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komponisto comments on [Poll] Less Wrong and Mainstream Philosophy: How Different are We? - Less Wrong
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A lot of philosophy is like this.
However, it takes a while to get to this point. The math in question dates essentially from the 19th century, while questions about time are ancient.
One would think that in over 100 years the philosophers would have caught on, if only they bothered to try.
Believe me, plenty of philosophers understand what an affine space is. Not enough, unfortunately, but still plenty.
Why then does SEP not mention it in the discussion of this A and B stuff? Certainly detracts from its credibility.
Because it is not relevant. B-theory time and A-theory time are not related like an affine space is related to a vector space. You can't get from B-theory time to A-theory time by picking an origin and calling it "the present". The whole point of the A-theory is that the present is not a static point in time. It moves. The particular mathematical representation you suggest doesn't capture this.
Right, I was pondering that, too:
Indeed the transformation does not capture this apparently moving origin. What does "moving" mean in this context? How would you describe it mathematically? In the block universe model, this is ought to be pretty easy by introducing a shifting origin, but it is probably harder in the growing block universe model. I need to think about it some more, feel free to point me to any mathematical references if you know of any. Though I do not think I will continue in this thread, due to the distracting karma burn it seems to extract, reminding me that, on average, people don't want me to.
This paper gives a reasonably rigorous mathematical treatment of the growing block model in the Newtonian, relativistic and causal set contexts. Also see this paper for a discussion of whether quantum gravity offers brighter prospects for A-theory than classical relativity. Let me know if you'd like ungated versions of either of these.