“It’s a quote mark,” Wendy said.
“Or the symbol for inches,” replied Pete.
“Bingo. Now look at the dash directly below the Sixty-three. It’s a minus sign. If you move the inches symbol down and the minus sign up, you get this . . .” Sam grabbed a pad, scribbled something, and turned it around for everyone to see:
Blaylock is telling us the starting square in his spiral is three inches.”
THEY QUICKLY REALIZED the mathematics needed to re-create the spiral were beyond their grasp. Blaylock had devised his bell-spiral combination based on his expertise in topology. To solve it, the Fargos needed an expert of their own, so Sam took a page from Remi’s book and called one of his former professors at Caltech. As it happened, George Milhaupt was now retired and living just seventy miles away on Mount Palomar, where he’d been playing amateur astronomer at the observatory since leaving the institute.Sam’s brief explanation of the problem so intrigued Milhaupt that he drove immediately to La Jolla, arriving two hours after Sam’s call.
Milhaupt, a short man in his mid-seventies with a monk’s fringe of white hair, followed Sam into the work space carrying an old leather valise. Milhaupt looked around, said, “Splendid,” then shook everyone’s hands. “Where is it?” he asked. “Where is this mystery?”
Not wanting to muddy the waters, Sam restricted his briefing to the Shenandoah , the bell, and the relevant portions of Blaylock’s journal. When he finished, Milhaupt was silent for thirty seconds, pursing his lips and nodding thoughtfully to himself. Finally: “I can’t argue with your conclusions, Sam. You were right to call me. You were a good math student, but topology was never your strong suit. If you’ll bring me the bell, your Fibonacci calculations, and a large sketch pad, then leave me alone, I’ll lock horns with Mr. Blaylock and see what I come up with.”NINETY MINUTES LATER, Milhaupt’s scratchy voice came over the house’s intercom system. “Hello . . . ? I’m done.”
Sam and Remi and the others returned to the work space. Sitting on the table, amid dividers, pencils, flexible measuring tapes, and a pad covered in scribbles, was a sketch:
As though playing a slow-motion game of musical chairs, the group walked around the table, eyes fixed on the drawing, heads tilting this way and that, until finally Sam said, “You’ve stumped us.”
“Do you see the tr notation in the upper right-hand corner and the numerals near the curve at the bottom left?”“Yes,” Sam said.
“That’s my handwriting, of course, but they were also inscribed on the inside of the bell. I suspect it means ‘top right.’”
Sam and Remi looked at him in surprise. “We missed that,” Remi said.
“Don’t feel bad. They were minuscule. Without my magnifying glass, I would have overlooked them, too. The tr notations were on the very edge of the bell’s mouth.”“You said ‘notations,’” Remi replied. “As in plural.”
“There were two. I have a second sketch, but aside from the order of the symbols, each is identical to the other. When I saw the two tr notations, I assumed they were intended as both orientation points and end points for a pair of spirals. As to why there are two spirals . . . I suspect that answer is hidden in the rest of that poem of his. As you can see, each X mark is accompanied by a designator; each represents a different glyph. I have a legend with all this written down.”“Amazing,” Sam said. “Imagine the patience all this took.”
Milhaupt smiled and rubbed his hands together. “And now I’d be happy to tackle Mr. Blaylock’s poem.”
Selma read it aloud.
“Well, I agree with your assessment of the first two lines,” Milhaupt said. “As for the other lines . . . I may have some ideas. First of all, this fellow’s a very abstract thinker-which is especially strange for a mathematician.”“He was a character,” Sam agreed. “We also think he may have been a few sandwiches shy of a picnic.”
“Ah, I see. That puts things into perspective. Well, the third line-‘From above, the earth squared’-suggests to me a pair of spirals that are to be viewed from overhead. The notations I found within the bell tend to validate that. Agreed?”Everyone nodded.
