Yes, I was not aware of the theorem, but I think you are right. Although I think that it is redundant in a way. So if we assume that experience is continuous, then we can still describe it discretely with an arbitrary amount of precision, by "rounding off" the qualities of experience to certain thresholds. I give the example in the article of "rounding off" the experience of light of wavelength 700.00001 nm to just the experience of 700 nm*.
We can of course choose our threshold for rounding off to be arbitrarily small. So we can describe continuous experience discretely with an arbitrarily large degree of precision. This, if I understand correctly, is the same thing we would have gotten out of invoking Poincare's recurrence theorem. Although, as I said, I have only just heard of it, and my understanding of it is only what I could get from a short bit of searching online.
*This of course assumes that there is a single determinate experience for every wavelength of light. This might not be true, but It still looks as though there is a single determinate experience for some wavelength of light under certain other conditions. And if we get that, we still have a definite measure of experience that we can round off. It is just cumbersome to make all these clarifications all the time.
Yes, I was not aware of the theorem, but I think you are right. Although I think that it is redundant in a way. So if we assume that experience is continuous, then we can still describe it discretely with an arbitrary amount of precision, by "rounding off" the qualities of experience to certain thresholds. I give the example in the article of "rounding off" the experience of light of wavelength 700.00001 nm to just the experience of 700 nm*.
We can of course choose our threshold for rounding off to be arbitrarily small. So we can describe continuous experience discretely with an arbitrarily large degree of precision. This, if I understand correctly, is the same thing we would have gotten out of invoking Poincare's recurrence theorem. Although, as I said, I have only just heard of it, and my understanding of it is only what I could get from a short bit of searching online.
*This of course assumes that there is a single determinate experience for every wavelength of light. This might not be true, but It still looks as though there is a single determinate experience for some wavelength of light under certain other conditions. And if we get that, we still have a definite measure of experience that we can round off. It is just cumbersome to make all these clarifications all the time.