“Suppose you hold your compliment and get a grip on your testosterone pump.”
He nodded.
She turned back to the road. “We begin here. A brisk walk downhill for two miles. It’s steep, but don’t run. It’s excellent preparation for what’s coming.”
“For what’s coming? What is coming?”
“There’s a big rock on the right at two miles. It’s just the right height for a bench. We’ll rest there and tighten our laces.”
Larson settled in beside her. He was breathing hard. “Difficult— to—keep—from— running.”
“Yes.”
She finished tightening her laces, then stood. “Now, dead run to the top. Last one does the breakfast dishes.”
Sheila had disappeared by the time Larson reached the top of the road. He sprawled on a pile of mulched oak leaves.
She appeared a moment later, a coffee cup in either hand. “Now, isn’t that better than rambling around in the chiggers and poison ivy?”
Larson took his cup, set it at the edge of the mulch, and closed his eyes.
“Six tomorrow morning?”
“You do that every day?”
Unless it’s raining or snowing.”
He looked at her. “You ought to have legs like a linebacker.” He shook his head. “And you sure don’t.”
“Maybe more good genes, but don’t forget about containing your compliments.”
He nodded. “Yes, ma’am.”
At four Lars on yelled across the room. “Banking’s done for the day. Quitting time.” Sheila didn’t react.
He crossed to her monitor. Rows of letters and numbers rolled down the screen.
“Not much plot. What is it?”
“Fortran coding. Instructions to the computer.”
“Tell me about them.”
“I’m about through here for the day. Let me postpone my answer until I can shower
and pour a glass of wine.” Half an hour later she appeared at the bottom of the stairway. The costume was another edition of T-shirt and cut-offs. “Wine or beer?”
“What wine?”
“A good California Merlot.”
“Wine, please.”
She poured generous glasses, then motioned for him to follow. “Back to our window seats? I like to sit there and watch the day end.”
He followed her. “Now, tell me about all those letters and numbers besmirching your monitor?”
“Besmirching? Good name for them today. What do you know about computers?”
“Microsoft Windows—WORD—EXCEL—the internet and the world wide web.”
“That’s all?”
“What else is there?” He paused. “Oh, I know there are other operating systems— whatever that means. Whatever runs the Apple computers and something called UNIX that someone else uses. That’s it.”
She shook her head. “It’s easy to forget who’s out there.”
“Meaning me.”
“And everyone else who uses applications, such as Microsoft’s, but gives no thought to how they work or who wrote them.”
“How about telling me about all that?”
“If you like.”
After four glasses of Merlot and two hours of lecture regarding machine language, source language, Fortran’s strength in the expression of mathematics, and compilers, Larson stood and stretched. “I think that’s enough for me.”
Sheila stood, too. “Yes. I sometimes find myself teaching for the joy of teaching and sometimes forget the makeup of the student body.”
Chapter 27
July 28
There was e-mail for Staranov from Ammonova: employing investigative tools developed by the u s securities and exchange commission and chicago board options exchange, i am now maintaining a twenty-four watch on the same markets as the american sec and cboe .
He responded:
excellent. how did you secure the sec programs?
Ammonova:
i remembered my Komitet training.
Staranov:
meaning?
Ammonova:
the SEC software was well guarded, but not so well that money could not provide access. The evening’s burgers were underdone and Gorgonzola as the cheese on a cheeseburger was a different experience, but the dinner was good and the Zinfandel was excellent.
Larson deposited his plate and flatware near the kitchen sink. “What’s the s ubject of tonight’s lecture?”
“What would you like to know—assuming the subject is within my area of expertise?”
“How about weather forecasting?”
She laughed. “I was thinking of sleeping tonight. That subject would—”
“Do your best. Aaron gave me a short lecture when we first met, but that was more than three years ago. Pretend you’re reading to me from one of those yellow Dummies’ books. Weather Forecasting for Dummies’.”
“All right.” She hesitated. “Weather forecasting is the prediction of what future weather will be.”
“May not have to start quite that far back.”
She ignored his comment. “A great deal of information—data—is required. Air pressure, temperature, humidity, wind speed and direction at various altitudes, and the like.”
“So you’re short on data?”
“No, we have an abundance of data. The problem lies elsewhere, in what’s termed initial conditions.”
“Initial conditions. Okay.”
“If the initial conditions entered into the predictive system are incorrect, the prediction will be incorrect.”
He nodded.
“Are you familiar with Lorenz’s butterfly effect?”
Larson shook his head.
“A third of a century ago an atmospheric scientist at MIT, Ed Lorenz, opined that the movements of a butterfly’s wings in one part of the world could affect the weather half a world away.”
Larson frowned.
“If a butterfly’s wings add to or subtract from a given air flow, then the hurricane that otherwise would have occurred does not. Or viceversa.”
