If you hang out with math nerds for an extended period of
time, they will inevitably bring up Erdős numbers.

So what is an Erdős number? And what does this have to do
with Kevin Bacon?

Most of us are familiar with “Six Degrees of Kevin Bacon”.
In this game, you try to connect any actor or actress with Kevin Bacon in the fewest
number of steps.

For example, Tilda Swinton was in “Constantine” with Pruitt
Taylor Vince who was in “Trapped” with Kevin Bacon. Thus, Tilda Swinton is
separated from Bacon by two degrees.

(To play this game online, go to http://oracleofbacon.org. It’s actually
quite hard to get a high number).

Back to our friend, Paul Erdős (http://en.wikipedia.org/wiki/Paul_Erd%C5%91s).
He was a famous Hungarian mathematician known for publishing the most papers
(~1525) of any mathematician (among other things).

An Erdős numbers is the degree of separation a mathematician
has from Erdős based on co-authorship of publications.

Say Person A published a paper with Person B who published a
paper with Erdős. Person A’s Erdős number would be two, and Person B’s would be
one. (Erdős’ Erdős number is zero). (For
a list of small Erdős numbers, see: http://en.wikipedia.org/wiki/List_of_people_by_Erd%C5%91s_number/)

Just like with actors and Kevin Bacon, it’s astonishingly
hard to find mathematicians with really high Erdős numbers (say over 10).

Side note: Interestingly, this will not be true in a few
hundred years. Because Erdős is dead, nobody new will ever have an Erdős number
of 1. In time, nobody will have an Erdős number smaller than 10!

This phenomenon of small degrees of separation is called the
“small-world effect”, named after encounters in real life when you meet a
friend of a friend and exclaim “what a small world”.

The small world effect isn’t just a series of coincidences. As
long as there are some random connections in a network, it becomes relatively easy
to connect any two people in the network.

An example of an un-random network would be if you could
only be friends with someone if they lived within ten houses of you. In this
case, it would be really hard to pass a message via friends between two people who lived on
opposite sides of the country.

In the real world, we can become friends with people who
live anywhere. Thus, you are connected to almost everyone in the world by a
surprisingly small number of steps.

To read more about network theory, I highly recommend Duncan
Watt’s pop-sci book “Six Degrees: The Science of a Connected Age” (http://www.amazon.com/Six-Degrees-The-Science-Connected/dp/0393041425).

He’s also a good author to practice reading research
articles, particularly the ones he co-wrote with Steven Strogatz (http://www.stevenstrogatz.com/).
(Full disclosure: Duncan Watts is one of my science crushes.)

So now you are fully armed if this subject comes up with a
group of mathematicians. And if they get too uppity, remind them that they will
never be able to have Erdős numbers smaller than two.

Bonus fact: Erdős referred to children as “epsilons”.

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