Rich Wilson wrote:
mega-snip

I give up.

This is good, Rich. Giving up the struggle, going with the flow, is a
good way to grasp mathematics once you arrive at the anti-intuitive.
I'm sure there is a little bottle of snake oil labelled Zen or Bushido
or something to account for it but it works in plain English too.

By the way, I'm Andre Jute. I started this thread a week or so ago.

Here's a thought experiment first devised by John Rawls, the Harvard
philosopher:

On a table behind a veil is a cake. How do you know the cake is there?
You don't. How do you know how many cakes? You don't. Your name is
Rich. You're standing outside the veil with Poor. He tells you there is
a cake behind the veil. You may choose to believe him or not. The fact
that he has a knife in his hand is irrelevant to your decision. If you
believe him, there is one cake, even if unseen. If you don't believe,
there is one imaginary cake, in his mind and maybe behind the veil as
well.

You raise the veil. There is a cake. How do you know there is only one
cake? Because there aren't two.

Poor suggests that one person cuts the cake into two parts behind the
veil and that the other person then chooses his part first. One person
cuts, the other person chooses.

What is the logic of this prisoner's dilemma game? It is in the
interest of the cutter to cut the cake into two equal pieces. (Unless
he's Hopi, but I throw that in just to show how well-read I am.)

All right. Poor cuts the cake behind the veil. The veil is lifted. The
cake is cut into two. You each take a piece. How many pieces are there
now? Two, of course, because you each have a piece and you are each an
individual person. Or two, because there is more than one. Or two,
because I tell you that the next number after one is two.

(Or just a single piece of cake because you are Borg without a concept
of more than one. But in that case you aren't there either, because
without numbers you won't build a pogo-stick, never mind a spaceship to
carry you here.)

Another possibility. Poor cuts the cake unequally. You choose the
bigger piece. The difference between your pieces is a negative number
by which his piece is smaller than yours. If you were to cut off half
that amount to equalize your pieces, it would be a negative number off
your cake and an equal positive number onto his cake, and both numbers
would be a real piece of cake.

Another possibility: Poor cut the cake equally but after you choose he
believes your piece is bigger. He even thinks he knows how much bigger
your piece is. The difference by which he imagines his cake to be
smaller is an imaginary negative number.

Cake size can be measured as weight or area on the cake plate. You can
take it from there. All this writing has made me hungry. I'm off to eat
my cake.

HTH.

BTW: Those numbers are in your hand. They're made of cake.

Andre Jute