Case of Lies

But you know the language of love, Nina thought to herself. “I would have said that you’re the wolf type,” she said.

“Predatory?”

“I do get this feeling of something with paws creeping up on me.”

“Puppies do that too. Then they roll over and beg for it.”

“Wolves call themselves puppies,” Nina said. “Let’s have another one of those.”

“Okay, the puppy thing isn’t going anywhere, I’m going to take another tack,” Mick said. He ordered another set of drinks and said, “Wow, look at that sunset.” They truly did have an angel’s view of the spectacle from their tower in the sky. The lake was flaming now, a sheet of red shading to indigo above.

Nina let her spine loosen. She was enjoying sitting opposite a charming younger man in a comfortable place, listening to his stories. She even wanted to tell Mick that, but…

He wanted to be in love. Did he care who he was in love with tonight? Did it matter if the splash of his erotic fancy had only accidentally encountered her one day, as she sat on the bank of the river of life staring drily at a book?

Maybe Mick could help keep this grim angry feeling about Chelsi from overwhelming her. It would be such a relief to lie in the freckled arms of this, uh, math professor… what kind of sheets would he have? A grid pattern?

Mick put his hand on hers.

“What are you thinking?”

“About something I read. I’m still reading about prime numbers.”

“The subject does tend to suck you in.”

“Mick, let’s talk about l-i-e-s.” She spelled the word out because she was not sure how to pronounce it in this context.

He took his hand back. “Isn’t it a little soon for that discussion? If I can momentarily adopt a masterful tack, well then I insist that topic will come up much later in our relationship. If ever.”

She laughed at his expression. “I mean in the mathematical sense.”

“Oh, good, ’cause it’s such an alarming word in its plain English sense.” He noted her glass was empty. Again. “Can I get you another one? No more for me. I’m driving.”

“I shouldn’t.”

“These things are small and weak. Like me.”

“Oh, well. Why not.” Di

“You want to know about lies, eh? Well, all sorts of lies relate to math. There’s a Chinese professor by the name of Li.”

“Not him.”

“There’s also a Norwegian mathematician from the turn of the century, named Lie. He gave his name to some concepts called Lie Groups and Lie Transformations.”

“Are they used in prime number theory?”

“Maybe. But if so, it’s way over my head,” Mick said. “So much genius has been wasted trying to figure out what the hell the primes are, and why they sit where they sit on the number line, that I’d have to look it up, and I might not know enough about that field to help.

“Here’s the thing about number theory: Any fool can ask a simple question that no genius can solve. Is one a number? What’s the square root of minus one? Why can’t you divide by zero? And the question that has you hooked: How come the primes, the building blocks of all numbers, can’t be located using some formula?”

“It’s true,” Nina said. “It seems so simple. There must be a pattern. I look at the list of numbers, and I think I see a pattern like a mist just behind the list. That there’s some simple little adjustment to be made, and they would fall into a regular sequence-2, 3, 5, 7, 11…”

“There’s a very great mathematician named Grothendieck who said you have to come at things this difficult with the mind of an infant,” Mick said. “Maybe the mystery will be solved someday by some retired postal worker who likes math puzzles. Meantime, let’s talk about one more ‘li.’ ”

“The li that comes close to predicting a pattern of prime distribution,” Nina said.

“Right. Let’s start with maybe the greatest mathematician who ever lived, the incomparable Gauss. Active in math in the late seventeen hundreds. A child prodigy. He kept notebooks, and he only published a small number of his discoveries. It’s said that his failure to let the world into his brain set mathematics back a century.

“When he was fifteen, he wrote a stu

“You said ‘log.’ A logarithm is some kind of root, is that right?”

Mick scratched his head and said, “I don’t think of it like that, but, yeah, it is a root. The natural log is the power a base number has to be raised to in order to equal the particular prime. Most people have had to study base 10 logs, but the scientific log is called the natural log, and…” He saw Nina’s eyes glazing over and said, “Yeah, it’s sort of a root,” and laughed.

“But not exact?”

“No. Close, but no cigar. Still, close was an amazing leap of creativity. Tantalizing, how close he came.”

“Are we getting closer to li yet?”

“Li. Hold on to your glass. Bring all brain cells into play. Grit your teeth. Ready?”

“Go for it.”

“Li means ‘logarithmic integral.’ It’s a refinement of the theorem that comes even closer to predicting the number of primes up to a certain number, and it gets more and more accurate as the numbers get larger. It still can’t predict individual primes, it just comes closer. Gauss came up with it later. It’s a root of a root, you might say. You make an x,y graph. Make a line representing the actual prime numbers, which of course we know up to a hundred digits or so. Make another adjusted line representing the lies of those numbers. The lines run extremely close to each other.”

He drew a simple diagram on his napkin. A right triangle-“The vertical axis is y. The horizontal axis is x, the number line. Where they intersect is zero”-then added another line starting from the zero point and extending out with an arrow at about a forty-five-degree angle.

“That’s the li line, which predicts how many primes there should be up to any point. But it only works approximately. Each prime is located at some random distance below the li line.” He drew a jagged stepped line which ran under the li line like a narrow staircase. “See where the actual number of primes are located? It’s as though the primes got pulled away from their line and have sunk at different rates.” He spread his hands. “To find out how and why this force acts to distort the prime distribution, I would sell my soul. Now I’m getting romantic. It’s because of those brown eyes of yours.”

Lights were winking on all across the forest now, leaving the mountains and the lake in their mysterious darkness.

“Then Riema

“I’ve been reading about that.”

“I have a really good book about it at home I could lend you. So this is co

“I told you, one of the witnesses is very interested in prime number theory.”

“Maybe he works for an Internet-security company,” Mick said.

“What?”

“Well, really big numbers can’t be factored-nobody can find the primes they’re made of-even with today’s computers. So a company called XYC invented a method of encoding financial and other information using that fact, so information couldn’t be hacked as it traveled from one Web site to another. The code lets you type in your credit-card number for certain eyes only. Ever buy anything on eBay?”