The Shaky Foundations of Science: The Theory of Falling Toothbrushes

I've been reading Classic Feynman, which has gotten me thinking about physics again, and science in general.

There are some problems you encounter when you try to figure how stuff works in the real world. Some of them are very clear to me; they're problems, but I understand them. There are other problems that aren't very clear to me, and hang around in the back of my mind like little nagging doubts. Let me explain.

This morning I was brushing my teeth and imagined that I knew nothing about physics and was trying to figure out what happens when you drop a toothbrush. That's all science is after all: you see stuff happen and try to understand it better and explain it.

So what would I do?

I'd start dropping the toothbrush and watching it. I'd watch it again and again. Soon I'd probably notice that it starts out slow and speeds up as it falls. Maybe I'd get a video camera and videotape the toothbrush falling and watch the tape frame by frame, and figure out exactly how fast it's falling. I'd notice that it falls at almost the exact same way every time. Sooner or later I'd come up with the Theory of Falling Toothbrushes, which might be stated as follows:

Toothbrushes fall at a constant acceleration: 9.8m/s²

So, is this a good theory? It has some things in it's favour, principally that it predicts the position of the falling toothbrush at a given time to within the error tolerance of most experimental setups you might imagine.

This theory is as good as a scientific theory can be. It has some problems, but, as far as I can tell, these problems are fundamental to scientific theories; that is, these problems exist for every scientific theory that could be invented.

Here are the problems I can see with this:

Category 1: Problems I Understand
These problems are not particularly interesting. They're just occupational annoyances that scientists face. I'll explain them here to distinguish them from the interesting questions.

Problem #1: Almost every physical process you can observe is very very complicated. For instance, when you drop a toothbrush, it bangs into air molecules, and starts out with a small bit of angular momentum since you can't drop it straight down. These will make your experiment come out a bit different every time, and the the complications they introduce will be incalculable. This is not news: The Theory of Falling Toothbrushes actually describes what would happen if you dropped a toothbrush from a perfect dropping machine that imparts no "twist" or "push" as it drops, in a perfect vacuum. If this was the only objection to the theory, it would still describe exactly how toothbrushes fall in a vacuum.

Problem #2: Theories are always doomed to remain theories. I haven't dropped my toothbrush in every possible location at every possible time to ensure that the theory accurately describes toothbrushes falling everywhere at every time. Therefore, my theory will forever remain a theory: I have pretty good confidence that this is how it works, but it's impossible to be sure. No matter how many ways I drop a toothbrush, I might be surprised one time to discover things don't go the way I expect. Sure enough I would. I would discover that at higher altitudes (in a vacuum), the toothbrush would fall slightly slower since I'm farther away from the center of mass of the Earch. If I dropped it from a great enough height, I'd see it gain mass and slow down as it approached the speed of light, according to relativity. If I dropped it from a great height not in a vacuum, I'd see it hit terminal velocity as the air particles bumping into it faster and faster offset the effects of gravity. This is fine too; I understand that a theory is a description of how I think things work from my experience, and I always might be wrong.

Category 2: Problems I Don't Understand
These problems I don't understand the implications of. Clearly they are not serious objections to science, since science has accomplished so much in spite of them. I don't know if they are fundamental issues with the underpinnings of science, or if I'm just confused and need to get straightened out.

Problem 3: At some point you have to jump from abstract to concrete, and I don't really understand the details of the jump.

When I think about a toothbrush falling, I'm working in the abstract math world. I'm assuming that actual physical "space" works exactly like mathematical 3-d space: there are infinite numbers of continuous points, and matter within that space exists within a closed surface with a certain density. That's a mathematical abstraction though that just kinda seems to work like reality, but they're only related by this foggy "I think it works a bit like that" feeling that I have no confidence in. So my description of how toothbrushes fall is really a set of rules for my toothbrush abstraction (my closed curve in math 3-d space with a density function within the surface). What do I really mean when I use that abstraction to describe the real world that actually has molecules and atoms and quarks, etc... etc... and is not an actual density function in math space? I don't know. I have kind of a foggy idea that you could make a set of rules that map your math model to predictions about what your measurement tools will read with various experiments. Kind of a real-world to math-model interface definition. I'm not really happy with my understanding of this yet though.

Problem 4: What the heck is this reality we're describing anyway? How do I know about toothbrushes in the first place? My rods and cones are stimulated to make a mental image of the toothbrush, and the sensors in my hands and mouth seem to tell me something is there. And I could taste it, smell it and hear it too. But that's all I've got! Who knows what it's like out there! Is there some kind of reality outside of my head? Seems to be that way; I think The Superhero exists and we seem to agree on what's out there. Does it make sense to talk about "out there"? All I know is what's in my head. Chris Langan addresses some of these issues in CTMU.

I think the way it works is that there's 2 separate problems: the mental to real-world (or math-model to real-world) mapping is one problem, and that's the one that's fuzzy for me. Then science sits on top of that and uses it, and has the problems in Category 1, which I've got under control.

That's all I've got for now; I'll report back when I figure it out!