Learned Philosopher and the World of Numbers: Plato’s Playground

Woooz, woooosh and boom. The learned philosopher popped, alive, onto a strange plane of existence. The space around him was pure white like untouched snow, stretching into forever on all sides of him. In front of him hovered a line which metamorphosed into two lines, then three, …then c lines where c is an arbitrarily defined number of lines. The first two lines formed a Cartesian plane of two dimensions, then three dimensions then c dimensions where c is an arbitrarily defined number of dimensions. This shape kept changing, starting from one line until it became a coloured-in circle, and then repeating itself.

Suddenly from out of the distance the learned philosopher could spy a marching troop of 1’s approaching with haste. Naked except for the kafiyahs around their necks, they were all chanting “1…1…1” in endless repetition, smacking their indefinite forms together, smacking their bodies as hard as they could. “What on Earth are you doing?” cried the learned philosopher.

“First,” cried the first one, “we are not on earth. This realm predates earth by a large number of integers. “Second,” at the mention of this word the rest of the 1’s booed and hissed. “Ah sorry, first first,” the other 1’s were satisfied, “we are trying to become one.”

“But surely you are 1!”

“I am 1, he is 1, she is 1 but alas we are many. Fate is cruel. For an eternity do we 1’s (the sound of the plural ‘s’ made 1 shiver) roam this endless land hoping to become one. What cruel God thought of us, I cannot imagine but he surely cannot be one.

Upon hearing this last 1 the 1’s all burst into a sequence of shouting 1.

“My faith declares that God is one” said the learned philosopher.

“ I am 1, he is 1, she is 1 alas but God is none”

“ You do know you’re quite odd!” cried the learned philosopher.

“Excuse me,” replied the first 1 “I am absolutely odd!”

The learned philosopher was taken aback at how offensive his statement had been. He looked around himself again; absolute nothing surrounded him like black fumes do the mouth of volcanoes.

“ I see you met my two friends.”

The learned philosopher noticed the Cartesian transformer but nothing else was in sight.

“Well, I haven’t quite been introduced to this…um fellow over here but he is the only one.

“1…1…1”

“Infinite Ian over here swims in his brother’s ocean Zane the Zero.

The learned philosopher was still thinking “what the fuck is going on” as the first one poetically described the mathematical landscape and the other 1’s kept chanting their name. The 1s now changed their voices to a subtle whispery repetition.

“For aeons, and aeons, Zane and Ian danced together, brothers in arms, transcendental twins joined by the hip. But unsatisfied, and bored of one another, Ian and Zane split! This rift between Zero and Infinity caused …dum dum…numbers! And so we came to be the children of nothing and everything.

“Oh boy, do you happen to have coffee here?” asked with a sigh the learned philosopher, begging for the sweet release of crushed beans on his now-tortured psyche, and realizing that he knew no way back home.

“So Ian and Zane stalk this plane,

together apart

And one by one we try insane

To become one. “

But no, alas, ergh, who was it now approaching from the nothing other than one’s elder one, two.