Yes, but there are exponentially more concepts than words. The words we have are sparse set of labels for particularly relevant combinations.

But yeah, the continuous dimensions can hide many more binary dimensions.

For example, 4-D rgba can be smashed into 1 continuous (or 64-bit) dimension, but that feels a bit like cheating.

So it sort of feels like 1000 64-bit dimensions is a tricky name. 64000 1bit dimensions.