Any vaguely mathematical publications that don't use TeX set off my crank alert[0], so I did some quick research on the author: he is an associate professor of computer science at Northeastern University, currently on sabbatical.[1] So it is unlikely for this to be crank-work.
Emanuele Viola is relatively famous in theoretical computer science, so he's definitely not a crank.
As far as TeX goes, Wordpress has a long way to go in terms of offering good native support for any TeX variant, so it's understandable that one might try to avoid it in that context.
I'm using LaTeX for Wordpress (https://wordpress.org/plugins/latex/) and it seems to do the job. However I agree that it's pain in a to find proper plugin and set it up and even more so if you ever want to change to some other plugin. For a platform that is a major writing instrument, it's a pity to be in this state.
Source: I've been using Wordpress to blog about math for over three years and have had a small amount of (indirect) contact with the Wordpress devs. Apparently they are considering alternatives to their current setup which renders tex formulas to images.
Lots of theories of everything these days. However, IMHO they all fail to address one fundamental point. And that is the issue of experiental consciousness, or, in other words, the fact that we experience that we are part of the universe.
Why is this fundamental to any theory of physics? One could argue that it can be addressed as something which is outside the universe, like an external observer watching in. But the important point is: this cannot be true, for I, and a lot of other people, are discussing experiential consciousness: it "loops" back on physics, so to speak. It interacts with it.
So, to me, it would seem that any "mechanic" theory of physics just can't be true, or rather, it can't be complete.
The only ways out of this, that I can think of, would be:
1. Experiential consciousness to be only an illusion. But then the question is: why is this illusion necessary? Why would physics plug the idea into my memory of consciousness? (possible answer: because in the worlds in which physics does not do this, I would not be conscious, but this is a circular argument). And thus this would go against Occam's razor.
2. There is choice is the universe (the universe is tree-like or DAG-like, and an observer could take a preferred route). Not really a satisfying explanation either, imho.
I might be in the minority here, but I think saying "any theory of physics should explain consciousness" is exactly like saying "any theory of physics should explain love" (or replace love with patriotism, friendship, capitalism, any other human concept). I don't see why consciousness is special: in my opinion it is an abstraction several levels removed from fundamental physics. In other words, to a neutrino flying through you, you are only barely distinguishable from empty space, and your consciousness (and love of music, appreciation of art, etc) means nothing.
Consciousness is more likely to be an emergent property than a fundamental component of a theory of everything. It is a property of systems of neurons; physical theories operate at a much lower level.
I don't agree with your claim that a theory of consciousness is fundamental to any theory of physics. In mathematics we have to deal with the possibility that the theorems we're trying to prove are "independent" of the system of proofs we're working in (such statements are known to exist and are neither provable nor disprovable, for example, the existence of certain numbers). As a consequence, any physicist working in a mathematical framework must consider the possibility that a theory of consciousness is independent of any theory of physics consistent with what we observe. In other words, it may be the case that physics, just like mathematics, cannot be both complete and consistent.
That premise is definitely true. It is a result of Gödel's Incompleteness Theorems. 'Physics' certainly satisfies the constraint: 'of sufficient complexity to encode the natural numbers'.
I wonder how you come to that conclusion, because physics is not proven to be of "infinite complexity" (loose statement).
Some things that we are used to from mathematics might not be true in physics. Take for example the fact that in mathematics the real numbers are uncountable. Now in reality (physics), the whole set of real numbers may not exist. It is only an abstract concept from mathematics. And while it may be possible to reproduce any real number in physics as some quantity, you are reproducing them as you go, making the "real" (physical) real numbers countable.
Pretty much any system of logic worth looking at (including any which the sciences may be based on and the one running inside each human brain) is going to at least be as complex as this set of axioms.
Also, you really should read the JR Lucas material-- it explains this. And, I'd suggest Nagel & Newman's _Godel's Proof_ for a great introductory explanation of the Incompleteness Theorems.
We don't know that the physical world has infinite precision. In particular, time doesn't even seem to be continuous as far as we can tell (cf. Planck constant). And we think there's a finite amount of mass in the universe, so how could we encode arbitrarily large natural numbers (as is required to model Peano arithmetic)?
We don't have to encode arbitrarily large natural numbers. Rather we have to encode the rules that allow us to construct them (which is quite simple actually). And, I think 'digital physics' is more compatible with Incompleteness implications than the alternatives; not less.
> are discussing experiential consciousness: it "loops" back on physics, so to speak. It interacts with it.
I think discussing it is independent of whether it exists. For instance, you could imagine a society of p-zombies that behaves exactly like ours, discussing the fact that they experience existence, without actually experiencing it (or you could program some computers to say the same thing).
As a side note, is "experiential consciousness" an established phrase, or did you come up with it? I really like that term. It seems the neuroscientists have commandeered the term "consciousness" to refer to only neurobiological consciousness, so I like the "experiential" qualifier you've added.
I thought of the "zombies" argument too. But I don't find it satisfying, because why would such zombies exist? It would go against Occam's razor. (Occam's razor does not offer a logical proof, but still has proven useful as a guidance).
No, indeed. I came up with the "experiential" qualifier, because the term "consciousness" is highly overloaded indeed, and I do not know the generally accepted phrase.
Well, Occam's razor is very subjective, dependent on what each person finds the simplest explanation to be.
Some people deny experiential consciousness exists at all (how they deny this, I'm not sure, because to me it is the one thing I am most certain exists), so to them the p-zombie argument would be the simplest.
[0] http://www.scottaaronson.com/blog/?p=304 [1] http://www.ccs.neu.edu/home/viola/