Friday, May 4, 2012

Kids that are twice more short than their parents

Hopefully that title makes you cringe. If I tell you that Bobby Jr. has two times less height than his dad, what does that mean? 

Let's suppose young Bobby Jr. is three feet tall and Bobby Sr. is six feet. Does that make Junior 2x shorter?  200% shorter? If he grows 2 times more will he be 6' or 9'?

So what am I complaining about today?

Well, a lot engineering effort goes into making things smaller and cheaper and apparently the standard language for describing reductions using fractions and percentages isn't adequate:
At UConn’s clean energy engineering facility, Maric has developed a prototype manufacturing process for the fuel cells that uses 10 times less catalyst material with little waste.
Wow 10 times less! So if the OLD process used 10 grams of catalyst, the NEW process would use 10g x 10 = 100g less, that is -90 grams.

I see this all over the place and especially when someone is trying to hype a supposed breakthrough. If the author had written, "that uses 90% less catalyst" or "that uses one tenth the catalyst" the meaning would have been perfectly clear and would have matched my mathematical intuition perfectly.

But apparently some deep quirk of human psychology makes us respond to the language of bigger even when smaller is better. "My cellphone is ONE TENTH THE SIZE of yours" just sounds wimpy but "TEN TIMES SMALLER" sounds grandiose.

Or perhaps a substantial population reading about fuel cells is too innumerate to understand the concept of one tenth? Maybe it's just a logical extension of that other travesty to mathematical intuition "x times more" that would cause us to describe 3' Bobby's growth thusly:
3' Bobby Jr. grew 2x more, so now he's 6' tall.
Okay, but now that we've cluttered up the meaning of the word "more", how do we describe percentage increases?
  • 3' Bobby Jr. grew 50% more so now he's 4' 6"
  • 3' Bobby Jr. grew 100% more so now he's 6' ?
  • 3' Bobby Jr. grew 200% more so now he's 6' ?  9' ?
That's not pretty. Accepting "times more" means that we have to either stop using "x% more" OR create a magic line at 100% more. So if a formerly 3 foot tall kid is now 99% taller, he's just shy of 6', but if he's 101% taller, then he's a little over 3' and if he's 200% or 2x taller then he's an even 6'. Ugh. It's enough to cause one to retreat into innumeracy!

So please, for the love of goodness and light, don't EVER let any variant of the gooey intelligence-sapping terms "x times more" or "x times fewer" ever be committed to text or speech.

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