Larson nodded.
“Now, what do you know about CHAOS?”
He laughed. “My mother’s description of my boyhood closet.”
She produced the obligatory chuckle. “CHAOS is—has become—a branch of mathematics that attempts to learn the behavior of a system at sometime in the future. Weather is one example, but there are many others.”
“Such as?”
“The outset of war, traffic flow, cardiac arrhythmias, and similar circumstances. Aaron’s original data were about the spread of measles. The theory is two-fold. One, no matter how complex, systems rely upon some underlying order and two, changes in initial conditions—for example, the butterfly—can provide very large changes in the behavior of the system.” She studied his face. “Do you follow?”
“I’m gaining on it. What about the mathematics of CHAOS?”
“Are far beyond the scope of tonight’s lecture.”
“But—”
“Does the term partial differential equation mean anything to you?”
“No.”
“Non-linearity? Entropy? Fractals? Complexity? Feigenbaum numbers?”
“No. No and no. And especially not those Feigenbaum numbers.”
She smiled. “I’m not trying to belittle your schooling. It’s a question of academic backgrounds and experience. We can proceed very well without your understanding Feigenbaum numbers.”
She started toward the kitchen. “More wine?”
“Please.”
“Therefore—”
“So, how does this relate to Aaron’s prediction of the stock market? I remember that it had to do with air pressure.”
“That’s correct. He thought he might be able to predict market changes in the same way as he was predicting air pressure changes. Identifying fronts, convections, and so forth.”
“Okay.”
“For example, if he predicted that the pressure over small cap stock
s would increase the following day, that meant that small cap stocks would rise.”
“Okay.”
“He found that by varying his inputs, he could predict the air pressure over any set of financial measures, but he couldn’t predict them all simultaneously. He had to concentrate in one area in order to secure meaningful data. He selected the Standard and Poor’s Five Hundred as his first target. His first step each day was to establish a zero level—analogous to standard air pressure of 760 millimeters of mercury at sea level.” She paused. “The analogy differs here. Standard air pressure is fixed, but the zero level for his stock market computations was variable and so had to be computed daily.”
“Okay.”
“Furthermore, he found something most important. The level was a measure of the reliability of his prediction.”
“Which is why I was to trade only when there was a high reading.”
“Precisely. You selected a threshold, did you not?”
“Eighty. Plus or minus. Positive eighty or more, buy. Same for negative, but sell. Any reading less than eighty either way, no trading.”
“Correct. And the timing of the validity?” she said.
Larson smiled—she was teaching again. “Good for just one day.” Larson raised his eyebrows. “Yes, yes—which is what you meant by the need for accuracy of the initial conditions.”
She smiled. “Very good. The analogy is not perfect. There could be special times when all such financial measurements might be up—announcement of a real peace in the Middle East—or all down—in the event of a presidential assassination.”
“I have it.”
They were silent for a while. “So where are you hung up?”
“The same the inputs Aaron received from the very beginning of his work are being retrieved. As I told you, I’ve run Augur for the last two hundred days. I have—”
“Big job?”
“No, a matter of seconds. But I’ve not found a single match between the Augur output and what I gave to you.”
Larson nodded.
“And so I’ve been examining his flow diagrams, the Fortran coding, and anything else I can think of.”
“And?”
“Not a glimmer.”
July 29
She had no news when they met for lunch. “But I’m not discouraged. Only an odd
number or a mistranslated symbol stands in my way.”
He nodded. “You may be redefining stick-to-itiveness.”
“The foundation’s too important for me to quit.”
She watched the data lines flow until sundown.
Larson showered, then opened a California Merlot and sat in front of one of the big windows. She sat beside him and laid her hand on his shoulder. It was the first time either had touched the other.
She yawned. “I’m not hungry. I think I’ll make it an early night.”
By nine, Larson had finished a third glass of the Merlot and a plate of Brie and crackers. He was about to go to bed, when he heard her footsteps.
“I dropped off, but it didn’t last. Perhaps a change of subject?”
“Sure. What?”
“Tell me about your operations.”
“My operations. You’re sure?”
She nodded.
“Okay. Nothing much to it. I—or Maggie, if I’m not available—ran your numbers through the computer. Then—”
“Wait. Your computer?”
“A ordinary Dell lap-top.”
“Employing?”
“A formula that Aaron devised.”
Sheila frowned.
“It decided what percentage of the assets to invest.”
“Invest meaning?”
“Buying S&P100 calls or selling S&P100 puts. And the same for the S&P500.”
“I know about the two indices, of course, but puts? Calls?”
“Index options. If I buy calls, I have the right to purchase at a fixed price—which is less than Augur predicts the market will close for the day. The reverse for puts—I have the right to force a sale at a price above the predicted close.”
