I finally finished Our Mathematical Universe (2014) by Max Tegmark. It took me a while — only two days left on the 21-day library loan. I often had to put it down to clear my mind and give my neck a rest. (The book invoked a lot of head-shaking. It gave me a very bad case of the Yeah, buts.)
I debated whether to post this for Sci-Fi Saturday or for more metaphysical Sabbath Sunday. I tend to think either would be appropriate to the subject matter. Given how many science fiction references Tegmark makes in the book, I’m going with Saturday.
The hard part is going to be keeping this post a reasonable length.
Back in the 1990s I bought The Nitpicker’s Guide for Next Generation Trekkers, by Phil Farrand. As the title suggests, it’s a somewhat tongue-in-cheek analysis of little inconsistencies Farrand spotted in TNG.
Part of the deal for me was that Farrand was a fellow computer programmer, so I expected he would approach it with more of an understanding of the possibilities of the future rather today’s limits.
By the time I finished the book, it was chock full of tiny Post-it note flags on the many dozens of pages where I had nits with his nits. The book literally bulged from all the inserted Yeah, buts.
No paper and no bulging here, but I have dozens of bookmarks, highlighted bits, and notes where, again,… I have nits.
As I said, the trick is distilling them into a post, and I’m already wasting words.
Tegmark’s Mathematical Universe Hypothesis (MUH) is that all of reality isn’t just described by mathematics, it is mathematics. There is no matter, there is no energy, there is no time, there is no change, there is just a mathematical structure.
Which raises the question: Where is this structure? How is it embodied?
Tegmark recognizes the conundrum of actually implementing a mathematical structure versus that structure just existing in some abstract sense. He asserts the Platonic abstraction is sufficient; implementation is not required.
So the answer is: Nowhere. It isn’t.
This is part of my objection to MWI (another theory I feel confuses the description for reality). Under MWI, reality is the Schrödinger wave-function, a mathematical structure. But unless MWI proponents can explain where or how the wave-function exists, MWI devolves into Tegmark’s belief — reality is mathematical.
He believes our universe is infinite, and that eternal inflation is true, which are also important parts of his argument. I’ve recently argued against the latter. The former raises some questions: time required to become infinite size; energy required to… etc.)
He embraces String Theory, another debatable physics quest, which he feels supports eternal inflation (and, hence, his Type II multiverse).
To be honest, he comes off a bit credulous to me. (His take on quantum computing seemed another example.)
There is a saying that one should have an open mind but not so open one’s brains fall out. Tegmark’s willingness to embrace these ideas (many of which Jim Baggott calls “Fairy Tale physics”) without skepticism felt vaguely evangelical. Or at least wide-eyed. He reminds me a bit of another wide-eyed evangelist, Brian Greene — someone Tegmark cites fairly often.
To his credit, Tegmark does characterize his idea as extreme. He even says he’s about the only physicist who believes this. (If his arguments haven’t convinced his fellow physicists, perhaps there’s a reason? Ironically, those who believe in MWI are definitely leaning his way.)
The other multiverse types feature separate universes. A distinct feature of multiverses is that separation. But our slice of the mathematical multiverse contains all other mathematical structures (at least in the Platonic sense). And in Tegmark’s view, Platonic is good enough.
Tegmark worked on a computer program to list mathematical structures. Essentially it assigns a Gödel number to them. This requires they be countable, which is questionable in light of Gödel’s results (that these are uncountable).
Tegmark acknowledges this, but skates right past it into a discussion about computational complexity. He wants to generate some of the structure by computation. The problem is he’s already denied time and change, which any computation requires (and Gödel still applies).
He seems to get hung on dilemma horns by needing many different types of infinity to support his arguments, but recognizing the inherent problems of that, he suggests maybe reality is rational. (A point I think might actually be true.)
But if it is, many of those infinities go away, and so does support for much of his argument. It feels like his own points are self-contradictory, which isn’t surprising since he may be arguing something nonsensical.
One thing I’ve noticed in these fairy tale physics stories is how they often contain what seems a show-stopper that proponents side-step.
MWI raises questions about energy and probability that, unless answered, seem to invalidate the theory. The BU raises questions about the flow of time and how that structure was ever generated in the first place.
On the flip side, both theories cling to tiny bits of flotsam to keep them floating. MWI clings to the Schrödinger equation being all that matters. The BU clings to a questionable (arguably contrary) interpretation of Special Relativity (to the point of claiming it’s proof).
