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Tag Archives: mathematics

Mandelbrot Antennae

*[click for big]*

I realized that, if I’m going to do the **Mandelbrot** in May, I’d better get a move on it. This ties to the main theme of Mind in May only in being about *computation* — but not about computation**alism** or consciousness. (Other than in the *subjective appreciation* of its sheer beauty.)
I’ve heard it called “the most complex” mathematical object, but that’s a hard title to earn, let alone hold. It’s complexity does have attractive and fascinating aspects, though. For most, its visceral visual beauty puts it miles ahead of the cool intellectual poetry of Euler’s Identity (both beauties live on the same block, though).

For me, the cool thing about the Mandelbrot is that it’s a computation that can never be fully computed.

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9 Comments | tags: computation, computer model, computer program, fractals, Mandelbrot, Mandelbrot fractal, mathematics, Turing Halting Problem | posted in Computers, Math

An old saying has it that *“March comes in like a lion and goes out like a lamb.”* That was certainly the case for us this year. February and early March were full-on old-fashioned winter, yet when baseball season started (in the USA) this past Thursday, the snow was mostly gone, and temps were in the 50s. (That’s the thing about winter: spring is pretty sweet.)

The end of March means the official end of the Mathness, but it’s not exactly the end of the math. The whole point of the rotation study was trying to understand 4D rotation, and I haven’t explored that, yet. I plan to, and soon.

But today, as an exit March, I want to talk about math phobia.

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9 Comments | tags: math anxiety, math phobia, mathematics | posted in Math

Last week we celebrated Albert Einstein’s birthday (he turned 140). Now we need another cake so we can celebrate the *other* March major mathematician’s birthday — **Emmy Noether** turns 137 today.

To my regret, despite that I frequently invoke her name (she co-starred with Albert in the Special Relativity series), her work in mathematics is pretty far above my head, and I’m simply not qualified to write about it. I can say that her work connects mathematical symmetry with physical conservation laws. She also made significant contributions to abstract algebra.

Just recently, I’ve begun to nibble at the edges of the latter in the form of group theory as a part of studying rotation.

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20 Comments | tags: algebra, cube, Emmy Noether, group theory, mathematics, rotation, square, tesseract | posted in Math

Back at the start of March Mathness I promised the math would be “fun” (really!), but anyone would be forgiven for thinking the previous two posts about Special Relativity weren’t all that much “fun.” (I really enjoy stuff like that, so it’s fun for *me*, but there’s no question it’s not everyone’s cup of tea.)

Trying to reach for something a bit lighter and potentially more appealing as the promised “fun,” I present, for your dining and dancing pleasure, a trio of number games that anyone can play and which might just tug at the corners of your enjoyment.

We can start with **277777788888899** (and why it’s special).

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2 Comments | tags: 277777788888899, algorithm, calculation, Collatz conjecture, computation, Mandelbrot, mathematics, multiplicative persistence, Numberphile | posted in Math

*Time for math!*

I have a special fondness for the month of March. For one thing, it contains the Vernal Equinox — one of my favorite days, because it heralds six months of light. (As a Minnesotan, Spring has much more impact than it did when I lived in Los Angeles.)

March is when the weather elves begin preparing for the April Showers that create May Flowers. It’s when baseball Spring Training is in full swing with the regular season looming (lately, even at the end of the month; this year on the 28th).

It also contains some important birthdays: Albert Einstein (3/14) and Emmy Noether (3/23), to name two, and in their honor I have myriad math posts planned!

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8 Comments | tags: 3Blue1Brown, Albert Einstein, complex numbers, Emmy Noether, mathematics, Mathologer, Numberphile, tesseract | posted in Math

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