23 February 2006

Thinking abount big numbers

In class today, Professor Haimes mentioned a case involving the carcinogenicity of saccharin. Apparently depending on the assumptions used in the model, there could be a factor of 100 difference in the level of carcinogenicity for saccharin. Think about that! That is not a 10% difference, it's 10,000%! I don't know how carcinogenicity is defined, but let's say it refers to the average increase in probability of developing cancer due to a given exposure. So that would mean that using a different set of (reasonable) assumptions, we could go from saying a given exposure to saccharin leads to:

  • 100 extra deaths per year... or 10,000 deaths!
  • a .1% additional chance of contracting cancer... or a 10% chance!

Let that settle in for a second. Can you really visualize that difference? With all this variability in our certainty how can we make a good decision about the carcinogenicity of a given product? How come we aren't told about this variability... instead just getting "CDC finds product X may cause an increased risk of cancer." Seems awfully important to me to know they aren't all that certain of the actual effects!

Oh, wait, I messed up, that wasn't a factor of 100. In the real case, it was 10 orders of magnitude, or a factor of 10,000,000,000. Yeah, ten billion. Neither I nor you can comprehend this massive number correctly. Instead just think, WAAAAAY more variability than you were thinking about a second ago. So let's look at those numbers again,

  • 100 extra deaths per year... or 10,000,000,000,000 deaths (um, everyone in the world 1,700 times over)!
  • a .1% additional chance of contracting cancer... or a 1,000,000,000% chance!

Somebody tell me why I'm wrong about this, because this is kind of scary.

No comments: