Mathematics of Change and Time

Someone has written on a public forum that the law of identity does not always hold, as things change. Thus, a seed becomes a plant; a child becomes an adult; and further on down the line.

There is a very great importance to this line of thinking. A belief that something is always itself is incomplete and does not allow for change. In matters of nature and physical world, such a belief will result in wrong calculations. And at the interpersonal level, seeing someone as remaining what they've known him to be from decades ago prevents growth, alteration and improvement and keeps leading people back to places that they by all righteous measure should have left.

Does something retain its identity? It does and it doesn't. What something is at a later point in time is a function of what it was in the past and the change that has taken place in the interim.

This is in no way a surprising conclusion; but it is something that does need to be said, as people tend to forget things of this nature.

I've ran some mathematical equations on this. Here goes:

(1) A = A                                          (law of identity)
(2) A1 = A0 + D                               (object changes over time, D is total change)
(3) D = t * dD/dt                               (change is time times the rate of change)
(4) A1 = A0 + t*dD/dt                      (substitute (3))
(5) A1 - A0 = D                                (from (2))
(6) A1 - A0 = t*dD/dt                       (substituting from (4))
(7) t= (A1-A0) / (dD/dt)                    (time equals difference divided by rate of change)
(8) t = D / (dD/dt)                              (substituting from (5)
                                                          (time equals change divided by rate of change)
(9) dD/dt = D / t                                 (rate of change is change divided by time)

Conclusions:

(1) For any given change, the faster the change, the less the time; the slower the change, the greater the time.

(2) The greater either the speed of change or the time, the greater the change.

(3) Infinite time or infinite speed of change creates infinite change.

(4) The object retains its identity as A0, with alteration by D, which is a factor of time taken to change and speed of change.

(5) With time, the identity changes in any number of possible directions.

(6) Time is part of the change process and is encoded in the changes that are made in the object being studied.

(7) Time and change thus results in alteration of reality; and time is woven into the fabric of reality, including things as they exist now and as they are yet to exist.