Musicians practice; actors rehearse; athletes work out; and mathematicians play with numbers. Some of the games they play may seem as silly or pointless as musicians playing scales, but there is a point to it all. That old saying defining insanity as doing the same thing over and over and expecting different results was never really correct (or intended to be used as it often is).
An old joke is more on point: “How do you get to Carnegie Hall?” (Asked the first-time visitors to New York.) — “Practice, practice, practice!” (Replied the street musician they asked.) The point of mathematical play can be sheer exercise for the mind, sometimes can uncover unexpected insights, and once in a while can be sheer fun.
As when finally solving a 65-year-old puzzle involving the number 42!
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 computationalism or consciousness. (Other than in the subjective appreciation of its sheer beauty.)
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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.
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.
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.
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).
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!
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.
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.
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!