I’m amazed that these philosophy types get paid to to write about and teach what is essentially a trivial point in math, affine spaces (removing absolute point of origin), no pun intended.. How annoying.
I’m pretty sure that you don’t understand the problem being discussed, but that’s an uncharitable impression. Could you indulge me in some further explanation of what you mean by, say, the reference to affine spaces?
I’m pretty sure that you don’t understand the problem being discussed
That’s quite possible, though, having studied some General Relativity, I probably understand a bit more about time than an average philosopher.
Could you indulge me in some further explanation of what you mean by, say, the reference to affine spaces?
Indulging, quoting some Wikipedia:
A-series (non-affine) “is past”, “is present” and “is future.” Here there is a fixed (for a given time) origin.
B-series (affine): “comes before” (or precedes) and “comes after” (or follows). Here there is no fixed origin (no “fundamental difference between past and future”, whatever the vague term “fundamental” might mean).
That’s quite possible, though, having studied some General Relativity, I probably understand a bit more about time than an average philosopher.
I’d love to ask you some questions about that, average philosopher to physicist.
Indulging, quoting some Wikipedia:
Okay, so given the distinction between affine and non-affine spaces, the question which (I think) remains is whether or not time is an affine space or a non-affine space. How is that to be resolved?
Right, A-theory’s origin has to be ‘the present moment’. I think A theory probably even excludes the possibility of a beginning of time (Hawking once wrote an article in which he had to coin the phrase ‘imaginary time’ to discuss the question of how long ago the big bang was). I’m sure that’s not an uncontroversial claim though.
This may seem like a kind of fringe metaphysical concern (and it’s certainly a metaphysical concern), but I think the question of the reality of change is probably the original philosophical problem.
Ahh, that. What would be an empirical difference between the two? If none, then there is nothing to resolve.
But that’s the whole question: is it affine or non-affine?
As to what empirical difference it makes (and whether or not ‘none’ means that the question is meaningless) is I suppose a matter for another survey question.
But, if you think Julian Barbour or EY are generally on the right track about the implications of quantum physics, then you’re a B-theorist. Fundamentally, the rejection of A-theory is the rejection of the reality of change. If you’re a B-theorist, change is on the map, but not anywhere in the territory.
Ah, again. See, it matters to me not in the least whether it’s A or B or something else, if they predict all the same things. (As far as I can tell, they predict nothing of consequence, so they are not interesting at all.) As for Barbour, his models have nothing testable in them, as far I know (replace time with “change”? so?), which is a big negative against them. Whether the “block universe” notion is a good one still remains to be seen, so far it is not instrumentally useful. I do not understand EY’s fascination with Barbour. At least MWI, when taken literally, has a chance of being falsifiable.
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.
A-series (non-affine) “is past”, “is present” and “is future.” Here there is a fixed (for a given time) origin.
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.
I’m amazed that these philosophy types get paid to to write about and teach what is essentially a trivial point in math, affine spaces (removing absolute point of origin), no pun intended.. How annoying.
I’m pretty sure that you don’t understand the problem being discussed, but that’s an uncharitable impression. Could you indulge me in some further explanation of what you mean by, say, the reference to affine spaces?
That’s quite possible, though, having studied some General Relativity, I probably understand a bit more about time than an average philosopher.
Indulging, quoting some Wikipedia:
A-series (non-affine) “is past”, “is present” and “is future.” Here there is a fixed (for a given time) origin.
B-series (affine): “comes before” (or precedes) and “comes after” (or follows). Here there is no fixed origin (no “fundamental difference between past and future”, whatever the vague term “fundamental” might mean).
I’d love to ask you some questions about that, average philosopher to physicist.
Okay, so given the distinction between affine and non-affine spaces, the question which (I think) remains is whether or not time is an affine space or a non-affine space. How is that to be resolved?
It does have an origin (the Big Bang) if you will, but that’s not the kind of origin you’d need for A-theory to make sense.
Right, A-theory’s origin has to be ‘the present moment’. I think A theory probably even excludes the possibility of a beginning of time (Hawking once wrote an article in which he had to coin the phrase ‘imaginary time’ to discuss the question of how long ago the big bang was). I’m sure that’s not an uncontroversial claim though.
This may seem like a kind of fringe metaphysical concern (and it’s certainly a metaphysical concern), but I think the question of the reality of change is probably the original philosophical problem.
First, I would not want to give a wrong impression. While I do have a PhD, physics is not my day job.
Ahh, that. What would be an empirical difference between the two? If none, then there is nothing to resolve.
But that’s the whole question: is it affine or non-affine?
As to what empirical difference it makes (and whether or not ‘none’ means that the question is meaningless) is I suppose a matter for another survey question.
But, if you think Julian Barbour or EY are generally on the right track about the implications of quantum physics, then you’re a B-theorist. Fundamentally, the rejection of A-theory is the rejection of the reality of change. If you’re a B-theorist, change is on the map, but not anywhere in the territory.
Ah, again. See, it matters to me not in the least whether it’s A or B or something else, if they predict all the same things. (As far as I can tell, they predict nothing of consequence, so they are not interesting at all.) As for Barbour, his models have nothing testable in them, as far I know (replace time with “change”? so?), which is a big negative against them. Whether the “block universe” notion is a good one still remains to be seen, so far it is not instrumentally useful. I do not understand EY’s fascination with Barbour. At least MWI, when taken literally, has a chance of being falsifiable.
I think that’s a pretty good ‘other’ answer to the question. Thanks for taking the time.
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.