Tonight J-Fav is out of the house, so I am left to my own devices here as T-Fav sleeps. In an idle moment I decided to submit an answer to New Scientist's weekly question in their "The Last Word" column. This week's question is:
Driving along in the car the other day, my four-year-old son asked why things that were closer to us were moving faster than those further away. What should I tell him? (Milton Inverdale, London, UK)
Here's my response, which is the real techie answer for the parent plus a little experiment for the 4 year-old:
We can answer this question and provide a simple manual "demonstration" that might appeal to Milton's 4 year-old. The complicated-sounding answer is that the type of optical system used by our eyes causes us to perceive a particular object as "smaller" the more distant it is; this is called foreshortening. Foreshortening causes nearby objects to appear to sweep past our vision much more rapidly than distant ones because it implicitly converts the angles subtended by the things you're looking at into distances on your retina. Therefore, nearby objects whoosh past your vision almost instantly because they have a high angular velocity with respect to the vertex of your pupil - but distant objects appear to creep along because they have a low angular velocity.
If our eyes were designed differently, with so-called "orthoscopic imaging," it would operate on the lengths of objects rather than their angles. That is, as you drove along in your car, everything would appear to move at the same rate. However, unless your eyes were very large, you wouldn't be able to see very far around the direction you're looking at!
You can demonstrate these things by placing your hand on a newspaper. Make a "V" with your index and middle finger and sweep it along the text. Your hand is the car, and the V is your field of view. You can see that the text near your fingernails takes a long time to move from one finger to the text, while the text closer to your hand transits more rapidly. In contrast, extend your index and ring fingers in parallel. When you sweep those along, every line of text takes the same amount of time to move from one finger to the other.
ps Fun diversion: check out NaturalMotion Euphoria, software for game developers that incorporates physics and AI to simulate really natural-looking motion of game characters. This is a big deal because it can replace "keyframing," a hard-coded approach. Anyway, take a look.