A review of Max Tegmark's book Our Mathematical Universe

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TL;DR: This thread is a review of the book Our Mathematical Universe.

This thread is a review of Max Tegmark's book Our Mathematical Universe. The thesis of Our Mathematical Universe is that not only does mathematics perfectly describe the universe, the universe is mathematics.. In this thread, I will give a very brief summary of the book, and I will list my takeaways from the book. A takeaway is information in the book that meets both of two criteria: 1# It is something that I did not know before I read the book and 2# It is interesting.

The book Our Mathematical Universe is divided into three parts. The first part is about describing the large things in the universe. The second part is about describing the universe at the atomic and subatomic levels. The third part of the book is about how the universe is mathematical.

The Sun was originally a gas cloud that was rotating or spinning. The core of the gas cloud was composed of hydrogen and helium. The outer parts of the gas cloud were composed of carbon, oxygen, and silicon. The cold parts eventually formed the planets of our solar system. The gas cloud that eventually became the Sun eventually "blew off" the planets. That is why all the planets in our solar system orbit around the Sun in the same direction.

A scientist with the last name Gamow predicted that our universe began with a hot Big Bang, and that plasma once filled all of space. Cold hydrogen gas is transparent and invisible. Hot hydrogen plasma is opaque and glows brightly. This means that when we gave ever farther into space, we should encounter old galaxies nearby, then young galaxies beyond them, then transparent hydrogen gas, then a wall of glowing hydrogen plasma.

Tegmark writes about how in the past, cosmologists were frequently wrong. Tegmark's examples of how cosmologists were frequently wrong in the past are how Aristarchos claimed that the Sun was eighteen times too close, and Hubble claimed that our universe was expanding seven times faster than it is actually expanding. Tegmark asserts that this phase of cosmologists being wrong is over. Tegmark argues that the fact that both the Big Bang nucleosynthesis and cosmic clustering gave the same measurement of the atom density, and the fact that both supernovae Ia and cosmic clustering gave the same measurement of the dark-energy density indicates that cosmologists are far more accurate today than in the past.

I keep losing my internet connection. So I am going to post this now. Then edit it so I know I don't lose anything.

 

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The scientist Bob Dicke told Alan Guth that there were two main problems with Friedmann's Big Bang model of the Universe: 1# The Horizon problem and 2# the flatness problem.

Scientists expected the temperature of the Cosmic Microwave Background Radiation to be different in different parts of the universe. Instead measurements and research discovered that the temperature of the Cosmic microwave background radiation is about the same everywhere in the universe. This is called the Horizon problem.

Scientists have measured space to be flat to high accuracy. The scientist Bob Dicke argued that the fact that space is flat is puzzling is Friedmann's Big Bang model is correct because it is a highly unstable situation. And we shouldn't expect unstable situations to last for long. This is called the Flatness problem.

Alan's radical insight was that by making just one strange sounding assumption, you can solve both the horizon problem and the flatness problem in one fell swoop--and explain a lot more as well. This assumption is that once upon a time, there was a tiny uniform blob of a substance whose density was very hard to dilute. This means that if one gram of this substance expanded into twice the volume, its density (its mass per volume) would remain basically unchanged, so that you'd now have about two grams of the stuff.

According to Einstein's theory of gravity, such a tiny nondiluting blob can undergo a most remarkable explosion that Alan called inflation, in effect creating a Big Bang. The whole inflation process, from beginning to end, could have been almost instantaneous by human standards, requiring less than 10 to the power of negative 35 seconds, less time than light takes to travel a trillionth of the size of a proton. In other words, exponential expansion takes something tiny that isn't moving much and turns it into a humongous, fast expanding explosion. In this way, inflation solves the "Bang problem", explaining what caused our Big Bang: It was caused by this repeated doubling process.

This is my review of the first 100 pages or so of Our Mathematical Universe. I am getting tired out. This is getting tedious. I might review the rest of Our Mathematical Universe on this thread in the future. The main text of Our Mathematical Universe is 398 pages.

 

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I invite everyone who reads this to give me feedback and ask any questions you might have about the book. If you disagree with anything that I wrote, please let me know.

 

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@jefferywinkler3 please give me your feedback on this thread

 

[Demystifier]

The map is not the territory. But Tegmark assumes that it is, and then develops this assumption to its logical conclusion. For me, it's a nice reductio ad absurdum.

 

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The map is not the territory.

What the heck does that mean? I am totally baffled. What map are you writing about?

