Max Tegmark’s “Our Mathematical Universe”

I am 2% in and am enjoying the book. Tegmark invokes Darwin early and perhaps I will go farther. Why did humans wonder “Where did everything come from?”? What’s the selective advantage in that? How things are turns out to being a clue about how things were. How things were turns out to be a clue about how things are now even if those things are not in plain sight now. Knowing how things are now bears on your choice of what to do to make your life better. All this is depends on the human ability to imagine alternate hypothetical situations—past, present and future. Our facility at this is strongly conditioned by keeping hypothetical and real situations separated in our head. This separation is what makes Everett’s multi-world hypothesis so hard to swallow.

L 205: Tegmark suggests solipsism as a solution to “What is Reality”. I don’t think so. Not that he thinks so but I think that he thinks that some think that. Perhaps, but I have not heard of anyone suggesting that.

L 264: I record here my plan to keep track of the dates of physical observations that support Tegmark’s ideas were made. I suspect that they were mostly before 1950. The use of computers began about 1950 and they helped fit the clues together and such progress continues today. At L 879 Tegmark notes modern telescopes able to see that really distant galaxies really do look younger—a dramatic corroboration of what was thought in 1950. Penzias and Wilson discovered the CMB in 1964 which was important. It was mapped in detail much later and that was also important. These discoveries made people pay attention to the pre 1950 ideas of Friedmann and Gamow. Smoot’s 1997 measurements of CMB fluctuations.

L 1177: I am glad that Tegmark is cautious about what happened before the universe was 1 second old. I am sceptical for what I suspect are different reasons. I was impressed with Weinberg’ “The First Three Minutes” which does not go back that far.

L 1406: I am unsatisfied with Tegmark’s description of how he draws conclusions from the CMB harmonics.

L 1768: I object here as I do on other presentations of inflation. If some bounded region of space now evolved from some earlier region of zero volume, then what region of space evolved into an adjacent region of space now? I suppose that the answer is some other zero volume region of space. The distance between these two earlier zero volume regions is, of course, zero and thus there is no mystery in them being alike.


How far apart were regions A and B at time zero? Zero! No problem communicating.

L 1805: The “Flatness Problem”. This is a problem from the perspective of the question “What are the solutions to Einstein’s GR equations?”. Those equations allow uniform positive and uniform negative curvatures, as well as the flat solutions. Of course they allow really bent solutions too. Teleology anyone?

L 1867: As Tegmark explains the inflation theory it sounds like a reparameterization of time. What is the advantage of the curve shown in figure 5.5 over a straight line thru the origin?

L 2631: Tegmark runs over the Anthropic principle quickly. At L 2686 he notes that “Anthropic” is a taboo word some places, but he likes it.

L 3545: You could write a Sci-Fi story about a universe in that set of measure 0. Perhaps that is where “General Magic” took place.

L 3638: The example in the Wikipedia article describes why you need density matrices. Tegmark’s figure 8.8 (location 3851) is relevant to the idea of the density matrix which relates the subject and object — “What does the subject know about the object?”.

L 3948: I had the great luck to talk to Wheeler once. He treated me too as an equal, which I clearly wasn’t. I asked him a question and he sent me a preprint of a paper about that question.

L 4122: Ah: the Measure Problem! (Head on at 5759)

L 4688: Tegmark draws a line between the words and the equations. I draw another line between two kinds of words. Our equations do not include information about what sorts of values expressions within those equations take on. This is an important lack in much mathematical literature today. I share Tegmark’s opinion about words that he gives as examples. I would not class my extra information as ‘baggage’. It, with the equations, is what is necessary to put into the computer.

L 4730: Tegmark describes reductionism. I think that Laughlin would not agree. I sort of side with Tegmark here until I hear a better story from Laughlin.

L 4747: “with equations that fit on a T-shirt”
There is more to mathematics than equations. Before you can “Shut up and compute.” you must know whether to use reals or complex numbers, or some value that denotes a point in a Calabi-Yau manifold. I am sure that Tegmark knows this but he must write a book.

