Man, in that second example, look at how much Bill Murray’s head widens between the first two formats.
Okay, what you originally said was that 4k was twice the resolution of HD. This is a common mistake. For example, people think that 1440p is twice the resolution of 720p, because 720x2=1440. But of course that’s only the vertical height. A 1440p display isn’t twice as “tall” as the 720p one but the same width, it’s twice as high and twice as wide. So it’s 4x the pixels, not twice.
As far as the definition of 4k - the DCI definition of 4K (4096x2160) came after the colloquial use of “4k” was used to refer to anything in that range, including what people would call “UHD 4K”, 3820x2160. Even though it’s not precisely correct, since 3820 is not 4000, this has been common usage.
Even by your own linked wikipedia page:
Which would support the usage of referring to UHD as “4k” is correct, because 4k is colloquially used as a class of resolutions that are pretty close rather than the specific DCI film projection definition of it. You will very likely see “4K Monitor” or “4K TV” used indefinitely referring to UHD units.
What you had was a fundamental misunderstanding - that you thought twice the vertical resolution meant twice the total resolution, not four times the resolution - and what you’re (defensively) accusing me of is a semantical misunderstanding, which is arguable because even your own cite also refers to the way I described it as being a valid interpretation.
Fair enough. I locked onto your use of the word “precisely” and missed the “twice as tall times twice as wide” statement that followed. You are correct that for twice the linear pixel count, there is four times as much information on screen.