Wonder of the Waves

by Jim Lombardo

  After introducing himself and his parents, and summarizing his achievements, Adam took some time to explain the basic structure and internal mechanics of the 3x3x3 Rubik’s Cube. He then rapidly solved a scrambled cube to the amazement of everyone, with the exception of Hannah. Before Adam had even begun solving the cube, she had created a mental image of the cube, had mixed it up randomly, and then after erasing from her memory the exact twists and turns that had taken her to this position, had explored various systems for returning the cube to its original solved position. It was rather easy for her. There were six faces on the cube. When solved, each face of the cube had a unique color—white, yellow, blue, green, orange and red. On the 3x3x3 cube, there were nine smaller faces comprising each single larger face. Three rows of three. Hannah recalled for an instant the game of Tic-Tac-Toe from the park. That had also involved a face, a two-dimensional square consisting of three rows of three. She considered how more deeply complex and intellectually provocative a square becomes when you add a third dimension, and wondered if you could ever add yet another dimension to a cube. This unknown reminded her of the questions she had about gravity. She wondered why the number of dimensions in space should be limited only to what the human brain, a collection of organic cells, could perceive. After all, there were sound waves that were outside the perceivable range of the human ear. That’s why dog whistles were invented. So the dog could hear the sound without humans being disturbed. There were also light waves in the electromagnetic spectrum that were beyond the perceivable range of the human eye. People could see violet light with wavelengths of about 380 to 450 nanometers, but not ultraviolet light, which has shorter wavelengths under 380 nanometers because they are physically blocked out by the cornea. So couldn’t there also be space dimensions that were out of the range of what human brainwaves could distinguish? She cordoned that question off to address later.

  On the Rubik’s Cube, she realized that the six center pieces on each face never moved from their relative position. They remained in place, regardless of how the cube was twisted or turned. In other words the small center white face always stayed in the center, and was always exactly opposite the yellow center face on the opposite side of the cube. The blue center face always sat opposite the green, and the orange was opposite the red. This meant that the six small center faces were already in the correct position. It was now simply a matter of placing and orienting the eight corner pieces, which had three colored small faces each, and placing and orienting the 12 edge pieces, the faces that were neither center nor corner pieces, each of which had two colored small faces adjacent to each other.

  As she mentally endeavored to solve the cube, she discovered that in trying to place and orient specific pieces, other pieces that had already been properly placed and oriented were disturbed. There had to be an order to the solution, and all solved pieces had to be taken into account when determining the proper sequence of twists and turns to make steady progress on the unsolved pieces. Initially she solved the entire cube one layer at a time, but then reversed the solution, and figured out that it would be more efficient to first solve a 2x2x2 corner section of the cube and expand that into a 2x2x3 rectangular box before completing the second layer, and moving on then to solve the final layer.

  Next, instead of relying on two separate sequences to first place, and then orient, the four final layer corner pieces, she devised complicated algorithms that placed and oriented the corner pieces in a single sequence, thereby reducing the number of twists and turns needed to reach the same endpoint. Just as Hannah completed this mental exercise, Adam was beginning his first solve for the group. During the 12 seconds that Adam was completing his solve for everyone, she playfully found a way in her mind’s eye to move the smaller faces from a solved position to a single face so that an orange letter H was created. The group applauded enthusiastically as Adam completed the Rubik’s Cube, and held it high above his head in triumph.

  Grace, at only eight years old, was a violin prodigy. She could already play a vast collection of classical and operatic pieces without sheet music, and had performed with symphony orchestras throughout the world. She made her way to a child-sized chair in the front of the room with her case. Like a seasoned professional, she removed her violin and bow carefully, adjusted the instrument under her chin, raised her bow with flair, and then launched into a two-minute long demonstration that was both amazing and moving to her listeners.

