From Mathematics

Number Gossip

Everyone has been posting abouit this but I have to put my 2 cents in the ring. Number Gossip is awesome. That is it, really my whole 2 cents. It is simply an awesome site that gives awesome info about any integer between 0 and 9999. Try it out, have fun with it. We just recorded episode 37 of C&P, which should be up Thursday night, and in honor of that here is what Number Gossip says about 37:

  • 37 is the smallest irregular prime (submitted by Andy Baker and John Kiehl)
  • 37 is the smallest left and right truncatable prime having more than one digit
  • 37 is the only prime with period length three: 1/37 = 0.027 027 027 …
  • 37 is the prime you get if a three digit number having the same digits is divided by its digit sum

Mathematical Opionator

Former guest on Strongly Connected Components Steven Strogatz has been having a rather good year. Not only did he appear on our podcast, he told part of the story from his new book The Calculus of Friendship, just finished it myself a couple of weeks ago it is a great read you should go and buy it, on the Numbers Episode of Radio Lab, and he now also blogs for the New York Times. Strogatz has become a part of Opinionator group of blogs over at the New York Times website where he is writing a series of posts about mathematics in wonderfully descriptive plain language, he started with a post about numbers and is now on roots. From that first post:

Children learn from this that numbers are wonderful shortcuts. Instead of saying the word “fish” exactly as many times as there are penguins, Humphrey could use the more powerful concept of “six.”

As adults, however, we might notice a potential downside to numbers. Sure, they are great time savers, but at a serious cost in abstraction. Six is more ethereal than six fish, precisely because it’s more general. It applies to six of anything: six plates, six penguins, six utterances of the word “fish.” It’s the ineffable thing they all have in common.

No matter who you are Strogatz’s exposition is plenty good enough to hold your attention, and the content is parse-able by anyone. If you are a mathematician go and read this to help reground yourself in the most basic contents, then go tell all the non-mathematicians you know to go read this so they know what the hell you have been talking about for all these years. (Strogatz Opionionator)

History of Mathematics Journal: 4

Early on this past week Professor Bhatnagar brought up the idea of mathematical funding, specifically how would any of us choose to fund mathematics if we were the government. The government of the United States of America currently funds mathematics through two main channels, the national Science Foundation and the National Security Agency, and many other side channels, Department of Defense, Department of Energy, etc. The National Science Foundation alone represents around 65% of the governmental funding for research in mathematics, and in their most recent budget they ask for an increase of $7.4 billion in total funding with an increase for mathematical research of 5%, a 16% increase in Graduate Fellowship money, as well as many other cyberlearning and outreach programs that will directly impact mathematics.

This resonated with me as I spent my weekend in the seat of United States of America’s federal power, Washington DC. I was there to participate in the Students for Free Culture, http://freeculture.org, annual Free Culture Conference. This conference is in the words of the creators: “A convening of the international free culture community for two days of networking, learning and acting. The vision is to bring together student activists and free culture luminaries to discuss free software and open standards, open access scholarship, open educational resources, network neutrality, and university patent policy, especially in the context of higher education.” The conference itself was a shot in the arm for me in particular, as it has pushed me towards really starting work on some projects that I have had on the back burner for a long time.

The conference, while concentrating a lot on education, spent a decent amount of time on politics, a subject that I have only allocated the minimal amount of interest to since I joined up and became on the few, the proud, the graduate students. It required that I open my mind and start thinking less like a mathematician, i.e. in closed logical fashion, where the strongest of formal arguments is obviously the correct one, and start cogitating in the way that normal people, and more specifically politicians, do on a daily basis. It was not the easiest thing for me to do, I would listen to some of the panelists talking about Net Neutrality or Open Educational Resources and immediately wonder why every does not just do things in the way that one of the panelists puts forth because it was obviously the best way. As a mathematician I often forget that most people do not think about the work in such a clean and dry way. One thing that became clear to me at this conference was that if I were the government I would spend as much money as I possibly could to make mathematics more open.

Read more

History of Mathematics Journal: 3

We started the week off talking about paradigm shifts. Paradigm shift, according to Wikipedia, was a term that was first used by Thomas Kuhn in his book The Structure of Scientific Revolutions in 1962 to characterize a foundational transformation in the dominant theory of a science. Since its introduction the phrase has had to go through one of itself to arrive at its current meaning of a over-arching change in any  area within the realm of homosapiens. In class quite a few paradigm shifts were discussed from the Calculus of Leibniz and Newton to the training regimes of the Williams sisters, but there is one that I feel is just as crucial and that is the invention of computational theory by Alan Turing.

One interesting way to look at the idea of a paradigm shift is through the lens of the Singularity that Venor Vinge was kind enough to give us. The term singularity is one that mathematicians are very comfortable as they are a term for where some mathematical object happens to not be defined.  Say we are talking about a function that is not defined at zero, then the function tends to behave oddly near this singularity. The same can be said for matter near black holes, which are called gravitational singularities. It was from these ideas that Vinge came up with the term Singularity, in this case referring to some point in the future when technology will stop increasing in speed at an algebraic level and start progressing at essentially infinite speed; usually this refers to AI or self-replicating machines. The reason that I feel this lens could be useful to look at paradigm shifts through is because of something that Singularity Science Fiction, the Singularity does have it own sub-genre of Science Fiction literature, author Cory Doctorow once said, that for all essential purposes the Singularity is the point at which human beings that were raised under the conditions caused by the Singularity are incapable of meaningfully communication with those born before the event. He went on to posit that human beings have already gone through multiple points of Singularity, the greatest of which would be the invention of spoken language. After which it is quite clear that meaningful communication with those who do not have spoken language by those who do would be, for any practical purposes, impossible.

While I do not believe that any of these paradigm shifts qualify as full Singularity events, I do appreciate the problems that those who learned mathematics after we had the calculus would have communicating the mathematics of, say a thrown projectile to those who came before the calculus was know. It is in this way that I wish to discuss Alan Turing and the beginning of computing. Read more

Even Newton Knew He Sucked

It turns out that is not just us here at ACME Science, and more patricularly Combinations and Permutations, that think that Newton was a waste; so di he:

The young Isaac Newton’s “debtor’s ledger of sins”:

  • Stealing cherry cobs from Eduard Storer
  • Denying that I did so
  • Robbing my mothers box of plums and sugar
  • Calling Derothy Rose a jade
  • Punching my sister
  • Striking many
  • Wishing death and hoping it to some
  • Threating my father and mother Smith to burne them and the house over them
  • Striving to cheat with a brass halfe crowne
  • Making pies on Sunday night
  • Squirting water on Thy day
  • Not turning nearer to Thee according to my belief
  • Setting my heart on money learning pleasures more than Thee
  • having uncleane thoughts words and actions and dreamses

(Gravity and Levity via Aisha)