Tag Archives: numbers

Two more books that I’ve read or skimmed

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And, here they are.

The Evolution of Useful Things. This was by Henry Petroski, may he rest in peace. I don’t know if I would call in fascinating, but it was an interesting look into how very simple things have been designed over the last couple of hundred years. Some of the examples included forks, paperclips, zippers, and more. He did circle back to forks in different parts of the book, so it seemed like he wandered in the topics sometimes. I may have skimmed or skipped some pages, since it was less than thrilling. But, I am looking forward to reading his book about — The Pencil.

Do Numbers Exist? A Debate about Abstract Objects. This was a philosophers pissing contest between Peter van Inwagen and William Lane Craig. I should have looked at the author list first, since I’ve known that William Lane Craig was a theistic apologist. They both brought up god even though I don’t see what god would have to do with the philosophy of whether numbers truly exist or not. They tried to get very deep into the philosophical weeds so that they could impress the readers with how much they know about how to use philosophical jargon over most people’s heads. In the end, I sided more with Peter van Inwagen, since he seemed to be of the mind that numbers actually exist. Most of the book was not really about numbers, but more about the existence of abstract objects in general. I liked the segment starting on page 211 about the concept — do chairs exist? It reminded me of the line by John Oliver — Do Owls exist? Are there hats?

I skimmed the vast majority of the book, but It did get me thinking about the existence of numbers. I think that the number pi exists. If there is an intelligent life form that has studied mathematics outside of our solar system, it also knows how to calculate pi, and it knows that it has an infinite number of digits (in whatever number base it uses). The fact that it is reproducible and exactly calculated in another part of the universe makes it exist. Also, why would god make a number such that it can’t know the last digit. It can’t know everything, since it can’t know every digit of pi. While a theologian might say that God knows the infinite, how does he or she know that god would know every digit of pi and e and all irrational numbers? Numbers just exist, and they were not created by a god. For some reason, these two debated about whether or not god created numbers. As uncreated things, they are still things. Hence, they exist.

The book — Fantastic Numbers and Where to Find Them

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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.