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.

Note:

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.

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