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
again.
Data from the individual frames is delivered sequentially as a
continuously
varying analogue signal with gaps provided for the blanking of the
electron
beam during the vertical and horizontal retrace. The signal is then
recorded
on the video tape using a helical scan recording head as set of
diagonally
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
serially
or, in older cameras, the analogue value sent for each pixel is the
integral
under a weighting function of the illumination of that pixel in the
period
immediately preceeding its transmission. Normally this weighting
function
is set so that the time constant is of the order of a 30th of a second.
For
some older cameras in use in the 60s the time constant was longer
leading
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
the
0th row would be updated with information for the 0th industry as an
average
of its input of other goods over the interval 1st jan 1996 to 31dec
1997.
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
period
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
interval
for alternate rows would be displaced by a year.
The same applies to TV pictures. If they are played at slow speed or
converted
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