L 4749: I love Tegmark’s partial ordering of physics theories and math theories.

L 4810: Tegmark suggests that isomorphism means identity. This is an awkward problem in our conventional formal logic. I think this problem does not detract from Tegmark’s ideas but it lays booby traps in the arguments. It is part of the reason I am queasy about nouns as noted below.

L 4831: Tegmark uses Chess to give an example of our ways of describing games, purely informally to formally.

L 4928: I think that Tegmark does a good job at describing ‘Mathematics’.

L 4958: Tegmark gets more real math ideas into the text, without equations, than most authors.

L 5658: Boltzmann brains in a comfortably sized volume, which is held at a comfortable temperature, will indeed achieve a configuration with statistical frequency proportional to eE where E is the entropy of that configuration. It is indeed for more likely that such a brain will delusional memories like yours without the remembered events having happened before, than the far less likely event that those earlier memories were real events.

L 5837: I agree that ∞ is a problem. Actually ∞ simplifies things in that it avoids saying how things end. That doesn’t mean that it is right.

L 5924: Tegmark has not let on that this Hilbert space habitat is occupied by just one point whose location defines the entire ‘universe’. Hilbert space has just c points but its infinity of dimensions lets the one point describe our ‘ordinary’ universe. I view the above orthodoxy like the Banach Tarski paradox—with a grain of sand.

L 5931: “Does the level IV universe really exist?” David Hilbert said mathematical existence is the mere absence of contradiction. When I do math I use nouns.

L 6131:

I accuse Tegmark of misusing “existing” here. Perhaps he is saying that infinite math is not consistent. I think that that is conceivable but then he should have said that. I suspect that at some extra cost useful math could be made finite. No one is making such an investment that I know of. I do not mind if Tegmark wants to posit finite math as the level IV universe; I think such a notion can be made precise.

L 6217: Alas many of the beautiful symmetries that mathematicians and physicists love are not known to finite math. You can draw a circle that is dense with rational points, but that is already infinite. There are curious finite approximations there to.

L 6240: I do not buy that initial conditions are figments. More accurately I see no need to exclude them. Conway’s Life game needs them.

L 6328: The question in my mind is whether Tegmark will hew to the old dictum: “Things are as they are because they were as they were.”.

L 6371: I think that the “Theory of Everything” that most physicists wish for is not required to reproduce the complete details of the CMB—only the statistical properties.

L 6588: I recommend Egan’s “Permutation City” as an introduction to most of these ideas written more like a novel.

L 6616: If Tegmark is planning to do away with cause-and-effect, he has some heavy explaining to do to explain it away.

L 6665: Regarding the 123 digit fine-tuning, the last time I studied that matter led me thru some of the least persuasive QM that I recall. I think that vacuum energy is in a queasy part of physics and will be redone someday.

L 6680:

Good point.

L 6873: I somewhat prefer star-lifting to Earth moving. I think they are both feasible but perhaps star lifting is slightly safer and prolongs our Sun’s life.

L 7028:

If they don’t we have nothing to fear; they will not be concentrating on how to protect themselves.

L 7036:

We got ours thru evolution. We got our worse angels thru evolution. It does not come automatically.
I like Tegmark’s use of words. Let me say what I think, as influenced by Tegmark’s words, but less by his ideas. I am convinced that math is not arbitrary. We can choose what math to study but not which numbers are prime. I am a skeptic about the universe. There is something going on and both I and Tegmark are part of it. My eyes glaze over however when people argue over whether the QM wave equation is real. I prefer not to use the word “real”. I suspect that I use nouns merely because I have not learned another way to think or talk. I don’t expect to learn another way. This is not a pretty ontology! But without “real” I can neither accept nor reject Tegmark’s MUH. I do enjoy it as literature however.
Greg Egan’s “Permutation City” takes these ideas seriously!

Tegmark’s site