The locust

The following short story was written in response to a perception-science exam question (in italics) sometime in 2021.

– At university, there is no Fall break, just more exams. Of course, your family is blissfully unaware of this fact, and they come over to visit. At least your young nephew is an adorable little fellow, who is already showing a keen scientific interest in the world around him. As you walk through the neighborhood park together, he spots a locust sitting on a branch. In happy excitement, your nephew runs to the animal to get a closer look. The locust is moving its head in a characteristic fashion, from one side to the other. The hypothesis that is entertained by your nephew is that the locust is trying to see around him. Before the little guy can even articulate this idea, however, the locust takes a big jump and lands on his nose.

After the tears from the unexpected shock have dried, your task is to educate the budding scientist and explain what the locust was really doing. You may assume your nephew is intellectually at the level of a second year BCN research master student. [~1000 words]

———————

Once your nephew is done crying, you take his hand in an avuncular fashion and walk him down the park path, allowing some time for his scientific curiosity concerning the locust to overwhelm any residual post-insect-assault sobs. Finally, when you can practically hear the gears turning in the boy’s young BCN research-master-level mind, he timidly asks, “Uncle, why was the bug moving his head in that funny way before it attacked me?”

“Because,” you reply ceremoniously, “that is the war cry of it’s people.” Your nephew tightens his little grip as the two of you approach a forest through which the path runs. “And it is not a bug, it is an alien.” Now the boy’s grip loosens in suspicion. “The bad blood between the Locustelians and Earth-people has simmered for many-a-millenia, and this act of brazen violence against our kind sets that simmer to a boil. It’s tantamount to a declaration of war!”

“Uncle!” The boy cries, now stopping with stamped feet and crossed arms. “Tell me the truth,” he demands with a furrowed brow, “and by truth I mean the science.”

“Well alright, if your asking for it,” you agreed nonchalantly with a sly smile, pleased that you have now got an audience of one on the hook for offloading all the great stuff you leaned in your Auditory and Visual Perception course. “Come along then. Science is best explained while walking.” The boy trots up to you and the two of your continue your stroll, now entering a canyon of verdant trees of many shapes and sizes. “Tell my what you see?” you probe.

“Trees?” The boy guesses.

“Exactly! Trees!” you exclaim, “Now tell me, do you see them moving?”

“Uncle! I asked for the science.”

“This is the science.”

“Oh?” the boy is surprised, and a ponderous look befalls his little face. “You mean how the trees move across my field of vision?”

“Yes, exactly,” you reply with vicarious pride in the boy’s collegiate level intelligence. “And now tell me, do the trees all move at the same speed?” The boy’s pondering resumes.

“The ones that are closer move slow and the ones farther away move more quickly.”

“Oh really?” you protest, “What if you focus on the ones farther away?”

“They switch! Now the farther ones stand still and the closer ones are moving!”

“Welcome, my boy, to the wonderful world of motion parallax.”

“Motion para-what?”

“Motion parallax.”

“Motion parallax? How does it work?” The boy inquires with intrigue, right-on-cue. You smile.

“Well if you really what to know. The crux of the matter is all in the fixation point and by that I just mean the point at which your vision is focused.”

“Is that like the little cross on the gray screen from all those experiments you’re always doing?”

“It can be, if that is what you are focused on.”

“Right now I am focused on the end of the path.”

“That is good. By doing so, you actually increase relevant depth information for your navigating of the way.”

“What? How?”

“Tell me, is the point your focusing on—at the end of the path—is it moving?”

“No not really.”

“What about the points around it?”

“Yeah maybe a little.”

“What about the points further around it.”

“Oh yeah, they are moving a lot!”

“In what direction?” you ask, priming the boy for his well-deserved ah-ha moment.

“Away from the fixation point!” he announces, with a little hop in his step, surely funded by the excitement of scientific discovery.

“That, my friend, is called optic flow. As an observer moves (and looks) forward, points across the retina move away from the fixation point. The further they are from the fixation point, the faster the move.”

“Uncle, what’s a retina?”

“That, my little scientist, is a question for another exam, but for now let’s just say it is the wall on the back of your eyeball that images project onto through your optic lens. Position, motion, and color inform us about features of the real world.”

“Uncle, I want to know more about the retina.”

“Kid, we should really be considerate of the word limit, we aren’t even done with motion parallax yet.”

“Oh, that’s right! How is motion parallax related to optic flow?”

“I’m glad you asked, kiddo. They are really two-sides of the same coin, both being caused by ‘the differential speed with which stationary objects move across the retinal image’(Stone 2012).”

“Why did you just wiggle your fingers in the air and say a name and date after that sentence?”

“Because I don’t want any trouble with plagiarism, of course.”

“Oh…” the boy trails off, lost in thought. A cool wind rustles the leaves all around them, some shimmering in beams of sunshine, dappling light onto the loam beneath. They both tighten their coats. Finally, the boy brightens up and queries, “So by considering the motion of objects across our retina relative to our own speed of motion and the angle between the object and our fixation point, we can approximate the distance of the object in question?” You nod steadily, radiating with pedagogical pride. Instead of answering, you allow the boy more time to think. “Any motion will work, right?”

“That’s right,” you answer flatly, suppressing your triumphant smirk.

“So the bug was moving its head side-to-side to estimate the distance it would have to jump to land on my nose?” The boy asks with profound excitement. You give him another moment and he finally adds, “Because of the ancient feud between our people and the locustelians?”

“Now you’ve got it.”

“Well that solves that, I guess.”

“Aren’t you forgetting something?”

“Huh, what?”

“What comes after science?”

“Oh that’s right, application!”

“That’s right. So how can we apply our new understanding of motion parallax to thwart future attacks by the locustelians and maintain intergalactic peace?”

“Squash-em?”

“I said peace.”

“Well, I don’t know then.”

“I’ll give you a hint kid. The distance estimation you mentioned above is define by an equation. d ≈ θ*v/s, where d is the distance of the object from the observer, v is the observer’s own velocity, and s is the speed at which the image of the object moves across the retina of the observer. Now tell me, how do we thwart the attack?”

“Ah, I see. If I bob my own head in the counter-direction of the bug’s head-bobbing, it will increase the speed at which the image of my nose moves across the retinas of the bug, thereby creating the illusion that my face is closer that it actually is. So it will jump and miss!”

“Now that’s what I call applied science kid,” you proclaim, with renewed hope for the future of human-kind. The sun picks up and birds are singing. An ice-cream stand moves with increasing speed across your retina. You really should get going, because unlike this kid, you don’t have a fall break and you do have an exam for your Auditory and Visual Perception course that starts in hour. Somehow, though, you feel this little didactic moment will come in handy later, so you decide there is time enough. “Say kid, I am proud of your hard work on that scientific problem. If I would grade it, I’d give it a 9.5, and moreover, I’ll give it an ice-cream. Go on, pick a flavor.” The two of you slow your synchronous gate and you take a moment to watch the many layers of trees slow their relative slides across your visual field, their differential inducing a phenomenological experience of the rogue dimension, placing you as a single point in a three-dimensional pool of light. You sway and the pool undulates in sympathy with your position. The motion calms you. You close your eyes.