My Erdős-Bacon-Sabbath Number: 11

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 continues

Now, 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 –
930 Saxophones

  • 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?

On the third Date of Christmas, my true love saw with me: “Stan & Ollie”


Yesterday, after a brief outpouring of angst about how complex it is – for me anyway, apparently not for anybody else – to search for a movie, Cathy and I decided to see Stan & Ollie at the Cineplex Varsity downtown.

Capsule review: we both loved it. Steve “Stan Laurel” Coogan and John C. “Oliver Hardy” Reilly are great and to my mind totally believable. I am not quite old enough to remember the glory days of Laurel and Hardy, but now I want to see more of their work. And this movie focuses on the team in the twilight of their career – I’d love another biopic about their early days!

Also Cathy and I need to learn the dance number from “Way Out West”.


Cineplex continues to tinker with the style in which they present a movie. Apparently our choices now include IMAX, DBox, Ultra AVX, VIP and a new thing called “Prime Seats” – which we chose; the best two rows in the theatre are reserved, slightly more comfortable, slightly wider seats. I don’t mind paying a couple of bucks extra for that. I wish searching for that option was easier. See earlier whiny post.

“VIP” means different things at different theatres, it seems. Sometimes it means “This is the kind where you can order a beer to your reserved seat” but not at the Varsity, where it now means “VIP is just our word for this particular theatre. Oh you want a reserved seat? That’s ‘Prime Seats’. And no we don’t wait on you at this one.”

I’m glad they’re working on refining the experience. Just like professional sports is discovering, people find it pretty comfortable watching on their big screen TV at home and it’s hard to get them out.

Also, people, PLEASE, stop talking when the movie starts. I had to give the couple behind me the half-turn a few times.


Searching for Movies

Cathy and I want to go to a movie tonight as part of the #12DatesOfChristmas and I can’t believe that in 2019, the process of searching for showtimes is still awful. It took me way too long this afternoon to come up with a list that might work.

How It Is Now

We live in the Greater Toronto Area, where most of the theatres are part of the Cineplex chain – although we’re lucky to have the excellent theatre nearby too.

By my count there are at least half a dozen movie theatres within a reasonable drive of here –, the 5 Drive Inn, two Cinepleces (Winston Churchill and Oakville) in Oakville, a Silver City in Burlington, a few more in Mississauga, and even Cineplex’s flagship Queensway in Etobicoke is only 29 km away. And for the right movie we might even venture to downtown Toronto.

We’re lucky to have this many choices. The Maps app shows even more than I thought –


And here’s’s main site –


why is this so hard

So why is it so hard to find a movie to go see? I’ve just spent way too long on the site searching. Their search process seems to assume you know exactly what movie you want to see, and in exactly what theatre. And I guess it’s good at that.

But it shows me WAY too many choices, or hides the info I really need.

Tonight, f’rinstance, I’d really like to see “Stan & Ollie”, the new Laurel and Hardy biopic starring Steve Coogan and John C. Reilly. If I search for that, here’s what Cineplex shows me –

Movie Search Results

I recognize a couple of those theatres – but Park Lane? Where’s that? [Spoiler: Halifax.] “Eau Claire Market Cinemas”? [Spoiler: Calgary] Why are you showing me these theatres thousands of miles away?

Fortunately I know that the Varsity VIP is in Toronto at least. Let’s check that out. Two or three clicks later after specifying the date, here are my choices

Show times

OK that’s fascinating but useless to know that the movie was on at 1:50 PM, several hours ago, and, I dunno, it’s 4:40 as I write this, have I got time to get to the 6:50 show?

Other search options aren’t much better. The actual show times for tonight are always hidden away, buried under the clutter of a bunch of movies I have no interest in.
Or, if I decide I want one of Cineplex’s reserved seat options, it shows me what theatres have that option, and I have to dig through to figure out which movies are playing that way.

What People Actually Want

My conjecture is that most people visit a movie theatre web site wanting to do one thing:

  • See a good movie tonight
  • Possibly in one of several different nearby theatres as long as I can get there in time
  • Have a generally pleasant experience

For me a pleasant experience at the theatre is sometimes “A nap in a comfortable chair in a dark room”, but the older I get, the more I like the idea of paying a slight premium for reserved seats so that we don’t have to gamble on how early to get there.

What Movie Theatre Web Sites Should Actually Show

Why can’t it be like this?
Let’s assume I want to see something tonight, and I’m not too particular.


And show me the results on a map – but only show me the ones I can reasonably get to from home –


Look, it’s 2019. You, Cineplex, have a computer. So do I. You know my location. I might be willing to share that. You know how long it takes to get somewhere. You can avoid showing me the 95% of things I won’t want, and pick out a couple I might like.

Help me out like that and I’m WAY more likely to go to the movies.

My emails with Jeff Bezos

One of today’s headlines reminded me that I too once had an interesting email conversation with Jeff Bezos.

Back in 2001, Amazon had rolled out a “gift list” feature, where anybody with an account could publish a list of things they wished other people would buy for them. And Jeff Bezos had his own public list. Some reporter mentioned how weird it was that the CEO of Amazon would want people to buy things for him.

Naturally I took a look. I liked Amazon, I had bought plenty of books from them, Jeff seemed like a good guy, and, crucially, his birthday was coming up. I thought it might be fun to buy him something inexpensive off of his list. And see what happened.

One of the cheaper items on the list was this set of car jumper cables. What the heck. One click later, I bought it and attached a gift message saying something like “Hey, happy birthday Jeff, I saw you wanted these, and I hope you don’t ever need them.”


Now, planning ahead, I also created my own gift list and added a few things to it – I forget what exactly, it might have been some fancy binoculars – just in case, you know, somebody wanted to reciprocate and give me a gift on my birthday from my wish list.

Well that didn’t happen, but I did get a nice thank-you email from Jeff Bezos thanking me for the jumper cables and agreeing that yes, he hoped he’d never need them.

So that’s my personal Emails with Jeff Bezos story.

PS. Also in writing this little post I have to say it is a great nostalgia trip going back through your old Amazon orders. The jumper cables were the first product I ever bought from Amazon that wasn’t a book or a CD …. and the very first thing I ever bought, in 1996, was “Dave Barry in Cyberspace”. Highly recommended, would buy again.

“I have heard your band”

You probably know that I used to be the Chief Centurion of the University of Waterloo Warriors Band (“One of the Bands in Canada”.) We were – and the band remains – a total bunch of goofballs, blowing off steam in a challenging academic program while supporting the Warriors etc etc etc.

Cleaning out the basement recently I came across a long lost box of Warriors Band memorabilia, including the letter below to Kitchener’s CKCO-TV and a reply. Reg Sellner’s response to our request to play the National Anthem for CKCO’s late-night signoff was a gem.



40 years later that still makes me laugh.