On 29/08/2017 3:17 pm, Russell Standish wrote:
I attach a brief PDF of what I have so far. It shows how observer moments, modelled as sets of bitstrings classified by looking at a finite number of bits naturally map to vectors in a complex vector space. There are some lemmas, proofs and conjectures (theorems I haven't managed to prove yet, but think are plausible).
I have had a look through your notes.I am not sure that I fully understand the direction you are heading in, but I have one or two comments to make at this stage.
You say: "A conscious observer of these strings will only examine a finite number of bits prior to making a decision on the meaning." This strikes me a tending to be a little dualist -- there is no-one examining any strings; some string or other corresponds to the actual observer (moment), so it is not "observed", it is the actual OM. Secondly, you take this string to be a fixed, finite length prefix, followed by an infinite string of "don't care" bits. I don't see that you can take the OM to be the leading section of the string -- it could occur anywhere, and there might be an essentially infinite string of lead-in "don't care" bits. But I don't think that this is necessarily a problem for your analysis. The assumption that the OM is a finite section of the string might be a bit strong -- why could it not be an infinite sub-section of the infinite string? The problem with infinite bit strings describing OMs might be that indexing becomes problematic.
The main difficulty I see is that you are simply analysing some properties of sets of strings. I do not see any way that you can characterize these strings as OMs. You start by picking out the set of strings containing an OM, but I do not see how you can ensure that manipulations of these strings necessarily leads to other possible OMs. What makes a string an OM -- other thanthe fact that that is how you select the string in the first place. Changing it in any way has not been shown to lead to some other OM. I don't see that an OM can match a number of different prefixes -- after all, the "prefix" is the OM! Of course, the same prefix might have any number of following "don't care" bits, so an OM is a union of atomic OMs, as you say.
I also don't really like the idea that the outcome of a measurement can be modelled via set intersection. OM A plus measurement outcome B is not necessarily the intersection of A and B. B is a measurement outcome, not necessarily an OM in itself. The OM representing A observing some measurement outcome B is surely some new OM, and it is not clear to me how it is to be related to either A or B without making some pretty strong assumptions.
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