Thursday, June 21, 2007
episode 3 of math abuse
-the incredible expanding toyota-
the mention of areas and volumes reminds us of geometry. this is another field ripe for innumeracy and math abuse. we can be influenced by the numbers that areas and volumes produce, or we can be influenced directly by geometry itself. the first abuse concerns volume.
in this case, we encounter the innumeracy i call dimensional dementia. understanding how areas and volumes behave can be tricky, which creates fertile ground for those who would impress or confuse us. here, for example, is how a recent television ad for the toyota camry began:
"How can it be that an automobile that'sa mere nine inches larger on the outside give you over 2 feet more room on the inside? maybe it's the new math!"
by appealing to "the new math", the advertiser sent a signal to the innumerate public: "Don't even try to think about this one. it's beyond you!"
cutting straight to the chase, a 9 inch increase in any of the toyota's 3 principle exterior measurements, (height width length), cannot possibly produce a change of 2 linear feet in any one of the interior dimensions. this suggests that the "2 feet more room" refers not to lenght, but to volume, 2 cubic feet to be precise. so should we be impressed when a mere 9 inch increase on the outside produces an additional 2 cubic feet inside? in fact, we should expect an even larger increase.
looking at the dimensions of the generic passenger compartment which are 3 feet(height) by 6 feet (length) by 4 feet (width). the volume is 3X6X4 = 72 cubic feet. any way you calculate the volume with an added 9 inches, the resulting increase is much larger than 2 cubic feet. increasing its width by 9 inches, for example, increases its volume by a whooping 13.5 cubic feet! heres the calculation. 9 inches = 0.75 feet. thus its final volume is 3X6X4.75 = 85.5 cubic feet. why then did the toyota company claim such a small increase in the volume of its compartment?
- I contemplated at 10:53 pm
