200% of Nothing

200% of Nothing, by A. K. Dewdney turns out to be a quick but interesting read.  The subject is “Innumeracy”; the mathematical equivalent of illiteracy.  He, and others, have a good point about innumeracy in America.  We accept, and even celebrate, mathematical ineptitude in a way that is horrifyingly inconsistent with the way we feel about illiteracy.  Contrast the comment “I’m just not a math person” with any similar statement about the inability or unwillingness to read.

Dewdney uses a collection of anecdotes to illustrate a number of the traps we fall into.  It is a decent introduction to ways you can be manipulated if you need it, and the anecdotes are entertaining if you are already well versed.  However, the book is a  bit superficial, and I suppose it is telling that I did end up with pages of notes on the interesting bits, as I have with most of the books I’ve read recently.

Statistics:
The media frequently leaves out information critical to the meaning of a statistic.
A public service advertisement in Sweden illustrates:

LAST YEAR 35 PEOPLE DROWNED IN BOATING ACCIDENTS.  ONLY FIVE WERE WEARING LIFE JACKETS. THE REST WERE NOT.  ALWAYS WEAR LIFE JACKETS WHEN BOATING.

The rate of life-jacket-wearing and the number of boaters are important, but omitted.  If only 1% of boaters wear life jackets, and 14% (5/35) of the dead were wearing them, then life jackets might actually be deadly!  To be even more extreme, what if only 5 Swedes wore life jackets in total, and they are all dead now?

Chance, Gambling, and Lucky Streaks
Dewdney spends a lot of pages on Gamblers fallacies.  Apparently, lots of people believe that past events will dictate future events.  If you flip a coin and get 5 heads in a row, then some mystical force of chance will require tails to come up soon.  This is mathematical and statistical nonsense.  However, if you get too many heads without reverting to the mean, you should start to doubt whether the coin being tossed is really “fair”.

In a lottery, all numbers are equally probable, but not all are equally memorable.  Nobody will choose 1,2,3,4,5 because that “will never happen,” even though it has the same likelihood as 13,27,29,40,51. It seems less likely only because it is less memorable.

If you can’t handle 1,2,3,4,5, then don’t play the lottery.

Street Math
Even without being a math whiz, you should be able to spot claims that just don’t make sense.
Dewdney relates the following problem to illustrate the way we divorce math from reality, and how schools fail to teach kids to make the move from abstract math concepts to applied math.

An army bus holds 36 soldiers.  If 1,128 soldiers are being bused to their training site, how many  buses are needed?

The critical step is to divide the number of soldiers by the capacity of the bus – 1128/36 = 33 1/3.
Only 70 percent of the high school students tested thought to use division.  Of these students, about two thirds seemed to be content with an answer including one third of a bus! (the answer is 34).  I think I would have done that.

Next Reads
Several of the online reviews I saw say that Dewdney borrows heavily from John Allen Paulos’ book, “Innumeracy”, and that Paulos does a much better job.  I don’t know if it’s true, but I found that Paulos has some other interesting books at our library that I will check out soon.

  • A Mathemeatician Reads the Newspaper
  • Once upon a number : the hidden mathematical logic of stories

The World’s Smartest Human Screws Up

In 1990, somebody sent a question to Marilyn vos Savant, author of the “Ask Marilyn” column in Parade magazine and holder of the Guiness Book record for highest IQ, that began a debate that still rages.

“Suppose you’re on a game show and you’re given the choice of three doors: Behind one door is a car; behind the others, goats.  You pick a door, say No. 1, and the host, who knows what is behind the doors, opens another door, say No. 3, which has a goat.  He then says to you, ‘Do you want to pick door No. 2?’  Is it to your advantage to swich your choice?”

I remember this issue of Parade, and the many “Ask Marilyn” columns that followed with angry and disbelieving comments and rebuttals.

So, what do you think?  Switch or Stay?

Marilyn said “Switch.”  This doubles your chance of getting a car.
This problem is small enough to write out all the possibilities to prove it.

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