Poem: The Infinite Root

The Infinite Root

We can indeed

commune with the infinite;

the dedicated heart and mind

in effortful pursuit of truth

will find it.

And so he did, this man:

he made a claim which claimed his life

taken from him by his own kind

who thought not revelation

more powerful than convention.

A square triangulated

uniting two entities

with just one line,

so the legend goes…

Measure the line joining opposing corners

asking is it possible that a fraction

could describe the length of the line in question

after we square it?

Choosing very carefully numbers, letters

representing integers of a fraction

fully reduced, simplified into lowest

terms, we continue.

Note that with more algebra, we can show that

one of these two numbers, the top one, will be

even since it’s equal to twice some other

integer out there.

With this information, we know this even

number can be carefully crafted, squared and

then by two divided; the bottom number

also is even.

What we just discovered has led us to a

simple contradiction since both the even

numbers make a fraction which must again be

simplified further.

Measure the line joining opposing corners

knowing that there cannot exist a fraction

that describes the length of the line in question

after we square it.

Suppose it is true.

Can you find the contradiction?

We can indeed

commune with the infinite.

—Derek Miller, 24 February 2015