Math’s Unfortunate Divorce from Meaning

Concepts are understood by the mind via spatial/geometric distinction. Concepts only make sense through abstract objects and the spaces they occupy in the mind.

The abstraction in mathematics has become divorced from this spatial reasoning, because doing so alleviated the perceived constraints of real-world geometry (imaginary numbers, negative dimensions, etc.).

The result is a tragedy in both pedagogy and application. Meaningless symbols to the uninitiated, whose original geometric origins (which contained far more implicit information than our abstract symbols) have been all but lost.

Worse, abstract concepts do not require a divorce from spatial reasoning, it requires a redefinition of space itself, which science ended up implementing in their models anyway.

Like removing a keystone species for the sake of “progress”, only to realize later it was critical all along. Now we have bland, vacuous marks and glyphs given as the starting point, when they should be the very last, most concise summary given for a system that is far richer.

Reclaim how the mind works, for yourself and others, before you spatter your page with the drained leftovers of history’s unfortunate divorce from meaning.