Tuesday, March 6, 2012

Proofiness: A look into how mathematics relates to American political life


Dearest readers,

This is my first post on The Virtuosi, so I thought I’d take a moment to introduce myself.  I’m a first year physics graduate student at Cornell, recently joined after 2 years working as an engineer first at a private firm and then at a national lab.  I myself have had lots of fun following the exploits of my estimable colleagues here on The Virtuosi, and I thought I could bring a new angle to the content here.   I would like to use this space to discuss how science interacts with everyday life in a cultural sense. How does science appear in popular culture?   How do political or social issues relate back to science? Those sorts of questions.  (I understand that there are plenty of other resources elsewhere that offer far more intelligent insight into these matters than I can, but in the very least this will give people a chance point them out to me as they yell at me in the forum below.)

Enough intro, here begins my very first blog post:

Being interested in how science is communicated to the public, I am an avid reader of popular science.   While academic types sometimes dismiss this kind of writing as shallow or otherwise uninteresting, I think science writers perform a very important function serving as a way to convey information about conceptually challenging topics to a general audience.   At their best, I find that these books serve as examples for how I can communicate my own ideas better, and in addition challenge my understanding of how science relates back to society in general.

This being said, I cannot recommend Charles Seife’s Proofiness enough.  The basic premise of this book is to explore the way that good mathematics is hijacked, twisted, or ignored in everyday life, and the ugly consequences of the tendency to misunderstand numbers and measurements.

Seife gives a number of fascinating examples of the ways in which numbers and math connect to American democracy.   American government functions through representation, and so the “enumeration” of citizens and their opinions through the Census and elections is an essential part of the democratic process. This “enumeration” is a counting measurement, subject to errors like any other.   And yet, the laws that govern how Censuses and elections are run ignore this fact.  Seife’s discussion of elections (and in particular Bush v. Gore) is fascinating, but I won’t spoil that here.   Here’s my take on the discussion of the Census that appears in Proofiness:

Consider a (vague) physics experiment.   I want to know how many particles are inside a box.  To figure this out, I have a detector that goes *ping* every time a particle passes through it.  I set up my detector inside the box and count the number of times that it goes *ping* in a certain amount of time.  I can then use that count to guess at the number of particles that I have in my box.   My measurement will let me estimate N to within some margin of error.  This process is perhaps unnecessary if I have only five particles in my box (in which case, I might just open the box and count what I see inside), but if I have 300 million particles in my box, it would be totally impractical for me to reach into the box 300 million times and count each one individually.

We can consider the Census to be just like this physics experiment.   I have N inhabitants (particles) living in my country (box), and I can use my detector (census replies) to count a certain number of people.  In principle, using well-understood statistical techniques of regression and error analysis, I can estimate to within a very good margin of error how many people live in each region of the country.   Instead, what the Census requires is that we reach inside the box (send representatives to every household that doesn’t reply by mail) and count every single person.   The whole process ignores the fact that even if we send a representative to every single household there will still be some margin of error in our counting measurements.   No such measurement can be made without errors.

The consequences of ignoring these errors, says Seife, can be that we waste money in attempting the impossible and trying to count everybody.  From a civic-minded perspective, this attitude towards the perfection of the Census can backfire.  For example, if undercounting occurs (i.e., certain households do not respond for some reason), the Census has no mechanism for correcting that miscount.   Counter-intuitively, the Census laws actually prohibit the use of any statistical techniques to correct miscounting.   The result is that those slow to respond are ignored and not taken into account when allotting seats in the legislature to represent them.

Proofiness is a fascinating book and a fun read, and I recommend you all look it up.  In addition, it serves as an excellent example of science writing that helped me to rethink how scientific ideas relate to everyday life.  I hope to invite consideration of these topics here and in future posts.

If you want to know more about the inspiration for this post, go here.

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