Something fascinating from an “amateur analysis” of the moon’s orbit — the sort of thing I’m sure a lot of people wish they did but never do.

In other words, the Sun exerts more than twice as much gravitational force on the Moon as the Earth does. Asimov argued that this means the Moon is really orbiting the Sun, with some perturbation by the Earth, and that’s why the Moon’s path looks like a slightly wobbly circle around the Sun.

We might look upon the Moon, then, as neither a true satellite of the Earth, nor captured one, but as a planet, in its own right, moving about the Sun, in careful step with the Earth. To be sure, from within the Earth-Moon system, the simplest way of picturing the situation is to have the Moon revolve about the Earth; but if you were to draw a picture of the orbits of the Earth and Moon about the Sun, exactly to scale, you would see that the Moon’s orbit is everywhere concave toward the Sun. It is always “falling” toward the Sun.

I was inspired by this short Randall Carlson episode to re-construct the diagram in Wolfram Mathematica.

It is a geometric construction of “the golden mean”, and then viewing it as a ratio, as the basis for a triangle, and as the basis for a pair of circles.

Here is a screenshot of that intermediate step:

For extra fun, there is a comparison of this ratio with a few interesting real-world … objects.

Here is a screenshot of that part:

But the real takeaway is how fluid it is to tinker with all this.

As I grow older, I really appreciate the “amateur joy” of all this 🙂

Here is the notebook published to the cloud, free to access publicly.

I had a T-shirt with a certain pattern that was fading out. I didn’t know at the time that this had a name, and later learned it was a geometrical pattern that had certain interesting connections. I won’t link to that here, but you can find it by searching for “Metatron’s cube” online.

Re-creating this geometrical pattern became a fun exercise within Wolfram Mathematica (which is such a useful and under-rated tool, btw, I can’t recommend it enough for anyone with the slightest interest in doodling, tinkering, learning, simulating …).

Nothing fancy, just a bunch of circles, points, lines, triangles. Good old-fashioned geometry.

I was able to experiment with a few different designs until I settled on one I liked. Mathematica allowed me to export what I had as a regular PNG file.

I still had to do some post-processing — to be honest, I’m sure there are tools within Mathematica for this, but I just used a photo-editing tool on my laptop to remove all the black and make the background transparent.

I had to pick a website to use for this, since there are so many options today. I went with something that I knew from many years ago, Zazzle, though again, I’m sure there’s something better right now.

Playing around with Mathematica for a few minutes.

Or rather, using it to play around.

I’m trying to figure out the “least B.S.” portions of “web3/defi/whatever”. So far, a limited goal is to follow along a couple of “stable, publicly used and usable” blockchains, and I picked Tezos and Cardano for this.

I built some probing views for each, as cloud notebooks:

Very elementary stuff, but it took a few minutes, and really shows how Wolfram (Mathematica) is a really great “computational explorer” right now.

P.S. eyeballing the two, at a very subjective, no-flame-war, just-this-instance level, Tezos seems to be stably handling about 2x transaction throughput compared to Cardano.