For several weeks I've been reading some of Max Tegmark's "Our Mathematical Universe" each morning. It's been a mind-bending journey, one which I'm about to complete -- just 26 pages left.
Tegmark argues that rather than mathematics just being able to describe the universe, mathematics actually is the universe. Along with everything else in existence, which includes four levels of the multiverse.
I'm enjoying the book. To me, Tegmark makes a lot of sense.
I've always wondered, Where are the laws of nature? Meaning, physicists can precisely model many of these laws via mathematical equations. But why should the universe be so orderly, so mathematical, so open to understanding by human minds capable of comprehending mathematics?
Some people argue that math is a human invention.
Well, if it is, how is it that this invention can be used by Einstein to reveal the mysteries of space and time with such precision? Or by Newton to come up with the laws that govern the motion of planets and everything else on a certain scale of reality?
I want to wait until I finish Tegmark's book before writing about what it means to me.
For now I'll just say that it is one of the most intriguing books I've ever read. Also, one of the most difficult to understand.
Not because Tegmark writes poorly or complexly. Quite the opposite. His book is very clearly written. It's some of the ideas that are diffcult to comprehend, because they are so far removed from everyday experience.
You can get a bite-sized taste of Tegmark's Mathematical Universe Hypothesis (MUH) in a Scientific American article he wrote: "Is the Universe Made of Math?" Excerpt:
Modern mathematics is the formal study of structures that can be defined in a purely abstract way, without any human baggage. Think of mathematical symbols as mere labels without intrinsic meaning. It doesn't matter whether you write “two plus two equals four”, “2 + 2 = 4” or “dos mas dos igual a cuatro”.
The notation used to denote the entities and the relations is irrelevant; the only properties of integers are those embodied by the relations between them. That is, we don't invent mathematical structures – we discover them, and invent only the notation for describing them.
In summary, there are two key points to take away: The External Reality Hypothesis implies that a “theory of everything” (a complete description of our external physical reality) has no baggage, and something that has a complete baggage-free description is precisely a mathematical structure.
Taken together, this implies the Mathematical Universe Hypothesis, i.e., that the external physical reality described by the theory of everything is a mathematical structure. So the bottom line is that if you believe in an external reality independent of humans, then you must also believe that our physical reality is a mathematical structure. Everything in our world is purely mathematical – including you.
I also searched my own blog for mentions of Tegmark, since it seemed like I'd heard of this mathematical universe notion before I started reading "Our Mathematical Universe." Google led me to a 2007 Church of the Churchless post, "What reality is really made of."
(Answer: mathematical structures)
Tegmark has been working away on his Mathematical Universe Hypothesis for many years. He talks in his book about how other physicists have told him that he should give up this obsession for the sake of his career, since the MUH is just so damn weird.
Well, I agree with Tegmark: scientists shouldn't shy away from entertaining really strange ideas, because the more we learn about the universe, the stranger it appears.
So I don't understand the extreme resistance to Tegmark's Mathematical Universe Hypothesis. For sure, it makes a whole lot more sense than religious theologies. HIs ideas are equally far-out, yet have the advantage of being grounded in some solid logic and reasoning.