Wow, great stuff, guys. Thanks for the FQXi link, "Bot"-tee'licious. That one could keep me busy for days. And it may give me inspiration for another blog. :)
OK, for the record, my vote is digital.
Thoughts...
- Discrete is not the same as digital. We (and I, in particular) shouldn't play fast and loose with those terms, as it has been pretty easy to use them interchangeably, but they aren't the same. Digital means that the amplitudes of a signal sample can be represented in bits. Discrete doesn't assume that. For example, a sequence like "0 1 0 1 1" is digital and discrete. But a sequence like "π 2π π 3π 0" is discrete because it contains a discrete number of samples, but it isn't digital because "π" (that's pi, in case it is hard to tell from the font) can not be represented digitally, being a transcendental number. Or rather, it would have to be represented with an infinite number of bits, which kind of defeats the purpose of being digital (see below).
- When Achim Kempf talked about space-time being both discrete and continuous, he is playing fast and loose with those two terms as well. In reality, you can REPRESENT a continuous wave with a discrete number. Take a sinusoid of frequency 1 Hz and amplitude 1. Let's represent that with the vector {1, 1}. So, a sinusoid of frequency 3.2 Hz and amplitude 2π would be represented by {3, 2π}. Now, sinusoids are continuous signals. So the representations of these signals can easily be made with discrete numbers. But so what? That's just an artificial mathematical assignment. The real question is whether the sinusoid itself is digital or analog - digital in the temporal domain and/or in the spatial domain vs continuous in either one. Kempf is saying that if there is some frequency beyond which there can is no content in a particular field, then that field can be represented discretely. That is true in the sense of the sinusoid example above, but I think that is missing the point - which is that the field doesn't come first! A field is an artificial construct that scientists come up with to identify some attribute of reality that has some value at various points in space and time. But, if space and time are digital, the field would be emergent from the rules of the bits.
- I would make a similar argument against Tong's paper. He says that integers are emergent just because the solutions to Schrodinger's equation are (for the most part) discrete, but only because they represent units of energy or whatever - very similar to the sinusoid example above. But that DOESN'T mean that underlying the mechanics of atomic states (that Schrodinger's equation describes) can't be a much deeper set of rules and some digital data. In other words, yes, integers may be emergent at the quantum level, but may be the source of everything at a much deeper level. So, the argument doesn't prove analog reality. Neither does his argument that we can't simulate the Standard Model on a computer. We couldn't simulate a mouse brain 10 years ago, but we can now. We couldn't recreate a high definition movie 10 years ago, but we can now. Give it n years and the Standard Model will be explained by deeper reality - on a computer!
- I still say that the best argument for digital vs. analog/continuous is that digital doesn't require infinities but analog/continuous does. And intuitively, I think we all recognize that infinities are impossible.
- I don't think the Holometer will settle the debate. It may lend support to a grainy reality, but that could still be generated but discrete continuous waves like Kempf talks about. Or by the bits and the rules that the guys in my post talk about.
Would love to hear more view and more votes!!!
