A little bit of thanks, and a math coincidence

November 23, 2023   Issue #648

Personal Stuff

Because I’m a person

When I decided to start writing a newsletter, I chose to write two issues a week; a free one on Monday and one for paid subscribes on Thursday. It didn’t occur to me at the time (it being early spring) that this meant I would always and forever more have an issue that came out on American Thanksgiving.

It’s a tradition to express what you’re thankful for on this day (ironic, perhaps, due to its history), and over the years I’ve taken the chance to thank you, the folks who read the things I write, especially here — the 2020 issue sums that up, as well as a video I made that I’ve reposted a few times, so why not again?

If I were to expound upon this topic again I feel it might become trite and seem insincere, when it most certainly is not. I meant what I wrote and said above.

In any case, to avoid that, here is a woefully incomplete and list in no particular order of random things for which I am grateful:

• Trees

• Mitochondria

• Chocolate

• Funny t-shirts

• Star Trek in all its forms

• Fresnel’s equations which describe how mirrors work

• Stellar nucleosynthesis

• My wife’s cranberry orange bread

• Icosahedrons (I just think they’re neat)

• The way vanilla smells

• Pencils made of real wood with actual working erasers

• Tiny adorable asteroid moons

• Puns

• …and the fact that I’m still alive after some things over the years have tried to make that not be the case. I’m glad you’re around too.

I’m also fond of math in general, about which I have something for you, but first this slight diversion…

Astro Tidbit

A brief synopsis of some interesting astronomy/science news

I tried reading this paper and its associated press release but I kept arguing with my relatives and then falling asleep while they watched football.

P.S. Yes, I know that’s not how this works but the joke was too good to resist.

Number crunching

Because I think math is cool, and I think that because it is

A fun thing happened on my new adoptive social media site Blue Sky. It’s still a lot smaller than Twitter was when I left, but there are enough folks there to make for some interesting conversations and discoveries*.

In my replies, someone posted that they had read my book, but did have one problem with it. I replied with my own feelings.

I thought this was funny. As always, your kilometerage may vary.

But then a friend of mine replied in that thread: Craig DeForest, a solar astronomer back in my old Colorado stomping ground, who is brilliant and has a vast amount of interesting info packed into his brain:

This caused my brain to make audible skidding noises. Wait, WHAT?

I did a quick bit of math in my head and knew he was right. What fun!

The Fibonacci sequence, for those of you who never saw the movie “Arrival”, is a sweet series of numbers where the next number in the sequence is the sum of the two before it. This is best shown by example. It’s taken for granted that the first two numbers in the sequence are 0 and 1. Add them together to get 1, and the series is then [0, 1, 1]. Add 1 + 1 to get two, and the series is then [0, 1, 1, 2].

See the pattern? Eventually the series become, [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 …] ad infinitum, literally.

What Craig was saying is that if you pick a number from the sequence after, say, 3, then the next number in the sequence is that many miles converted to kilometers. So, 5 miles is 8 km. 8 miles is 13 km. Etc.

This turns out to be pretty accurate. 5 miles is 8.05 km, accurate to about 0.6%. 8 miles is 12.87 km, accurate to 1%. If we go way out in the sequence, like to the pair 1597 and 2584, it’s accurate to about 0.5%.

You can convert km to miles by going the other way, of course. 8 km is 5 miles, and so on. It’s not too far off.

Why does this happen? Coincidence! Sequences like this tend to behave this way, such that dividing one number by the one before or after it is nearly a constant. In this case that constant is about 1.62 — the Golden Ratio — which coincidentally is close to the ratio of kilometers to miles (1 mile = 1.609 km).

Is it useful? Well, not hugely, unless you a) happen to need to convert a distance in miles to a distance in kilometers and the number happens to be in the Fibonacci sequence, and 2) you have the Fibonacci sequence memorized to the appropriate element.

Oh and you don’t have any sort of mobile device handy that can just do the conversion. Or you can’t multiply by 1.6 (or 0.6 to go the other way) in your head.

Still, it’s neat, like the fact that there are pi x ten million seconds in a year (accurate to better than 1%).

In a Universe of numbers, coincidences are inevitable. Happily, some of them are also fun.

* Note Bluesky is still in beta, and I don’t know when it will open to the public at large. Hopefully soon, as long as they figure out how to, y’know, keep off the Nazis and MRAs and the rest of those fetid gangrenous-brained zombies.

Et alia

You can email me at [email protected] (though replies can take a while), and all my social media outlets are gathered together at about.me. Also, if you don’t already, please subscribe to this newsletter! And feel free to tell a friend or nine, too. Thanks!