Some emails resulting from the posting earlier. Roy Simpson worked with me at Standard Telecommunications Laboratories in the late 1980s on AI topics. His background is physics. As usual with email, read from the bottom up.
On the issue of the physics - QM (quantum mechanics) link and the branching aspect of time, an interesting gap appears in QM as discussed in Penrose's Road to Reality. Accordingly the area is "Multi-body Relativistic QM" - it sounds a mouthful, but the reason it hasn’t been developed is because it would seem to introduce multi-dimensional time -which no-one can make sense of.... and yet this area needs developing..... For various reasons I begin to think that there is a "Worldview" issue involved here. Worldviews are essentially psychological so maybe there is a connection here too.
Thus it seems likely that the psychological aspect of time will be closely linked to AI and also to the physics of time (and its perception). All these components need to converge on a good explanation.
I was more interested in the 'psychology' of time-past and time-future. I appreciate your point and the arguments work I think with directed graphs in general. The concept of 'time' comes in with the idea of an order relation on events, I suppose, but it doesn't have to be a total order. Note the diverse models of the various modal logics which have been applied to time modelling - forwards and backwards branching time as well as linear time.
The underlying physics would be the real boundary condition, but it's not clear to me that you get a good answer. The ontology behind QM is completely obscure (there are no classical events, only amplitudes). Since classical (Einsteinian)physics is effectively time-reversible, then I guess you have a total order. But perhaps it all breaks down again at the Planck length or something, where space-time meets quantum effects.
The piece was really a note to self, and would need a fair bit of work to reach conference paper standard, even if there was a place to put it. I DO think that the 'AI level' has something to add to the discussion of the 'psychological arrow of time', especially given the inadequacy of the treatment given by physicists who normally write about this stuff and who lack AI-based formal models.
----- Original Message ----
From: Roy Simpson
To: Nigel Seel
Sent: Sunday, December 10, 2006 10:52:10 AM
Subject: Recent Blog on Time Asymmetry
I am not clear whether the article notes that there is a distinction forward and reverse in Turing Machine operation.
If we consider a TM obeying function f so that e.g. f(1)=5, f(2)=6,f(3)=7,f(4)=5, ... then we can film a (any) sequence of inputs and the corresponding outputs. We run the film in reverse to observe the non-functional relation g. Non-functional since g(5)= 4 and g(5)=1.
So there is an asymmetry between f and g. To restore g to being a function (and so the reverse flow looks behaviourally like the forward flow) it is necessary to introduce another parameter - the Order - into the type and description of g. So f: Nat --> Nat, but g: Nat X Nat --> Nat, but g is now functional.
Arguments like this might suggest that the origin of temporal properties is fundamentally a computational one rather than a physical one, as commonly assumed.