Spelvin extricated his gangly frame from the chair and sauntered up to the whiteboard hanging from the wall behind Dmitri’s chair. His Dilbert-like appearance and techie fashion statement—Coke-bottle glasses and a rumpled, white shirt with a plastic pen holder clipped to the front pocket—was no doubt responsible for the amused expressions of Dmitri’s students.
Spelvin proceeded to draw an x,y plot containing two curves. “For the dataset I analyzed, the bottom plot is the correlation profile for the spatial coordinate, and the top curve is the correlation profile of the spatial coordinate with respect to the previous symbol. The profiles derived from the whale song data are nearly identical to the profiles that characterize a classic two-player board game. Are there any questions?”
Spelvin’s query was greeted by stunned silence. What could anyone say, thought Dmitri? The arc of their careers and their lives had collided head-on with the perplexing proposition that they’d decrypted a game in the middle of a whale song. This was uncharted territory. Knowing his students needed more background information, Dmitri decided to jump-start the discussion.
“Last night after Greg left, Joel and I worked until midnight to examine the data with a fine-tooth comb. The more we learn, the more certain we are that this is indeed a game.”
Greg’s face appeared puffy. He mumbled, “Sorry, I’m a bit hung over after a late night celebration with Michelle, but the suspense is killing me. What else did you discover?”
“In the beginning of the alleged game,” Spelvin said, “we confirmed that the circular symbols were drawn in an alternating clockwise and counterclockwise fashion.”
“As if the two players were identified by the direction of the spin,” added Dmitri.
“You say it’s a classic two-player board game. So where’s the board?” asked Seema.
“Ah,” answered Dmitri. “To quote Churchill: ‘That’s a riddle wrapped in a mystery inside an enigma.’ However, the most likely conclusion is that the board is some kind of a template synthesized in the auditory processing region of the whales’ brains. Their minds draw and memorize the symbols acoustically. It’s similar to the way we visualize the Speakeasy word grams in the frequency domain on our computer monitors.”
Andrew raised his arms chest high. “Look ma, no hands. Want to play a board game? Then let’s just use the one inside our heads.” He was greeted by groans.
“As incredible as that sounds, it’s not far from the truth,” interjected Dmitri. “However, we need to wrap our minds around the ultra-precise control required to generate and image these acoustic shapes. It’s almost unbelievable that—”
“And think about the memory capacity required to retain the image of all the symbols generated during the game,” interrupted Greg. “Like chess masters who can play single or multiple opponents while blindfolded.”
Spelvin frowned. “Greg, your notion strains the bounds of credulity. We’d better be certain we’re not diving off the deep end.”
“Greg’s chess-master metaphor is not implausible,” Dmitri responded. “The human brain is hardwired to process twenty times more visual- than sound-based information. John Lilly’s dolphin communication experiments confirmed the cetaceans process twenty times more audio information than visual. QED: Their big brains have evolved to process sound with the same level of sophistication as our brains have evolved to process images. Human chess masters play blindfolded as a challenging novelty. Our fingerless cetacean friends have no choice but to image a version of the game board in the frequency portion of their brain’s audio processing region. Oh, and by the way, Joel, tell everyone about our other breakthrough observation.”
“Oh, yeah, I forgot to mention that the signature three-concentric-circle, bull’s-eye pattern occurred at the point in the profile corresponding to the end of the game.”
“Checkmate,” Dmitri exclaimed triumphantly.
“So what kind of a game is it?” asked Seema.
“Well, once you realize you’re looking at a two-player game format, the patterns look eerily similar to the strategy of the game called Dots and Boxes,” answered Dmitri.
“I used to play that with my kid brother,” Andrew grinned. “I didn’t realize it was such a whale of a game.” His remark elicited another chorus of groans.
“I may know this game. How is it played?” asked Seema.
