Perspective
Ron Graham
There’s been a wide body of research on the way outfielders chase after fly balls over their heads. (Believe it or not.) You might think that the most efficient way to go after that ball before it lands behind you is to run straight back. But outfielders don’t actually DO that. They run a curved path, forcing their view of the ball to have two dimensions. If the outfielder only looks over his shoulder, his perspective of the ball is one-dimensional. (He can get a stiff neck, too, but that’s another story.) And that one dimension appears to him to be almost unchanging, moving along with him, until the ball is close enough to ground level that its apparent change in size is noticeable.

This is one example in nature that shows us that we need at least two dimensions of perspective to be able to "see" distance. If you wear a patch over one eye, you’ll find that you can follow objects moving from side to side in your field of view, but your depth perception is clearly not what it is when you use both eyes. And to know where something is, you need to be able to pick up three dimensions.

Satellites show us this in another way: in order for a spacecraft’s position to be determined, it generally needs two reference points. One reference point (often the Sun or another star) gives the spacecraft two dimensions; a second (generally an Earth station or the Earth horizon) gives the third dimension. If the Sun or star is invisible to the spacecraft at any time (which usually happens a couple times per Earth orbit), the spacecraft has to "guess" where it is until the Sun is visible again.

GPS shows us this in still another way: once the spacecraft knows where it is, it locates a GPS receiver on Earth. It needs another two pieces of information: the distance of the receiver from the spacecraft, and how long it takes for the spacecraft to bounce a signal off that receiver. Both the spacecraft and GPS are using a technique called triangulation to determine position -- they need three dimensions just as does the human eye.

Perspective is important in art, as well -- the artist must provide us three dimensions in order for us to locate everything in the painting.

Perspective is important in our writing. In business, you usually can’t send a nontrivial memo unless reviewed by the boss first. You usually can’t publish an article unless at least reviewed by an editor -- if not by several. In the Old Testament, every fact was to be confirmed by "two or three witnesses." (Throw an extra one in there in case one is unreliable. Redundancy.) The idea is that readers are not expected to take actions on the basis of a single point of view.

For a writer to provide perspective to the reader is not just a matter of having others edit the written work first. The writer also has to have some feeling for the way the human eye works, and provide ways for the reader to locate information on the page. The importance of visual cues to the reader's perspective can't be overstressed. Ways you can provide perspective within your text include

  • Highlights (e.g. bold and italic and underscoring)
  • Lists (for ALL nontrivial enumeration)
  • Tables (for ALL nontrivial matched pairs and triplets of info)
  • Section headings (if you have more than one logical section)
  • Graphics (for ANY information not readily adapted to text)

You don’t necessarily need all of this. But it’s unlikely that you can get away with none of it.

Assignments

Use two concentric tubes (paper towel or toilet paper tubes will do), and connect them at one end with rubber bands spaced at 60 degrees radially. Once they're connected, you can turn one tube relative to the other and the rubber bands converge to the common center, as shown:

tube problem

You can use the combined tubes as a "robotic grappler," where you control its location by looking through the tube, and grab a loose (and hopefully extended) object with the converged rubber bands. What are the sources of error? How can you operate this system successfully?

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