Some years ago I found myself waiting for someone near Times Square with my thesis advisor. We had a bit of time to kill when the question came up - "of the people walking by, how many are physicists?"
There are a few ways to approach the problem, but both of us were experimentalists. He took a piece of notebook paper out and with a marker wrote a number on it and held it over his head.
Sure enough - a few people stopped to talk and all of them turned out to be physicists or astrophysicists. 137 turns out to an approximation of the inverse of the fine structure constant - a coupling constant characterizing the strength of the electromagnetic interaction and something central to any quantum electrodynamic calculation. If you encounter the number - even on a roadside - the first thing that leaps to mind if you are a physicist is this important constant of nature.
I don't know why anyone would want to attract physicists, but we showed this worked experimentally. Are there numbers that people might identify people in your profession, sport, or hobby?
People do have favorite numbers and societies have "lucky" and "unlucky" numbers. Douglas Adams clearly liked 42, but many seem to have a fondness for small integers and in Western societies primes seem to be favored. There is certainly the stigma of numerology, but there are also aesthetic choices and understanding this more deeply would be fascinating.
This morning I heard a piece by Robert Krulwich on NPR (summarized in his blog post) that pointed to a study currently underway to look for patterns in favorite numbers - the sort of thing that those of you who are anthropologists will love. You can ask to be notified when the results are published next year.
The history of numbers is rich and fascinating - a fascinating work on the subject is The Universal History of Numbers by Georges Ifrah. I recommend it with a few reservations as it is only a starting place and far from a universal history - some of its entries are disputed. But it is an excellent entry point to learning about the development of some of the most explosive change civilization has witnessed.
Oh - my favorite number? If I'm restricted to integers I've always liked 17 and 23, but my all time favorite is the irrational real constant e - namely 2.71828182845904523 ...
It is deeply embedded in useful expressions of how science describes nature and is also important in mathematics. e is part of Euler's Identity - one of the most beautiful relationships in all of math: .
some of its early digits are curious making it very easy to remember.
2.7 then 1828 is repeated twice, then 45 90 45 - just like the angles in an isolates right triangle, and then 23 which is a favorite small prime of mine ..