Changes

For example, relative to a frame of observation that is left implicit for now, one is permitted to make the following sorts of inference:  From the fact that <math>A\!</math> and <math>\operatorname{d}A</math> are true at a given moment one may infer that <math>(A)\!</math> will be true in the next moment of observation.  Altogether in the present instance, there is the fourfold scheme of inference that is shown below:

For example, relative to a frame of observation that is left implicit for now, one is permitted to make the following sorts of inference:  From the fact that <math>A\!</math> and <math>\operatorname{d}A</math> are true at a given moment one may infer that <math>(A)\!</math> will be true in the next moment of observation.  Altogether in the present instance, there is the fourfold scheme of inference that is shown below:

{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:96%"

{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:96%"

|

|

{| align="center" border="0" cellpadding="8" cellspacing="0" style="text-align:center; width:96%"

{| align="center" border="0" cellpadding="8" cellspacing="0" style="text-align:center; width:96%"

| &nbsp; || From || (''A'') || and || (d''A'') || infer || (''A'') || next. || &nbsp;

| &nbsp;

| From

| <math>\overline{q}\!</math>

| and

| <math>\overline{\operatorname{d}q}\!</math>

| infer

| <math>\overline{q}\!</math>

| next.

| &nbsp;

|-

|-

| &nbsp; || From || (''A'') || and ||  d''A''  || infer ||  ''A''  || next. || &nbsp;

| &nbsp;

| From

| <math>\overline{q}\!</math>

| and

| <math>\operatorname{d}q\!</math>

| infer

| <math>q\!</math>

| next.

| &nbsp;

|-

|-

| &nbsp; || From ||  ''A''  || and || (d''A'') || infer ||  ''A''  || next. || &nbsp;

| &nbsp;

| From

| <math>q\!</math>

| and

| <math>\overline{\operatorname{d}q}\!</math>

| infer

| <math>q\!</math>

| next.

| &nbsp;

|-

|-

| &nbsp; || From ||  ''A''  || and ||  d''A''  || infer || (''A'') || next. || &nbsp;

| &nbsp;

| From

| <math>q\!</math>

| and

| <math>\operatorname{d}q\!</math>

| infer

| <math>\overline{q}\!</math>

| next.

| &nbsp;

|}

|}

|}

|}

</font><br>

<br>

It might be thought that we need to bring in an independent time variable at this point, but an insight of fundamental importance appears to be that the idea of process is more basic than the notion of time.  A time variable is actually a reference to a ''clock'', that is, a canonical or a convenient process that is established or accepted as a standard of measurement, but in essence no different than any other process.  This raises the question of how different subsystems in a more global process can be brought into comparison, and what it means for one process to serve the function of a local standard for others.  But these inquiries only wrap up puzzles in further riddles, and are obviously too involved to be handled at our current level of approximation.

It might be thought that we need to bring in an independent time variable at this point, but an insight of fundamental importance appears to be that the idea of process is more basic than the notion of time.  A time variable is actually a reference to a ''clock'', that is, a canonical or a convenient process that is established or accepted as a standard of measurement, but in essence no different than any other process.  This raises the question of how different subsystems in a more global process can be brought into comparison, and what it means for one process to serve the function of a local standard for others.  But these inquiries only wrap up puzzles in further riddles, and are obviously too involved to be handled at our current level of approximation.