We sat in silence for several seconds, heads bowed. Then Nathan was given the cue to serve salad and the talk began to flow. Dexter broached the subject of our duel and explained the idea for those who were unacquainted with it. "Ray is suggesting that if you throw together all of Sherlock Holmes' maxims..."

"Thumbrules," corrected Zelda.

"Right, thumbrules," said Dexter. "If you throw these all together into Sherlock-in-a-Box, the program should be able to solve not only Arthur Conan Doyle mysteries, but those written by other authors as well. Including me," he added. "How about giving the group an example, Ray?"

"Sure," I said. "There's one from A Scandal in Bohemia. Quite an interesting story. One of the few in which Holmes doesn't get his man."

"That's especially true," said Zelda, smiling at me, "because his adversary was a woman. Irene Adler, wasn't it?"

I smiled back as many around the table chuckled. "Yes, it was. Thank you for the correction."

"Any time." Her eyes twinkled mischief, which was strangely reassuring. At least they weren't twinkling malice. I hadn't spoken to her since her excursion on my sailboat yesterday.

"Anyway, there's a thumbrule that had to do with fire. Irene Adler has hidden an important photograph that Sherlock Holmes needs to find. So he sets a fire in her drawing room." I retrieved my thumbworn copy of Conan Doyle from my laptop case, but found myself able to recite from memory. "'When a woman thinks that her house is on fire, her instinct is at once to rush to the thing which she values most. It is a perfectly overpowering impulse...'

"You have to remember that Sherlock Holmes was a little chauvinistic," I continued. "The new thumbrule generalizes both the gender and the type of emergency. 'If in an emergency a person rushes to an object, then he or she values that object most.' Now, if you throw in some facts like 'there is a fire' and 'a fire is an emergency' and 'a woman rushes to a painting,' Sherlock can reason that the painting is what the woman values most."

"Very interesting, Ray," said Dexter. "But perhaps you've made the thumbrule too generic. Women are more sentimental creatures than men, after all. A man, I think, would run to put out the fire."

"Oh, come on, Julius," Zelda said. "You're threatening to sound more chauvinistic than Sherlock."

"I wouldn't change it," said Father Zebediah. "After all this time it's still a fact that women are more emotional, men are more logical. Like the book says, women are from Venus..."

"Yeah, yeah," said Zelda. "And men have a penis."

"I think what Zelda is trying to say is that I have to modernize Holmes' gender bias and turn-of-the-century worldview to be able to take on a modern mystery," I said.

"I don't disagree," said Dexter. "But you may have your work cut out for you. There's another Holmes story that reveals his keen insight into a woman's heart. The Case of Mistaken Identity or something."

Dexter must have been doing his homework. "Yes," I said. "A Case of Identity. It deals with a bad love affair. Holmes and Watson are watching a woman standing on the sidewalk outside their office. She's trying to decide whether or not to approach them." Finding the passage, I began to read.

Oscillation upon the pavement always means an affaire de coeur. She would like advice, but is not sure that the matter is not too delicate for communication. And yet even here we may discriminate. When a woman has been seriously wronged by a man she no longer oscillates... Here we may take it that there is a love matter, but that the maiden is not so much angry as perplexed, or grieved.

Laughs and playful groans sounded all around the table. "A brilliant deduction!" said Zelda. "The damsel no longer oscillates, and therefore is perplexed, and cares naught that the matter is too delicate for communication, nor that she has a pimple on her delicate white behind. What a pile of male chauvinist pig manure."

---

---

The funeral progressed through the High Mass. Miriam followed it intently for awhile, but then shook her head sadly and turned to me as I continued to play with the computer. "Show me how it works."

I tapped on a few keys until the Sidney Paget picture of the brooding detective puffing on his pipe appeared on the screen.

"You might be a little disappointed," I said. "I ran Sherlock several times this morning. He asks a few questions that I can't answer and then grinds to a halt." I shifted the computer on my lap and typed, "Who performed the cult ritual?"

