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 -

• 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?

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.

Alfie Kunz

I was sorry to learn that Alfred “Alfie” Kunz, noted composer and conductor, passed away last week at 87. Here’s a bit about him from the University of Waterloo, where he was music director for many years, and a career retrospective from the Record.

He had a huge musical career all across the K-W area but I remember him most from his UW days. And I want to share some memories of a time before the Internet when nothing ever got written down in a way that it could be searched for later.

Alfie was one of the first people I met when I started at Waterloo in 1977. I hardly knew anybody and had no clue about extra curricular activities but somehow learned that there was a UW Concert Band that rehearsed on Wednesday nights in the Arts Lecture Hall, and I quickly signed up - and also joined the UW Stage Band, that he also directed, and I think I might have even been in the UW Orchestra at one point.

Waterloo actually had a full time Director of Music on staff and it was Alfie’s job to run all these ensembles, up until UW president Burt Matthews eliminated that program in 1979. We were upset! I recall we even wrote a protest song about it -

Tune: Yes, Jesus Loves Me
Matthews hates us, this we know
For the budget tells us so,
Peripheral programs gotta go,
Music's of priority low.

Burt Matthews hates us,
Burt Matthews hates us,
Burt Matthews hates us,
The budget tells us so.

It didn’t do much good though. UW killed its extracurriular music program, and although I was grateful that Conrad Grebel College picked up a few of the pieces - and even made concert band a credit course, which it never was in my day, not that I’m bitter - it was never the same.

I made some great friends in Alfie’s concert band - in fact, it was through the concert band that I learned that the Warriors Band even existed. All I knew about the Warriors Band was that they were a total bunch of goofballs occasionally on TV, and as a proud new student, there was no way I’d ever join that ragtag ensemble.

Needless to say, many members of that ragtag ensemble were also in Alfie’s concert band, including clarinetist Ken Fudurich, who talked me into coming to my first Warriors basketball game one night after concert band practice. We trudged through the snow from the arts lecture hall up to the gym, only to find it deserted, and Ken concluded “Oh, maybe tonight’s game is actually at Laurier, not here.” And we hiked down to WLU, found that the game had already started, Ken introduced me to Warriors Band CCWB Mark Hagen, who was overjoyed to find another trombone player besides himself… and when someone in the WLU crowd held up a sign saying “Waterloo’s Band Sucks”, I knew I’d found a new home.

But that’s kind of another story. Back to the Concert Band for a moment.

I met a lot of great friends in that group, many of whom I stay in touch with today. I recall an end of year banquet at which Alfie thanked the graduating seniors, and I thought “I gotta stick around, I want to hear that speech about me some day.” Alas, we never got the chance after UW pulled the plug. But, we made some great music. Popular tunes, Christmas selections, interesting Alfie compositions - including one Oktoberfest-themed overture where the trombonist had to stand up and play a drunken, wobbly version of “Ein Prosit”, and I think Rob Gibson had seniority and got to play it instead of me. I hoped we’d do that one again a few years later so it could be my turn but it never happened.

I can recall a raucous concert with the UW Concert Choir, in which they were all behind our Stage Band, singing “Hey Jude” by themselves, and we begged Alfie to let us play along on the chorus even though we weren’t quite sure what key it was in, and it sounded great and Alfie loved it.

I remember a grand afternoon concert Alfie called “Tea and Symphony”, and we all had special “Tea and Symphony” T-shirts, and it wasn’t until much later in life that I understood that that title was some sort of pun on a movie title.

I can remember recruiting some of my new Warriors Band friends to join the Concert Band too. The concert band was chronically short on percussionists and I told Alfie I might know some - thinking, of course, of the many skilled musicians in the Warriors Band, and also thinking of the drummers in the Warriors Band - and I brought Jim Snyder along one time to help out. Except Jim couldn’t make the practice before the big concert, but he came along to the big concert, and I can still recall the shocked look on Alfie’s face as he cued the percussion section at some crucial spot in the opening number and BOOM, there was a huge crash on the cymbals played by someone Alfie had never seen before.

I also remember one weird band rehearsal when we were roaring away on something, triple-forte, and an older man we had never seen before barged into the room, yelling, and grabbed Alfie and threw him to the floor. Huh? We found out later it was a professor whose late night research was being disturbed, and he was of course totally out of line and had to apologize later to the whole band. But the band persevered.

I sure had friends in that band. It kept me sane while I was trying to figure out how university worked. It was a refreshing counterpoint to the disorganized mayhem of the Warriors Band - and Alfie was always a great supporter of that other group too. He composed The Black and White and Gold, UW’s official school song, and of all his hundreds of serious compositions, I bet that one’s been played the most.

Jim Spence. Rob Gibson. Rosalee Mitchell. Ginny Lyons. Ken Fudurich. John Oldfield. And many more great friends from that group and I’m adding their names here in case they stumble across this post in a google search some day. I’ve got some pictures at home that I’ll scan and post when we get back.

A few years later when I was still in the waterloo area, Alfie called me, looking for a trombone player to help out at some gig at one of the German clubs, and I hemmed and hawed and then didn’t actually show up. I felt guilty about that for twenty years afterwards - and was happy to discover that Alfie was on Facebook, so that I could apologize to him - and he forgave me, much to my relief, and we had a good chat about how much fun we’d had.

Thanks, Alfie. A lot of us wouldn’t have made it through UW without you.

Rest in peace.

Here’s a holiday treat. I ordered some of these unusual candy canes for Christmas.

https://mcphee.com/collections/candy-canes

Unfortunately, my first choice - Mac & Cheese Candy Canes - was (and still is) out of stock, so I had to settle for Clam, Bacon, Pickle and Rotisserie Chicken.

They are delightfully packaged, but you are probably more interested in what they taste like. Well, they taste like clam, bacon, pickle and rotisserie chicken. Some of my family appreciated the fidelity of these flavours, others immediately spit them out (but at least they tried them) and some flat-out refused.

I think a better strategy would be to order a variety, unpackage them and set them out in a bowl and see what happens if people just randomly take one.

My niece took a few to a party and planned on telling people that the clam/bacon/pickle/chicken ones were actually Vanilla, Strawberry, Lime and Root Beer flavours. I need to find out how that worked out.

Note: Archie McPhee sells all sorts of fascinatingly odd products but they won’t ship to Canada! Booooo. I had to have them shipped to a hotel I was staying at in the US. It was a little awkward bringing them back through Canada Customs - I declared that I had some candy, and the border agent said, “Well, did you bring enough for all of us?” I’m glad I didn’t share with them. I need to be able to cross the border in the future.