While lying on my bed, I became intrigued by plus one and
minus one and what happens to them. For example,
pairs can be made in four ways, pp, pm, mp, mm.
If we are multiplying the numbers, the result is obviously one or the
other. If they are the same pp or mm,
they end up p, but if they are different, either mp or pm, then they end up
m. This seems obvious.
In the general case instances of two qualities can be paired
under an operation four ways. The result
is a single one of them and which one depends on whether they are the same or
different. But is this always so?
This gives the intuitively right number of answers: two of
each. Totalling two ones, two, and two
minus ones, minus two.
Take parenting with the two sexes. Partnerships of the same sex produce no
offspring, the result is not m or p, but a zero. In the previous general example, there was no
zero.
So what is the mathematical generalisation of this
case? If we take the plus one and minus
one but instead of multiplying them, we subtract them, we end up with p-p=0,
m-m=0, p-m=2, m-p=-2. Why marriage
should be equivalent to the operation of subtraction is not clear. Perhaps when two people cleave to each other
they cancel out their individuality in the way two oxygen atoms make a neutral
molecule where a single one is charged. If
we add the numbers instead of subtracting, we end up with the result that two
ps will produce another two ps and two ms similarly, while the mixed pair produces
nothing. It is clearly the wrong model
for marriage, but perhaps arbitrarily so.
With division, the result is the same as for multiplication.
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