You can hear the most interesting and compelling things from the most unexpected sources. In March, NPR’s “Science Friday” aired an interview on the subject of math with Kyne Santos, who wrote an unusual book about math. Ira Flatow did the interview. The following is from the transcript of the interview (click here for the full transcript):
KYNE SANTOS: I wrote this book for college students, high school students, adults, people who maybe don’t have a great relationship with math. I want to help repair that relationship, and show them that math doesn’t have to be this challenging, cold, hard, calculating subject that you remembered in school. It can be something that’s fun and inspiring and is actually present in everywhere we look around the world around us. I just want to show people that you can just love this universe. And math is the language of our universe.
IRA FLATOW: Yeah, that’s another way of saying, and you say this in your book, that math is magical.
KYNE SANTOS: Yeah.
IRA FLATOW: Right.
KYNE SANTOS: It is magical.
IRA FLATOW: And you rarely hear people who are not mathematicians who are not involved with math talking about it being magical. Make an argument for me about math being magical.
KYNE SANTOS: I mean, I’ll talk about pi since we talked about that. Pi is everywhere. You can use it to make a dress, but it’s also got infinitely many digits and yet we only need a few of them to make a dress. And we only need even 15 of them to land rockets on the moon.
With the first 40 digits of pi, you can estimate the circumference of the entire observable universe within atoms with margin of error. And yet, it has infinitely many digits. And it may or may not have your phone number, your credit card number encoded within it… the entire works of Shakespeare and the Bible. I think infinity is just this magical concept, and yet, it exists in our own heads.
IRA FLATOW: Yeah. And speaking of pi, you talk in the book about how many different cultures discovered it independently. That it was something that had to be discovered.
KYNE SANTOS: Yeah. I think the other magical thing about it is — if it is in our heads, then why did so many people discover it independently around the world? You had the ancient Egyptians, the ancient Greeks, ancient China, India, Mesoamerica all coming up with number systems, all coming up with their own expressions of pi and algebra and sort of landing on these similar math concepts.
There’s two schools of thought. You can say that math is sort of invented by us and exists in our heads or it’s out there in the real world.
IRA FLATOW: Yeah.
KYNE SANTOS: If it’s invented in our heads, well, it works really well.
IRA FLATOW: Right.
KYNE SANTOS: And it is so good at describing the universe. And if it’s out there, then where is it? Is it in the sky? Is it in the —
Where is it out there if it’s a physical thing? I don’t know.
IRA FLATOW: Yeah. It’s kind of spooky. I mean, in a good way.
Yeah? Where is math, anyway?
For much of human history the question of “where is math?” has led to the idea of the transcendent. It has led to the idea that, ultimately, math is in the mind of “God”. I use quotation marks here because this idea is separate from the major monotheistic religions, so the “God” here need not be the God of Adam, Abraham, Noah, and so forth. Pi and infinity contribute to a robust construction of ideas regarding “fides et ratio”, faith and reason.
It makes no sense that we humans invented pi, like we invented the zipper. Santos and Flatow use the word “discover” with math, because, well, what other word would you use? The universe existed without zippers, and if the zipper had not been invented our clothes would have a lot more buttons. But circles, and pi, were in the universe (Where? In the sky?) before the first person figured out, or discovered, that the ratio of a circle’s circumference to its diameter is 3.14159….
Ditto for infinity, which is within pi, as Santos says. How can infinity exist in our heads? We are not infinite. Our heads are not infinite. We are, as far as science can tell, material things; finite collections of atoms undergoing chemistry — or as was said in a Star Trek: The Next Generation episode, finite “bags of mostly water”; nothing more. How did we bags get ahold of the idea of the infinite?
We do not see infinite around us. We do see indefinite. We see the universe being large beyond measure, for example. But that is equally true for the number of grains of sand on a seashore and they are not infinite in number. They are indefinitely large in number. We cannot count them, yet we know they are not infinite.
Infinite is something completely different. It is alien to who we are and to the world we see, but we have conceived of it nonetheless. Magical indeed, Kyne Santos!
If you are supposing that Santos is making these statements as part of some effort to sneak a little anti-materialist philosophy/theology onto Science Friday and thus into the wider culture — if you are supposing that the next thing Santos is going to do is start talking about Thomas Aquinas — well, that seems unlikely. Santos is a “drag queen” (and writes the book as such; hence, it’s an unusual book about math). “Drag queen” is a concept that does not mesh well with a lot of traditional religious thought. That makes Santos’s observations about math so unexpected, interesting, and compelling; an affirmation of an important idea in the realm of “fides et ratio” from a person with no particular reason to be providing that affirmation.