  There was a math genius named Arja who had recently competed in the Mental Calculation World Cup held in Norway. At ten years old, she had beaten all participants, including adults. With one of the administrators following along with a calculator, Arja had everyone in the front row, one by one, call out random four-digit numbers and then immediately proclaimed the total of all the numbers added together. Hannah agreed with the final sum, and for sport had also quickly computed what the grand total would be if the digits in each four-digit number were put in reverse order. After the applause had ended, the woman with the calculator multiplied a random number by itself and then called out, “Arja, what is the square root of 942,841?” After brief consideration, Arja replied confidently, “971.”

  “Correct!” replied the administrator incredulously, and the room was filled with applause. Hannah refrained from clarifying the girl’s incomplete answer, because she didn’t want to show her up. But she knew that the correct answer was actually positive 971 and negative 971, since negative 971 multiplied by negative 971 also equaled 942,841.

  There was a linguistics savant from India who by the age of four could read four different languages, and now at seven could read, write and was fluent in six languages. Also participating in the study was the recent winner of a nationally televised Child Genius Competition hosted in Los Angeles, as well as the winner of the annual National Spelling Bee, who had clinched the title with the word, pneumonoultramicroscopicsilicovolcanoconiosis.

  Robin, though socially awkward, was a savant with an uncanny ability to memorize facts and figures relating to ornithology, the study of birds. His preoccupation with this subject had overtaken his life to the point where he was begging his parents to let him sleep in a bird-like nest he had constructed in his bedroom, rather than his bed.

  While in the midst of introducing himself timidly, his mother poked him in the arm with a stiff finger. “Do the bird calls,” she said in a harsh whisper.

  With full concentration and solemnity Robin announced, “The White-throated Sparrow.” He then began whistling for about 30 seconds in what resembled a high-pitched Morse code. After the applause ended, he continued, “The Mourning Dove.” He cupped his hands together and blew into a slit between his thumbs in such a way as to make a low cooing sound, producing a vibrato occasionally by flapping the fingers of one hand.

  Hannah, at the tender age of just under three and half years old, was by far the youngest participant, but easily the most well-known. The introduction she gave was probably unnecessary, but she obliged everyone with a short story about her life. She emphasized how ecstatic she was to be joining other children with whom she had something in common, and that she was looking forward to getting to know them all. In truth, her intellectual capabilities and potential far exceeded everyone in the room, though her parents had never allowed her to compete against anyone.

  When the introductions were over, a few researchers and administrators stood up individually to make orientation presentations, and answer questions from the parents and children. There was not much offered regarding the details of the study itself, but Dr. Burstein stressed that the children would have fun. There would be no studying and no tests, which was met with wild cheering from all of the kids, with the exception of Hannah who always loved those exercises. There would be team games, puzzles, and mysteries to solve together, debates, and discussions about various topics of interest in groups of different sizes, as well as plenty of time to simply enjoy socializing. Dr. Burstein thanked the parents
for their generosity in allowing their children to participate. She distributed contact information, and finished by saying she was looking forward to seeing the parents back in a week for the pizza celebration.

  Three days into the study, Hannah sat with Robin in a fourth floor classroom accompanied by two researchers who were trying to organize materials for a detective game they would have the children play. The two youngsters would have 30 minutes to work together, trying to solve a sequence of riddles to crack a mystery involving a missing piece of candy. The researchers would monitor the kids’ emotions and social interaction as they collaborated together on the challenge, designed to generate angst and conflict, because it had no solution.

  “Sorry, I gotta go downstairs to get the last page that didn’t print out. Be back in a few, guys,” said one researcher.

  The remaining researcher nodded and then yawned while stretching her arms high above her head. “You kids mind if I open the window to get some fresh air? It’s scorching in here.”

  “Sure, Kate,” Hannah agreed.

  The woman got up and unfastened brass latches on the bottom of two aged, leaded-glass windows that were about six feet high. She then began laboriously turning an old crank handle to swing them fully open. A cool breeze wafted into the room. The sound of wind weaving through the tree leaves below entered, and a few birds called out in the distance.

