Although he openly admits that he is not the first to propose the ideas, the way they are presented is quite interesting. The proposal is based on two hypotheses. The first of these is close to my heart, while the other one, is, hmmm, courageous. What are the two hypotheses?
External Reality Hypothesis (ERH):
There exists an external physical reality completely independent of us humans.
Mathematical Universe Hypothesis (MUH):
Our external physical reality is a mathematical structure.
ERH seems to be quite widely accepted, although in the light of Quantum Mechanics results we must remember that the external physical reality might be very different from our intuitions. It might be nonlocal, unreal, quantum - pick the name you prefer. The key point, which I hold dear, is independent of us humans.
Now, the aim of the papers is to argue for the necessity of MUH. There are great reasons for this: it would solve the mystery of why is the Universe, in so many of its aspects, so well describable by mathematics.
It could also change our perspective on the Theory of Everything and science:
If the mathematical universe hypothesis is true, then it is great news for science, allowing the possibility that an elegant unification of physics and mathematics will one day allow us to understand reality more deeply than most dreamed possible. Indeed, I think the mathematical cosmos with its multiverse is the best theory of everything that we could hope for, because it would mean that no aspect of reality is off-limits from our scientific quest to uncover regularities and make quantitative predictions.
However, it is even more difficult to break the bounds of our limited imagination and intuitions and perceive our universe as some mathematical structure, which is by definition an abstract, immutable entity existing outside of space and time. What is `mathematical structure' anyway? Set of abstract objects and rules that connect them? How complex should that structure be to describe the seemingly infinite variety of our observations, the probable complexity of the Universe? Most people, even physicists and mathematicians, would not venture into his abstract space at all.
But - why not? Our human perspective is rather limited and inadequate. Even for `almost normal' phenomena. It suggests that Sun circles the Earth when we observe it moving across the sky. It does not help us in understanding how a light bulb works, or a hard disk in our computer. Why should our intuitions be more usable when we talk about the question of ultimate reality? Tegmark even uses our inadequacy as a `proof' of the Mathematical Universe hypothesis (although I detect some measure of tongue-in-cheek there):
Ultimately, why should we believe the mathematical universe hypothesis? Perhaps the most compelling objection is that it feels counter-intuitive and disturbing. I personally dismiss this as a failure to appreciate Darwinian evolution. Evolution endowed us with intuition only for those aspects of physics that had survival value for our distant ancestors, such as the parabolic trajectories of flying rocks. Darwin’s theory thus makes the testable prediction that whenever we look beyond the human scale, our evolved intuition should break down.
We have repeatedly tested this prediction, and the results overwhelmingly support it: our intuition breaks down at high speeds, where time slows down; on small scales, where particles can be in two places at once; and at high temperatures, where colliding particles change identity. To me, an electron colliding with a positron and turning into a Z-boson feels about as intuitive as two colliding cars turning into a cruise ship. The point is that if we dismiss seemingly weird theories out of hand, we risk dismissing the correct theory of everything, whatever it may turn out to be.
It is like saying `it must be true because I do not understand it'. Well, perhaps it is worthwhile to remember our limitations and to be sure that we do not dismiss some possible solutions because of these limitations.
But the papers are certainly worth reading.