Right. The DCT, in theory, is completely lossless. But the reason that the "other space" is helpful for us for compression is because our eyes and ears are more

Right. The DCT, in theory, is completely lossless. But the reason that the "other space" is helpful for us for compression is because our eyes and ears are more interested in comparing relatively than absolutely. So you don't need the exact high-frequency content, just the relatively correct high-frequency content. As discussed, "high-frequency" just means stuff that's moving very fast. In sound, that's compared to pitch. In a JPEG image, that means a given pixel's brightness. This is what the DCT is exploiting -- that we can adjust the high-frequency terms and it will still look OK to our eyes. https://magcius.github.io/dctx/ https://magcius.github.io/dctx/