Math – Kai Strandskov Music

March 14, 2021March 19, 2021

Pi

Pi is at the very center of the human experience. It’s the number intrinsic to cycles. The rising and setting of the sun? Pi. The cycle of the moon? Pi. The seasons? Pi. The tides? Pi. The motions of the stars and the planets? Pi. Eclipses? Pi.

On a 2d axis, a point on the circle is represented by the horizontal distance (x) and the vertical distance ( y ). And there is an angle represented by how far you’ve traveled around the circle. There is a connection to this angle and the coordinates. If the angle is t, then your location on the circle is (cosine t, sine t). When you travel half way around the circle, you’ve traveled pi radians, and a full circle is 2pi radians. Then, the cycle repeats again as you travel around again.

I think we’re all familiar with the sine wave. It’s the vertical component of your location as you move around a circle. If you graph just that motion, you see a beautiful periodic wave that cycles forever, every distance of 2pi.

You can transform the sine wave to fit different kinds of periodic data. The stock market? Pi. Infection rates? Pi. Roller coaster paths? Pi. The length of a river? Pi. Biological mechanisms defining stripes on a zebra? Pi. A swing set? Pi. Your car’s transmission? Pi. The shocks on your car? Pi. Your steering wheel? Pi. The famous Euler probabilistic curve? Pi. Sound waves? Pi. Square waves used in synthesizers? Pi. Anything and everything cyclical involves Pi. Happy Pi Day!

November 21, 2012November 21, 2012

Trying to push the boundaries

If you search up images of fractals, you see what hippies are into. But you also see some cool patterns that are pleasing to the eye. It turns out DNA is really like fractal seeds–using concepts of iteration and recursion–and so all of life as we know it on Earth is much like a fractal pattern too. Pretty cool. That’s probably why fractals are so pleasing on the eye. It would suck to look around at the world around us and have it be ugly. Compare Julia sets with ferns, as a good example.

Anyway, fractals are also fascinating because you can zoom in and zoom out and yet always see the same amount of complexity. You can probably search up some animated fractal .gif files that zoom in. Try the Mandelbrot set. That’s a good one for that. You keep zooming in, and you keep seeing the same pattern getting repeated. Pretty cool. (It’s like a heat map of how quickly complex numbers approach infinity when you keep squaring them.)

But notice this: The animated gifs don’t zoom in and out on areas where there is no clear pattern. It’s just the pattern that’s the most interesting. With fractals like the Mandelbrot set, the pattern is actually just the borders between regions of space. As you zoom in on the borders, they stay interesting.

It’s the borders where the excitement happens. The boundaries. That’s what people care about. Like the boundaries between land and sea. Tide pools are brimming with life. The boundaries between earth and sky. The boundaries between the chorus, the verse, the bridge, and the solo. The beginning of the song, and the end. The boundary of a black hole, or basketball hoop, or a nation. The boundary between inside your body and outside your body. The boundary between where relativity and quantum mechanics matter more. The boundary between the performer and the audience. The boundary between control and chaos. The boundary between love and hate. The boundary between being full and being sick. The boundary between truth and fiction. The boundary between repetition and redundancy.

I think boundaries really matter. Play with them. Explore them.

October 27, 2012December 14, 2012

I’m not good at Math

I would hear that a lot when I was a math tutor while pursuing my BS in Math at Southern Oregon University. My college classmates and my private students from high school would often tell me this straight up.

But the stark reality is that math is not any harder than anything else. Now, if you came to me and said, “I’m not good at being an astronaut”–that, I could believe. You have to have a PhD, or numerous other degrees, you have to have great social skills, you have to be physically fit, you have to be adaptable, and you have to manage stress. You have to be a Warrior. You’ll probably drop out and never get selected. Genetics plays a large role.

Math is not like being an astronaut. No, you just are not interested.

I don’t know when this whole thing started. But for some reason, if you don’t like math then you get to blame your genetics. As if you have an allergy, and the only cure is less math. So, why go to a tutor? Are tutors like magic wizards that grant you a passing-grade spell?

Don’t tell me you hate all the repetition. How many times have you listened to your favorite song?

But above all else, don’t tell me you’re not good at math. And especially, don’t tell me you’re stupid.

Be honest. You hate math. So let’s find out why that is, then let’s get you a C+ in your algebra class and move on.

I’m not good at math, my ass. You know what you’re not good at? Excuses.