Thursday, October 13, 2011

seconds, superseconds, Savitt, and Markosian

Steven F. Savitt assumes "But if this process, the pure passage of time, exists, it should
be possible to say at what rate it occurs." in his "Comments on Markosian’s “How Fast Does Time Pass?”".

I don't see why it a priori should be possible to say at what rate time passes. Savitt and Markosian had previously defined "rate" to be of the form "meters per second". It takes at least an argument to say that from the existence of the pure passage of time, we have to now make sense of "seconds per second".

Nevertheless, it is possible to make sense of "the rate of time's passage". [reference coming] said it seems like time passes at a "rate" of
1 second per 1 supersecond
Here a "supersecond' is a unit of a second dimension of time. (On this blog I have also expressed it as a "rate" of 1 clock-second to 1 qualitative-second.)

But, I claim, there is no need for a third dimension of time. There is no need for
1 supersecond per 1 superdupersecond
because superseconds are such that they are rates relative to themselves:
1 supersecond per 1 supersecond
is sufficient. There is no separate third or higher dimension of time. The sequence of meta-times stops with superseconds. (Though it's necessary to have both seconds and superseconds). I don't see what's wrong with that.

Can one have a category without identity morphisms? I read about this somewhere a while ago. Then, we're concerned with a category with two objects, seconds and superseconds. An arrow roughly means "passes relative to", so there are arrows from seconds to superseconds, and arrows from superseconds to superseconds, and that's all. There are no arrows from seconds to seconds nor from superseconds to seconds.

could you use non-wellfounded sets? e.g.
1 supersecond = {now, 1 supersecond}.

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