"His first hypothesis is that figuring out the numbers in the boxes will identify the cultists. When he can't work that out, he stops and asks us for the answer."

"And we can't tell him because we don't know."

"Correct. He poses other questions, but eventually he fails. We can't get any further until we figure those numbers out, or Sherlock does."

On the screen, Sherlock Holmes continued to puff on his pipe. Behind the detective's unruffled exterior, I knew Sherlock was jumping in and out of his thumbrules, backward chaining until he came to a dead end, meaning he had insufficient data. And insufficient data meant he had to ask a question.

"Any second now," I said. Finally the graphic of Sherlock Holmes disappeared, replaced by a question. But it wasn't the one I expected. It read, What is distance from west portal to maze?

I looked at Miriam in surprise. "I entered some facts about the maze while we've been up here. Sherlock must have connected it with our mystery."

Miriam seemed to tremble and looked unsteady. The funeral was taking its toll.

"Maybe we should leave," I said. "We can do this later. I'll measure the distance from the doors to the maze after the funeral is over."

Miriam hugged her chest and took a deep breath, as though willing herself to be calm. "No need to measure it," she said. "It's one hundred twenty five feet."

--- section removed as Miriam explains how with "sacred geometry" all distances are derived from a starting length)---

I was genuinely impressed. As well as having an aesthetic feel for beauty, Miriam was obviously mathematically inclined. I realized that the two were in balance in this building. But I wondered why Sherlock would care about the distance to the maze. I dutifully typed in the number that Miriam had given me.

Sherlock digested the response. "Look what he's asking now," I said, angling the screen toward her. What is shape of maze?

I typed in "Round."

Does maze have half-circles on circumference?

Half-circles on the circumference. I recognized this phrase. I had entered it into Sherlock to describe the sketch we had found.

I hefted the binoculars again to examine the maze. Its inner circle had six smaller half-circles connected to its circumference, reminiscent of the petals of a flower. The flower illuminates the time and the place. A chill quivered through me. I entered "Yes." The program responded with, What number half-circles has maze?

Six. The same number as was on the sketch. I temporarily suspended Sherlock-in-a-Box, and brought up the picture of the Numbers of the Rose sketch on the computer.

There was indeed a resemblance between the circles on the sketch and on the maze. "It looks to me," I said to Miriam, "that we were wrong to think that the figure on the sketch was a rose. It's actually the center of the maze."

I checked to see if she had made the same connection. Her face had gone pale and she looked as though she were going to faint. I quickly set the computer down. "Miriam, are you okay?" I touched her shoulder. "Do you want to leave?"

She pushed my hand away. Slowly, methodically, she began to tap a closed fist against her chest. I was afraid she was having trouble breathing. Then I understood the gesture. She was praying.

"Give Sherlock his answer," she said.

"Are you sure, Miriam? Maybe we should..."

"Do it, Ray."

I typed in the answer. "Six."

Does rose window have vertical shaft connected to circle?

I looked out to the distance of the western entrance to the stained glass window. I typed in "No."

Does maze have vertical shaft connected to circle?

I looked through the field glasses at the maze. "I don't see any vertical shaft coming from the inner circle."

"That's because of our perspective," Miriam said softly. She took the binoculars and held them to her eyes. "If you follow the path of the maze from the opposite end, it joins the circle just like it shows in the picture." She set the glasses down and looked at me. "From ground level, no one would connect the pattern in the maze to the pattern in the sketch because of the perspective. And you didn't recognize it from here because you were looking at it upside down."

The use of the word "you" instead of "we" wasn't lost on me. Miriam had already deciphered the sketch, probably when I had shared Jon Matthias' comparison of the boxes to walking a winding path. "It has to be looked at from the other direction, from a height," she continued.

"You mean it has to be looked at from the rose window?"

Miriam brought a handkerchief to her puffed eyes. I was beginning to realize that there was more to her grief than the death of an old friend.

