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Tag Archives: mathematics

Folded into the mixed baklava of my 2018, was a special mathematical bit of honey. With the help of some excellent YouTube videos, the light bulb finally went on for me, and I could see **quaternions**. Judging by online comments I’ve read, I wasn’t alone in the dark.

There does seem a conceptual stumbling block (I tripped, anyway), but once that’s cleared up, quaternions turn out to be pretty easy to use. Which is cool, because they are very useful if you want to rotate some points in 3D space (a need I’m sure many of have experienced over the years).

The stumbling block has to do with quaternions having not one, not two, but three *distinct* “imaginary” numbers.

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16 Comments | tags: complex numbers, math, math theory, mathematics, natural numbers, number systems, numbers, octonion, quaternion, real numbers | posted in Math, Sideband

I seem to be doing a lot of reblogging lately (a lot for me, anyway). But I’m on kind of a math kick right now, and this ties in nicely with all that.

4 gravitons

You’ve probably seen it somewhere on your facebook feed, likely shared by a particularly wide-eyed friend: pi found hidden in the hydrogen atom!

From the headlines, this sounds like some sort of kabbalistic nonsense, like finding the golden ratio in random pictures.

Read the actual articles, and the story is a bit more reasonable. The last two I linked above seem to be decent takes on it, they’re just saddled with ridiculous headlines. As usual, I blame the editors. This time, they’ve obscured an interesting point about the link between physics and mathematics.

So what does “pi found hidden in the hydrogen atom” actually mean?

It doesn’t mean that there’s some deep importance to the number pi in nature, beyond its relevance in mathematics in general. The reason that pi is showing up here isn’t especially deep.

It isn’t trivial either, though. I’ve seen a few people…

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2 Comments | tags: math, math theory, mathematics, physics, pi, quantum physics, science | posted in Math

When I was a high school kid, my dad and I sometimes played a game where one of us would make up a secret code, write a message in that code, and the other would try to decipher the message. We generally used simple substitution ciphers, so it was an exercise in letter frequency analysis and word guessing.

There’s a cute secret code I found in a book back then that really stuck with me because of the neat way it looks. It also stuck with me because it’s so simple that once you learn it, you really can’t forget it.

So for some Saturday fun, I thought I’d share it with you.

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1 Comment | tags: Alan Turing, Alienese, cipher, code, decipher, decoder ring, Freemasons Cipher, Futurama, math, mathematics, one-time pad, Pigpen Cipher, secret code, substitution cipher, The Simpsons | posted in Basics, Math

But my brain is full!

You may have noticed that, in a number of recent posts, the topic has been math. The good-bad news is that there’s more to come (sorry, but I love this stuff). The good-good news is that I’m done with math foundations. For now.

To wrap up the discussion of math’s universality and inevitability — and also of its fascination and beauty — today I just have some YouTube videos you can watch this Sunday afternoon. (Assuming you’re a geek like me.)

So get a coffee and get comfortable!

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6 Comments | tags: algebraic numbers, math, math and sex, math ontology, mathematics, numbers, Philosophy of Math, Theory of Mathematics, transcendental numbers | posted in Math, Opinion

Oh, no! Not *math* again!

Among those who try to imagine alien first contact, many believe that mathematics will be the basis of initial communication. This is based on the perceived *universality* and *inevitability* of mathematics. They see math as so fundamental any intelligence must not only discover it, but must discover the same things we’ve discovered.

There is even a belief that math is more real than the physical universe, that it may be the actual basis of reality. The other end of that spectrum is a belief that mathematics is an invented game of symbol manipulation with no deep meaning.

So today: the idea that math is *universal* and *inevitable*.

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41 Comments | tags: alien math, cardinal numbers, cardinality, counting, counting numbers, first contact, Leopold Kronecker, math, math origins, math theory, mathematics, natural numbers, numbers, Philosophy of Math, rational numbers, real numbers, Theory of Mathematics | posted in Math, Opinion

It was never the plan for this blog, but I’ve found myself several times writing about morals (for example: here, here, and very recently here). In those posts I touched on what morality means and how we might define it. I make no claim to breaking new ground or having anything particularly insightful to say — just my 1/50th of a buck based on my own observations, thoughts, and experiences.

The last week or so a set of three thought threads wound through the loom of my mind and seemed to form an interesting fabric. They have to do with the nature of morals, the usefulness of reason, and our modern sense of otherness.

Today I’m going to try to make something out of that fabric.

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53 Comments | tags: alien contact, David Brin, Dogma of Otherness, dolphins, Ernest Hemingway, Immanuel Kant, intelligence, is and ought, mathematics, morality, morals, Otherness, rational thought, reason, Rebecca Goldstein, Rodin, Steven Pinker, The Thinker | posted in Philosophy

Computing…

I’ve written here before about chaos theory and how it prevents us from calculating certain physical models effectively. It’s not that these models don’t accurately reflect the physics involved; it’s that any attempt to use actual numbers introduces tiny errors into the process. These cause the result to drift more and more as the calculation extends into the future.

This is why tomorrow’s weather prediction is fairly accurate but a prediction for a year from now is entirely guesswork. (We could make a rough guess based on past seasons.) Yet the Earth itself is a computer — an *analog* computer — that tells us exactly what the weather is a year from now.

The thing is: it runs in real-time and takes a year to give us an answer!

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2 Comments | tags: analog, analog computer, chaos theory, digital, Information Technology, math, mathematics, orbital mechanics, Pluto, Pluto is a planet, solar system, three-body problem, weather, weather prediction | posted in Math