Paul Erdős received an honourary degree at my University of Waterloo B.Math. convocation ceremony. Don’t know the name? You should; he was one of the great mathematicians of the 20th century. And highly quotable! One of my favourites –

A mathematician is a machine for turning coffee into theorems.— Paul Erdős

He had no fixed address, and travelled the world doing math research, staying in the homes of other mathematicians along the way, and publishing more mathematical papers than any other mathematician in history. He was a superb choice for an honourary degree.

I was a bit of a slacker in my undergrad days and only vaguely knew of Erdős, but to this day, I can remember a professor telling us about the Erdős-Feller-Pollard correspondence. I can’t tell you what that correspondence is, but I definitely remember the term “Erdős-Feller-Pollard correspondence.”

I remember he led off his convocation speech like this (approximately)

I travelled from Hungary to Waterloo for this event, and then I am going to Los Angeles, and after that to Australia and then back to Hungary. So I am travelling 360 degrees around the world to receive one degree. A total of 361 degrees.

polite laughter from audience, Erdős continuesNow, 361, that’s an interesting number. It’s 19 squared. I remember when I was 19 …

## Erdős numbers

Everybody has an Erdős story as he kept constantly travelling and collaborating, and in the math world, there’s an idea called the **Erdős number.** You could define it recursively.

- Paul Erdős is Erdős 0.
- If you collaborate with someone whose Erdős number is N, then your Erdős number is N + 1.

So, if you co-wrote a paper with Erdős, your Erdős number is 1 (and you have exalted status in the math world). If you collaborated on a paper with someone who was Erdős 1, you are Erdős 2, and so on. There are 511 people with an Erdős number of 1, and there can be no more, since Erdős passed away in 1996.

People take this fun idea very seriously, and compile huge databases of Erdős numbering. See the Wikipedia article for starters. All 56 winners of the Fields Medal, the most prestigious prize in math (since there is no Nobel in math) have a finite Erdős number. 159 of the 200 Nobel Physics prize winners have an Erdős number, all ranging from 2 to 12. (I should check and see what the number is for Waterloo’s Donna Strickland, recent Nobel Physics winner hmm. It’s probably pretty low; there are several people connected to Waterloo with an Erdős number of 2 or less.)

Someone even wrote a paper analyzing the Collaboration Graph from a graph-theoretical perspective with the observation that it would have some interesting property if only two specific authors had collaborated on something; those two quickly whipped up a math paper on some trivial topic to ensure the graph stayed interesting.

## famous people with Erdős numbers

And Erdős received another honourary degree from Emory University on the same day that baseball legend Hank Aaron also received one. Someone thoughtfully arranged to have a baseball autographed by both Erdős and Aaron; thus, Hank Aaron has an Erdős number of 1.

Lots more info at the Erdős Number Project web site. I’ve always loved this math silliness. Einstein was Erdős 2. Marie Curie, Erdős 7. (thus, Pierre Curie, Erdős 8.) Bill Gates is Erdős 4! (During his brief stay at Harvard, Gates came up with an algorithm in a combinatorics class that was later formalized in a paper by Harvard computer scientist Christos Papadimitriou, who is Erdős 3.)

## so what is MY Erdős number?

Charlie Colbourn taught at Waterloo and was Erdős 1, as a result of a 1985 paper – which I’m sure you read – “A conjecture on dominating cycles”, B.N. Clark, C.J. Colbourn, and P. Erdös, Proceedings of the Sixteenth Southeastern Conference on Combinatorics, Graph Theory, and Computing, February 1985, pp. 189-198. Looking through his c.v. I recognize a few people I remember from grad school who wrote with him, and who are thus Erdős 2, and I am very jealous.

He collaborated on at least one paper with Kellogg S. Booth, who was the director of Waterloo’s computer graphics lab where I hung out as a grad student. Booth is Erdős 2.

Booth and John Beatty co-directed the graphics lab and published various things. Beatty is Erdős 3.

Beatty was my master’s supervisor and about the only scholarly thing I ever wrote was my master’s dissertation, “Software for the Tektronix Geometry Processor”, and he heavily critiqued and edited it. So I can claim a tenuous link to being **Erdős 4**.

## kevin bacon

This probably reminds you of the whole “Six Degrees of Kevin Bacon” thing where people compute a distance between actors and Kevin Bacon. Bacon is 0, people in any movie with Bacon are Bacon 1, etc. The definitive source for this info is the Oracle of Bacon.

This of course, leads to the idea of the “Erdős-Bacon Number”, which is the sum of your Erdős and Bacon numbers.

## black sabbath

Taking this idea to another extreme, music has the Sabbath Number. How close are you to collaborating with Black Sabbath. Naturally this leads to the greatest of all numbers…

# Erdős-Bacon-Sabbath Number

I kid you not. People track the combined Erdős-Bacon-Sabbath number. No, seriously.

Stephen Hawking owns the lowest known Erdős Bacon Sabbath number – 8.

- Erdős Four. (I’m surprised it’s that high.)
- Bacon Two. According to the Oracle of Bacon, Hawking appeared in “Queer Duck: The Movie” with Camryn Manheim; she appeared in “Cop Car” with Kevin Bacon.
- Sabbath Two. Stephen Hawking made a guest appearance on Pink Floyd’s album “The Division Bell”. Dave Gilmour of Pink Floyd played one number on the “Rock Aid Armenia” album which also featured Tony Iommi of Black Sabbath. Therefore, Hawking’s Erdős-Bacon-Sabbath number is an amazing EIGHT.

Brian May – guitarist of Queen, Ph.D. in astrophysics – is Erdős-Bacon-Sabbath 9. Also amazing. There’s an interesting list of celebrities with small E-B-S numbers.

## ok ok ok what’s mine

This is going to be a stretch. I can very tenuously claim to be **Erdős 4**.

### my bacon number

Bacon? Hmm. Let’s see. back at Waterloo I was the musical director for the annual 1987 FASS show. That year, the star of the show was **John Watson**, a student at the time who went on to an acting career. You might remember him from the classic commercial for Maple Leaf Foods. Back Off. Get Your Own Sandwich.

John, who I hope might vaguely remember me, has done a few things – here’s his demo reel

John appeared in “Haven” with the late Natasha Richardson. She was in “The Favour, The Watch and the Very Big Fish” with Bob Hoskins. Hoskins was in “Balto” with Kevin Bacon. So John is Bacon 3, and I can stake a very weak claim to being **Bacon 4.**

### my sabbath number

Sabbath, hmm. This will be tricky.

Let’s start here –

- In 2004 (and again in 2009) I played with the Shuffle Demons in their Saxophone World Record Attempt. 930 saxophones in Yonge-Dundas Square! (Playing the theme from “Hockey Night in Canada.”) (I don’t exactly play the sax but I have an alto, and learned just enough notes to play along on the ‘easy’ part.)
- Richard Underhill of the Shuffle Demons has played with the Neville Brothers.
- The Neville Brothers song “Voodoo” on their album “Yellow Moon” was co-written by Tony Iommi of Black Sabbath.

Neville Brothers: Sabbath 1

Richard Underhill: Sabbath 2

Me: **Sabbath 3**

## my grand total

I am proud to claim the Erdős-Bacon-Sabbath number of 4 + 4 + 3 = 11.

So what’s yours?