?

Log in

No account? Create an account
 
 
02 September 2002 @ 02:40 pm
200% of Nothing, by A.K. Dewdney  
The subtitle on the book cover reads: "From 'Percentage Pumping' to 'Irrational Ratios' -- An Eye-Opening Tour through the Twists and Turns of Math Abuse and Innumeracy." That's pretty accurate.

And one of the blurbs on the back cover quotes Arthur C. Clarke:

"In today's world, "innumeracy" is an even greater danger than illiteracy, and is perhaps even more common. Advertisers and politicians exploit is; intellectuals (self-styled) even flaunt it. I hope that this wise and witty book will provide cures where they are possible, and warnings where they are necessary.

"It's also a lot of fun. I can guarantee that 100%."

What can I add to that? Well, a couple of things. It really is an interesting book, and was a surprisingly easy read. However, I think I may have to read it again before too long -- I need to develop some way of internalizing my recognition of many of the math abuses so clearly illuminated here.

Also, I'm having a really hard time understanding why the likelihood of a false positive or false negative on, say, an AIDS test depends on the incidence of the disease in the population I come from. Sounds like voodoo statistics to me. Does this mean I have a different likelihood of a false positive if you consider me as coming from the population of "over-50-year-old white males" than if you consider me as coming from the population of "North American sf fans"? Just doesn't make sense to me.

On the other hand, I have no trouble at all with the fact that the law of averages demands that if I've just flipped a coin 800 times and have obtained 800 "heads," the chances of getting "heads" on the next flip is exactly 50/50.

In any case, the bottom line is I highly recommend this book.

 
 
Current Mood: didactic
Current Music: Gryphon - About As Curious As It Can Be
 
 
 
the laughing leaping waterminnehaha on September 2nd, 2002 07:07 pm (UTC)
Have you read Innumeracy, by John Palos? That's the book that started the topic.

B
Fred A Levy Haskell: bridgefredcritter on September 4th, 2002 03:48 pm (UTC)
No, I haven't. I think I may have arrived at 200% of Nothing from How We Know What Isn't So: The Fallibility of Human Reason in Everyday Life, by Thomas Gilovich (one of the most important books ever written, IMVHO).

I take it you're recommending Innumeracy? Thanks! I'll pick up a copy and put it on my "to be read" shelf.
the laughing leaping waterminnehaha on September 5th, 2002 09:38 am (UTC)
I can lend it to you if you want. (I'm pretty sure it's around here somewhere.)

B
the laughing leaping waterminnehaha on September 3rd, 2002 09:06 am (UTC)
"Also, I'm having a really hard time understanding why the likelihood of a false positive or false negative on, say, an AIDS test depends on the incidence of the disease in the population I come from. Sounds like voodoo statistics to me. Does this mean I have a different likelihood of a false positive if you consider me as coming from the population of "over-50-year-old white males" than if you consider me as coming from the population of "North American sf fans"? Just doesn't make sense to me."

Let's see if I can do this.

First of all, you either have the disease or not. That's a fact, not a probability. The probabilities are about the test, and not about the patient. The probabilities arise from the amount of indecision in the test, which is partly based on the facts we have about the patient.

So if there was a perfect AIDS test, then the probability that you had the disease would be 100% or 0%, depending on the outcome of the test. No indecision.

Given an imperfect AIDS test, the probabilities would be different. Given additional demographic information about you, we can make those probabilities less variable. Knowing that you are in the group "Over-5o white males" or "North American SF Fans" counts as additional demographic information.

The likelihood of a false positive is, in part, a function of the prevalence of the disease in a given population. A test might have a 50% false positive rate in general, but because the disease is so prevalent in OFWMs the false positive rate might be 30%. Or, because the disease is so rare in NASFF, the false positive rate might be 70%. If you are both a OFWM and a NASFF, the false positive rate will be somewhere in-between.

This is simply a measure of the indecisiveness of the test, not the patient. You either have the disease or you do not. If you went to a NAACP dinner, the probability that you were a Caucasian would be some number. If you went to a KKK rally, the probability that you were a Caucasian would be another number. Your race never changes, just the information about the situation you are in.

Caveat: I have not read the book, and I am assuming that this is what the book is talking about.

B