tisdag 10 maj 2016

Bergson and Deleuze on Duration of Time (and Irreversibility)

Duration of thinking.
Duration of smoking.

Both Bergson and Delueze say something essential about time by stressing the concept of duration or "thickness of the present" as a transformer changing past into future. To Bergson and Deleuze change is thus a fundamental aspect of time, and maybe time can simply be identified with change.

Deleuze makes a distinction between a more simple elementary concept of time represented by the Greek god Aion as the simple tick of a clock in linear progression with an infinitely thin present tick as an infinitely thin cut between past and future, and a more complete concept of time represented by Chronos as the duration transforming past to present. One of Bergson's masterpieces is Duration and Simultaneity.

Chronos thus represents the continuity of a phenomenon or being under change, where the past is transformed into present into future in a continuous change which loads the present with history, and which then gives time a direction. Aion represents discontinuous time without history and direction with every tick the same.

We understand that Chronos gives a fuller picture of time than Aion, which is the view of Einstein with his space-time events without history which has created so much confusion and misunderstanding.

Chronos concept of time is present in the generic mathematical model of a time-dependent problem as an intial value problem of the form: Find a function $u(t)$ of a real variable $t$ named time, such that
• $\frac{du}{dt} = f(u)$ for $t > 0$
• $u(0) = 0$
where $f(v)$ is a given function of a vector-valued real variable $v$. Here the differential equation in time-discretized form expresses the transformation of the state $u(t)$ from one time instant $t$ to the next $t + dt$ with the length of the Chronos duration equal to the time step $dt > 0$, carrying along (some of) the history of previous states, in an update of the form $u(t+dt) = u(t) + f(u(t))dt$ with $u(t)$ carrying the history and $f(u(t))dt$ the change.

With the duration of the present equal to the time step, we understand that the length of the duration of the present is not given once and for all, but like the time step can be smaller or bigger depending on the precision of time resolution of an underlying continuous evolution in time we may choose, and like the time step is never zero.

The irreversibility of certain processes as time evolution of $u(t)$, then is expressed in the initial value problem as stability in forward/increasing time and instability in reverse backward/decreasing time. The reversibility or irreversibility of certain processes is thus determined by stability aspects with actual physical processes being represented by intial value problems which are stable in forward time, and irreversible physical procesess being represented by intial value problems which are unstable in backward time and thus not realizable as physical processes.

The 2nd law of Thermodynamics as the law of irreversibility of certain physical processes thus can be based on stability which is a physical property, instead of probability which is unphysical and has ruined modern physics.

It is more illuminating to give evidence of irreversibility as physicsl break-down or blow-up of unstable processes, than to say following Boltzmann that natural processes have a tendency to move from improbable to probable states (rather than the opposite), which is an empty tautological statement.

PS1 Concerning simultaneity, which is so important to Einstein, one may say that physics does not care about this concept, because in physics things happen locally and if two particles collide they do it at the same time. It would be ridiculous to report as a curious fact of a new physics that you met a person in a certain street corner at 1.00 pm once during a day according to your clock, while the person you met insisted that he/she met you once at 2.00 pm according to his/her clock the same day at the same street corner.

This would not be accepted as evidence of new physics, only as evidence that at least one of the clocks was off time. Right?   And yes, Einstein's physics is at most epistemology but not real physics, according to Lorentz.

PS2 Concerning time as change, one may identify time with motion as change of position, of the Earth, of the arms of a clock or with propagation of light. The basic question is then to answer how motion is possible as a solution of Zeno's Paradox of the arrow which at each moment is still and yet moves or changes position. A resolution is presented in posts on Zeno's paradox.

PS3 Bricmont and Sokal as Fashionable Nonsense accuses Deleuze and Guattari of using mathematical language in imprecise way in philosophical texts, which may be more or less meaningful, but forgets that Einstein in a scientific physics text is even more imprecise which is not meaningful.