Is the moment of change numerically identical with the time it occurs?

Is the moment of change numerically identical with the time it occurs?

If the moment of change is today at noon, is that the exact same time as today at noon, whatever it is else happens then?

It may be a trivial yes, but few things are all that trivial, and I wondered about ' 'numerical identity' and times, if only due to the elegance of the phrase

• Indeed this may not be that trivial. Numerical identity means identity only in terms of abstract numerology aspect in such a way that you can say one planet is numerically identical with its sun. And in phenomenology time cannot be infinitely divisible down to an instant, only down to some psychophysical duration, then do you think an instant point in physical time assuming it's continuous is numerically identical with a duration?... Commented Aug 16, 2022 at 1:35
• If you're talking about Kantian numerical identity (not confined to him, but he's all I've read the most of, on this count), he used different sectors of pure space to showcase how things could be numerically distinct yet qualitatively equivalent. For time, we would have to show that change-time was not the same pure period of time as occurrence-time, we'd have to show that the two times did not "geometrically" coincide. Commented Aug 16, 2022 at 3:09
• I'm guessing both of you lean toward temporal series being best represented as a series of points in space-time @KristianBerry may I ask whether, supposing a moment of change does not exist, that means that there is no point in space-time that coincides with it, and whether or not "so what? Perhaps a dim witted question (and I should have stuck with the title)
– user62133
Commented Aug 16, 2022 at 4:18
• @not_again, I think the idea of times and spaces as being more "zone-like" in general is given as an option in Kant. Remember, Kant did not have the real-numbered calculus, but an infinitesimal one, and his sense of indivisible points was as empirically inaccessible objects. So a fluid motion that was not just points staggering along discrete lines seems available to his dynamics. Unfortunately, I've never read his actual treatise on physics so hard to say how he cashed such options out. Commented Aug 16, 2022 at 4:24
• On standard accounts, no. The problem is that "moments" do not designate entities (in realistic ontologies), and are rather only abstractions of them, what Frege called "senses". So the context shifts the designation from entities to senses, and numerical identity of senses is highly sensitive to connotations, as in Hesperus/Phosphorus. Since the "moment of change" connotes change in something and "today at noon" does not the senses are not identical, see SEP. Commented Aug 16, 2022 at 4:50

No. One describes an action the other describes a point in time. The action can be repeated the point in time can (as far as we know today) not be revisited so they describe a similar thing but they are not identical. Also what conceptually is the "moment of change"? Like when did something truly start, end or reveal itself to have changed? So it might be more of a time frame than a spot anyway.

• I dunno if describing an action can't describe a point in time
– user62133
Commented Aug 16, 2022 at 12:16
• One part is that an action is a time interval not a point. The other is a bit more tricky. Like picture your classical sine wave. Would you consider the peak and valleys to be identical? Like if you're only interested in the amplitude than they probably are and you could see that whole wave represented in one circle, but suppose your tracking a water wave and putting a rubber ducky on one of them, are they still the same? Commented Aug 16, 2022 at 12:51
• well the moment of change is arguably an instant.
– user62133
Commented Aug 16, 2022 at 13:10

The phrasing of your question is ambiguous, so it is open to interpretation. I cannot be sure what you mean by the 'moment of change' or by 'numerically identical with'. However, in modern physics there is a difference between an event, or a change, and the time at which it occurs. A change may have several attributes, for example it will generally have a spatial location, whereas the time at which it occurs is just one coordinate labelling the position of the change.

In an everyday sense, most changes are not instantaneous (although you can break down a change into parts of increasingly shorter duration), so you cannot sensibly associate them with a single instant of time in any event.

The numerical value of the time at which a change occurs is in any case entirely arbitrary. For example, you might consider an event to have happened at noon, while someone in another time zone might say it happened at one O'clock, and both those times are simply conventions- there is no absolute numerical value associated with a point in time.

Asking if a change is numerically identical with the point of time at which it occurred is rather like asking if it is numerically identical with the distance at which it occurred, measured from some arbitrary origin.

I' unaware of the implications of the question, but here are me two cents ... for what they're worth.

The numerical designation of a moment is dependent on the starting point from which time is measured. This year is 2023 in the Gregorian calendar, but is 1472 in the Armenian calendar, 2973 in the Berber calendar, you get the idea. Check out 2023.

The real identity (is this a mystery novel?) of a moment would be better defined in terms of the events that take place in it, assuming each moment's events are adequately unique.

A moment of change is not numeric and so it can't be numerically identical with some other thing.

With the advent of Einstein's Special Relativity, moments of change - that is events - that are simultaneous in one perspective need not be in another. Thus the notion of a global time breaks down and so also global simultaneity and thus global time breaks down.

What we do have is local simultaneity.

A minimum of two measurements is required to numerically describe a change: initial and final. The "moment of change" is the time between these two measurements and is described as an interval rather than a single point.