“Can you give a simple example?” asked Seema.
Dmitri nodded and wrote the numbers 4 and 2 in the middle of the diagram. “If you have a simple language which consists of four words, then two times two equals four, so the information content is two bits. If you double the number of words in the language from four to eight, then two times two times two equals eight. So any message written in that language contains up to three bits of information.”
“Got it,” replied Seema. “Every time you double the number of word entries in a language’s dictionary, the information content measured in bits increases by one. It’s a base two logarithmic scale.”
“Yes, good. It’s similar to the way earthquakes are measured on the Richter Scale.”
“Except that’s a base ten logarithmic scale,” said Andrew. “A magnitude seven earthquake is ten times more powerful than one that registers magnitude six.”
Dmitri wrote the numbers 8,000 and 13 on the board. “So, for the English language, nearly all messages can be expressed using 8,000 of the most commonly used words.” He tapped the number 8,000.
Seema reached for her iPhone and played with the touchscreen. She touched her palm on the whiteboard where Dmitri had written the number 13. “According to my calculator, if you multiply the number two thirteen times, it equals 8,192, which is the power of two closest to 8,000.”
“Exactly,” replied Dmitri. “The information content of messages sent in the English language is therefore thirteen bits.” He gestured toward Andrew. “Why don’t you continue?”
Andrew nodded. “However, that’s the maximum possible amount of information in the source message, assuming that all of the words are equally likely. But in fact we know that many English words are used more frequently than others. The probability of each word is also dependent upon syntax, its placement in a sentence, and the context of the neighboring words.” He paused. “Engineers exploit these statistical dependencies and redundancies to design more efficient sets of code words that compress the amount of data required to transmit or store a message. It’s so cool, like freeze-dried food. Just remove the water and add it back later.”
“‘Freeze-dried food.’ That’s a good one, Andrew. Can I borrow that gem for one of my lectures?”
“Sure, boss, just remember to give me credit.”
Andrew’s smile reminded Dmitri of the tooth-whitening ads gracing the walls of his dentist’s waiting room.
“So, to finish up, Seema,” Andrew continued, “these data compression formulations are essential to all types of digital communication technologies such as Internet file transfers, wireless iPad and iPhone transmissions, and the storage of audio and video information onto CDs and DVDs.”
Despite his own tension, Dmitri cast a smile of satisfaction in the direction of his protégé. “Because of these redundancies, the actual information content of the English language can be compressed from thirteen to ten bits per word.” He crossed out the number 13 on the board, writing a 10 directly above. “So, the Columbia team used similar techniques to compute the redundancies of the periodic units in the whale songs. Interestingly, they measured the information content of the Hawaiian whale songs to be a measly one bit per sound unit.”
“Jeesh,” said Andrew. “There’s no comparison. That’s one bit for whales compared to ten bits for human speech, measured on a logarithmic scale.”
“Exactly,” said Dmitri. “They concluded that human language conveys hundreds of times more information than humpback language. The implication is that, although the whales sing a pleasant tune, they don’t measure up to the higher standard of human intelligence. But, and this is vitally important, like a self-fulfilling prophecy, the stigma implied in their findings might discourage others from investigating cetacean languages.”
Andrew sighed. “So it sounds like all the work’s been done before and the answer is nada. Doesn’t that leave us out in the cold?”
“Well, let me repeat. They’re comparing their measurement of the humpback’s phonemic-like alphabet of about a dozen symbols to the entire lexicon of the 8,000 most commonly spoken English words. Does that seem reasonable to you?”
Andrew exclaimed, “You’re right! You get it, Seema? Like apples and oranges, they’re comparing the amount of information in a dictionary of 8,000 words to the information content of the twenty-six letters of the English alphabet.”
“Which is only about one to two bits per letter, about the same as the whale songs,” replied Dmitri.
“What a crock,” said Andrew. “How’d they decide that the basic acoustic units of whale songs are similar to human words instead of letters or phonemes?”