Tegmark’s MUH floats largely on the observation that particles are characterized by numerical properties: mass, charge, spin, etc. From this he derives the idea that particles are therefore nothing but those numerical properties.
But what causes those properties to manifest? Why are they there? To me, reducing particles to just their numerical properties confuses the description — the measurements — for the thing.
It confuses the map for the territory, so it strikes me as a weak premise.
(As an aside, the MUH and BU, because both are static, are incompatible with quantum mechanics which appears random and dynamic. This is why Tegmark needs MWI — to account for apparent randomness in a static system. But MWI makes a hash of probability.)
The show-stopper I see here involves time and our sense of time flowing.
The MUH has the same time flow problem as the BU. Both say time and change don’t exist. The BU posits a static four-dimensional block that contains all of spacetime. The MUH posits a static mathematical structure describing what amounts to a BU.
So where does our sense of time flowing come from? Why do we all seem to share the «now» as well as a mutual past?
Those denying the fundamental nature of time often point to Einstein’s Relativity as demonstrating that time isn’t real. I think this misses a key point: proper time — our personal time — never changes. Neither does anyone else’s. It always and ever moves at one second per second.
Tegmark’s answer is that our perception of «now» is based on our sensory inputs and memories, and, at any given point along the timeline there is a corresponding sense of «now».
Fine, but why does it occur serially at a fixed rate? Why do we share that rate (when we’re in the same frame of reference)?
I think time is fundamental, and, if so,it falsifies the MUH (and the BU).
As an aside, Tegmark speaks freely of “change” and “process” just as those who believe in strict determinism often still speak of “deciding” or “choosing.” It’s almost as if their subconscious was trying to tell them something. 😉
As another aside, despite advocating the MUH, Tegmark does not believe in the VR Hypothesis. For one thing, the VRH evolves in time as it’s calculated Matrix-style, which is contrary to the static MUH view.
Speaking of asides, Tegmarks refers to his four flavors of multiverse as Levels, but I have trouble seeing them as levels (unless we mean like in video games).
I can see a Type II multiverse (eternal inflation; universes with other laws) as being a higher level than a Type I multiverse (this infinite universe), since II clearly includes I.
But a Type III (MWI) doesn’t require either of the first types. It could be true in a single finite universe. Type IV, likewise, isn’t an extension of the other types; they are not required first steps.
So I’ll call’m Types.
Another characteristic of fairy tale physics is its tendency to resort to what amount to philosophical arguments and to then take them as givens.
Two huge offenders in a lot of hand-waving books are the Anthropic argument (I refuse to call it a principle) and the Doomsday argument. They make an appearance here, of course, and are taken as reasonable.
The Anthropic argument is seen as in tension with the Copernican principle (which also doesn’t deserve the term principle). The resolution to that tension is some kind of multiverse — the Copernican principle is seen as winning.
And yet Tegmark himself asserts a belief that, not only are we the only intelligence in the galaxy (something I believe), we’re the only intelligence in the visible universe.
Which, if so, makes us Ptolemaic. This universe literally does revolve around us.
Tegmark uses the infinity of multiverse Types I, II, and III, to put Copernicus back in the win again.
But it is a fact that  there might be just one finite universe and  it just turned out the way it did and  since it did, here we are, deal with it.
In the last section of the book, Tegmark turns to social argument, making a plea for a better, more educated, world. He refers to our one spaceship Earth and how we’re all in this together.
Regardless of all that infinity, we ultimately do have just this one very small, very brief, reality. Tegmark isn’t too impressed with what we’re doing with it, and I have to agree with him on that one.
He’s very concerned about the dangers of AI. He’s definitely on the alarmist side. Given his mathematical views, it’s no surprise he asserts that consciousness is what information processing “feels like” (an idea not only with no supporting evidence, but with all known evidence falsifying it).
As such, he believes in the possibility of a superior AI that could, in turn, build even more superior AI. The speed of computers compounds the risk considerably.
He said something else I agree with: This century is unique in that, for the first time, we have the power to wipe ourselves out. If we survive it, we’ll probably have mastered the impulse. But right now, right here, our million year history is at stake.
Tegmarks suggests his theory does have a possible falsification: If he’s wrong, scientists should discover something they can’t explain with math.
I couldn’t help but think of wave-function collapse. The big complaint theorists have there is the lack of mathematics to describe it.
I also wonder if the results of Turing and Gödel might apply. Both demonstrated limits to mathematics — things it can’t explain.
Stay narrow-eyed and skeptical, my friends!