Hello everyone, and welcome back to the AlmaMAC! I’m your host Adam and today we have the second part of my interview with Sawayra, the inventor and original host of the AlmaMAC. Last week we talked about why she started this radio show, and what direction we are going to take it from here. You can listen to that over on our website, scientificanada.ca . Today I’m bringing you the second half of that interview where we finally dig in and learn about the research Sawayra does. Spoiler, she is working through a dual PhD/MD program, but she will explain all of that in the interview. So let’s not waste any more time and jump right in!
Before we go, I just wanted to let you know that we have a new article up on the site. It’s about this really interesting result from statistics that says not all digits come up with the same frequency in nature. It’s called Benford’s law, and what it says is that in large naturally occurring data sets, the leading digits of the numbers in the set don’t look as random as you might expect. In fact, it’s been shown that 1 comes up almost twice as often as 2, which comes up almost twice as often as 3, and so on. And it’s true of a heck of a lot of things too! From the population of cities, the height of buildings, to the surface area of rivers, the results predicted by Benford’s law seems to show up over and over again. And it’s so robust a result that forensic mathematicians sometimes use it to try and find data that’s been tampered with, like research data and financial data, the latter of which has been used as evidence in court.
This may sound like mystic numerology, but Benford’s law is something you can prove mathematically. The full proof is not super exciting, but the reason it works has to do with how natural systems relate to the logarithmic scale. That’s the scale that slide rulers use, and it lets you represent numbers over several orders of magnitude on the same line. Instead of spacing the numbers 1, 2, 3, 4, etc evenly on a ruler, a logarithmic ruler would space 0.1, 1, 10, 100, 1000, 10000 etc evenly. Seems like a weird thing to do, but if you think about trying to plot the population of all of canada’s cities on one scale, logarithms seem a bit more reasonable. Now, what Benford’s law says is that if you have a collection of data that works more naturally with logarithms, then if the numbers don’t depend on each other (like the populations of cities), then the data will look like its been picked at random off a logarithmic scale. Now, pull up a log scale, and you’ll see the gaps between 1 and 2 , be it .1 to .2 or 1 mill to 2 mill, are larger than the gaps between 2 and 3, 3 and 4, etc.
It’s a surprising result, but it actually seems to work with a whole lot of data. Some data it doesn’t work with, though, is the US presidential election data. There are many many papers, blog posts, articles, podcasts, etc that explain why election data shouldn’t follow Benford’s law, but that hasn’t stopped some US politicians from trying to use it as proof of election fraud.
In the article, which is up on scientificanada.ca , I don’t talk about why Benford doesn’t work on election data (though I link to some good articles that do). Instead I talk about why I think math, stats, and Benford’s law specifically are sometimes used to try and push political agendas.
Thanks again to Sawayra for well, for everything. Follow her on twitter @SeeingAWay .
If you liked the show, check out the other stuff we have going on at scientificanada.ca
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So, thanks again, and see you next week!