Isosceles Triangle

An Isosceles Triangle
looks in the mirror,
and finds itself un-reversed.
"My base angles are equal,"
it says.


On Doing Math
The scientific training,
teaches how to discover.

The artistic training
teaches how to uncover.

The mathematician uncovers,
only to discover --
new things to uncover.


Paradox

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Paradox

All Cretans are liars
said Epiminedes,
a Cretan,
a classic Paradox.

If Epiminedes tells the truth
then he must be lying.
And if he is lying,
he is telling the truth.

Sounds like a
contradiction,
doesn't it?
But a paradox is
different from
a contradiction.

Contradictions
are not allowed:
because
P and Not P
implies any Q.
In other words,
a contradiction
implies
any proposition.

"The Pope and I are two".
said Russell,
"If 2 = 1, then
the Pope and I are one."
Thus went Russell's proof
that he was the Pope.

But a paradox
is different,
its more valuable.
It increases
the size
of your universe.

Russell's paradox
showed the gaps
in set theory
and set the stage
for the next
leap forward.

Paradoxes
are the stuff
of which
giant leaps
are made.


Lots more here.