The Bindu of a Naked Numbskull

Portrait of Thomas Aquinas painted by Carlo Crivelli, 1476
"How many angels can dance on the point of a pin?" is a question first asked by such truth-seekers as Aquinas in the glorious age of scholasticism, when metaphysical nitpicking, hair-splitting and name-calling were the order of the day.

Counting angels is not easy when they’re standing still, let alone jitterbugging on emptiness. And if the dimensionless point at the end of a pin were as infinitely rich in potential as the bindu of Hindu metaphysics, to count the angels you'd need some really tight air traffic control.

But if the point were a dome, and the angels were very thin, how many could dance on the head of a bald man?

Becoming bald is a process involving a diminishing number of hairs. But let's get specific. At the loss of which hair, precisely, can the label "bald" validly be applied? Or, if you're loading straw onto the back of a camel, what is the number of the straw that breaks the camel’s back?

Most if not all questions about moving from one state to another involve a paradox. According to the ancient Greek philosopher Zeno, motion is an illusion, and yet he sat on many stools. Paradoxes are like boogeymen: they seem scary and threatening but when you look closely they lack substance. Most if not all paradoxes emerge from the inherent limitations of human thought and language. Resolving them is simply a matter of accurate definition.

For instance, baldness could be defined as the mean headhairiness density of 0-2 hairs per square centimetre across more than 94.2% of naked numbskull.

Alternatively, we could apply a reductive definition paradigm based on recursion theory. If a full head of hair comprises, say, a million hairs, baldness could be defined as the phase transition marked by the loss of hair #999,678, and absolutely and totally bald, as the end-state marked by the loss of hair #1, i.e. the ultimate hair (hair #2 is the penultimate).

Similar methods can be applied to counting straws and camels.

Now if there’s no bijection, this post can draw to an ignominious close.