I agree with you that systems which are not totally constrained will show a variety of outcomes and that the relative frequencies of the outcomes are a function of the physics of the system. I’m not sure I’d agree that the relative frequencies can be derived solely from the geometry of the system in the same way as distance, etc. The critical factor missing from your exposition is the measure on the relative frequencies of the initial conditions.
I haven’t actually made a statement about frequencies of outcomes. So far I’ve only been talking about the physics and geometry of the system. The relevant aspect of the geometry is the proportions of possibilities, and talking about proportions as I said requires the assignment of a measure analogous to length or area or volume, only the volume-like measure in question that I am talking about is a “volume” in a phase space (space of possibilities) rather than normal space.
I do eventually want to say something about frequencies and how they relate to proportions of possibilities, but I didn’t do that yet.
The prediction of equal frequencies is critically founded on a state of information, not a state of the world. It’s objective only in the sense that anyone with the same state of information must make the same prediction.
Yes, but you’re talking about the prediction of equal frequencies. Prediction is something that someone does, and so naturally it involves the state of information possessed by him. But there’s more going on than people making predictions. There’s also the coin’s behavior itself. The coin falls heads-up with a certain frequency regardless of whether anyone ever made any prediction about it. If you toss a coin a few million times and it comes up heads about half the time, one question you might ask is this: what, if anything, caused the coin to come up heads about half the time (as opposed to, say, 3⁄4 of the time)? This isn’t a question about whether it would be rational to predict the frequency. It’s a question about a cause. If you want to understand what caused something to happen, look at the geometry and physics of it.
I agree with you that systems which are not totally constrained will show a variety of outcomes and that the relative frequencies of the outcomes are a function of the physics of the system. I’m not sure I’d agree that the relative frequencies can be derived solely from the geometry of the system in the same way as distance, etc. The critical factor missing from your exposition is the measure on the relative frequencies of the initial conditions.
I haven’t actually made a statement about frequencies of outcomes. So far I’ve only been talking about the physics and geometry of the system. The relevant aspect of the geometry is the proportions of possibilities, and talking about proportions as I said requires the assignment of a measure analogous to length or area or volume, only the volume-like measure in question that I am talking about is a “volume” in a phase space (space of possibilities) rather than normal space.
I do eventually want to say something about frequencies and how they relate to proportions of possibilities, but I didn’t do that yet.
The prediction of equal frequencies is critically founded on a state of information, not a state of the world. It’s objective only in the sense that anyone with the same state of information must make the same prediction.
Yes, but you’re talking about the prediction of equal frequencies. Prediction is something that someone does, and so naturally it involves the state of information possessed by him. But there’s more going on than people making predictions. There’s also the coin’s behavior itself. The coin falls heads-up with a certain frequency regardless of whether anyone ever made any prediction about it. If you toss a coin a few million times and it comes up heads about half the time, one question you might ask is this: what, if anything, caused the coin to come up heads about half the time (as opposed to, say, 3⁄4 of the time)? This isn’t a question about whether it would be rational to predict the frequency. It’s a question about a cause. If you want to understand what caused something to happen, look at the geometry and physics of it.