  Robin sat quietly, with a disturbed look on his face.

  “So, is Robin your real name?” Hannah inquired, wondering if his bird-like moniker was more than a coincidence.

  “Uh, it’s kind of a nickname. My real name is Robert. Nice how such a minor thing in your life, like your name, is chosen by somebody else,” he said sarcastically. “It shouldn’t be that way.”

  “Well, luckily it’s chosen by people who love you, so it shouldn’t ever be too horrifying, like...Robert,” Hannah offered with a grin, though her attempt at humor seemed lost on the boy. “Once there was this unconventional musician named Frank Zappa who named his daughter Moon Unit. Imagine going into a job interview with that at the top of your resume.”

  Kate, who was eavesdropping on their conversation, leaned forward in her chair with interest, and it squeaked, grabbing Robin’s attention. The woman craftily reclined back into a normal position and pretended to look down at some papers. She needed to remain as inconspicuous as possible since all of the children’s exchanges were considered important research data, regardless of whether or not they were engaged in an experiment.

  “So, I see you like birds. When did this obsess-, I mean, interest start?” Hannah asked.

  “It’s okay to say obsession. I guess that’s what it is,” Robin acknowledged.

  He peeked over at Kate and then lowered his voice. “I’ll tell you if you really want to know. It all began the morning of July 14th, four years ago. We had gotten in this really bad car accident the week before that kinda freaked me out, and my parents wanted to cheer me up, I guess, so they bought me this new black bike called a Typhoon, my first two-wheeler. Learned to ride it that same day. Anyway, the next morning, just as it was starting to get light out, I woke up and was dying to try it again. So I rolled outta bed and got dressed quietly, cuz my big brother and me shared a room, and I didn’t want to wake him up and make him mad. I snuck outta the house, got my bike from the garage, and took off. We live on a main road, on a corner, and I rode down this side road called Salisbury Street, which has a bunch of houses, but’s a dead end. Nobody was out cuz it was so early. I pedaled as fast as I could until I got to the end of the road, and then pulled over to the side cuz I was outta breath. That’s when I first saw my bird.”

  Robin paused as he relished the recollection. “He was on top of the last house, right in the middle of the roof, just perched there, looking down at me. It was a Classic American Robin with a dark orange breast. He called for me with a few chirps, and then we looked at each other for a really long time. We both knew what was going on.

  “The next morning, I went out there again, and of course he was there. This went on every morning for the rest of the whole summer. He only took a few days off when it was raining and lightning out. But he probably just didn’t want me coming out on those days, you know, so I’d stay safe and all. Anyway, the first day of school, I couldn’t ride my bike to see him that morning. I remember being scared cuz I was starting kindergarten. I couldn’t even eat my scrambled eggs. But when we got to the school, there he was, up on the roof of the place, watching over me. And it’s been like this now for four years. I see him all the time, like from my hospital room when I was stuck in there after my asthma attack. I coulda died, but there he was, sitting on a wire right outside my window for me. I told my parents about him, and they made fun of me. Said I was nuts and that’s why I didn’t have any buddies like my brother. They said it’s not the same bird, but it is. They don’t understand.”

  As Robin spoke, Hannah sat perfectly still, with laser focus on his every word. Like Kate, she also considered this conversation important research data.

  Robin continued his monologue with unabashed homage. “I don’t think my bird is God, but I do think that birds are kinda like angels. Each one of them has a special mission. Just think about them for a while, listen to them, learn about them, and you’ll see. I could tell you all sorts of stories about birds.”

  The boy became happily animated as he continued. “Like once there was this Viking explorer named Floki Vilgerdarson, who found Iceland. He took a cage full of ravens with him, and every once in a while he’d release one. They were common ravens by the way, the scientific classification is passeriformes, corvidae, corvus, corax. When the ravens circled the boat, he knew they weren’t near land. But when one finally headed off in one direction, he had the ship follow it to land. Don’t try to tell me that a bird is just a bird.” As Robin finished speaking, the exuberance drained from his face, and he cast his eyes down glumly.

