[OPE-L:6481] [PAUL C] Re: time: continuous and discrete

Gerald Levy (glevy@pratt.edu)
Mon, 20 Apr 1998 17:09:50 -0400 (EDT)

---------- Forwarded message ----------
>From wpc@faraday.org Mon Apr 20 02:05:26 1998
From: Paul Cockshott <wpc@faraday.org>

I am afraid that the analogy does not work.

A cine film camera takes typically 30 frames per second.
A TV camera using the PAL standard takes 60 interlaced frames
a second. An interlaced frame contains information about every second
scan line, thus the 0th frame contains all the even lines of the picture

the 1st frame all the odd lines, then the 2nd frame all the even lines

Data from the individual frames is delivered sequentially as a
varying analogue signal with gaps provided for the blanking of the
beam during the vertical and horizontal retrace. The signal is then
on the video tape using a helical scan recording head as set of
oriented magnetic stripes, one per scan line.

>From a temporal point of view there is only a minor difference between
this and a cine camera. Depending upon the technology of the actual
detector in the camera the information for a frame may either be
collected synchronously for the entire frame and then transmitted
or, in older cameras, the analogue value sent for each pixel is the
under a weighting function of the illumination of that pixel in the
immediately preceeding its transmission. Normally this weighting
is set so that the time constant is of the order of a 30th of a second.
some older cameras in use in the 60s the time constant was longer
to the sort of smearing one saw on the broadcasts from the moon of
Niel Armstrong.

The economic analogy would be an input output table with 730 rows whose
data were
updated in total every 2 years. The alternate rows would be updated
each year, with one row updated each day, so that on the 1st of jan 1998
0th row would be updated with information for the 0th industry as an
of its input of other goods over the interval 1st jan 1996 to 31dec
On the 2nd Jan 1998 the 2nd
row would be updated with the flows into that industry over the period
2nd jan
1997 to 1st jan 1998, etc.
On the 1st jan 1999 we would get the data for the 1st industry over the
1 jan 1997 to 31 dec 1998.

The result of course would be an i/o table that is not internally
consistent since
each row would apply to a different time interval. The time capture
for alternate rows would be displaced by a year.
The same applies to TV pictures. If they are played at slow speed or
into stills, any moving vertical edge acquires a sawtooth structure due
to the
inconsistency of time intervals at which alternate lines are samples.

Allin Cottrell wrote:

> This is a bit off-topic, but given the degree of interest in
> matters of temporality on the list, maybe not too far off...
> I'd like to come up with a nice analogical explanation of the
> difference between discrete and continous time in economic
> modeling, for pedagogical purposes. I thought of this:
> discrete time modeling is like a movie (discrete frames =
> periods) while continuous time modeling is like a video tape
> made by a TV camera. Anyone know if the second half of the
> analogy actually holds up? Thanks.
> Allin Cottrell
> Department of Economics
> Wake Forest University, NC