On the whiteboard, Dmitri drew a diagram depicting the principles of the Dots and Boxes game. “Starting with an empty grid of dots, players take turns adding a single horizontal or vertical line between two adjacent dots. A player who completes the fourth side of a box earns one point and takes another turn. The game ends when no more lines can be placed. The winner of the game is the player with the most points. Beginners play more or less at random until all the remaining boxes are joined together into chains of varying lengths. If you’re not careful, a bad move can give an opponent the opportunity to build a long chain.” He drew an example of boxes in a chain.
“Yes, that’s the game I’m familiar with,” replied Seema. “So in the whale’s version, the circular squiggles are the dots, and they are acoustically drawn onto an imaginary grid of dots?”
“And in their version of the game, they don’t draw any lines,” interjected Greg. “Instead, a box is completed when all four corners on the imaginary grid are occupied by their sound-generated symbols.”
“Remember, we’re not literally saying the grid is square or rectangular,” replied Spelvin. “Only that we measure a geometric correlation between the placement of the symbols. Human versions of the game are played on triangular and hexagonal grids. There’s also a variation in Bolivia played on an Incan Cross grid. Think about how challenging that would be.”
“Joel, your knowledge never ceases to amaze me,” replied Dmitri. “So, everyone, according to Joel’s calculations, and by our own biased visual interpretation of the Speakeasy plot, we aren’t certain they’re literally playing Dots and Boxes. Just that it’s game-like and similar.”
Joel addressed Dmitri’s graduate students. “Game-like in that we measure maximum randomness at the beginning, followed by a series of increasingly correlated maneuvers,” he explained. “I have to admit I was so shocked by the initial implications of the patterns, I spent half the night investigating other alternatives.”
Dmitri laughed. “Despite your cynicism, Joel, I knew you couldn’t resist the challenge.”
Spelvin arched his thin lips into a sheepish grin. “Of course, you’re all familiar with the Nobel Prize-winning game theorist, John Nash.”
“Yeah,” replied Greg, “A Beautiful Mind. A stimulating portrayal of the fine line separating genius from madness in brilliant mathematicians, present company excluded.” He cocked his hat at a sideways angle.
“Of course,” said Dmitri, suppressing a grin.
“I loved the movie.” Seema sighed. “Especially with Russell Crowe as Nash.”
“Such credible character casting,” replied Andrew. “Gladiator morphs into a brilliant, bumbling mathematician. If there’s ever a movie based on A Brief History of Time, I expect the director to cast Brad Pitt as Stephen Hawking squawking about black holes.”
The room erupted with laughter.
“Okay, folks, let’s get back to business,” interrupted Dmitri. “Joel, you were saying . . .”
Spelvin flipped another coin. “Nash’s theories were instrumental in the field of economics. Nash himself was inspired by the first great game theorist of the twentieth century, the German Ernst Zermelo. In 1913, Zermelo’s theorem proved that, for every two-player game with clearly defined rules, a winning strategy always exists for one of the players, as long as both players know all the preceding moves. To understand this theorem, it’s helpful to illustrate how the moves of the two-player game correspond to a tree structure with many branches.” He began to draw a branching structure on the whiteboard. “Each branching path in the tree corresponds to the range of options available on the player’s next move, a
s defined by the rules. The theorem applies to games like tic-tac-toe, checkers, and even to chess.”
Dmitri pointed at the whiteboard. “So, according to the theorem, a computer like Deep Blue should always win a game of chess when pitted against a human. Some of us know, however, that the 1997 world champion won a few of those games.”
“Touché, Dr. Dmitri,” exclaimed Spelvin. “Yes, according to Zermelo’s theorem, a computer should be able to trace through all of the alternative paths to converge upon the optimal winning path. However, a tree structure for the game of chess would have on the order of 10120 branches to consider. In comparison, according to the Standard Model of physics, there are only 1080 particles in the known universe.”
“Okay, Joel,” said Greg, “so even the universe’s most powerful supercomputer can’t play the perfect game of chess. How did you apply Zermelo’s theorem to the whale song data analysis?”
