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People born after 2000 have never seen the cosmic microwave background on their TV set.
(startrek.website)
A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. A showerthought should offer a unique perspective on an ordinary part of life.
The trope of video/audio breaking down into static is an easy shorthand that is unlikely to be forgotten, probably even well after all the devices capable of doing so have long since been buried in the landfill.
It's especially hilarious in media depicting the far-flung future, where apparently all technologically advanced space men and their communications devices -- not to mention high powered central supercomputers and so on and so forth -- somehow still work over NTSC television signals. Even by the early 1980's it should have been entirely predictable that in "the future" anything like that would be digital, considering we already had widespread digital audio media (CD's), and digital video was already making inroads into the computing industry.