Some people are smart because understanding comes easily to them. I, on the other hand, might argue that what smarts I have come from what I don’t understand. <\/p>\n
Take, for example, mirrors. There is a basic rule about mirrors that many take for granted, and that is when we focus on a mirror image, we focus not on the mirror but on the things it’s reflecting. Optometrists use this all the time to avoid having twenty-foot-long rooms. Using mirrors, light bounces from the eye chart letters twenty feet before hitting the patient’s eyes; hence the 20 in 20\/20. (20\/20 means that at twenty feet, you see at the same clarity as a normal human. Some few see more clearly; 20\/10 means you see an object at twenty feet as clearly as it would appear at ten to most people.)<\/p>\n
But this presented problems to me because I could not understand how it worked. Here were my questions:<\/p>\n
How does my eye know how far to focus in order to see the other object clearly? If I’m looking at a mirror that’s reflecting something out of my line of sight\u2014a plain cube, say\u2014how would I know, without a context, where to focus to see it at the appropriate clarity for my vision? How know if it was five inches a side, or five feet? All my brain knows is that the cube is some distance farther from me than the mirror. Yet somehow my eye focuses. (Briefly I wondered why, if my brain can “decide” how distant a thing is, it can’t “pretend” it’s closer so my myopic eyes see it clearly? I’m a highly near-sighted person who sees clearly about six inches from my eyes, after which the world begins to blur. Don’t worry, I figured it out.)<\/p>\n
Why can’t I take a picture of the mirror itself, or glass, for that matter? Saying it’s because they’re transparent only raises the issue of what, exactly, makes transparency possible in the first place. A thing that both allows an unimpeded passage of light through, but can also reflect that light almost perfectly? <\/p>\n
It was all too weird for me.<\/p>\n
But I understood the basics of refraction, and eventually (I’m ashamed to admit how long this took) I came up with a mental picture to understand this at least partly. <\/p>\n
First, I had to acknowledge that transparency was not a focusing issue (more about transparency later). Then I imagined a camera, an object, and a mirror at the points of an equilateral triangle. The mirror is angled so that it reflects the object to the camera, and the camera to the object.<\/p>\n
The camera’s view includes both the object and the mirror. But the representation of the object the camera sees via the mirror has traveled twice as far, and so is less clear. As was my understanding, until I thought of this.<\/p>\n
Then another question occurred to me. If the camera is absorbing both its direct view of the object, and the reflected view, perhaps a piece of film with both those bits of information was more accurate somehow than simply seeing the object clearly. Then I imagined multiple mirrors, each angling a different aspect of the object onto the same point. The results would have much more complete information about the object than a simple photograph. We might not interpret it well on a flat surface. Then I thought of holograms, and suddenly my understanding of the interference pattern that creates a hologram, and the apparent chaos of a piece of holographic film, improved sharply. <\/p>\n
Most of the things in my life that I understand well originate like this, with something obvious to others but not to me. And that’s why I say that I’m smart because I’m stupid.<\/p>\n
Still, I’m also stupid because I’m smart. There are a bunch of cuttlefish in a lab in Pennsylvania that are demonstrably better able to learn than I am, Here’s why:<\/p>\n
Jean Boal, an associate professor at Millersville University, studies cuttlefish intelligence, as well as that of other cephalopods. She has devised a fairly complex test, demanding not only learned association, but unlearning it and learning a new one, then going back and forth in a process called serial reversal learning. They’re pretty good at it.<\/p>\n
The cuttlefish goes through a door, into a tank within a tank. It’s small, with opaque walls. To both sides of the cuttlefish are two openings into the larger tank, and in front of it is an object such as a plastic plant.<\/p>\n
The two openings are marked differently, one framed with broad, vivid stripes, one a solid color. Both appear to be open to the cuttlefish, but one is closed using a transparent piece of plastic. If the object in front of the cuttlefish is a plastic plant, then the solid-framed doorway is open. If the object is a rock, then the striped doorway is open. <\/p>\n
Cuttlefish are smart enough to figure this out, and act accordingly to obtain access to the rest of the tank. <\/p>\n
Here’s why I’m not as swift as a cuttlefish. There are two good routes to my workplace, one on the highway, one on a street paralleling the highway. If I stepped out the door to see a mockingbird sat on my mailbox, and this was followed by a wreck on the highway necessitating my taking the street route, I would not correlate these things. Even if every time the mockingbird was on the mailbox there was a wreck on the highway, I sincerely doubt I would notice the correlation. For one thing, I’m smart enough to have a lot of things on my mind, which might make noticing and retaining and associating the data more difficult. For another, I’m informed enough to understand the basics of physics, and this tells me that birds on mailboxes are not catalysts for car wrecks. So the very simple association the cuttlefish makes would be beyond me.<\/p>\n
Dr. Boal say that “the ultimate question is, am I smart enough to find out how smart they are?” Well, Dr. Boal, I can tell you one thing\u2014they are most definitely smarter than I.<\/p>\n
Transparency and reflection are still interesting to me. Think about it. Here’s a piece of glass, and it allows light to pass through in a straight line, unimpeded so far as we can tell (I’m assuming no impurities are present to tint or otherwise distort the glass). We look through the piece of glass, and we see what’s on the other side. But that same piece of glass can, if I view it from the right perspective, reflect all that light instead of letting it pass through. And my brain lets me see it clearly, despite the focusing distance being farther than the glass itself. Water and other things are similarly challenging. <\/p>\n
It’s as though the property of the transparent object\u2014allowing light through, or reflecting it\u2014is dependent on the perspective and behavior of the observer. I know this is very obvious. But it seems to me that this is a good analogy for some of the more mysterious behaviors in the universe. It’s not that something magical is happening. It’s that we’re seeing different facets of the same thing, and we just can’t see the thing itself yet. Because it’s transparent.<\/p>\n
Originally posted on LiveJournal<\/p>\n