Defining Time But let's say that we can make this idea clear. Then a new problem arises. There is no time for change in an instant. Let f(t) be the state of object. If we understand change as the non-equality of f(x) and f(y) at two times x and y, then clearly we can't put x and y in the same instant unless x = y. But then f(x) = f(y) and we don't have change. — 0rff
So there must be a minimum time taken for us to realize that now has changed, or the instant has changed.
The practical problems do not as such concern me. Mathematics fails to capture the full essence of some phenomenon, especially if the phenomenon is qualitative.
I apologize if the reply seemed meagre. It was all I could think of at the time.
We notice change. We seek change. We await change. The invention of abstract, scientific time comes fairly late in the game. We had to institute this time. — 0rff
I think is a good point. This is our limitation. It is hardly appropriate to ask the Universe as to care about it. The now simply changes and we notice it. At all times.
We notice that one moment at all times. The other moments are lost in the past. Anything that would attempt to define time mathematically otherwise, would be trying to capture that past.
At this point the role of the arrow of causality or arrow of time comes into account.
So, time currently can be said to be comprised of two factors, one now, the other causality.
I wish to point out that causality is not needed per se.
It is natural to think that when quantifying a qualitative phenomenon, somethings are lost in the process.
Regarding your earlier reply, where you point out that now could be a real number.
I think your approach is correct, but we are looking for continuity there. What way is there to know if indeed time is continuous, at all points, if all we can do is observe the now, and some data from the past?