# The Transitive Kernel Who Never Squared Pi

The field was in darkness.
The groups were in place.
Our ideals were prime
As we stared into space.
And above us, our captain,
He stood like a king.
But to us he was just
A Euclidean Ring.
Now don't get me wrong,
I respected that Ring
'Cause he knew his domain
Was an integral thing.
But our Ring was not perfect,
And quite a far cry
From the Transitive Kernel
Who never squared pi.

And well ordered too.
Their union was strong,
Though their subsets were few.
Was indexed and null,
Transfinite and bounded,
And exceedingly dull.
Despite his equivalence,
My respect he commanded;
He was cardinal, countable
And not underhanded.
But his continuum powers
Could not begin to compare
To the Transitive Kernel's,
For no pi did he square.

All tense were the conics,
With their foci unnerved.
Their tangents unstraightened
And their ellipses uncurved.
Directrix his name,
So tangent, so normal,
You'd swear him insane!
But he did have experience,
And could asymptote fine;
Let's face it, can you
Draw an infinite line?
But drawing such lines
The Kernel could do,
And also, he never
Raised pi to the two.

The statistics were calm
And their mode was apparent.
They were highly significant
And greatly invariant.
Their head man, a t. Student,
Was a mean derivation,
A dimensionless moment
In my estimation.
However, in fairness,
He was a linear guy,
95% confident
and square tested by chi.
However, this man,
Though square tested by chi,
Was not like the Kernel
Who refused to square pi.

There were matrices there
(Just to cover our flanks).
And a number of ranks.
They were led by Hermitian,
A conjugate fool,
And broke Cramer's rule.
Yet he was a determinant,
And unusually singular.
He was symmetric and transpose,
And upper triangular.
But this man was no Kernel,
At least that I reckoned,
For the Transitive Kernel
Ne'er put pi to the second.

The vectors slept waiting,
Cross-product and curl.
Their commander, Laplacian,
A unit del dot,
Was seen as a vector
Whose brain went to rot.
Nonetheless, he was scalar,
And quite sturdy too,
And incredibly healthy,
And quite well-to-do.
But the Kernel was better,
Both in health and in wealth,
And never did he
Multiply pi by itself.

The differential equations,
Their solutions were general,
Were partial, exact;
Their exactness, incredible.
Their kernel, Runge-Kutte,
(His type now defunct)
Was ordinary, initial,
And usually drunk.
Nevertheless, he was brave,
Homogeneous, exact,
No courage he lacked.
But he was not like the Kernel,
Who never did try,
To compute or to find
The second power of pi.

The compact topologies,
A latticy crew,
They were coarse and cofinite
And metrizable too.
They followed an officer -
Hausdorff, I think -
A regular fink!
Notwithstanding, this man
Was a bit homotopic,
Bicompact and open,
A man pseudometric.
But compared to the Kernel,
His strong points were few;
The Kernel, he never
Placed pi with a two.

There were differences, sums,
Trochoids and cycloids,
Quartics and quintics
Plus oblated spheroids.
Like Fresnel and Catalan,
Minkowski, Laguerre,
Green and Jacobian.
But the greatness alone
Did not mean we would win.
We knew we would win, though,
And none of us die,
Who never squared pi.

A burning orange spheroid
Distantly rose.
We were in residue classes,
Our perimeter closed.
Our bases, orthogonal,
And our complex inversion
Was beta hexagonal.
But none of them knew
Just what they should do.
Oh, where was the Kernel?
We needed Him so,
And in just a few moments
We'd be fighting His foe.

I was sent to go fetch Him,
That continuous slope,
That dual choice function
In whom rested our hope.
I translated myself,
Off the field to the woods.
An explosion then cubed me
Right there where I stood.
Swiftly I spiralled
And was thrown to the floor
When that gamma explosion
Was followed by more.
They were under attack,
My men over there,
But where was the Kernel
Who pi never squared?

They fired their antilogs
(As I Leibnitzed in shame)
But without the Kernel
Didn't know where to aim.
They reflexed and injected,
But all was improper,
The men were misled
As they fell in the slaughter.
As their men dropped like phis.
But soon they too fell,
Then the field lay in silence,
I stood there a moment,

I Stoked through the forest
Complementing my way,
Trichotomized visions
Of the dead of that day.
For the tent of the Kernel
Approaching with null,
Was he captured and tortured
Then shot through the skull?
Why did he leave,
Leave us to die,
This transitive man
Who never squared pi?

I went through the tent flap,
His back facing me,
He was working at something
Which I couldn't see.
What was it this Guy
Was doing while he
I looked at his paper
(As I shivered with fear)
Number and figures,
Their meaning was clear.
I stared at this man-god,
Then I took out my slide rule

Why did I kill him,
This great Number One?
Quite simply, I killed him
Coefficiently he
In other words, committed
A terrible crime.
He was guilty of mapping
In modulo three,
A crime that in lawbooks
You never will see.
For the Transitive Kernel,
Who left us to die,
Was only computing
The third power of pi.

MarkRandell