 

[Demystifier]

What the heck does that mean? I am totally baffled. What map are you writing about?

https://en.wikipedia.org/wiki/Map–territory_relation

 

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The map is not the territory. But Tegmark assumes that it is, and then develops this assumption to its logical conclusion. For me, it's a nice reductio ad absurdum.

Why do you think that Tegmark assumes that the map is the territory?

 

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Here is my extremely brief review of page 101 to the end of Our Mathematical Universe.

On page 104 Tegmark writes the following: "Another puzzling feature of inflation is that it causes accelerated expansion. In high school, I was taught that gravity is an attractive force, so if I have a bunch of expanding stuff, then shouldn't gravity instead decelerate the expansion, trying to ultimately reverse the motion and pull things back together? Again, Einstein comes to the rescue with a loophole, this time from his general relativity theory, which says that gravity is caused not only by mass, but also by pressure. Since mass cannot be negative, the gravity from mass is always attractive. But positive pressure also causes positive gravity, which means that negative pressure causes repulsive gravity! We just saw that an inflating substance has huge negative pressure. Alan Guth calculated that the repulsive gravitational force caused by its negative pressure is three times stronger than the attractive gravitational force caused by its mass, so the gravity of an inflating substance will blow it apart."

The elementary particles are completely described by their quantum numbers, and appear to have no intrinsic properties at all besides these numbers.

The scientists Hugh Everett originated the thesis that the wavefunction (whatever that is) never collapses.

Neils Bohr and his colleagues invented wavefunction collapse to explain why experiments seemed to have definite outcomes. But Everett realized something amazing: even if experiments didn't have definite outcomes, it would still seem as though they did.

Everett juxtaposes the Copenhagen interpretation with the Everett interpretation. The Copenhagen interpretation is that the wavefunction collapses. The Everett interpretation is that the wavefunction never collapses. The author Max Tegmark agrees with Everett that the wavefunction never collapses. Therefore, the author Max Tegmark disagrees with the Copenhagen Interpretation.

The Level I multiverse is everything in space that is outside of the observable universe. The Level I multiverse has physics just like the physics in our universe. The Level II multiverse is all of space outside of our observable universe that has Laws of Physics that are different than the physics in the observable universe. The Level III Multiverse could be very close to our universe, just in a different Hilbert space in a different dimension. There is a Level IV multiverse, but I don't remember how Tegmark described the Level IV multiverse.

Then Max Tegmark wrote a lot about decoherence, but it just went over my head. I am not a physicist. Then Wojciech Zurek continued his decoherence research beyond what Tegmark had re-discovered, and Zurek showed that decoherence does one more important thing for us: not only does it explain why large objects never seem to be in two places at once, but it also explain why conventional states (such as only being in one place) are so special: out of all the states that quantum mechanics allows for large objects, these conventional states are the ones that are the most robust to decoherence, and therefore the ones that survive.

 

[Demystifier]

Why do you think that Tegmark assumes that the map is the territory?

Because math is a mental map, but he assumes that math exists outside of our mind.

 

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@berkeman
@jefferywinkler3
@Ibix

What do you think about Demystifier's post #5 on this thread? Do you agree with @Demystifier ?

 

[Ibix]

I haven't read Tegmark so I can't comment on the book.

However, on the frontiers of physics we have not settled what the correct view is and there can be vigorous debate between experts. A frequent problem with popularised texts is that they reflect the author's personal interests and biases, and they are not always clear about when they are talking about "stuff everybody agrees", "stuff everybody agrees except those oddballs who work for Prof XYZ", "stuff me and my mates agree on", and "stuff not even my mates agree with me on". It would not surprise me if Tegmark has written with more certainty in some places than is really defensible, and it doesn't surprise me that working physicists like @Demystifier disagree with his stance on some topics.

 

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I haven't read Tegmark so I can't comment on the book.

However, on the frontiers of physics we have not settled what the correct view is and there can be vigorous debate between experts. A frequent problem with popularised texts is that they reflect the author's personal interests and biases, and they are not always clear about when they are talking about "stuff everybody agrees", "stuff everybody agrees except those oddballs who work for Prof XYZ", "stuff me and my mates agree on", and "stuff not even my mates agree with me on". It would not surprise me if Tegmark has written with more certainty in some places than is really defensible, and it doesn't surprise me that working physicists like @Demystifier disagree with his stance on some topics.

Even though you haven't read Our Mathematical Universe, you could still read posts #1, #2, and #9 on this thread and tell me if it is consistent with your knowledge of physics.