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A Sermon by Donel McClellan
A Sermon by Donel McClellan
Hot Topics for the
Summer: What is your
ErdÅs
Number?
Matthew 6:25-34 - Pentecost 8 - August 3, 2003 St.
Gregory’s Episcopal Church in San Francisco is famous, among other things,
because a part of the Sunday liturgy is a dance in which the whole
congregation participates. Around
the sanctuary are contemporary icons of people the congregation has selected
as Dancing Saints. Many familiar names and faces are
there may be found there: Martin Luther King Jr., Mary and Martha of Bethany,
Raoul Wallenberg, Hildegard of Bingen, Erasmus, Emily Dickinson, Oscar Romero,
Helen Keller, and Stephen Biko. Then, there are names unfamiliar to most
people. One of them is Paul ErdÅs. The
church identifies this unusual saint with this description:
Paul ErdÅs
lived his life as an itinerant mathematical angel, traveling constantly and
unexpectedly, showing up on other mathematician's doorsteps when they found
themselves stuck in developing exciting new theories. ErdÅs
would stay long enough to help find a way through the difficulty, then move on
to the next person who needed a hand. ErdÅs
lived very simply, depending on his friends to tend his needs as he offered
himself in support of the work that others were doing.[1] Indeed,
Paul ErdÅs
was a kind of contemporary saint. Mathematicians count him among the top ten
math geniuses of the last century. ErdÅs
was born in Hungary in 1913, the son of mathematics teachers. He showed
himself to be a math prodigy at age three when he discovered negative numbers
by subtracting 250 degrees from 100 degrees and coming up with 150 degrees
below zero. As an older child he would amuse himself by solving problems he
invented, like the time it would take a train to travel to the sun. An only
child whose two sisters died of scarlet fever a few days before he was born,
Paul ErdÅs
was pampered by his mother. One friend said he never buttered his own toast
until he was 21 years old. He never married, never had a home, a car, or a
bank account. He was a mathematical minstrel traveling from country to country
visiting mathematicians and collaborating with them. Carrying a half-empty
suitcase he traveled from meeting to meeting staying with mathematicians
wherever he wandered. When he arrived on someone’s doorstep, Paul would greet
his potential host by saying, “My mind is open.” This was an invitation to
join him in a mathematical dialogue. Then he would work furiously for a few
days and move on once he had exhausted the ideas or the hospitality of his
host. It is said that ErdÅs
was capable of falling asleep at the dinner table if the subject of
conversation was not mathematics. When he retired at night he would say to his
host, “We will continue tomorrow, if I live.” He did live until 1996 when at
age 83 he died of a heart attack while working on a math problem. One of
our members, Dr. John Reay, has met Paul ErdÅs
several times. I asked John to tell me something about him. John remembered
that in 1965 he was on sabbatical from Western, teaching at Michigan State
which hosted an international conference on geometry. John writes:
One evening Betty and I invited all the participants (from all over the
world) to our home for a social party. Paul ErdÅs
showed up an hour in advance. He wouldn't let Betty take his coat, but instead
walked thru our kitchen, opened the door to our basement and hung his coat on
Betty's dust rags. Then he wanted to see our "epsilons" as he called all
children. Betty showed him our two boys, aged 4 and 1, [asleep] upstairs.
Paul took off their blankets, had a good look and then kissed each one before
covering them up and going back down stairs. John
continues:
That was the year that I found out what a fierce ping pong player he
was. He would hold the end of the paddle handle in several fingers, letting
the paddle droop as if it weighed 40 pounds. He looked too weak to hit the
ball back, much less be a serious player. But his little flick sent the ball
back like a lightning shot. I could never win one game from him. I played him
again at University of California Davis, 23 years later, and he was still as
strong a player as ever.