“That’s the point! They just assumed that each 2.5-second vocalization was a distinct acoustic entity, regardless of the details of the frequency modulations within each unit. Heck, an entire human sentence averages about 2.5 seconds and consists of numerous words and many more phonemes.” Dmitri’s gaze intersected Andrew’s, and then Seema’s. “That’s why our team should focus on analyzing these units for phonemic changes, similar to human speech, on a much smaller timescale.”
“It’s beginning to make sense,” said Seema. “Nevertheless, we can’t ignore the fact that these songs contain a very limited set of acoustic symbols grouped into repetitive patterns.”
“Seema, you’ve hit the nail on the head.” Dmitri’s face registered his approval. “So here’s the thing to know. Only the male humpbacks sing these Aquarian shanties and they stage their productions almost exclusively during the breeding season in Southern waters like Hawaii, Mexico, and Bermuda. Since marine biologists hypothesize the songs serve a mating function, who are we to argue? So, if you’re trying to analyze a humpback vocalization for linguistic codes and information content, which source data are you going to use? A mating song or vocalizations linked to communal behavior during the feeding season?”
“I get it, boss. It’s like comparing the conversational IQ of a couple at the dinner table versus when they’re trying to make a baby. What’s the information content of oohing, aahing, and moaning? Not even one bit per symbol.”
“Exactly, Andrew. Imagine extra-terrestrials evaluating human intelligence from the satellite-television transmission intercept of a porn video.”
“No wonder we haven’t been contacted by the ET’s,” said Seema.
“Correctamundo!” Dmitri punched a fist at an imaginary foe. “So although the researchers acknowledge that the linguistic structure of humpback songs is a barometer of their intelligence, the information measurements decree it to be a low-level intellect. Since the medium is the message, the results are a fait accompli, conditioned by anthropocentric bias.”
Seema stared directly at Andrew. “I’m surprised there’s even one bit per symbol considering how puerile guys are when they’re showing off.”
When Andrew rolled his eyes and made a silly face, Seema laughed and poked him in the ribs. Dmitri wondered, not for the first time, if the nature of their relationship was more than academic.
“Maybe the whale mating song is more like a rap song or a Twitter post to lure groupies?” Seema uttered a series of high-pitched tweets. “Something like, ‘Meet me at the Fluke and Fin for a breach.’”
Dmitri smiled, glad that she too felt free enough to be playful in his office. “Precisely. Just as you’d expect for a mating ritual, their songs are stylized communications with low information content. But maybe this is just the tip of the iceberg of an information-rich language. There’s bound to be more dense and meaningful dialogue when the humpbacks are engaging in a moveable feast.”
“Or if the pod is planning this season’s bubble-net, fashionista designs,” added Seema.
“So I take it we’re gonna be research contrarians?” Andrew asked.
“Absolutely! Instead of a Masters and Johnson study, we’ll focus our analysis on the less melodic vocalizations in the Alaskan recordings when they’re not in the breeding mode and their communications are hop
efully more diverse. And we’ll analyze their microstructure for the more fundamental phonemic units of language, not just these big stylized units in the songs.”
“Aw,” Andrew moaned, “that’s too bad. I was hoping to pick up some pick-up lines from the big boys.”
Seema groaned. “Sorry to inform you, Andrew, but the information content of your jokes can be measured in fractional bits.”
Andrew chuckled with the percussive dots-and-dashes rhythm of Morse code.
To stifle his own laughter, Dmitri bit his cheek. “Okay, let’s get back to Seema’s original question. How do we identify acoustic symbols in the vocalizations? As Andrew knows from our voice codec work, there’s the traditional technique of correlating the shifting frequency patterns in a spectrogram to likely phonemic units.”
“And as we previously discussed,” replied Andrew, “adapting speech recognition techniques to this task could be our full-time occupation for weeks on end.”
“Ah, so now I have to reveal my second transformative experience in Maui,” Dmitri said. “Thanks to a speech therapist, who will be nameless,” he winked at Seema, “and a deaf twelve-year-old boy, I believe we have another exciting option for attacking the problem. Have either of you heard of the Speakeasy speech-therapy computer program?”