She smiled. “I have it.”
“You’re happy at learning something new?”
“Yes, always. Please go on.”
“I divided my purchase or sale into small pieces and sent the orders to my various brokerage houses via the internet.”
“Encrypted?”
“No. I tested the idea at one time, but the necessary decoding at the brokerage end proved to be too slow and errorprone.”
“All right.”
“Then I was finished. I sold out at the end of the day. Maggie handled it, if I wasn’t going to be there.”
“If you didn’t sell out?”
“The brokerages closed my position automatically at four o’clock eastern time.”
“If one failed?”
“The brokerage paid for the mistake.”
“If not?”
“No brokerage was going to lose my business over a loss caused by its own personnel.”
She nodded. “How many brokerages?”
“Twenty-two when I was running full blast.”
“Why so many?”
“To minimize interest in what I was doing.”
“Where were they.”
“Just beyond, but as close to the International Dateline as possible. Australia and the Far East.”
She frowned.
“I wanted to have my trading completed before most of the world knew what I was doing.”
“But if you didn’t have the prediction until ten o’clock Eastern time, it was already late in the day in, say, Tokyo.”
He smiled. “Very observant, but business for those people is tied to Wall Street’s working hours. There was no shortage of staff ready to execute my orders.”
“Interesting.” She yawned. “I think that will do it.”
“Do what?”
“Your explanations have diverted my mind. I’ll be able to get back to sleep. Thank you.”
“My pleasure.” Larson watched her climb the stairs, then reached for the last of the Merlot.
July 30
Larson closed his book, then stopped beside the computer. “How was your
afternoon? Anything?”
She shook her head.
“Sheila, I wonder if it isn’t time to move on.”
“Move on?”
“Look for new worlds to conquer.”
“Quit? I don’t want you to—”
“I think we—meaning you—have given this about as much time and effort as is
indicated. Is there anything you haven’t tried?”
She hesitated. “No.” She hesitated again. “And I suppose I am tired.” Larson stood. “I’m going to the shower.”
Half an hour later, Larson strolled around the living room. He looked at the
mathematical artwork, then pointed to the figure still lying on the floor.
“You haven’t done anything with your new artwork.”
“No time since he brought it.”
“Do you remember that we talked about it at the time? You said it might have a
different meaning for you someday.”
“Yes.”
“What’s the formula?”
Sheila closed her eyes. “r equals a multiplied by two multiplied by the parenthetical
one plus cosine Theta.”
“Forgive my lack of mathematical education and tell me what r, a, and cosine Theta
mean?”
“a is a variable, r is another variable, and the angle Theta is a third variable. In a right
triangle, the cosine is the relationship between the side adjacent to the subject angle and
the hypotenuse.”
“Relationship?”
She was impatient. “Side adjacent divided by the hypotenuse. A fraction—expressed
as a decimal. The cosine of a thirty-degree angle is—” She closed her eyes. “Point
86603.”
“Mud.”
“Trigonometry.”
“Sheila, I—”
She raised her hand.
“What—”
She stared at the lights in the mountains.
Larson watched her face. The expression was rapt.
She hurried to her computer, opened the UNIX partition, and constructed a threevariable matrix.
Larson peered over her shoulder. “What’s up?”
She switched to the NOAA mainframe.
“Pick any day you can remember as having been a good day.”
“April 29. This year. The biggest single day I ever had.”
“What was the reading you received?”
“The OEX was 247. The Wall Street Journal reading was 12, which gave a d in
dying’.”
“Never mind the direction. Just the intensity.”
“As I said, 247.”
“All right. The Augur output for that day was—was—66.”
“Okay.”
“Now, what do we observe?”
Larson shrugged.
“We see that there had to have been another, final computation.”
“And?”
“Aaron called some of the readings to me via telephone, but on those days when I
was in the office, I received the day’s reading from him directly.” She paused. “It was
always written on a piece of scratch paper. Never a printout. What does that tell us?” Larson shook his head.
“What if the final step in the generation of the reading was a handcalculation?” “Hand?”
“Paper and pencil. Or a simple calculator.”
“Okay.”
“The requirement for a final step could have been a security measure. Augur could
be stolen, but without the final calculation, the thief would have nothing—which is where
we are.”
“Okay.”
“Now, what did Aaron do to the Augur output to convert it to a final, true reading?” “Fog.”
“Could be anything. Perhaps just a numeric transformation. Add six, multiply by the
square root of yesterday’s high temperature in Calcutta, subtract your cat’s age.” “Okay.”
“What’s 247 divided by 66?” She closed her eyes. “Three point seven four.” She
hesitated. “All right, give me another day, any day.”
I’ll have to get my book.
He returned turning over pages. “185.”
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