What I like most about math, are its quirks. Not the real world applications, sizeable equations and formulas, but things that make you go “huh, neat”. It’s why I love Numberphile so much, while the math involved sometimes goes way over my head, the things they tell about are, to me, really interesting, even if it has no real use. Math can be fun, it’s unfortunate that a lot of the fun parts are hidden behind concepts that can be difficult to grasp, with or without a good teacher. Some people got a brain for that, others are for example better at picking up languages. I’m fortunate that I’m pretty decent at both.

One of the most famous mathematicians is Paul Erdös, a Hungarian who’s mostly known for solving math problems that were unsolved for decades or even centuries. He was an oddball, as Time magazine called him (his wording had a lot of idiosyncrasies) and lived very frugal. He usually was travelling from one science convention to another, his only possessions in a suitcase. These lectures as well as the money coming from awards were more than enough for him to be self-sustaining, all other earnings went charity. Some cash was set aside to be used as award money: Erdös wanted to get young people into doing more math, as well as stimulating people into solving still existing problems, pinning a monetary reward onto it (though not all problems are solvable by kids or mere amateurs). A famous example of such an Erdös problem is the Collatz conjecture, better know as the 3N + 1 problem. Simply put, take any positive, whole number. If it’s even, divide it by two, if it’s odd, multiply by 3 and add 1 (the 3N + 1 part). Do this over and over again and for any number you start with, along the way you’ll always wind up with a 1 somewhere. The proof of this hasn’t been found yet, and there’s still a 500 dollar price tag for solving it.

Devoting his entire life to mathematics and nothing else, Erdös wrote about 1500 papers, more than any other mathematician and likely to be the record holder for quite a while. He saw math as a social engagement and wanted to co-write with as many other mathematicians as possible. Academics is already a small world and the concept of “six degrees of separation” is rather applicable. This led to the creation of the Erdös number. It’s a degree of separation from Erdös, who obviously has an Erdös number of zero. Someone who collaborated with the man directly, has an Erdös number of one, while someone who collaborated with that collaborator, but not directly with Erdös himself, gets a two. You have a three if you haven’t collaborated with Erdös himself or someone with a one, but have written a paper with someone having an Erdös number of two. This continues on and on, until you are somehow connected with Paul Erdös (going all the way up to at least 15). The median of all mathematicians who have an Erdös number is five, 511 of them have an Erdös number of one. Note that you don’t need to be a mathematician to have an Erdös number: mostly physicists and statisticians, but also linguists, biologists, chemists, physiologists and economists are known to have Erdös numbers, mostly through key figures in the respective fields like John Tukey and Eric Lander. Famous examples are Albert Einstein (2), Wolfgang Pauli (3), Richard Feynman (3) and Noam Chomsky (4). Unfortunately, with the death of Erdös in 1996, no one can obtain an Erdös number of one anymore.

This phenomenon has been adapted into other fields with their own big names, but the more prominent is the Bacon number, where the same principle is linked to actor Kevin Bacon (stemming from the game “Six Degrees of Kevin Bacon”). It all started when in 1994, Kevin Bacon claimed he had worked with everybody in Hollywood, or someone who’s worked with them, garnering quite some media attention. Bacon initially disliked the idea, but came to embrace it for what it is, even launching a charitable organization, using its popularity for the greater good. In any case, the Bacon number was born. Actors like John Lithgow, Gary Oldman and James McAvoy have a Bacon number of one (“Footloose”, “JFK” and “X-Men: First class” respectively), while Matt Smith, Daniel Radcliffe and Ian McKellen have a two (using “The Crown”, “Harry Potter” and “X-Men: Days of Future Past as connection points). Though difficult to verify, only about 12% of Hollywood can’t be tracked to Kevin Bacon by any means. Kevin Bacon is, however, not the most connected thespian in Hollywood. Through the use of algorithms and information on IMDb, the real “Centers of Hollywood” include Donald Sutherland, Dennis Hopper and Harvey Keitel.

It’s only a small step to the creation of the Erdös-Bacon number now, which is simply adding up the Erdös and Bacon number for a person. These numbers are of course much more rare as the person in question needs to have a connection in both the academic and entertainment world. Carl Sagan is one of these, combining an Erdös of four and a Bacon of two, giving him a six in total, the same number as Richard Feynman (his separate Erdös and Bacon numbers are both three). Stephen Hawking has appeared next to John Cleese in “Monty Python live (mostly)”, giving him a Bacon number of two (John Cleese appeared next to Bacon in “The Big Picture”), while his Erdös number is four, making his Bacon number lower than his Erdös number while you’d expect otherwise.

As for actors themselves, a few examples are Natalie Portman, having a Bacon number of 2, but also having co-authored a paper (she has a degree in psychology) leading to Erdös in five steps, getting her the Erdös-Bacon number of seven. Another actress, Mayim Bialik, who is a neuroscientist just like her well know character in “The Big Bang Theory” (Amy), is as close as miss Portman. Even Colin Firth is connected to both Bacon and Erdös, though Firth’s name is only formally credited as co-author on a neuroscientific paper titled “”Political Orientations Are Correlated with Brain Structure in Young Adults” when he suggested such a study could be during a BBC Radio 4 interview. This paper included the neuroscientist Geraint Rees who has an Erdös number of five. Colin Firth himself has appeared with Bacon in “Where the Truth Lies”, adding his total Erdös-Bacon number to another seven. However, there is one man who has an Erdös-Bacon number of only three, though the connection used is a bit unconventional. Hank Aaron is connected to Kevin Bacon through Susan Gardner (the movies “Summer Catch” and “In the Cut” being relevant), but his Erdös number of one is through both Erdös and Aaron signing the same baseball. It’s debatable if that actually counts, but a cool story nonetheless. There is a bit more to this whole story, but you can read up on that here.

If adding Erdös and Bacon numbers isn’t enough yet for you, you might want to look into Erdös-Bacon-Sabbath numbers, where Black Sabbath is included as yet another connection needed through songs or musical collaborations. A few examples of people having such a number are Firth, Portman and Bialik again (as well as Chomsky, Feynman and Hawking), but also Adam Savage, Terry Pratchett, Douglas Adams, Condoleeza Rice, Imogen Heap, Brian May (remember, the dude’s an astrophysicist), Brian Cox and Buzz Aldrin. Even Thomas Edison makes that list. Not all of the connections are as sound as the original Erdös or Bacon numbers, but why be a spoil sport about it.

So is this useful in any way? Not at all. But it’s fun. Why can’t math be fun once in a while. And obviously for me on a personal scale, it adds to my already encyclopedic knowledge of movies and their cast. None of my numbers are defined, so I’m infinitely removed from Erdös, Bacon and Black Sabbath. Maybe I should work on that.

This blog was brought to you by: Black Sabbath – War Pigs