  “I love birds too, Robin. I’ve studied them, once for an entire day,” Hannah said in an upbeat manner, hoping to cheer him up. “Is that book of yours all about birds?” she asked, reaching out with both hands. The boy jumped out of his chair, clutching the huge binder to his chest and turning away to protect it.

  “No! I mean…yes, but I-I don’t like showing it to people.”

  “Well, you can share it with me ’cause I’m a fellow bird lover myself.” Hannah got up and moved towards Robin. She raised her arms up just high enough to touch the bottom of the binder. Then she playfully jumped up and grabbed for it, taking hold of a piece of paper that was sticking out. As the boy pulled the book further away from her and she dropped back to the floor, she inadvertently tore a small scrap of paper out of the book.

  Robin shrieked, and his eyes bulged in anger. Hannah let go of the paper, but because they were right next to the window it was sucked up by a gust of wind and began sailing across the room.

  “GET IT!” Robin ordered in a panic, clenching his book now so forcefully that his knuckles turned white. Kate and Hannah both started after it as it darted to the opposite side of the room, climbing almost up to the ceiling and hovering for a second before swooping down under a desk. Hannah got down on her hands and knees, and, with Kate watching carefully, she dutifully retrieved the paper. Just then, there was a loud thumping sound behind them.

  “I have it!” Hannah announced, thrilled to share the news, but when the two turned back towards Robin the room was empty. The tattered binding rested open on the floor beneath the open windows. Another blast of wind fanned across the tome, brutishly flipping a few of the exposed pages. Each sheet was crammed with minuscule handwritten notes and numbers along with tiny sketches of different types of birds, and parts of their anatomy. Kate’s mouth dropped open, and she covered it with her hand.

  “Where’s Robin?” Kate asked, looking fearfully around the room. She jackknifed forward to check under all the tables. “Oh, my
God. Hannah, stay where you are,” she ordered.

  Kate ran to the window, stuck her head out and peered down, gasping for breath. “Oh, no…please!”

  She scoured the ground for Robin, but saw only bushes, grass, and a squirrel scampering cautiously across a flagstone walkway, scurrying a few feet at a time, then freezing to check for danger, before resuming. Hannah watched as Kate cocked her head in confusion, before scanning up and over to her left. The woman gasped again and stood motionless in horror, unable to get any words out. Robin was perched precariously about six feet away from the window on an extremely narrow cement ledge that was angled slightly downward. With his significant girth, it seemed to be defying the laws of physics that he was not falling forward off the ledge.

  Hannah disobeyed Kate. She pulled a chair up to the base of the window, climbed up, and poked her head out right from under Kate’s chest, startling her.

  “Be careful, Hannah! You’ll fall out!” the woman cried. She squeezed the tot firmly with both arms, trying in vain to recall a single thing she had learned from her extensive crisis training. But her nerves had reduced her to a mere observer.

  Hannah surveyed the scene, noting this was a situation in which gravity could present a much worse problem than the spring-loaded seat cushion scenario. For an instant she appreciated the physical manifestation of an analogous emotional condition. It dawned on her that throughout their entire lives, humans existed on top of a towering, razor-sharp precipice in a figurative sense, with no control over when they would fall off and die. She wondered if this was at the heart of generalized depression and anxiety.

  You wouldn’t need anything specific going wrong in your life to have the blues or to be anxious, with this impending drop dwelling in your subconscious, she thought. Maybe people overwhelmed by these uncomfortable feelings are simply more tuned into the reality of their ephemeral physical existence than others, and they struggle emotionally, like Robin, searching for ways to cope. Knowing that their loved ones face this same predicament is trying as well. Theirs isn’t an inferior way of thinking at all. Quite the contrary. It’s the product of a heightened thought process, a more highly developed self-defense mechanism. In the final analysis, a superior mind.