You might argue that Andy Pandy isn't the kind of thing which could have a square root. You're clearly the kind of person who strongly believes in typed programming languages. I'm the last person to deny the utility of polymorphic typing - caught so many errors that way - but you'll never wean me from my love of Lisp: (sqrt AndyPandy).
Even so, trying to find an x such that x2 = Andy Pandy is a stretch. We plainly need to identify an operation 'multiply' over a set which includes Andy Pandy, who is not often known as a number.
In modern mathematics we define operations like 'plus' and 'times' axiomatically. In some sense both these operations are the same: group operations over different sets (integers; non-zero rationals being one pair of examples).
Can we instantiate the group axioms over a set involving Andy Pandy?
The operator 'marries and produces one child ' which we'll call * might do it.
Mother * Father = Child.This is a very modern relationship permitting terms like:
- Mother * Mother
- Father * Father
- Mother * Child
The identity e produces clones (e is a kind of null-person):
Mother * e = Mother.Each individual has a unique inverse, for example,
Mother * Mother-1 = ewhich implies everyone has one entity with whom they are infertile.
With this representation of the group axioms, we seek an X such that
X * X = Andy Pandy.Here's the group table, the cyclic group of order three, with Mother as generator.
So there you have it. The square root of Andy Pandy is her parthenogenetic mother.
* "... that Andy Pandy was transgender .."
† Andy Pandy's own procreative propensities? Let's not go there, children!