Brain surgery on a thumbrule system isn't all that risky or difficult. You simply dissect the knowledge base to examine the thumbrules and facts. You check to make sure you haven't missed anything critical. Then you retrace the chain of reason to test the thinking process. If you arrive at the correct answer, then you stop. If you don't, then you tinker.

I had to tinker. Yes, Sherlock-in-a-Box had arrived at one correct answer: [spoiler content removed]

So what went wrong? A thorough check showed that my thumbrules were okay. They were internally consistent and logically connected. I decided that my work to incorporate the deductive reasoning of Sherlock Holmes into Sherlock-in-a-Box was a success.

The problem lay elsewhere. Sherlock was indeed smart. When stumped, he tried another tack, based on a different thumbrule. If he still couldn't reach a conclusion, it was because he lacked facts. Fed enough facts, he would eventually arrive at an answer. Once he found the answer, he stopped.

That was the problem. He stopped at the first answer, because to him there was only one answer. But in the real world, different people came to different conclusions, depending on their belief system, which made them gauge the facts differently. Clues ranged from truth to half-truth to bald-faced lie. Dexter had put his finger on it. To a computer system, a fact was a fact. There was no range or degree of "truth"; black was black, not white or gray.

My duel with Dexter was a few short days away, scheduled for Friday evening. In order to deal with the red herring that Dexter was sure to throw my way, I had to guide Sherlock to operate in a world of gray. Late into the nights that followed Zebediah's death, I worked hard to manipulate the mind of my idiot savant. Once again, Sherlock Holmes himself led me to the answer.

----------------------------

I spent all of Monday, June third, on the floor of my living room amidst a pile of Doyle's books. At one point I placed Regina's picture next to me; someone to chat with when I needed a break from talking to Sherlock. But I was less inclined than usual to ask her opinion.

Sherlock Holmes had some thumbrules to offer about red herring. "Circumstantial evidence is a very tricky thing," the fictional detective explained in The Boscombe Valley Mystery. "It may seem to point straight to one thing but if you shift your own point of view a little, you may find it pointing in an equally uncompromising manner to something entirely different." There it was again. Point of view. Which was colored by your belief system. The thumbrule was good, but there was still something missing, and I was beginning to feel desperate.

Tuesday morning found me asleep on the floor when Jon Matthias knocked on my door. "Wake up, Ray," he yelled through the screen door. "I come bearing gifts."

"Gifts?" I groggily sat up. Matthias let himself in and plopped down beside me, balancing a paper bag from which he produced a box of Krispy Kreme donuts. He seemed chipper and alert, while I struggled to overcome my sleep deprivation.

"I need some help," I told him. "I've got a little problem that I can't seem to work out."

It took much more than a minute to explain the way Sherlock worked - and didn't work. It took another hour to debate the mathematics behind why Sherlock thought only in black and white. Another half hour to discuss the sleuthing heuristics that I had found in Conan Doyle's books of novels and short stories, which were still scattered all over the carpet. The last passage that I quoted, from The Hound of the Baskervilles, finally struck the chord.

"Holmes tells Watson that he looks for "the region where we balance probabilities and choose the most likely."

Jon, who had been a fountain of ideas to this point, was silent. He grunted and reached into the bag for the last donut. Finally he spoke.

"Probability statistics," he said.

"Probability statistics?" I asked.

"Yes. That's the answer. Add a weighting factor to the thumbrules. Some rules are better than others in certain situations. Put a weight on them when you enter them into Sherlock. Or, if you want to get fancy, add belief system thumbrules to decide what weight to give them under what conditions. That way Sherlock can examine two possible solutions, weigh them against each other, and choose between them."

The intensity of our conversation escalated. When the donuts were gone, we babbled in excitement as we walked to the store, bought more donuts, and returned home. At midnight, when Matthias finally left, we were halfway there.

When Zelda visited me early the next morning, I was all the way there.