The Whale Song Translation: A Voyage of Discovery To Neptune and Beyond (36 page)

“If the definition of music is sound-sculpted time,” said Seema, “this is sound-sculpted mathematics.” She glanced at Dmitri.

“That’s a beautiful description, Seema,” replied Dmitri. His comment painted a broad smile onto her face.

“They’ve achieved a mastery of sound,” said Greg, his tone expressing stupefied elation. “The sounds of songs, and now, the sounds of language—a mathematical language!”

“It’s not like Uber is drawing with pencil and paper and has the benefit of visual feedback to achieve such precisely proportioned figures.” Dmitri traced a finger over the shapes on the display. “Just as the juveniles imaged the logical game symbols, Uber’s taken his prowess of memory and precision acoustic control to an even higher level of expression.”

“Except I’m seeing an irregularity in the elliptical symmetries.” Greg paced his words as though he were deliberating. He appeared pensive. “I think there’s something more here than meets the eye. Look.” Greg slid a finger across the peaks and valleys depicted in the waterfall plots on Andrew’s PC workstation monitor.

“You’re right.” Dmitri combed an anxious hand through his hair. “It’s surprising that the energies of the third and fourth higher-frequency peaks are about the same as the first two lower-frequency peaks.”

“Which is very different than for human speech and for the juveniles’ game vocalizations, where only the first two peaks were dominant.” Greg’s voice was charged with excitement. “I think Uber is encoding vital information using all four frequencies.”

“What are you two suggesting?” asked Melanie. “The basis of the Speakeasy system is the visualization of the two-dimensional word grams. Remember our discussion last month? Since we’re restricted by the properties of our vocal tracts, we only use the two lowest resonant frequencies to encode the symbols of language.”

“Which is why the symbols of our language are inherently processed in only two dimensions, limiting the number of symbols we can generate,” answered Dmitri.

Like the Invisible Man, McPinsky’s disembodied voice loomed from the speakerphone. “As the human brain evolved to adapt these symbols in various ways, it’s no accident that the types of games we play are also of a two-dimensional nature.”

“But the spectral plots indicate Uber is generating four different frequency peaks of nearly equal energy intensity, Professor,” replied Greg. “I think we should assume he has an entirely different physiology, which gives him independent control of the four peaks.”

“Chris,” asked Dmitri, “could the humpbacks utilize air sacs of different dimensions, like Helmholz resonators?”

“Over the years, we’ve autopsied a few humpbacks that have washed ashore,” replied Gorman. “We’ve confirmed their respiratory system is connected to a series of structures that look like flotation sacs. Maybe those have been adapted for the generation of sound?”

“Or maybe,” said Seema, “their respiratory system has multiple tubal structures, acting like independent vocal tracts?”

“This is all fascinating,” said Dmitri, “but the Coast Guard’s breathing down our necks, and I am, after all, responsible for the launch. Maybe they’ll be more lenient if we tell them we’re ready to cooperate.”

“I hear you, Dmitri, but my gut tells me this could be really, really big!” answered Greg. “I’d like to try one more thing.”

“And we’re still surrounded by the whales,” said Lila. “The Coast Guard can’t touch us.”

“Okay, Greg,” said Dmitri. “What do you suggest?”

“Possibly because of my hearing deficiency, I’ve developed an acute visual sensitivity to the structural details of mathematical functions like the ellipses on the screen. I’m saying we may need to examine these vocalizations at a deeper level. Andrew, I know I’m pushing the envelope here, but is it possible to display Uber’s three lowest frequency peaks in 3D perspective?”

“Like a 3D version of Speakeasy?” asked Melanie.

“That’s the idea,” replied Greg, “except we won’t need to wear funny glasses.”

“Thought you’d never ask,” replied Andrew. “I always prepare for contingencies when I write new applications and, besides, we already discussed this back at SoCalSci. I actually did
design the program to plot the Speakeasy data in 3D x,y,z coordinates. It’s only because I’ve forced the data points to a value of zero in the third dimension that it’s defaulting to Melanie’s two-dimensional version of Speakeasy.”

