# Talk:ATD 1018-1039

## Page 1036

**output . . . can be the indefinite integral of any signal**

- (Discussion mostly removed from the page annotations)

Techno-mathematical-sounding nonsense. The photographic medium does not record any time information for use in such a reconstruction.

(note by Sonni: this is not true. A photograph is the recording of a picture by means of capturing light on a light-sensitive medium *during a timed exposure*. The time of exposure may be reduced, but is never zero. Thus, what is recorded on a photograph is always the amount of light emitted between time t and time t+dt, and even though it's only with high dt that your picture will get visibly blurred, every picture is, in a sense, blurred, in an usually imperceptible amount. So if we analyse the light emitted as a function of time, taking a photograph is indeed a recording of the variation of the function related to a very small variation of time, that is a way, simplistic but substantially correct, to define the derivative. The real problem here is that, once you have a single photograph of an event, you are in possess of a single value that your 'derivative' takes: so you can't calculate its integral in a "closed" form. What you can do is, in a very short interval around the time you're analyzing, assume that the integral is a straight line with your "derivative" as the inclination: and that's exactly what we do when, seeing that the long exposure portrait photograph we've just taken has come out blurred , we scream to the subject: -why on earth did you move?-)

However, what is suggested here is that every photograph potentailly generates a family of integrals (indefinite integral) f(x)+C, where C (the Constant of Integration) can be changed (f(x)+1, f(x)+2, f(x)+3...) [1]--alternate integrations, if you will (see below). This is in fact an elegant mathematical, or, better, 'pataphysical, expression of the phenomenon of looking at a single photograph and imagining it as part of a movie (which is after all just a sequence of still photographs), or of many possible movies--the movie is the integral of the photograph. This is techno-mathematical nonsense of a very particular kind: an example of 'Pataphysics [2], which its originator, the absurdist novelist and playwright Alfred Jarry [3](1873-1907) defined as "The science of imaginary solutions". His fictional creation Dr. Faustroll explains that 'Pataphysics deals with "the laws which govern exceptions and will explain the universe supplementary to this one". One can imagine any number of possible "movies" or world-lines, for the subject of a photograph, any number of alternate histories and supplementary universes.

Many of the other pseudoscientific and "Techno-mathematically nonsensical" explanations and phenomena in this and the following sections, in fact in all of AtD, could be excellent examples of 'Pataphysics: The science of imaginary solutions.

- That is a very useful lead!

Obtaining a mathematical solution of any physical problems is the FIRST step in solving the problems. Once the solutions are obtained one goes to the SECOND step: applying boundary or initial conditions. f(x) + C above is only a set of mathematical solutions which is not the real solution to any possible physical problems until, say, some initial conditions for a particular real problem are given. In other words, one does not just use indefinite integration to obtain answers for physical problems in real world which require initial conditions. For a well-posed initial value problem, each initial condition corresponds to ONE AND ONLY ONE value of C. So there will be ONLY ONE possible solution !!!

- For a well-posed problem. This one isn't. There is no physical constraint that leads us to the one and only one correct value of C. Even if you grant the premise that we can "integrate" a photograph, we still don't have enough boundary conditions to get the unique physical solution. You can see—granting that premise—that
*the gentleman is walking in a straight line*and*the gentleman is walking in a circle*are both valid solutions if the photograph shows a gentleman walking.

(note by Sonni: this is not because we don't know the boundary conditions, but because we know only a single value of the derivative. Having a single photograph is just like knowing that the velocity of a car at a certain time is 100 km/h: this isn't enough to tell where the car will be in 5 minutes, because I don't know how the velocity will vary, but it IS enough to guess where it will be in 1 second. And if I knew the value and direction its velocity takes every, let's say, 5 seconds in the next 5 minutes, I can make a prediction of the complete path it will take in that time - and that's HERE that I would need to know the boundary conditions to refine my prediction from the infinite possible parallel paths to the only one path it will effectively take. This is a process similar to making a movie from a given set of stills.)

- You can't extract time information from a still photograph. Sorry, Sonni. You may be able to measure the range of positions of an object during the short time (delta-
*t*) when the shutter was open, but you cannot determine speed or direction of motion. In 'Pataphysics, yes, and that happens here, but in conventional physics,**no,**that information has been put through a transformation that has no unique inverse. And since the photograph does not contain a derivative, and therefore we can't integrate it, the argument about "the next 5 minutes" is vacuous. Volver 14:28, 23 January 2008 (PST)

- You can't extract time information from a still photograph. Sorry, Sonni. You may be able to measure the range of positions of an object during the short time (delta-

When a photograph is affected by "motion blur", you CAN determine speed and direction of motion: you measure the distance between the two extreme positions that are recorded on the film, you scale it to take into account the reduction due to perspective, you divide by the time of exposition, and then you have measured your speed, and direction. I don't see how this can be denied. And then, what is a normal photograph but a blurred photograph where blurring is but imperceptible? This does not mean that you can't measure the speed: only that the measurable speed is practically zero. Another matter entirely is deducting, from this single value of speed and direction (whether it is zero or not), what will happen next. This is of course impossible. We agree on that, but nonetheless the comparison between a still photograph and a derivative of motion still holds :-)