## Wednesday, April 23, 2008

### Postscript to "When is 325,000 Greater Than 325,425?"

When I originally blogged this item, I had an idea about an alternative interpretation but I couldn't quite express it. Now, I think I can.

When we see a high-precision number, we perceive it as being associated with something particular (e.g., this pig). When we see a rounded number, even if it is smaller in magnitude, we perceive it as being associated with an interval or collection of numbers (e.g., the collection of pigs in the drawing). That's more or less what's going on between Sylvie and Bruno; she's thinking round numbers about the collection of pigs, whereas Bruno is focused on the particular four pigs that he can see immediately.

An interval is a range of numbers that could encompass the precise number and therefore, by definition, exceed it. So, for example, $325,425 is larger than$325,000 in absolute magnitude, but the latter could be interpreted (i.e., perceived in our mind) as representing the interval $325,000 to$326,000, which encompasses \$325,425. Hence, the particular may be perceived to be smaller than the general. The Cornell researchers did not test for this effect.