“The fourth line-‘From praying hands my day is quartered, the gyrare once, twice’-is a bit trickier, but as we’re fairly certain about the overhead view issue, the ‘praying hands’ may represent two hands of a clock, pointing toward midnight. I suspect the words ‘my day is quartered’ mean Mr. Blaylock has divided his ‘clock’ into four sections-midnight, three, six, and nine. And finally, following this logic, the line ‘the gyrare once, twice’ probably means we’re to rotate our first spiral to the three o’clock position and the second spiral to the six o’clock position.”
Milhaupt demonstrated, rotating his sketches, the first on top with the open end of the spiral pointing to the right; the second below that, the open end of the spiral pointing downward. He looked at each member of the group in turn. “Thoughts?”No one spoke up.
“Me neither,” he said. “How about the last line of the poem?”
Selma recited it:
Words of Ancients, words of Father Algarismo Remi said, “As for the first part-‘Words of Ancients’-we have a hunch what Blaylock means.”“You’re referring to those Aztec glyphs inside the bell?” Milhaupt asked with a Cheshire smile. “I have no idea of their translation, of course. I assume you do?”
Sam nodded. “They’re from the Aztec calendar-thirteen months, thirteen corresponding symbols.”
“Clearly Mr. Blaylock was absorbed with the Aztecs, yes?”
“‘Absorbed’ isn’t the word we’ve been using,” Remi said.
Sam said, “The second part of the line-‘words of Father Algarismo’-has us stumped.”
“I am happy to say I have your answer. At last, my love of obscure mathematical history has come in handy. There is no Father Algarismo, you see. It’s another one of Mr. Blaylock’s tricks. Algarismo is the Portuguese derivation of the word ‘algorithm.’ Quite simply, it means digit.”Remi said, “Then, translated, the last line reads, ‘Words of the Aztecs combined with numbers.’ Sam, you’re the cryptography guy. Is any of this ringing any bells?”
Sam nodded. “Maybe. I seem to remember a page in his journal that was nothing but dots. Did I imagine that?”
“No, I remember it,” Wendy said. “I’ll find it.” She disappeared into the archive vault.
“I can see the gears turning in your head,” said Remi. “What’s going on?”
“I don’t think we’re meant to combine Aztec words with numbers. I think we’re meant to translate them. For example, take the symbol for ‘flint’ and replace the letters with corresponding numbers.”Remi was jotting along on her pad:
6 , 1 2 , 9 , 1 4 , 2 0
“A simple substitution code,” said Milhaupt.
“Right,” Sam said. “I think Blaylock’s spirals are just window dressing. Look at the two rotated sketches. If you straighten out the ends of the spirals, you get a horizontal line of glyphs and a vertical line of glyphs.” “Essentially a grid,” said Remi.
Wendy’s voice came over the intercom. “Sam, I found that page you mentioned. It’s on the screen.”
Selma grabbed the remote and switched on the TV. As Sam had described, the page consisted of nothing more than groupings of seemingly randomly placed dots-row after row, column after column.“How many clusters?” Sam asked.
Remi was already counting. “One hundred sixty-nine. Thirteen down and thirteen across.” She smiled. “Same number as your spiral grid idea, Sam. And the same number of months in the Aztec calendar.”Milhaupt said, “We have a winner. Now you just need to plug your dots into the grid and figure out what it all means.”
HAVING CHASED BLAYLOCK’S RIDDLES for what seemed like months, Sam, now certain he was closing in on his quarry, attacked the “Blaylock Dot Grid Mystery” with a gusto that took him through the evening and into the early-morning hours of the next day.
Translating the Aztec-Nahuatl glyphs first into their Anglicized meanings and then into numbers was straightforward but time-consuming. Once done, he began plugging the dot clusters into their corresponding rows and columns until he had what looked like an LSD-inspired Sudoku puzzle on steroids. Next he began experimenting with various cryptographic methods, hoping to stumble upon something that clicked. Shortly before midnight, he found just that: a binary-type system where the dots’ positions determined which numbers in the grid were used.After hearing Sam’s theory, Remi said, “You’ve worked this out? Tested it?”
“I did. Aside from the ‘empty’ clusters, they’re all latitude and longitude coordinates. This is a map.”
