Does Math Make Research "Better"?

Yes -- if you don't know much math, that is. A new study finds that even academic scholars perceived research to be of higher quality if there's some math involved -- even if the math makes no sense. The experiment threw an irrelevant mathematical equation into research paper abstracts, and asked scholars of different fields to evaluate the quality of the research:

Mathematics is a fundamental tool of research. Although potentially applicable in every discipline, the amount of training in mathematics that students typically receive varies greatly between different disciplines. In those disciplines where most researchers do not master mathematics, the use of mathematics may be held in too much awe. To demonstrate this I conducted an online experiment with 200 participants, all of which had experience of reading research reports and a postgraduate degree (in any subject).

National Treasure 2.7 Deciphered

In one of my previous posts, I asked for help interpreting a rather bizarre dream imagining a new plotline for a National Treasure movie. These movies often involve deciphering secret codes, and so did my post. My [day]dream was actually an aid to help me remember 40 digits of the irrational, transcendental constant of Leonhard Euler, e.

Here is the dream again with numeric annotations in brackets:

What Would it Be Like to Climb 26 Years of Federal Spending?

Data is often difficult to comprehend, especially when the numbers are huge. As Sanjoy Mahajan points out, the $14.3 trillion national debt seems impossible to fathom. It's not a numeracy problem; it's more a question of how to divide the gigantic number into parcels we can understand. Mahajan suggests using smaller measures we can handle - namely thinking about debt in per capita terms.

Fortunately there are also some media tech folks to the rescue. This spring, two computer engineers from Minneapolis challenged designers and coders to come up with a visual program to help the public understand the U.S. federal budget. You can see the winners here. If you want a fun way to understand the cuts that Obama's talking about, the game Budget Climb lets you physically experience 26 years of federal spending data in a virtual reality, interactive format.

A Stack of Bills Reaching to the Moon: How to Quantify Our National Debt

Now that the U.S. national debt is in the headlines, the media is awash in astronomical numbers such as $14.3 trillion (the current debt). Everyone realizes that this number is incomprehensible. Even back in 1981, when the national debt was only about $1 trillion, the debt was still incomprehensible. Thus, speechwriters for Ronald Reagan created, or at least popularized, a widely used attempt to give it meaning. Speaking to Congress in February 1981, Reagan said:

A few weeks ago I called such a figure, a trillion dollars, incomprehensible, and I’ve been trying ever since to think of a way to illustrate how big a trillion really is. And the best I could come up with is that if you had a stack of thousand-dollar bills in your hand only 4 inches high, you’d be a millionaire. A trillion dollars would be a stack of thousand-dollar bills 67 miles high.

This comparison is often quoted as a stack of one-dollar bills 67,000 miles high (perhaps because thousand-dollar bills don't exist). No matter which denomination you use, I give the explanation an A for effort, but an F for performance. For I have little idea of how far 67,000 miles is. I know it’s way too far to walk and even too far to fly (jumbo jets have a maximum range of around 7,000 miles). But is it large as a national debt? I have no idea. Perhaps a large national debt would reach all the way to Mars. The connection to a height has merely replaced one meaningless idea ($1 trillion) with another meaningless idea (a stack 67,000 miles high).