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Hugh's right.
To make a science lesson out of this, let's see if we can apply Shannon's
channel-capacity theorem. That is,
capacity = analog bandwidth * log(signal-to-noise ratio)
where for composite video the bandwidth is less than 6 MHz, and we can
estimate log(SNR) to be something like 10 bits.
Contrast this with the monitor I've got here, which is putting out
80 Hz refresh * 1280 horiz * 1024 vert * 3 colors * 8 bits apiece
Collecting results, we have
composite video: 6 * 10^6 bytes per second
computer monitor: 314 * 10^6 bytes per second
(i.e. 80 * 1280 * 1024 * 3)
At this point, we need not wonder why the composite video looks five or ten
times worse. Indeed a better question would be why it looks _only_ five or
ten times worse, not fifty times worse. Most of the answer has to do with
perceptual coding. There are certain things that the human eye cannot
perceive, such as high-spatial-frequency color changes. The composite
video signal is verrrry cleverly coded to exploit this, assigning its
precious bandwidth to the sort of things that are most perceptible in
"ordinary" scenes.
/snip/