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?
Thanks for a vast number of answers to this question, many of which were probably more suited to undergraduate level than to a four-year-old. However, one notable group of wags insisted on sidestepping the answer at all costs. Among these was the inevitable 鈥淎sk you mother鈥�, from Tony Turner of Tuross Head, New South Wales, Australia. Stephen McIntosh of Hull, UK, suggested: 鈥淵ou are far too intelligent for a four-year-old鈥� have a lolly.鈥� More encouraging was the answer from Dave Oldham of Northampton, UK, who offered: 鈥淚f you can ask a question like that at four years of age it won鈥檛 be many more years before you can explain it to me.鈥� And congratulations to Peter Gosling of Farnham, Surrey, UK, for his unashamedly literal view of the world. His advice was: 鈥淚 think you should tell your son that it is illegal for him to be driving at four years old.鈥� 鈥� Ed
鈥� When my son (now nearly 10) was a similar age, I tried to explain this phenomenon during a train journey. First I pointed out that objects further away look smaller. I used his hands to show this: if he held one hand close to his face and the other at arm鈥檚 length, the one at arm鈥檚 length appeared smaller, even though he could put his hands together to confirm they were the same size.
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Secondly, I showed him that it takes more objects to fill the same amount of visual space if they are further away. For example, if the hand further away is half the apparent width of the one closer, it takes two hands to fill the same width.
鈥淚t takes more objects to fill the same amount of visual space if they are further away鈥�
Finally, I got him to think about something moving, such as an index finger traced slowly from one side of his palm to the other. If it moved at the same speed when it was further away, it travelled the same actual distance (a palm鈥檚 width), but seemed to have travelled only half as far. So it would take twice as long for it to look like it had travelled the same distance. I then summed up by explaining that the distant things were not actually moving slower, they just looked as if they were.
I also had to explain why it looked as if the trees and houses were moving when my son was sure that they weren鈥檛 really. First, I got him to move his hand in front of his face, and then to hold his hand still but move his head from side to side. In each case he could see that the hand seemed to move across his vision in the same way. I told him that the two movements were equivalent and he seemed to accept that.
The other passengers on the train thought I was a little strange, but it kept my son quiet.
Keri Harthoorn, Stoke-on-Trent, Staffordshire, UK
鈥� The answer is that the type of optical system that is used by our eyes causes us to perceive a particular object as 鈥渟maller鈥� the more distant it is 鈥� a phenomenon called . As our vision system converts the angles subtended by the things we are looking at into apparent distances on our retina, this causes nearby objects to sweep through our field of vision much more rapidly than distant ones. So while distant and nearby objects are within the same field of vision, those further away take longer to pass across it, as they have a low angular velocity, than those that are closer.
You can demonstrate this by placing your hand on a newspaper. Make a 鈥淰鈥� with your index and middle fingers 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 next, while the text closer to your hand moves more rapidly.
Gregg Favalora, Arlington, Massachusetts, US
鈥� One way to demonstrate this process is to put a toy car on a path representing the road, with an object placed 30 centimetres ahead and 30 centimetres to the side of it. Show your son how the object goes from being diagonally ahead to diagonally behind the toy car when you move it forward 60 centimetres. Then do the same thing, but with the object 3 metres ahead and 3 metres to the side. This time the car has to travel 6 metres to cause the same change in the angle at which someone in the car would view it. Also point out that it takes much longer for the car to travel 6 metres as for it to travel only 60 centimetres.
Eric Kvaalen, Cambridge, Massachusetts, US