Some of you might be wondering what it is about this Karplus-Strong algorithm that has got me interested. Of course, long time readers of my blog might well have wondered that about any of a number of things that I’ve written about. What is it about checkers that prompted me to write a checkers program? What is it about prime numbers or pi that made me write programs to compute them? What is it about the FFT? What is it about FPGAs and computer architecture? Why did I find Brian Beckman’s Physics of Racing intriguing?
I think it has something to do with hidden complexity.
Consider for example the Karplus-Strong algorithm that I coded up. It’s relatively simple: just a few lines of code. But it has complex behavior: behavior that is in some sense surprising. It’s hard to see from examining it how it can generate the kind of sounds it produces. Ken Steiglitz’s book doesn’t really provide enough background on how it works until 100 pages in, and even then, there is a lot of subtlety which isn’t really apparent. There is genuine genius in the dozen or so lines of code that make it up: genius that hints at hidden knowledge and new ideas.
Ditto for checkers. Payne did some of the first analysis of so-called “First Position” back in the late 1700s. These are some of the most basic checker positions: two king versus one king and one man endgames. Yet, inside these positions are some deeply complex principles, principles which still make writing a good checker playing program difficult.
Beckman’s Physics of Racing provides some insight into how race cars actually work. Making a car go fast around a track is more than just weight and horsepower. It’s about understeer and oversteer. It’s about balance. It’s about friction and slip.
There is more in these systems that are evident from first glance. In many cases, mathematics provides an insight into the underlying structure and complexity. Computers can lend insight into systems which are too complicated to understand from first principles. And in the end, engineering and actual physical implementation provides us with the glory of music, the fun of games, and the thrill of racing.
Richard Feynman once famously mused that science provided a glimpse into a kind of deep beauty. Rather than paraphrase him, I’ll let him talk…
The world of mathematics and physics and computing provides us an opportunity to explore the deeper inner beauty of things in new ways. And geeky as it is, that’s what I think underlies some of the themes I explore on this blog.
There, glad I got that off my chest. Now, back to work.