Tag Archives: mathematics

Another book — Do Dice Play God?

This book is by Ian Stewart. No, not the 3rd baseman who played for the Rockies and the Cubs about 15 years ago, this Ian Stewart is a Professor of Mathematics at the University of Warwick.

Thus, the book has a British focus, and some of his examples are based in the UK, but that is ok.

The subtitle is the Mathematics of Uncertainty. The title is a play on the statement by Einstein, “God does not play dice with the universe.” While god may or may not play dice, do dice ever play god?

Ian says that there are six ages of uncertainty, and he does not cover them in the order that they were found for various reasons. Chaos theory was discussed out of order from when it was found by humans.

  1. The first age of uncertainty involved gods, prophets, fortune tellers, seers, and the like. They could try to predict the future. They could supposedly explain what was going on in the world.
  2. The second age of uncertainty came about during the scientific advances in the 1500-1700s. This is when Newton’s laws defined how gravity works, and it explained how we could predict where the planets will be in the future. If we could predict the movements of planets, would it be possible to predict everything, including human behavior?
  3. The third age came with greater understanding of mathematics and probability. Gamblers, astronomers, mathematicians, and many others would like to know the odds of a future event happening.
  4. The fourth age came with quantum mechanics, and our understanding of never really knowing the location or the momentum of atomic and subatomic particles. These ideas took off in the early 1900s.
  5. The fifth age is when chaos theory was developed.
  6. The sixth age is our current situation. He said that it is “characterized by the realisation that uncertainty comes in many forms, each being comprehensible to some extent.” (page 10.) Mathematics can help us understand the universe a fair bit, but much of the world and the universe is “still horribly uncertain.” For example, we are better at predicting the weather about 5-7 days out, but predicting the weather 10-14 days out is still a crap shoot. Predicting climate change is different matter.

One thing I found fascinating was an oil droplet experiment that made teeny oil droplets behave like both waves and particles. This made Newtonian sized objects behave more like atomic particles. (See pages 233-235.) I had not heard of this experiment since I left physics back in the 1980s. But, it looks like that has been debunked as of 2018. Oh well.

Overall, I enjoyed the book, and I found it interesting. It would probably be best for people who have already had some college-level math or 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.

Here’s Looking at Euclid

Took me several months to finish this one, and I finally did a couple weeks ago. I particularly liked Chapter 4 the Life of Pie and Chapter 7, Secrets of Succession.

I’ve always like how pi has digits that go on forever, since it is an irrational number. The Secrets of Succession chapter covers sequences of numbers. It mentions the Online Encyclopedia of Integer Sequences, which I had never heard of before. For example, the Fibonacci sequence has many notes, while other sequences are not as full.

I am reading another book that connects numbers with physics, and I learned that Fibonacci was not his real name. “The man’s full name was Leonardo of Pisa, or Leonardo Pisano in Italian. He was born in about 1175 in Pisa, a Tuscan town famous for its Leaning Tower. The name Fibonacci [pronounced fib-on-ach-ee] is short for ‘filius Bonacci’ or ‘son of Bonacci.’”

Overall, if someone is mathematically inclined, it is a fun read.

Is God a Mathematician? – The book doesn’t answer that question

I recently read the book, Is God a Mathematician by Mario Livio. I picked it up at the JeffCo Libraries Whale of a Book Sale. I figured the book would not answer the question posed by the title, but I thought it would talk a little bit more about logical proofs for or against an all powerful being. In a way, I am glad that it did not do that. It was mostly on the question, is mathematics invented, or is it discovered?

My favorite chapter was probably chapter 5 on statistics and probability. I learned a little bit more about how games of chance helped influence mathematical thought. They discussed games of chance on pages 138-140, but it was involving dice. I thought that card games influenced mathematical thinkers more when it came to chance and probability of winning various hands of cards. That didn’t seem to come up in the book.

I guess I am on the side of the fence for mathematics being discovered. I think that prime numbers and the number pi exist with or without human involvement. It is just up to us to find them in the world of mathematics. But, math is more than just numbers, it also involves concepts such as functions, and algebraic concepts of unkowns in formulas. There is a lot of math in physical concepts such as waves of light or the Navier-Stokes equations in fluid dynamics. That math would still exist even if we did not find them. Other intelligent life forms would probably also know about pi, prime numbers, the speed of light in a vacuum, E = mc2, and the Navier-Stokes equations.

However, we can invent different ways to communicate the concepts of mathematics, just as calculus can be communicated using different terminology. So, the way to communicate mathematics can be invented.

Anyway, it was a good book. It was not earthshaking, and it did not answer the main question in the title, but it was an interesting read.