“I just assumed, a-priori, that the rules of the game were the same as for Dots and Boxes. I programmed my laptop to build a set of tree structures based upon the actual whale song symbol locations. I then constructed an alternative set of trees based upon the current position in the actual game and generated the next set of branches according to the rules for Dots and Boxes.” Spelvin scribbled two sets of tree structures, appearing side by side, onto the whiteboard. “I then compared the theoretical best solution tree to the tree corresponding to the actual moves in their game and, bingo, I calculated with 85% confidence that it’s Dots and Boxes.”
“Amazing!” Andrew shook his head.
Although both Seema’s and Andrew’s faces were wan with fatigue, Dmitri saw their mouths agape, dazzled just as he was by Spelvin’s expertise and findings. “That’s pretty impressive, Joel. It confirms your initial correlation measurements.”
The hyper Spelvin drummed his fingers to his temple. “It’s highly suggestive but still not definitive enough to publish. We need more conclusive proof.”
“If this is indeed the type of game we suspect it might be, we have a duty as scientists to confirm the discovery,” said Dmitri. “If these beings participate in games as a form of social engagement, that’s irrefutable evidence of a highly evolved intellect. Since the game requires a prodigious memory and precise control to generate the game-symbol frequencies, it’s probable they’ve adapted the use of acoustical symbols to other forms of communication.”
Seema leaned forward in her chair and peered at Dmitri, her eyes wider than he’d ever seen.
“Dmitri, buddy, you’re preaching to the choir.” Greg laughed. “Where do we go from here?”
“I have a plan for obtaining the irrefutable proof that Joel demands.”
Spelvin responded with crossed arms. “And how do you propose to do that?”
Dmitri paused for a few seconds, the glimmer of his smile gradually growing more playful. “We challenge them to a match, of course.”
The room exploded in a tumult of gasps and groans.
“No, really.” Dmitri pounded the table. “I’ve already given this some thought. During our recent trip to Maui, Greg and I discussed this issue with Chris Gorman. He wanted to be informed if we found new evidence about language in the songs. Once we brief him, I’m confident he’ll cooperate in a follow-up experiment in Hawaiian waters, particularly since whales are still dying in Maui.”
“What kind of experiment are you proposing?” Andrew asked.
Dmitri replied without hesitation. “We configure a research vessel with underwater hydrophones and speakers. Given their ongoing whale song recording program, Gorman’s institute probably has the equipment. We sample the game portion of the sound track of our whale song recording and rebroadcast the symbols, one at a time. We select the particular frequencies that are appropriate to the context of the game.”
Spelvin grimaced. “Problem number one: How do we entice a forty-ton grandmaster to sit down for a game with a research vessel? Problem number two: How do we ensure that the game develops according to the strategy we’re hypothesizing?”
Spelvin clenched his arms to his chest, telling Dmitri he’d need to be more convincing. “Let me address your first challenge, Joel. Since we would rebroadcast recorded samples of actual Maui whale vocalizations, they are more likely to respond.”
“Right,” said Andrew. “They’d think it’s one of their own that’s communicating.”
“That could be a problem,” said Greg. “Our current knowledge is based upon the few symbols whose frequency combinations we discovered in the only game in our possession.”
“Okay then.” Dmitri paused and gulped some coffee. “We can sample the current data and then build a special synthesizer that generates the tone pairs corresponding to any possible symbol in the game.”
“Like a musician’s sampling keyboard, a whale synthesizer.” Seema placed her hands on the table and mimed a keyboard solo. “That’s right up my alley. It also reminds me of my music professor’s definition of music as ‘sound-sculpted time.’ The whales are using sound-sculpted time to represent images in space—frequency space, that is.”
“That’s an interesting analogy, Seema.” Dmitri’s fingers appeared to tap out a tune. “Okay, so assuming we have a synthesizer of prerecorded samples that sound whale-like, we would broadcast a sequence of tones every thirty seconds, corresponding to the random locations on the game board. If we’re fortunate enough to detect a cetacean response, then that brings us to Joel’s second challenge.”
“Wait a second,” interrupted Spelvin. “How do we recognize an appropriate response on a boat in the middle of the ocean?”
