by Jonathan Kujawa
A few weeks ago the Numberphile website posted a short video. The video discussed an “astounding” sum and got considerable press (the video has 1,523,719 views so far). It appeared on both Slate and 3QD. The sum? It's:
3QD included links to the firestorm the video created (I know, I know, I too was shocked that the Internet was up in arms over something). But I was surprised by the kerfuffle. The Numberphile videos I had seen featured James Grime giving well thought out discussions of interesting bits of math. I am happy to recommend them to anyone.
This video, however, is complete rubbish [1]. The hosts cram a remarkable number of mathematical outrages into 8 minutes. But they all come from a single anthropological source:
Mathematicians are Sherlocks and physicists are Mycrofts.
Both Sherlock and Mycroft Holmes are brilliant, devoted to reason, socially awkward, and sometimes downright unpleasant. But just the same we appreciate and even sometimes like them. Where they differ is in means versus ends.
Sherlock follows his reasoning wherever it leads. He never hesitates along the path of reason no matter the final outcome. As he says, “when you have excluded the impossible, whatever remains, however improbable, must be the truth.'' Sherlock believes that he serves only The Truth. The means justify the ends.
Sherlock's brother, on the other hand, is perfectly willing commit all manner of sins as long as the end result is the desired one. The ends justify the means. In the TV series at least, Mycroft serves Queen and Country. He has the luxury of an ultimate authority to judge what is right and what is wrong.
Just so, physicists have Mother Nature. They are free to commit all manner of (mathematical) abuses because they know at the end of the day Mother Nature will judge their work as right or wrong. All sins are forgiven if they give an answer which matches experimental data. Indeed, less than a minute into the Numberphile video the hosts show our seemingly ridiculous sum on page 24 of a standard reference on string theory. And indeed it's true that this sum is used in string theory, quantum physics, etc.
It is entirely reasonable for physicists to take this view. By playing fast and loose they travel farther and see more. They can do this safe in the knowledge that Mother Nature will eventually catch them if they go too far. And it should certainly be said that physics has always been a rich source of new ideas and insights for mathematics.
