Though Scott permits in his review that physical reality and mathematics are isomorphic, he shies away from considering that they are equivalent. Why is that? I submit that it is prejudicial to consider that there is a reality beyond the pure logical pattern of mathematics. Objectively it is a leap to conclude that there is a physical reality, or some spiritual reality, at all. A century or two ago the existence of god was a given, an axiom really, and even now it seems it is mostly the philosophers and scientists who have the mental freedom against instilled faith to be capable of denying the existence of a supreme being. It is science, primarily, that has endowed thinkers with that freedom.

The mathematical universe concept has, similarly, given me the freedom from an instilled faith in reality, and the mental clarity to deny the existence of realty. Why should anything exist beyond logic, i.e. mathematics, and the patterns that are intrinsic to it? What we experience is the richness of such patterns and nothing more, and we ourselves are such patterns, and nothing more. All else I believe is illusory. And it is not I that must prove that reality does not exist; rather it is up to those that believe in reality to prove that it does.

]]>He also shows a “letter” that lists not only his street address, zip code, town, state, and country, but also his planet, Hubble volume, post-inflationary bubble, quantum branch, and mathematical structure.

I am aware that this review is rather old, but I feel the desire to add something here:

From my point of view, the object of investigation of physics is per definition restricted to **our** Hubble volume, **our** post-inflationary bubble, and **our** “mathematical structure”. Speculations about other Hubble volumes, other post-inflationary bubbles, or other “mathematical structures” are per definition metaphysical.

The same could be said regarding alternate histories that might have occurred in other quantum branches–only that this would have to be addressed more to historians than to physicists.

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Tegmark claims in his book that assuming a bigger universe does not violate Occam’s razor since sometimes the whole is (definition-wise) simpler than one of its parts. True, but:

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The fact is that some things cannot be too simple and still satisfy a certain property; for example, since we don’t believe that a single atom possesses consciousness, then we must conclude that below a certain threshold of complexity no device possesses a human-level consciousness.

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Thus, E(x) = “x is a mathematical structure” could be TOO simple (/simplistic) a definition for existence, and so “existence” corresponds to a more complicated condition which means that only a proper subset of the set of mathematical structures actually exist.

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Furthermore, notice that his “simple” definition entails the existence of unboundedly complicated structures, while assuming that only the members of U (mentioned in my previous entry) exist does not.

So why is positing that all those extremely complicated structures actually exist is simpler than assuming that they do not?!

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Therefore, I don’t think there is any purpose, reason or advantage in assuming the existence of anything greater than the set U.

]]>U = {u(a_1,a_2,…a_n) | the a_i range over all allowed values}.

One could ask why not simply posit that a universe exists iff it is describable by an equation in U?” Tegmark replies by asking what is so special about these equations and not other structures?

Well…

A. It seems that he uses a Copernican argument, the problem is that one can use this argument ad infinitum, which implies that one has to stop somewhere.

I think that one should probably stop when assuming the existence of a greater encompassing environment violates Occam’s razor (so adding type I parallel universes might not violate it since we have a theory that suggests them —inflation— and we do not have a simpler theory that does not, and yet consistent with the data).

I believe that all those “self-sampling” or anthropic arguments can be carried out inside U, so there are no logical or scientific imperatives to consider a bigger collection of universes.

B. Also, I think that the claim that “a full mathematical description equals the thing itself” is based on Leibniz’s principle of the identity of the indiscernibles. So, first of all, there are problems with considering this principle as absolutely valid (see entry in the Stanford EOP); also, as acknowledged, “existence” might not be a mathematical property.

But assume it is, and let us consider the predicate

E(x) = “x is a (Tegmark) mathematical structure”, so it is 2nd order (one could say that E(x) is actually meta-mathematical in the Tegmarkian sense… ).

Now, using similar arguments by Weinberg relating to the cosmological constant being non-zero but small, we can ask “what is the likelihood (again, the measure problem!) that E(x) is as Tegmark suggests?” (and not, say, that E(x) = “x contains observers”, which seems more appealing to me). So, if we look at the power set of the set of mathematical structures, the likelihood is low that E(x) corresponds to the empty set, or to the entire set, and it is more likely to be somewhere in between. So here is a way of turning his thinking on its head, since E(x) being the entire set would be “too special”.

Thus, I don’t see any ontological or scientific problem in assuming that U is the only collection that has the property of “existing”; I also think there might be ways to hold the position that only our universe exists (the ‘Copenhagen’ approach) instead that all the other members of U also exist (the ‘MW’ approach).

]]>If we agree with Searle that consciousness is concrete and information is not, Tegmark, who has recently hitched his wagon to Tonnoni, cannot be right. It seems as though consciousness can only be constituted by information that is physically realized. However as soon as you accept consciousness as some form of physically realized information you run into Putnam’s (1967) ‘multiple realizability problem’. Pereboom formulates it as:

“Since mental states can be realized by indefinitely many kinds of neurophysiological states, and perhaps by many kinds of non-neurological states, mental states are not reducible to neurophysiological states.”

Pereboom thinks the problem is serious enough to force us to abandon both type and token identification of mental states with microphysical states.

I believe that one’s position on the physical realization of information depends on one’s position on the ‘thing in itself’. Substance physicalism distinguishes between substance as nothing beyond a co-occurring cluster of relational properties and substance as the categorical base of those relational properties. So one can either view the electron as a cluster of relational dispositions (its effects on other physical systems) or as ‘the thing in itself’ possessing these dispositions. Insisting that ‘properties are the properties of something rather than nothing’ and accepting the existence of such ‘physical but non-relational’ properties underlies much of Russellian Monistic theories because and is a physical candidate for both the categorical base of physical properties and a possible form of intrinsic phenomenality.

Here we can ask whether it is possible for information to be physical in the sense that it exists, but in a non-relational/non-dispositional state. Is it possible for a collection of (Q)bits to be physically realized in such a way that they only exist for each other (like Lewis’ world-mates with purely internal actualization conditions ) and are impossible to access by other bits? And most importantly for our purpose, Can physically realized information shed its relational properties and still exist? I think that these questions are related and that the answer to the last question is yes. That is easy to see by considering not only Bekenstein’s Bound which is independent of physical realization but also Aharonov’s Quantum Cheshire Cat where particles become separated from their properties. (I asked him a few weeks ago whether such particles are similar to the Bekenstein’s ‘naked bits’ and he agreed its possible.) Also in QM physical properties can sometime violate causality as long as information does not. Information seems to be more basic than relational properties. It is also more intrinsic, as Mike Steiner points out, information is Lorenz Invariant while mass is not. You cannot turn a mass in an inertial system in to a black hole nor can you increase its bit number by moving faster. (you will think that your copy is smarter than you and your copy will think that you are smarter than it.) It is more intrinsic than mass.

It seems as though if such naked bits were to exist we could both preserve some of Tegmark’s intuition and at the same time solve the multiple realizability problem.

Of course the question is whether the brain can instantiate physics strange enough to generate such naked bits. The fact that the brain is ‘a bit conformal’ may help.

Ill leave you with a question: Whats the smallest number of (Q)bits that can refer to itself?

All the best, Uzi. ]]>