"Anyway, over generations there grew among the nobility a taste for mathematics, and eventually this taste solidified into a caste. Men only, for they claimed that women did not have the agility of mind to embrace the myriad complexities of numbers and forms. As I told you on your first night, Tirzah, the Magi, as these mathematicians came to be known...command power through contemplation of the One, and of all numbers and forms that the One generates.

"Gradually, their power and influence increased. The Magi loathed the magic of the Elementals, because they said it was unpredictable, reliant on chance and the whims of the Soulenai. Their magic, they claimed...was powerful because of its verdy predictableness and because, once its rules and parameters were understood, it could be manipulated to the Magi's needs. They work their magic according to set rules! Tables! Parameters! Can you imagine that?"

I cleared my throat and read, praying my voice would remain steady and not irritate him with a stumble.

One, three, nine, eighty-one. A form in itself. Three lines of three, nine lines of nine, the square of beauty, breed into more beauty. Life is numbered from conception to death, rising from and declining into the One. There is beauty in numbers. This beauty is called Regularity, and its essense is Predictability. Everything else is unworthy. Eighty-one, nine, three, One. Life is numbered, all elements of life can be reduced to numbers, life is nothing but the predictability of numbers. There is nothing but numbers. Nothing. Nothing but the One.

I stopped. I could go no further. Tears filled my eyes.

"I was nine when I wrote that. The age of beauty I think, for nine is a special number in itself. ....Tell me what you think of it, Tirzah."

I answered trughtully. "I find it sad, Excellency."

"How so?"

...

"I find it sad, Excellency," I said slowly, "that a boy so young should find life so sterile."

"One day I heard two Magi briefly mention the numbers one, three, five, seven, eleven. They are another progression, perhaps." I prayed Boaz would not read the lie in my voice....

"You have given me only five numbers, and in themselves they do not make a progression. What follows the eleven?"

"I do not know, Excellency."

...

"There is only one thing those numbers have in common."

"Yes, Excellency?"

"They are all incomposite numbers, except the One, of course, which exists outside and beyond the others."

I did not have to pretend confusion. "Excellency?"

He sat forward, so I could see his face more clearly. "Incomposite numbers are those which cannot be factored, they cannot be divided except by themselves or by the One. They are thus indivisible."

"Then they would hold a special relationship to the One, Excellency."

"You are very good, Tirzah," he said softly, his eyes keen, and I thought I had gone too far...."And you are correct. Incomposite numbers hold a very special relationship to the One. They not only have a direct relationship with the One, they are in a sense different expressions of the One."

"So, from eleven the next would be thirteen? Then...seventeen?"

"Precisely, Tirzah. And then on infinitely. Perhaps we will make a Magus of you yet."

"Threshold is a mathematical formula expressed in physical form to provide a path into Infinity. The Song of Frogs is a mathematical formula expressed in music to provide a path into the Place Beyond."

"That's wonderful!" I cried. "Do you mean that if we learn the formula then we can travel to and fro between this world and the Place Beyond?"

....

"No...What I said" - and his voice was tight with strain - "was that the Song of the Frogs is a mathematical formula that will provide a pathway to the Place Beyond....but there is a catch, as there was always a catch with the Threshold formula -- although none of the Magi minded about that."

"And the catch is..." Isphet asked quietly.

"It's a one-way trip," Boaz said.

...

"Can you teach us this Song?" Yaqob asked. "Can you show us how it works?"

"I can't see why not. Listen..." and Boaz expounded the mathematical properties of the Song of the Frogs in exquisite detail.

None of us understood a word he said.

"Boaz, can you explain it in simple terms? None of us have had any training in the mathematics. And what you say..."

Boaz frowned. "That was the simple explanation. But I will try to put it a different way."

All we learned was that only someone with a mathematical background could understand this cursed Song.