Tag Archives: physics

Love and Math: The Heart of Hidden Reality by Edward Frenkel

Here is another book about mathematics. In this book, the author talks about his absolute love of the beauty of mathematics, and how it explains physical properties, such as features of subatomic particles and in quantum physics. For example, mathematicians postulated the existence of some particles before they were even found based on symmetry in the underlying mathematics.

I was particularly interested in this book, since the author attended college right around the same time I was going to college (he is one year younger), and he experienced the changing world at the same stage that my wife and I did. Even though he is one year younger, he graduated from his high school one year earlier than me at age 16.

In the book, he explains how he was singled out in the mathematics test to attend Moscow State University (or MGU) as a Jewish person. When he went in for his math test, the testers grilled him, and they found a reason to reject his application even though he is brilliant. Moscow State University does not accept people who are even just one quarter Jewish. He ended up going to the Moscow Institute of Oil and Gas (also called Kerosinka and officially called the Gubkin Russian State University of Oil and Gas) which has a pretty good applied mathematics program. They accept Jewish people. This allowed him to attend some lectures (first by jumping a fence, then getting an ID card) at Moscow State University, even though he wasn’t a student there. (See Chapters 3 and 4.)

In 1989, he received a Harvard Prize Fellowship to attend Harvard for a Semester to learn from some of the best mathematicians in the world. Most of the other recipients had graduate degrees and/or PhDs, while he just had an undergraduate degree from Kerosinka. He worked hard to prove that he belonged there with the fellowship.

He ended up staying in Boston for longer than a semester. He was able to get his PhD in just a year between 1990 and 1991. Below is his dissertation.

Frenkel, E. V. (1991). Affine Kac-Moody algebras at the critical level and quantum Drinfeld-Sokolov reduction.

After he gets his PhD, he works on the Langlands Program. This attempts to be a grand unified theory of mathematics. As noted at Wikipedia — “The Langlands program consists of some very complicated theoretical abstractions, which can be difficult even for specialist mathematicians to grasp.” Frenkel tries to explain some of the math in the program, and I caught some of it, but not very deeply. At the end of the book, he talks about the movie that he worked on, The Rites of Love and Math. The book was published in 2013, while the film came out in 2010, so the film preceded the book.

The book — Fantastic Numbers and Where to Find Them

The subtitle has — A cosmic quest from zero to infinity. It was written by physicist Antonio Padilla.

I was thinking this would be more math focused, but it is more about how a physicist explains very large and small numbers. That is fine with me, but it had a different bent from what I was expecting. With topics such as Tree(3), the Googolplex, Graham’s Number, zero, and Infinity, I thought it would be more mathematical than physics. I was particularly looking forward to the chapters on Graham’s Number and infinity.

The author is based in England, so it had British spellings, and it mentioned a lot of British and European sports. That is ok.

I did not expect Usain Bolt to show up in the book. The first chapter is about how Usain Bolt managed to run so fast in 2009, that he could slow his clock down by a factor of 1.000000000000000858 (I counted 15 zeros, but maybe I am off by one), and no human had ever slowed down their time that much. This is because of time dilation as objects approach the speed of light. As objects approach the speed of light, they also appear to have more mass, and they contract in size.

In the book, some of the things that I learned more about were:

  • Black hole head death. Which is “if you tried to picture Graham’s number in your head, then your head would collapse to form a black hole.”
  • Tree(3) — I am still not exactly sure why it is less than infinity, but I found some math articles to clarify that, but they were over my head. He did not explain that good enough for me. I guess it has to do with Kruskal’s tree theorem.
  • Where the name Fibonacci came from. That was not his real name.

In trying to explain how there are different levels of infinity, we learn about different sets. There are countable infinities, and then there are uncountable infinities. These concepts drove Georg Cantor mad.

Sometimes, the topics discussed seemed disconnected. For example, in the chapter on Infinity, he ends up talking about String Theory. I am not quite sure how he ended up there from the concept of infinity.

He changed the story of Schroedinger’s cat to be one of the Queen of England’s Corgi dogs. I found that to be a little odd.

It was an interesting read, but he does go off into tangents about the holographic universe, but that is his thing, so just be wary of the loose and strange connections he makes.

Time Travel by James Gleick

I was hoping this book would discuss more of the science concerning the possibility (and unpossibility) of time travel, but he covered more of the older science fiction that discussed time travel.

It all starts with a discussion of the H. G. Wells book, The Time Machine, that was published in 1895. That seems to be the impetus for much/most /all? of the time travelling science fiction that follows in his footsteps. I’ve not had the pleasure of reading the Time Machine, but now that I know it exists, I will give that a read.

He then goes on to talk about and explain how other science fiction authors address the concept of time travel in new, different, and unique ways.

The two chapters that cover more of the science and philosophy of time travel are Chapter 11 on Paradoxes, and Chapter 12 on What is Time. The main paradox that is discussed concerning time travel back in time, is the problem that one could kill their grandfather. Personally, I don’t think that one could circle back in time to affect the present. Time operates like a function on a graph. For every point in time along the x axis, there can only be one y answer. Like a mathematical function, time is not allowed to backtrack.

But, it may be possible to jump to the future. All one needs to do is travel at the speed of light, or nearly the speed of light, and one can essentially travel into the future while aging very little. The main problem is that it takes a huge amount of energy to get a mass of any weight close to the speed of light. This was mentioned, but it was not talked about all that much.

If you want to get an overview of the science fiction of time travel, this is your book. If you want a scientific overview, this will have pieces and parts, but that is not the focus of it.

For a more in depth look at the concept of time, the Order of Time by Carlo Rovelli, may be better. I read that book a couple years back, but I found it to be a little obtuse. I seem to agree with many of the people who gave that book 3 stars.