Pi 3/14/21

Thoughts by Richard Bleil

Happy Pi Day!

Yes, every March 14 (3/14) we celebrate all things mathematical, like pi (3.14). Pi is one of those funny natural irrational constants of the universe, the same anywhere you are in the universe with digits that continue forever. To be “irrational” means the digits not only extend to infinity, but also never repeat. In other words, 1/3 has digits that continue to infinity, but they repeat (0.3333333333). This, in and of itself, is a triviality. You see, irrational numbers cannot be expressed as simple fractions. The number 0.333333 (etc.) is 1/3. The closest fraction expressing pi is 22/7, but this is only approximate. The fraction 22/7 is 3.14286…, while pi is 3.14159… This is close, with only a 0.04% difference, but if you’re navigating between galaxies this small difference could make the difference between finding yourself with the Rebel Alliance or the Empire. Pi is actually the circumference of a circle (the length of the edge of the circle) if the diameter (the maximum distance from one side to the other) is 1. In other words, a circle is pi times larger around as it is across.

These irrational numbers abound in nature. The value of e, which is the constant that is the base of the natural log, is 2.71828… and is also irrational. This constant arises naturally in a number of distribution and growth problems, such as interest in investments or banks. Natural processes, for example in grade distributions, often fall according to an equation that utilizes this constant.

There are a number of irrational constants as well. The charge of electrons is related to Faraday’s constant (96,485.332…). Boltzmann’s constant relates temperature to kinetic energy, and the list goes on. It should not be a surprise that so many universal constants are irrational. It’s actually not difficult to prove that there are literally an infinite number of irrational numbers between any two rational numbers. Keep in mind, this means to digits well beyond our computer capabilities to calculate them; I mean literally taking the digits out to infinity. It’s a fascinating topic, actually, that I’ll not expand upon here.

You’re welcome.

Mathematics is the language of science. My degree was heavily based on mathematics. As a theoretical chemist, I write mathematical models of chemical systems. My mathematician friend is often irritated with me because, as a scientist, I can do what he cannot. I can use as “proof” how my models fit experimentally determined curves. In mathematics, all proofs must relate back to already accepted mathematical laws, so when I bypass steps saying, “and this fits experimental data”, he’s not a fan. I just laugh.

In science, Lord Kelvin is known by most people, I’m assuming, as the absolute temperature scale named after him. He was a British physicist, mathematician and engineer born in 1824, as I understand it. He became famous for his mathematical modeling of electricity and his work in thermodynamics. I know him as having uttered probably the most influential phrase in science I’ve heard, one that has guided my own personal pursuits when he said, “If you can put a number to that of which you speak, then you truly know something of the topic. If not, then you know nothing at all.”

I guess I shouldn’t be using quotation marks as this is probably not accurate, making it a paraphrase rather than a direct quote. Oops, to be true to Lord Kelvin, I should have used zero quotation marks, rather than two. But the reality is that many scientists (perhaps even most) are not terribly well versed in mathematics beyond statistics. We use statistics constantly to calculate errors in our experimental values, but my science uses far more. Physics, generally speaking, is most strongly founded in mathematics, followed by chemistry and then biology. I had a very good friend majoring in biochemistry when I was in graduate school. The day that she was ready to defend her thesis, the final step in a doctoral program, she came to me and said that she uses logarithms frequently but didn’t really understand them and asked me to explain them to her. She was (and I’m sure she still is) a shining star in the department, probably one of the students in our class in my humble opinion. While it might be reasonable for most people not to understand logarithms and powers, that she didn’t understand what they tell us was somewhat of a surprise. I did not doubt her intelligence then, and still do not today, but it was surprising.

Mathematics is like a compressed language. A mathematical equation speaks volumes to us in a very compressed manner. The ideal gas law, PV=nRT, immediately tells me the relationship between pressure and volume, pressure and moles, pressure and temperature, volume and moles, volume and temperature and moles and temperature. It literally took me 19 words just to tell you what this equation tells me, as opposed to six simple characters. I understand that many people don’t like math, but I hope my readers have at least come to appreciate it a little bit more. As for me, I will forever love mathematics.

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