“Nope,” replied Andrew.
Seema shook her head.
“Until recently, I hadn’t either. It was developed by a research team in New Zealand to correct the pronunciation of people with hearing loss. They cleverly exploit a visual representation of the primary frequencies of the consonant and vowel phonemes.” Dmitri drew an example of a Speakeasy word gram on the whiteboard and briefly described the relationship between the tone-pair frequencies and the shapes. “Are you with me?”
Both students nodded. “We’re chill, boss.”
Dmitri continued. “It’s designed like a videogame to provide real-time visual biofeedback. Compared to all the data in a spectrogram, it calculates and depicts a concise set of variables in the frequency domain. Speakeasy is the optimal tool to determine if the whale’s language is frequency modulated like our own. I brought a copy of the program back from Maui. I’d like Andrew to preview and prep the whale song data using the spectrum analyzer. Then Seema can massage the data for the Speakeasy analysis. Any questions?”
Andrew raised his hand again. “Have you booked our flight to Stockholm for the award ceremonies?”
“Very funny.” Dmitri kept a straight face while opening a jewel case and removing a CD. “This disk contains all of PICES’s recent digitized whale vocalizations.” He held it aloft, hummed the first four notes of Beethoven’s 5th, and considered their symbolic meaning—Fate knocking at the door. “Think positively since, for all we know, it could be the cetacean Rosetta Stone.”
Andrew grabbed the CD case, and the two students waved their goodbyes. Dmitri reflected upon his good fortune, happy to be the mentor of two such delightful and competent individuals. Their team chemistry was superb.
It had taken all of his self-control, however, to appear cheerful during their discussion. Prior to their meeting, he’d scanned the online edition of the Honolulu Star-Advertiser. Now he clicked on the window he’d previously minimized and glanced again at the headlines: MORE WHALES STRANDED IN MAUI . . . DEATH TOLL MOUNTS. Dmitri hadn’t wanted his students to be spooked by his anxiety over Melanie’s peace of mind or his desperation for a language breakthrough. He required every ounce of their talent. They’d need to be as relaxed and upbeat as possible during their investigation of the whale songs. Maybe, with their creativity, their help, he could actually break the codes to unlock the gates that guarded the interspecies Tower of Babel. It could be the whale’s best hope for survival.
TELL ME I’M NOT CRAZY
SoCalSci University, Los Angeles, California—the next day
Dmitri whistled Gershwin’s Rhapsody in Blue as he approached the Engineering Department’s Signal Processing Lab. He was in a much better mood now that he’d finished the early afternoon lecture for his undergraduate signal processing class. The intellectual challenges of his work and the stimulating interactions with bright young minds often helped to balance his emotional swings.
He swiped his magnetic card, punched in the security code on a wall-mounted keypad, and entered a dimly lit, windowless anteroom. The lonely space was jam-packed with rows and racks of electronic equipment. Banks of gizmos and gadgets, studded with garish chorus lines of pulsating LED status lights, oozed waves of electromagnetic radiation. The mind-numbing roar of an army of cooling fans besieged him. He’d worked in rooms like this before, sometimes experiencing headaches and disorientation.
Dmitri hurried through a central corridor, flanked by columns of hardware, and parted a pair of double-swing doors. He found Seema and Andrew huddled together at a computer workstation crowded with test instruments, their faces masked by a fluorescent blue glare. They gazed at two video screen displays of various frequency plots, presumably from one of the whale song recordings.
Dmitri tapped Andrew on the shoulder. “How’s it going?”
“Look at what we found.” Andrew pointed at the monitor.
Dmitri recognized the peaks and valleys of a waterfall plot, a way to represent time-varying, two-dimensional information in three dimensions. The sequence of two-dimensional frequency plots, each resembling the rising and falling of a mountain range, receded into the depth dimension of the monitor like a series of cascading waves. He studied the peaks and valleys of the power levels across the spectrum of frequencies. “This section over here,” he pointed, “looks like amplitude modulation of three fixed frequencies.”