[2] One of
the remarkable things about Paul ErdÅs
is that he published more than 1500 mathematical papers in his lifetime. He
solved some enduring problems in numbers theory and founded a field called
discrete mathematics which is a foundation for computer science. Even more
remarkable was the extent of his work with other mathematicians. At last
count, over 507 collaborators published papers with him. I can
imagine that, if the world of mathematics honored saints, Paul ErdÅs
would be among them. In fact, in a way mathematicians have created a kind of
beatitude for him by making him the center of a special universe. Paul ErdÅs is given the number 0. If someone
has published a paper with him, their ErdÅs
number is 1. Publishing a paper with someone who published with ErdÅs
gives one a number 2 and so on. John
Reay has an ErdÅs
number of three. Branko Grunbaum of the University of Washington has a joint
paper with Paul ErdÅs,
and hence has ErdÅs
number 1. Professor Bill Bonnice of the University of New Hampshire has a
joint paper with Grunbaum, and ErdÅs
number 2. John Reay published a joint paper with Bill Bonnice in 1967 and
therefore has an ErdÅs number of 3. It is
possible that you are beginning to wonder where all of this is going, so let
me try to explain. One of the theories Paul ErdÅs
explored was the mathematical nature of networks. He suggested that networks
were randomly arranged. A network is a cluster of people, or computers, or
cells in an organism or stars for that matter. If one
considers the network of living mathematicians, and assumes a random
distribution, one would expect that ErdÅs
numbers would range from 1 to several hundred. Surprisingly, that is not the
case. Most mathematicians have rather low ErdÅs
numbers. This is
the basis of the popular theory that there are six degrees of separation
between any two human beings. For example, in an average of six personal
relationships I might be connected to a Sherpa in a remote Tibetan village. A
friend from college may know an anthropologist living in New York who knows a
Swiss mathematician whose mountain climbing partner has worked with the Sherpa.
It
seems that networks of websites on the internet, human beings, and molecules
in a chemical reaction all obey the same basic laws. To take the example of
this church, not everybody knows the same number of people in the
congregation. Newcomers, for example, begin by knowing only a handful of other
members. Shy folks know fewer people than more gregarious folk. More
importantly, there are a few people in the congregation who know almost
everybody. These people are connectors. If you know a connector, you are
likely to become acquainted with others faster than you would on your own. The
reason most mathematicians have low ErdÅs
numbers, is that there are a number of mathematicians who collaborate widely.
They are connected to dozens of hundreds of their colleagues. By publishing
with someone who has published with one of the connectors, your chances of
having a low Eros number are enhanced. A
healthy network is one in which the nodes are well connected to connector
clusters. A healthy church is one in which every member has multiple ties to
others in the congregation. If we were to consider First Congregational Church
of Bellingham numbers you might get something like an FCCB 5 for attending
worship. Joining would bring you to an FCCB 4. Participating in a smaller
group in the church would make your number FCCB 3. Volunteering as a member of
a board, a church school teacher, or choir member would bring the number down
to FCCB 2. In other words, the more connections you make within the
congregation, the stronger our network will be.
Whatever your FCCB number is, you have another important ranking. That is your
relationship to God. Jesus was clear in the Sermon on the Mount that your God
number is always 1. As Jesus expresses it:
"Stop worrying, then, over questions such as, 'What are we to eat,' or
'what are we to drink,' or 'what are we to wear?' Those without faith are
always running after these things. God knows everything you need. Seek first
God's reign, and God's justice, and all these things will be given to you
besides.”
[3] In the
tradition of the Reformed faith, you are not related to God through a minister
or priest, which would make your God number 2. You have a direct relationship
through Jesus who invites everybody to be a brother or sister. That gives you
a God number of 1. You are
always in a direct relationship with God. It is a two way street. God counts
the hairs on your head and provides for you as generously as for the birds or
wildflowers. You respond by participating in God’s creative care for other
people and the creation. In this way a strong network is formed. The Creator
and creative people work together to fulfil a vision of peace and justice for
the world. Whether
or not you have an ErdÅs
number, your God number is always 1. Thanks be to God.
[1].
http://www.saintgregorys.org/GodsFriends/Vol8/No2/Dancing_Saints.html
[2].
Personal conversation and email from John Reay
[3].
Matthew 6:33
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