It's January, and thankfully we weren't slipping on the sliding ice when we congregated at Blackstone Library to learn about networks from Professor Daniel Spielman.
A collection of connected elements (people/internet sites/computers/proteins - pretty much anything that can be connected) forms a network. For example, one is all too familiar with the concept of social networks; similarly, in biology there are networks connecting proteins; in engineering there are electrical networks. Each element in the network is called a node or a vertice, and the connection between two elements is called an edge or a link. If you know the characteristics of an element, you can predict the characteristics of other elements connected to it, which is why if you have a LinkedIn profile or a Facebook profile, you may be prompted with suggestions to connect with specific individuals. These predictions are based on refined algorithms that have been developed to make rapid calculations behind the scenes. What is particularly fascinating is if you looked at a particular social network, while connections exist because of some shared features between individuals, many other features may be divergent. Very complex networks that look like a pot of cooked angel hair pasta can be simplified into manageable clusters and then further studied. For example in a network of high school classmates, political views may span the spectrum. Each classmate has his or her own network.The question is, can you make a reasonable guess about the political views of someone who you don't know directly in this complex social network? Mathematicians study these networks (they refer to them as graphs), and develop elegant algorithms to yield fast and clean answers to such questions. Such algorithms can be applied to understanding and interrogating networks in general.
Dan took us through a captivating afternoon where we learnt about the history of the field of networks and how even map coloring played a role in the field - you may have encountered your school geography teacher telling you that you could use only four colors to color a map, and adjacent countries should have distinct colors. While the topic of networks and how mathematicians and computer scientists develop methods to understand them may seem daunting, Dan simplified it for us in a manner that can be broadly understood and shared with us how he is trying to continually improve existing protocols to study and understand networks. It definitely gave us a greater appreciation of the under-the-hood contributions of mathematicians to making the world a little more manageable!
Professor Heeger started the afternoon with telling us about subatomic
On a note related to networks, Lewis Carroll had developed a game he called Word-links or Doublets, where two words were connected to each other through a number of steps, and each step involved the change of a single letter in the word; each new word had to be a word in the English dictionary. Perhaps the most famous Doublet challenge is this - can you evolve ape to man in five links?
Solution: APE - ARE - ERE - ERR - EAR - MAR - MAN
There is of course a shorter link:
Solution: APE - APT - OPT - OAT - MAT - MAN
For a compilation of Lewis Carroll's Doublets, visit - http://www.explorethemidwest.com/Doublets__a_word_puzzle__by_Lewis_Carrol.pdf
Note that he ends the preface to the book as follows:
"I am told that there is an American game involving a similar principle. I have never seen it, and can only say of its inventors, "pereant qui ante nos nostra dixerunt!"
I had to check what the Latin translated to, and according to Merriam-Webster, it is this: "may they perish who have expressed our bright ideas before us." Brilliant!
Thank you, Dan, for an informative afternoon. It was worth the wait!
In closing, a network joke -