the observer as a boundary condition. The theory, more precisely, which physical model is "true," may be indeterminate. This indeterminacy would be analogous to quantum indeterminacy applied to the cosmic scale. This would correspond to the "I" being equally "at home" in multiple different worlds or equivalently that multiple worlds would be in a superposition with respect to the "I."
George
David Nyman
GL: I do not accept as primitive an independent mathematicalism/arithmetical realism. I think that math and logic are co-emergent with the consciousness of the observer. In addition physics is also co-emergent with the observer. So in a sense the "I" or first person is primitive-emergent. "I", math and physics are all anthropically linked.
DN: Hi George. I agree with the substance of this, and similar intuitions lie behind my recent posts. Perhaps to avoid seemingly inevitable terminological confusions over the "I" and the first person, I might put it that a 0-personal self is primitive-emergent, and 1-persons or observers emerge from self-relative localisations of this.
GL: The simplest theory of everyting is that everything exists. But this is hardly satisfying. A useful theory of everything should bring in the observer as a boundary condition.
DN: Yes, perhaps one could say that the 'self' is the 'everything' that exists, but that the self is not finite. Finitude manifests as the spontaneous symmetry-breaking of the self, or self-relativisation, which is then equivalent to self-actualisation in terms of the co-emergence of observers and physics. Math and logic in turn would emerge as aspects of the observer description of co-emergence, not the physical description.
GL: This would correspond to the "I" being equally "at home" in multiple different worlds or equivalently that multiple worlds would be in a superposition with respect to the "I."
DN: Yes, this is a good way to phrase it. Relative co-emergence of 1-persons and physical structures would then equate to observer-dependent decoherence from the superposition of multiple worlds with respect to the self. Any arbitrarily finite degree of actualisation from the 'plenitude' - or which model is 'true' - may indeed be indeterminate. To paraphrase somebody or other, perhaps even a TOE need be infinite enough to save the appearances, but not more so. So as an aspect of such a theory, the plenitude allows us to extract any arbitrary limit of possible observed relationships from 'infinity' by postulating, as you say, the observer (or any possible observer) as the boundary condition.
David
Wei Dai
These two justifications are about equally attractive to me. I also have a
couple of other justifications.
Aesthetic: If anything doesn't exist, it's non-existence would constitute an
element of arbitrariness, given that anything exists at all. We shouldn't
accept arbitrariness unless there's a good reason for it, and there doesn't
seem to be one.
Pragmatic: We have to accept that there is at least a non-zero probability
that all possible universes exist. Unless there is reason to believe that
the probability is so small as to be negligible (and I don't see such a
reason), we will need to consider the everything ensemble when making
predictions and decisions. Given that, why not believe that the probability
is one? The probabilities for all other possible collections of universes
can be "folded" into the measure over the everything ensemble in such a way
that all of the predictions and decisions come out the same way as before.
Brent Meeker
> Jason wrote:
>> I have seen two main justifications on this list for the everything
>> ensemble, the first comes from information theory which says the
>> information content of everything is zero (or close to zero). The
>> other is mathematicalism/arithmatical realism which suggests
>> mathematical truth exists independandly of everything else and is the
>> basis for everything.
>>
>> My question to the everything list is: which explaination do you
>> prefer and why? Are these two accounts compatible, incompatible, or
>> complimentary? Additionally, if you subscribe to or know of other
>> justifications I would be interesting in hearing it.
>
> These two justifications are about equally attractive to me. I also have a
> couple of other justifications.
>
> Aesthetic: If anything doesn't exist, it's non-existence would constitute an
> element of arbitrariness, given that anything exists at all. We shouldn't
> accept arbitrariness unless there's a good reason for it, and there doesn't
> seem to be one.
It would be a peculiar kind of arbitrariness that had a good reason for it. :-)
But what constitutes a "good reason"? Does a good reason have to show that the result is inevitable? or merely probable?
>
> Pragmatic: We have to accept that there is at least a non-zero probability
> that all possible universes exist.
This seems to be a tautology: P>0 <=> "possible". The question is what is possible and in what sense of "possible". Certainly many things are logically possible: flying pigs, Santa Claus, and victory in Iraq. But if we assign a non-zero probability to one of theses we are just quantifying the uncertainty of our knowledge.
Brent Meeker
Russell Standish
> >> I have seen two main justifications on this list for the everything
> >> ensemble, the first comes from information theory which says the
> >> information content of everything is zero (or close to zero). The
> >> other is mathematicalism/arithmatical realism which suggests
> >> mathematical truth exists independandly of everything else and is the
> >> basis for everything.
> >>
> >> My question to the everything list is: which explaination do you
> >> prefer and why? Are these two accounts compatible, incompatible, or
> >> complimentary? Additionally, if you subscribe to or know of other
> >> justifications I would be interesting in hearing it.
Another justification is rather indirect. Following the arguments in
Theory of Nothing (also mostly available in "Why Occams Razor" and "On
the Importance of the Observer in Science"), a number of really curly
philosophical problems melt away in a blaze of understanding. I refer
here to
1) Occams Razor
2) The problem of Induction
3) Why anything bothers to exist
4) The Hilbert space structure of QM
Of course its not all plain sailing - the problem of the Occam
catastrophe means that the Anthropic Principle is rather mysterious,
rather than trivially obvious as it is in naive realist theories.
However solving 4 unsolvable mysteries in exchange for having another
one is not a bad deal, and is a pretty good justification for taking
these theories seriously.