Daily Archives: March 24, 2009

Jack Schwartz (L), Dave Shields, c. 1975

The only known photo of me with Jack Schwartz.

I was going to call this post “Soldering On with Jack,” but on closer inspection I see he is holding a wire-wrapping tool.

I’ve kept a copy in the top drawer of my desk for decades.

Jack *always* wore a sweater, just as R. P. Feynman always wore a long-sleeved white shirt.


Jack Schwartz on String Theory

Though I forget the exact occasion, I do recall once working with Jack when he to spend some time untangling a rat’s nest of wires.

After straigtening them out, he conjectured that there must be a theorem in this, but that it would be very hard to prove:

A Conjecture by Jack Schwartz:

If you put some strings, ropes, or wires on a table, then no matter how carefully you set them down, they will soon became entangled, as though an unseen agent had been at work.

I would have then remarked on Thomas Edison, if I had then known what I learned a few years later while browsing through the supplement to the Oxford English Dictionary:

Usage of the term “bug” to describe inexplicable defects has been a part of engineering jargon for many decades and predates computers and computer software; it may have originally been used in hardware engineering to describe mechanical malfunctions. For instance, Thomas Edison wrote the following words in a letter to an associate in 1878:“

It has been just so in all of my inventions. The first step is an intuition, and comes with a burst, then difficulties arise — this thing gives out and [it is] then that ‘Bugs’ — as such little faults and difficulties are called — show themselves and months of intense watching, study and labor are requisite before commercial success or failure is certainly reached.

The conjecture remains to be proved. It is a knotty problem.

The World is Flat and Small: Jack Schwartz on Six Degrees of Separation

During a phone call with Peter Capek earlier today I mentioned the incidents that led to my starting this series of posts on the theme, “The World is Small and Flat.”

Peter agreed, and we then spoke of Six degrees of separation.

I then told Peter about a conversation I had with Jack Schwartz, the eminent mathematician and computer scientist who died earlier this month at the age of79. He was a professor at NYU’s Courant Institute of Mathematical Sciences (CIMS).

Sometime before President Nixon resigned from office, Jack and I were having lunch in a small restaurant in Greenwich Village when he told me of another occassion when Professor Peter Lax of CIMS was having lunch in an equally cheap and obscure restaurant. [1]

The phone rang and Peter was told that the White House was on the line, and wanted to speak with him.

Jack then commented that the White House had an incredibly efficient group of telephone operators. [2]

We then on to discuss how any two people could exchange a letter, and how many “hops” it would take to do so.

The problem was to give each person just the name of the other, their country of residence, and their profession or some other quality about them.

Each would then write a letter to the other, and each would try to get the letter to the president or prime minister of the other’s country with the fewest hops.

Thus there would be a race to the top, in which each would try to get the letter to the head of their country in the minimal number of forwardings, or hops.

Once the letters reached the leaders then one leader could forward the letter to the other, who would then forward it back down the chain.

For example, if I were told to exchage a letter with a Russian computer scientist, then I would give the letter to Jack, he would give it to Peter, and Peter would send it on to the White House.

The Russian computer scientist would have as their goal to reach Academician Andrei Petrovich, who would then forward it to the Kremlin. Just a few hops would be needed.

In this particular case, even fewer hops would be needed since I had visited Ershov in Novosibirsk, Siberia, in November 1973.

Jack also mentioned that he had spent some time in Turkey around 1960. He said that he had learned that a small number of people ran the country, and that he had met many of them.

Jack then conjectured that seven hops would usually suffice, and that just six would often be enough.


1. I will write of my many “Lunches with Jack” when time permits.

2. CNN’s Anderson Cooper was one of the speakers at my daughter Jen’s graduation ceremony at Yale in 2006. He said that he had recently gotten a request that he make a donation to Yale while he was on assignment in some remote corner of the world.

He then went on to say that if President Bush really wanted to track down Osama bin Laden, then all he had to do would be to ask that Yale should award bin Laden an honorary degree. Copper said there would be an uproar, but the objections would die down within days, because the Yale Alumni Fund would soon locate Mr. bin Laden, and the rockets that would kill him would arrive within a few minutes after the letter reached his hands.

The World is Flat and Small: John Cocke and Rabbi Michael Shields

I had a wonderful phone call earlier today with Peter Capek, a friend and colleague for over forty years, both at CIMS and IBM.

During the call I learned of an amazing coincidence, proof yet again that the world is much smaller than most of us think.

Peter said he heard me mention, or write in an email, the phrase “Lake Norman.”

I said that would have been because my son Michael is Rabbi of the Lake Norman Jewish Congregation. I mentioned that Lake Norman is about twenty miles north of Charlotte, North Carolina, and was built by a power company in the 1920’s.

