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The easiest way to correlate it is think of audio like a digital picture.
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You have to be careful with digital photography analogies.
Going from 960x960 to exactly half, is NOT 480x480 (it would actually be one quarter the size).
Imagine a 2x2 pixel image (4 pixels like a box).
If they were like a checkerboard (black/white) and you need to 'downsample' to only 2 pixels worth of info, which would be black/white/etc...?
In real life, the image gets a little 'fuzzy'.