Tongues of Fire

Day 5 or 6 (maybe even 7)

I'm standing at the back of the classroom gazing at this four foot eight girl and the monstrosity of the blackboard behind her. I feel like we're locked in an intense battle, ready to pull out the pistol and fire, but she's bracing everything with calm and poise and I realize I'm the one with a problem. A Math problem, this time. It's back to a sunny day and there is a towhee chipping in the trees near the school. I had sent the rest of the students on an extended break mainly because they would be nothing but a distraction.

'Melinda, how many natural numbers are there?'

'One.'

'One? How can that be? What about "2"? Isn't that a natural number?"

'Yes.' And she went and wrote "1+1=2"

'I see. What about infinity? That's not countable.'

'Infinity only works as a set. And the set is also a natural number and is one'.

'What about the bijection of two sets? Set "B" cannot be the same set as set "A".'

'No, but it's the pair of the first set. It doesn't exist without set A. And she went and wrote this:

(lilies) (white)

(pansy ) (blue)

(hyacinth) (pink)

On top of one of the chestnut cabinets laid a vase of pansies, miniature lilies and hyacinths. Pansies were blue, lilies white and the hyacinths pink. It was Principal Bale's idea to give the room a splash of color and fragrance.

'Ok. I get your point. White is the pair of lilies and the color cannot exist without the object it describes. But it's still a bijection, in Math terms.

'It's an appropriation, more than a bijection.'

'Meaning?'

And she went and crossed out "white" and instead wrote "blue, yellow, pink.."

I couldn't finish my 'Right'. She started defining the set of the natural numbers with the following bijection:

(1) (yellow, green, blue, white...)

(2)

(3)

'I don't get it. That is no longer a set. Or a bijection.

She then went to write "1" at the center of a circle and drew radiuses from "1" to different points on the surface of the circle. At those points she again wrote: "Yellow", "Blue", "White", etc.

'"1" is yellow to the left, blue to the right, pink at the back and so forth."

I was slowly getting to the realization where this was heading and it made me shiver to the cover.

'Well, Melinda, if "1" is "blue" to the right... how many points are there between "1" and "2"?

She wrote: "aleph _{1}". I brushed my fingers against my forehead and my temples and wiped the sweat that was welling up.

'Melinda, is this a fake aleph _{1}? I mean... I mean... should this be aleph _{2}? Is there, between "1" and "2"; between the natural numbers and the real numbers; is there a set between aleph _{0} and aleph _{1} that we don't know about?' And I was preparing for the worst. That this nightmare would carry on and that she would be giving the right answer. That I would be rooted to that spot, at the back of the room and that if she would come right at me and I wouldn't be able to move or close my eyes.