“As if playing multiple organ pipes of different lengths,” replied Seema.
“But this section on the right looks like the inter-frequency modulations of vowels,” added Andrew.
“Like the human vocal tract.” The words surged through Dmitri’s lips on a wave of rising pitch. “The anatomy and physiology of their vocal system could be even more complex than our own. Seema, since you’re interested in the design of novel musical instruments, how about a project to reverse engineer a model of the humpback’s vocal tract from these waveforms?”
“Very interesting,” replied Seema. “Like a whale French horn or bagpipes.”
“Don’t do it,” said Andrew. “The whaling nations could use that thing like a duck call to lure the whales to their doom.”
Seema glared at Andrew and then faced Dmitri. “By the way, you were right. There’s nothing above four thousand hertz in these frequency plots.”
“Curiously in the same range as human speech.” Dmitri leaned over Andrew’s shoulder to peer at the monitor.
“I applied more than the usual amount of pre-emphasis to the higher frequencies,” said Andrew.
Dmitri backed away. “Not that easy to position a microphone close to a whale.”
“Ahh, so that’s why the high-end frequencies are so attenuated.” Seema tapped the screen.
Andrew rotated his chair to face Dmitri. “We decided to test-drive the analyzers by comparing the Maui whales to the Tongan humpback data. The grouping of the resonance peaks is of a different pattern. We think their songs exhibit a dialect unique to their region.”
Seema laughed. “It’s so cool, as if the Tongans have an Oxford English accent and the Hawaiians speak American English.”
“Intriguing,” said Dmitri, “but remember, we’re here to decode discrete phonemic units from these frequency patterns, not to discover the next great whale rapper for American Idol.”
“How about a trip to Maui?” suggested Seema. “We could drop some speakers into the ocean, play back the recordings, and just lay back and listen for feedback.”
“Don’t forget the mai tais.” Andrew lifted an imaginary glass to his mouth.
“Nice try.” Dmitri glanced at his watch. “In fifteen minutes, Melanie’s calling us from Hawaii.” He saw their quizzical expressions. “The speech therapist, rig
ht? She’ll instruct you in the operation of the Speakeasy interface. I’ve committed to a workshop in Santa Barbara tomorrow, so let’s reconnect in a couple of days. If Speakeasy reveals anything interesting in the Alaskan vocalizations, don’t hesitate to text me. Right now, I’ve got a meeting in the dean’s office. Goodbye and good luck.”
* * *
Seema stretched and Andrew yawned. It was early morning, and they were still camped-out in the Signal Processing Lab, their workstation cluttered by Styrofoam cups and Chinese take-out boxes. All night long, they’d tried to make sense of the Speakeasy images and the captivating relationship between the humpback’s vocalizations and the word gram shapes on the monitor.
Seema pointed at the screen. “As Dmitri suggested, these sharp turns are the most likely regions to find cetacean phonemes.” She mumbled through a blanket of fatigue.
“Pretty ingenious suggestion,” replied Andrew. “Like the discovery of super-massive black holes from the time-lapse pictures of stars orbiting around them.”
“Unfortunately, we’ll need more persuasive evidence than visual observation.”
“We’d have to do a statistical analysis of the Speakeasy data. It’ll take at least a week to code and test.”
“Let’s discuss it later.” Seema slumped over, resting her head on the table top. “It’s almost morning, so let’s get some sleep.”
“Give me just a few more minutes,” said Andrew. “We’ve focused our attention on these dense episodes of frequency modulation that Dmitri’s interested in.” He indicated a second monitor that displayed the non-Speakeasy, time-varying waveforms. “We’ve totally ignored the other sections of the recording. What about this?” He pointed to a sparse region of sound blips separated by many seconds of silence. “Let’s analyze this segment before calling it a night.”
“Oh, what’s the use? It looks like noise to me.” Seema lifted her head, leaned back in the chair, and stretched like a feline.
The Whale Song Translation: A Voyage of Discovery To Neptune and Beyond Page 11
