Dora's College Graduation - Part 2 (Bronxville, NY, May 2004)

Evelyn came, too.

With some favorite teachers and friends:





Preparing on Metro North...

Dave's College Graduation - Part 2 (Berkeley, CA, May 2000)

Dave lived in a dorm his first year, then tried one of the bigger Berkeley coops, but then found the small coop he really liked.

Dora's College Graduation - Part 1 (Bronxville, NY, May 2004)

OK, Sarah Lawrence is really in *Yonkers*, but for understandable PR reasons, they call it Bronxville, so I will too. It was a great day.



Getting ready.

The family, including not-quite-yet-sister-in-law Allison.

Advisor, friend and mentor Monica tells a story...

...that seems to end with a funny face, to everyone's amusement.

Dave's College Graduation - Part 1 (Berkeley, CA, May 2000)

Dave's college graduation, the 2000 graduation of the UC Berkeley College of Engineering, was a large event, held in the Greek Theatre.



Yes, that's Dave with the orange hair, done for the occasion.

Dora and Margaret (Palo Alto, CA, August 1992)

Missing from the Greenmeadow posts (Part 1 and Part 2) are these great pictures of Dora and Margaret Cooke (and one of Margaret's little sisters). The first, shot during a hot Nintendo session I guess, has a nice view of the livingroom of the house we stayed in for 3 summers. The second shows a typical Eichler, across the street

Paul Erdös, xkcd and Me (Montreal, Canada, 1968-69)

This one is a little obscure, and of interest to few, but I can't resist. xkcd is a web comic with a lot of (usually sophisticated) computer science and math humor, and is often very insightful and often very funny (excellent Wikipedia article here).

Elizabeth first pointed me at today's xkcd. My friend Giuseppe also sent it to me from Italy, saying, "I'm sure you will appreciate it, especially the awareness of being one in a thousand that can do so :-)" The comic (linked below) is about Paul Erdös and Erdös Numbers. Erdös was a completely remarkable mathematician, brilliant (that is a serious understatement), and eccentric in many, many ways. I highly recommend the Wikipedia article about him, it captures his character well. He was essentially homeless, and not equipped for modern life, but rather traveled from one mathematical institution to another, often towing his mother along, being put up by those he visited. He was an amphetamine addict, and a lot of his life was necessarily organized by another, the important mathematician Ron Graham.

In his travels, he collaborated with very many mathematicians, often several at a given place. A massive body of significant mathematics appeared with him as a co-author. It was joked that he had once written a paper with a train conductor on his way between institutions. Because he coauthored so many papers, the concept of Erdös numbers arose. It's a little like (but way predates) the Six Degrees of Kevin Bacon. If you wrote a paper with Erdös, you have Erdös number 1. If you wrote a paper with someone with Erdös number 1, you have Erdös number 2, and so on. In general, your Erdös number is one more than the lowest number of any of your collaborators.

Low Erdös numbers are a source of humorous but serious pride among mathematicians, so I am really proud to have an Erdös number of 2. Here is an alphabetical list of all 8,674 people with Erdös number less than or equal to 2, including his more than 500 direct collaborators (who thus have number 1). I got my 2 by writing a paper with Ron Graham and Frank Harary, who each have number 1. The one-page paper is below. It, and the short paper (by just me) that preceded it, are pretty much the sum of my mathematics research career. I had solved a problem in Graph Theory (by constructing a counterexample to a conjecture), and this was an easier (but less powerful) alternative solution. (This was during the nanosecond that I thought I would call myself Joshua Fisher when I published, so that is the name that's there, but it's me.)

But I also had a more direct interaction with him: I taught Paul Erdös how to throw a frisbee. I was a graduate student in math at McGill University during 1968-69, and Erdös visited our department, gave a talk, and worked with some people. (In 1973, my advisor at McGill, Will Brown, wrote a paper with him.) He came to our department picnic (bringing his mother along, in a wheel chair). He saw me throwing a Frisbee with a friend and asked me about it, saying he had never seen one before (the modern Frisbee first appeared in 1964, and was just getting popular). I showed him how to do it, and we threw it back a forth a few times. He seemed thrilled.

The xkcd strip and most of my paper are below.

You Saw It Here First (Asheville, NC, June 2009)

Recall the amusing cover (well, it amuses me) of the IEEE Solid State Circuits magazine, covering my invention of VLIW architectures, and their subsequent success. It said, "Part 1". I was just sent the cover of Part 2. They used a picture from the Fisher Picture of the Day; the historic shipment of the first commercial VLIW processor. Now there are hundreds of millions of them, but that was the first.

Jones Beach (Jones Beach State Park, NY, early 1950s)

At the same time that my family was driving across the Bronx to go to Orchard Beach, Elizabeth and her family were driving across Long Island to go to Jones Beach, another Robert Moses megaproject.

After we met, Elizabeth and I started going to the beach via subway a lot (first Brighton, then Rockaway). When we got a car, it was off to Jones Beach. We'd wake up really early, and try to get a coveted spot in parking field 9, with its very private beach (closed for the past 20 years due to beach erosion). With all that beachgoing in our backgrounds, I guess it's not surprising that we now live in a beach resort.

I've already included a picture of Elizabeth, Paul and their father at Jones Beach. Here are more pictures of Elizabeth and her family at Jones Beach.


This one shows the art deco buildings along the boardwalk. It looks about the same today, including that odd rectangular structure in front of it, and with the addition of some ugly blue awnings.




Wait a minute! What's this doing here. It's 36 years later.

Orchard Beach (Bronx, NY, about 1951)

From a New York Times article a few years ago, At Orchard Beach, people remember summer days when their apartments felt like steam baths, and how a trip here meant not just relief but an escape from a harder-edged world.

Among my most enduring memories from my childhood were trips that my parents and I took across the Bronx to Orchard Beach. These always involved lots of my parents' brothers and sisters, and were usually arranged on very short notice. Sometimes it would be after dark, unbearably hot, and no one could sleep, so we would pile into whatever car could be scared up (usually one of Bud's). We'd sleep on the beach.

I don't know who is with Willa here, but you can see Paul and me in the background. Also in the background are the colonnades, the front of the bath house, now a NYC landmark. Here's a current picture on Flickr. Orchard Beach is in Pelham Bay Park, yet another Robert Moses megaproject from the 1930s, and NYC's largest park.


With one of my omnipresent comic books. I had a vast collection of the humorous kind: Donald Duck, Mickey Mouse, etc. My 20 year old parents read them too, and embarrassedly insisted they were doing it to vet them for me. I believed them at first.

My mother at about 23.

And two pictures of my grandmother, with Willa, and then with me.

The Cash Register (Bronx, NY, early-mid 1970s)

When we lived in Montreal, in 1969, we saw this old NCR brass cash register in a shop, for $50. A little ahead of our time, we knew we had to have it. It worked really well. The hard part was getting it home--we finally convinced a cab driver to help us get it into his trunk, and help us get it home. It always took a lot of planning as we moved it from apartment to apartment during the 1970s, since it was really heavy. At some point, we just gave up and sold it to one of the used restaurant supply places on The Bowery.

Sam and Bud (San Diego, CA, January, 1996)

As I've written, my parents' brothers and sisters became friends. As teenagers, Sam and Bud were close friends. Bud called me after my father died, and he told me that he talked to Sam for a long time, something nice that came out of my father's death.

Here are the two of them at my parents' 50th Anniversary celebration, obviously having a good time:

Dora's Jr. HS Graduation - Part 2 (Brookline, MA, June 1996)