Peter then spoke of John Cocke, the legendary computer scientist, one of the five smartest people I have ever met.

I knew that John came from North Carolina and that he came from a very wealthy family.

Peter confirmed this. Moreover John’s father was Norman Cocke, and the lake is named after John’s father, Norman Cocke!

It’s a small world indeed.

My son is the Rabbi of a congregation that takes its name from a lengendary figure in the history of computer science.

I also take this as further proof that fewer gifts are more precious than The Gift of a Name.

Mazel Tov!

A Mathematician’s Mathematicians: Professor Herb Keller, and his Notation for QED

I decided to change my major from Physics to Mathematics at the end of my junior year at Caltech. When I returned to the campus in September, 1965, I was told that my advisor would be Prof. Richard diPrima. I learned as I started to write this post that there is an award named in his honor, The SIAM Richard C. DiPrima Prize.

Prof. diPrima was the first person I met who was also a member of NYU’s Courant Institute of Mathematical Sciences (CIMS), then and now the world’s foremost school of applied mathematics.

He was a wonderful man. I recall vividly our first conversation, in which I said I had decided to change my major since I had learned how to program, and found that, especially when done in applied mathematics, programming was much more fun than physics.

He said that was very important, for if you found something that you enjoyed doing, then all the rest would take care of itself.

We didn’t do much mathematics together. He suggested I do an independent study project with a former colleague of his from CIMS, Prof. Herbert “Herb” Keller, who was spending the year visiting Caltech.

Herb was a wonderful teacher and mentor. He suggested as a project that I wrote programs related to the Kruskal Solitrons, and I had a lot of fun working with him.

Fun. It is ALL ABOUT FUN. Never forget that, and the details will take care of themselves.

Herb returned to CIMS in September, 1966, the same month I began my graduate studies there.

I took his course on Ordinary Differential Equations in the first, or perhaps second, year.

His classes were a great joy. He would start with a substantial theorem or topic, and then spend the rest of a two-hour class proving the theorem, or digging into the details. His passion for mathematics was evident in every sentence he spoke, or every equation he wrote on the board.

Whenever Herb finished a proof, he would not write QED but a symbol of his own devising.

QED stands for “Quod Erat Demonstrandum” and is the standard way of marking the end of a proof.

Herb instead wrote one of the following symbols:

– o –
o – o

I of course copied this into my notes, and continued to do so for all the other proofs I went through during my remaining years as a student of mathematics

I have continued to use this notation to this day, to mark the end of an important paragraph, or the end of a first draft, and so forth

Of course, each and every time I do I think of him, and what a fine man he was.

Herb left CIMS to become a professor at Caltech within a year or so. I read recently that he had died at the age of 83, and that he had been an avid bicyclist in his later years.

I also had the great good fortune to have Eugene Isaacson as my professor for at least one, and I think more, courses.

The good fortune is doubled in that I count among my many great professors both authors of a classic work on numerical analysis, Analysis of Numerical Methods, known to mathematicians as “Isaacson and Keller.”

Prof. Isaacon was also a wonderful teacher. He also had a striking resemblance to my favorite author, the man after whom this blog is named, A. J. Liebling. I often think of the other when I think of one of them.

Professor Herbert “Herb” Keller – May His Memory Be a Blessing.

– o – o – o – o

The World is Flat and Small: Bruce Robinson

This past Thursday I attended an event for Caltech alumni in New York City. This was only the third or so time I had done so. The most recent was a few years back when the alumni attended as a group a performance of a play about R. P. Feynman in which Alan Alda played the title role.

I was sipping a glass of wine when I asked the man standing to me if he had gone to Caltech. He said that he had not, but had attended a choral school near Princeton, New Jersey.

When I asked him what he did, he said he was an agent for playwrights.

I said that one my relatives was the playwright Bruce Robinson.

He said he was Bruce’s agent and reached over to shake my hand.


– o –

The World is Flat and Small

Several recent incidents have convinced me that only do we live in a Flat World, we also live in a small world.

The world is both Flat and Small, as I shall try to demonstrate in a series of posts on this topic.

I will begin with two incidents. Both happened within the last few days. They led to my claim that the world, viewed as a social network, is much smaller than most people think.

Dr. Barbara Cooper: Work to Keep Anxiety At Bay

One of my wife’s oldest friends is Dr. Barbara Cooper. My wife recently told me that Barbara had suggested it was important to work, because working would help keep anxiety at bay, especially in these troubled times when so many of us, as am I, are unemployed and seeking employment.

This is a profound observation, and so I am posting it here to share the thought with others.

Barbara’a web site is College Counseling Info.

Barbara has asked my help in updating her web page, and I have already created a Ning site to help her do so. I’ll let you know when the new version is available.

Thanks Barbara!

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