“He’s right,” said Dmitri. “Since Andrew had adapted his thesis’s 3D plotting routine for this experiment, we’d decided to maintain the 3D option for both transmit and receive functions.”

“That’s great,” said Greg. “What about computing the frequency and the amplitude of a third peak?”

“Like I said,” replied Andrew, “I live by my Boy Scout leader’s maxim, ‘Prior planning prevents piss-poor performance.’ My peak analysis program loops through the frequency data for as many peaks as I specify. Right now, it only searches through the data for the two lowest-frequency peaks. To search for the three lowest-frequency peaks, I only have to change a single input parameter in the setup menu. Then it’s a piece of cake to image the symbol location in the three-dimensional perspective of a Speakeasy plot.”

“For God’s sake, man, that’s fantastic!” Greg thrust his arms triumphantly into the air. “Do it now and replay the recording of Uber’s vocalizations of the ellipses. Seema, while we’re waiting, do you think your symbol synthesizer can be modified to broadcast three different frequency peaks at the same time?”

“Like Dmitri said,” replied Seema, “we’d already planned for that option. Even though my program is restricted to synthesizing tone pairs, I have the option to generate two tone pairs at the same time by the superposition principle. If you only want three peaks, I’ll zero the output energy of the fourth peak.”

“That’s brilliant, Seema!” exclaimed Dmitri. “I didn’t realize you’d finished that. You two are amazing.”

“Okay, I’m ready,” announced Andrew. “I’m replaying Uber’s recording back into the Speakeasy program which is now set up to analyze and plot the first three peaks. They should be appearing on the Speakeasy display any second now. Look, there’s the first ellipse.”

They waited silently for the time it took to plot all four of the ellipses.

“Are you kidding me?” howled Greg.

“Oh, my,” uttered McPinsky. “Is this what I think it is?”

“Yes,” answered Dmitri, surprised that his mentor’s voice had quavered with such emotion.

“What is it?” asked Mark.

“Could you elaborate, Professor?” Melanie echoed.

“It’s a sublimely succinct calling card,” answered McPinsky, “rendered in the universal language of mathematics and written by the acoustic hand of the Megapterans. This is a message for the ages, transcending the proverbial ‘take-me-to-your-leader’ cliché. In Carl Sagan’s book
Contact
, he postulated that the first confirmed radio communication from an ET civilization was mathematical—a repeating series of the first 261 prime numbers.”

“It’s rather elementary, Watson,” interjected Greg, facing Dmitri. “I’m visualizing the acoustical mastery of the mathematical expression of three-dimensional geometric figures. Uber has independent control of the rotation of these figures in all three dimensions. These ellipses are rotated independently by forty-five degrees around each of the three x, y, and z axes of the 3D plot.”

To make his point, Greg traced his fingers across the shapes on the screen, and Dmitri muttered, “Amazing.” The static figures not only appeared to be rotated clockwise relative to one another, but in the 3D perspective of the x,y,z coordinates, they also seemed to pivot into the depth of the screen as well.

When the boat momentarily swayed, Dmitri clutched the back of Andrew’s chair. “This is the mathematical basis of inertial guidance systems such as gyroscopes and gyrocompasses.” In awe, Dmitri reached out and touched the figures on the monitor. “Could this be how they navigate?”

Gorman spoke in a quieter tone now, as if mystified. “I never imagined this—”

“What are they talking about, Mom?” asked Mark. “What did the whale say?”

“Honey, it’s even difficult for me to understand, but I think the whales are drawing 3D pictures with their voices.”

“Awesome!” exclaimed Mark.

Melanie turned her attention to the researchers. “You know, for thousands of years, what we heard as grunting or barking sounds is really a language of mathematics. Humans have adapted the written language to express both the representational symbols of the alphabet and the pictorial symbols like the Chinese ideograms. Likewise, as I see it now, the humpbacks have adapted their voices to express both the primitive logical game symbols, and in the pictorial mode, the ideograms of geometric figures in 3D no less.”

“So whaddya think now, Chris?” asked Lila.

“This is way beyond my grasp,” replied Gorman. “I’m relying on Dmitri and Greg to interpret the meaning of these signals.”

