in fact, a very brief review of the most elementary functions
gives one the impression that almost all functions that reach a
singularity involve division of two distinct forces or what is essentially
the same, a logarithm. examples include rational funtions
(f(x) = -1 / (x - 5)), logarithmic functions (f(x) = -ln(5-x)), and
trignometric functions (f(x) = tan(x)).
thus a speculative leap: at least two interacting forces are
necessary to reach a true mathematical singularity, and no single force
can "grow" to infinity in finite time. that is, faster-than-exponential
growth (x!, e^(x^x), etc.) does not imply singularity per se.