# Energy, Information, and Geometry

When I was around eight years old, I had a Mickey Mouse record player with built in settings for neutral, 33 RPM, 45 RPM, and 78 RPM in my room. I’d spend hours playing records on that thing. For fun, I’d listen to a record at the wrong speed, see if I could hear the frequency ratios and then map them back to the correct speed. If I listened to a 33 RPM record at 45 RPM, the pitch would be off by 45/33. I tried to imagine the ratio between them (1.36). While other eight-year-olds were outside playing ball, there I was there on my bedroom floor trying out different combinations of records and speeds.

One day, I put the record player in neutral and walked my fingers along the record. I wanted to see if I could hear when it hit the right pitch. This little game led to puzzling discovery. I realized that if I used the point of the needle as a guide, in order to keep the record at the right pitch, I had to change the speed of my fingers as I walked them from the outer to the inner rim. This meant that, from the perspective of the needle, the speed of the record changed over time. When I graphed it out in my head, I saw that the needle traveled one outer diameter per unit of time on the outer rim and one inner diameter per unit of time on the inner rim. The velocity of the needle (inches/second) changed as the needle moved over the surface of the record. Yet the pitch of the music stayed the same. Why?  This didn’t make any sense to me at all.

I disassembled the record player to see if I could find out why the pitch didn’t change. I looked at the speakers and the speaker wire. I thought that it might have longer wires to compensate for the varying speed of the needle over the surface of the record. I couldn’t figure it out, but I was not going to give up because I knew that there was a physical answer to the riddle.

As I struggled with the mystery, my brother walked in and asked what I was doing. I explained and it took him all of a second to fire back: “Mark, it is just recorded that way. The grooves hold the information and it is stored to compensate for the change in speed.” I was looking at the record player for the answer, but the answer was in the way the information was stored in the grooves of the record itself.

I was dealing with an energy and information system. The energy was the sound; the information was the speed of the record, the pitch, the grooves on the vinyl, and the location of the needle at any given time. And the two were related through the system’s geometry (the grooves in the record vs the speed of the needle), which showed the relationships between the components, the path of the information flow, the speed of the system, and the rates of change.

Once I figured this out, I knew it was possible to imagine all kinds of dynamic systems by understanding the scale, speed, time, color, rules, and distance between things. And not only that, I saw that it is also possible to map these things onto a spatial model that shows me how the whole thing works.

This observation has been useful.