I had a similar experience working with products of numbers of the form (a+b)/(c+d), and then I showed it to John Conway (lucky me, I had access to the master), who instantly recognized that I had only stumbled across a known realization of GL(2).

Sigh...

Also (hehe): quantum theory, everything is quantized. So as far as I understand physics, indescribable numbers aren't god's numbers, they're actually our own invention.