“Sorry if I’ve skipped over the details about the setup, but my mind is racing ahead. Our team will provide a PC workstation, high-performance laptops, and a special version of the Speakeasy program for doing the audio-to-video conversion of any acoustic response. We’ll have the same capabilities for viewing the data as we did last night in the Signal Processing Lab. A word gram display of the symbols in frequency space.”
“I understand.” Spelvin maintained a grudging tone. “But what about my second challenge? What’s our plan for playing the game? I’m assuming we implement the strategy for that type of game and, if we’re right and we’re lucky, they might even respond.”
“Yes, and depending upon the location of their responses on the Speakeasy frequency plot, we’d select our next symbol from Seema’s palette of synthesized tones.” Dmitri nodded at Andrew. “I’d like you to code a script and an application that links with Speakeasy and automates the procedure Joel just outlined.”
“No problem, boss. Interspecies videogames are my specialty. Maybe I could get a patent and market it to Sony.”
Seema shook her head. “Remember to donate your profits to the Save the Whales Foundation, Mr. Entrepreneur.”
“Hey!” Greg, who’d been reclining in his chair, suddenly sat upright. “I just thought about another embellishment. Just as the deaf Speakeasy subjects have visual feedback of their own vocalizations, why don’t we offer the humpbacks a similar light show?”
Greg’s proposal evoked blank expressions until Seema posed the question on everybody’s mind. “How do we convert a research vessel into a floating movie theater?”
“Dmitri, don’t you remember our Molokini snorkeling trip? The boat had a glass bottom for viewing the tropical fish.”
Dmitri’s eyes glimmered. “That’s brilliant, Greg! We feed the Speakeasy images to a large, flatscreen monitor fastened to the glass and pointing down into the water.”
“You took the words right out of my mouth,” replied Greg. “There’s one small problem, however. I read somewhere that a humpback’s eyes are spherically shaped, like a fisheye lens. We won’t know if the images on the display will appear distorted to them.”
“Everybody slow down,” interjected Spelvin. “We’re possibly sliding down a very slippery slope. What about the Star Trek Prime Directive: Do not interfere with alien cultures. Who knows how the whales would
react to bright, flashing lights, especially to shapes that dance to the frequencies of their own vocalizations?”
“God forbid,” chimed Seema. “I remember an incident in Japan a few years ago. While children watched an episode of the Pokémon cartoon series, some had epileptic seizures triggered by rapidly flickering images of a particular frequency. Since we have no clue about humpback brain physiology, we’d better proceed cautiously or else we could become unwitting villains.”
“The ACLU would take that case in a heartbeat,” said Andrew.
“I agree,” replied Dmitri. “We would only activate the external visual display after assessing the progress of the acoustic experiment.” After a long pause, he stood and yawned. “Let’s take our ten-minute break.”
“It’s getting too exciting to stop now,” said Andrew.
Everybody seconded the sentiment.
“Okay,” said Dmitri, sitting back down. “Greg, I’m reminded of Melanie’s tutorial in the Maui Speech Lab. She described the two modes of symbols used in written language: the pictorial form, like the Chinese ideograms, and the representational form, such as the characters of the alphabet. Intelligent beings with no physical capacity to communicate in the written format would likely adapt their acoustic symbols to express both modes, don’t you think?”
“Like the whale game where the symbols represent the placement of pieces on a game board,” added Andrew.
“Yes,” said Greg. “In hindsight, it makes so much sense that intelligent creatures, who’ve developed the symbols of language, would utilize those symbols in the playing of games. Playful behavior in mammalian species serves the dual purpose of social interaction and training for activities crucial to their survival.”
“I get goose bumps thinking about this cryptic message.” Seema’s soulful eyes panned Dmitri and Greg. “The clues to their intelligence have been waiting to be discovered for possibly thousands, maybe even millions of years. It wasn’t until humans developed a technologically advanced society that we became capable of interpreting the purpose of their vocalizations. I can’t believe we’re the beneficiaries of this golden opportunity.”
The Whale Song Translation: A Voyage of Discovery To Neptune and Beyond Page 14