Uber’s vocalizations resumed. He blasted away, over and over. As the cabin groaned with his roars, the geometric figures danced on the screen.

“His control is unbelievable!” shouted Greg. “He just keeps retracing the same rotated figures with perfect precision.”

“Oh, my God,” uttered Dmitri. “Look, now he’s rotating in the reverse direction, first counterclockwise, then clockwise.”

The whale’s booming voice finally ceased.

“I think he’s waiting for an answer,” said Andrew.

“Who are we to refuse,” remarked McPinsky. “Don’t you think we should engage him in a three-dimensional version of the game?”

“That’s an intriguing idea, Professor,” replied Dmitri, rubbing his hands together in anticipation. “Seema, is your synthesizer ready to broadcast that extra tone we discussed?”

“It’s all set up and ready to go. I’ve even incorporated it into the random-tone-generation program. You want me to start with that?”

“Yes,” said Dmitri. “Fire it up and cross your fingers. Hopefully, we’ll see a response.”

With the addition of the third tone, the sounds of Seema’s computer-synthesized game symbols had a richer quality. The Speakeasy translations of the first few, ring-shaped symbols appeared to float in the three-dimensional perspective of the Speakeasy display.

“Works like a charm,” said Greg.

“Now the game becomes all the more challenging,” said Dmitri. “In addition to forming boxes in all three dimensions, a higher-level goal is to complete as many cubes of eight vertices as possible.”

“I remember the original
Star Trek
television series,” said McPinsky, “where Spock and Kirk played a futuristic version of three-dimensional chess. I never imagined I might witness such a match between humans and another earthly species.” Dmitri sensed a degree of anticipation in McPinsky’s voice that he’d never heard before.

“Hey, Andrew,” replied Greg. “There’s still something fishy about the shapes of the ellipses in three dimensions. Can you give me a raw data printout of the power levels and the frequencies of the four peaks?”

“Fishy!” Dmitri heard Mark repeat, and he saw the boy was smiling.

“Sure enough,” replied Andrew. “You’ll see the printout appearing in a couple of minutes, right over there.” He pointed at the printer located on the adjacent desk.

“What are you up to, Greg?” asked Dmitri.

“I’m not sure yet. Give me a few minutes to do some calculations.”

“Hey, guys,” said Andrew. “I’m hearing game symbol responses from Uber.”

“Okay, Seema, get ready.” Dmitri tensed. “I’ll give you the 3D coordinates and you feed them into your synthesizer.”

Lila rushed over to Andrew’s workstation as Uber’s first ring-shaped symbols appeared. “Look at the screen! You were right, Greg. He’s playing the game in three dimensions. God, can this be happening?”

Dmitri slapped Greg on the shoulder. “You’re a genius, pal.”

As before, Uber projected the loop-shaped acoustic game symbols left and right, up and down, onto the LCD display. Now, however, the researchers could see that the placement of the symbols also receded into the depth dimension of the 3D Speakeasy soundscape.

The match magically unfolded before their eyes. The circular symbols appeared to levitate in the three-dimensional perspective of the x,y,z plot. Now that the game had been translated into a higher dimension, the Turing test, the ultimate gauge of intellectual aptitude, was being performed upon a stage of even richer complexity. As the game progressed, boxes were transformed into cubes. The scoreboard’s mounting tallies confirmed the undeniable truth that, despite all of his training, Dmitri’s mind was not nearly as adept as his cetacean counterpart’s at manipulating the rules of logic in the extra dimension. The transcendent breakthrough more than compensated for his humbling defeat.

* * *

Ensconced in the executive leather chair in his home office, Professor Theodosious McPinsky stared at the revelation painted upon his computer monitor—the Speakeasy rendition of Uber’s 3D game masterpiece.

To celebrate the occasion, he uncorked a rare, vintage bottle of his father’s favorite Scotch whisky. He yearned to share this special moment, so he filled two tumblers and placed the second drink next to the framed photo perched upon the desk. Then he raised his glass and toasted the lovely woman in the photograph, who perpetually smiled back at him. Savoring the Laphroaig single malt, he gazed longingly into the eyes of his departed wife, Emma, his own eyes wet with tears.