Welcome to all that found us through Sum Idiot’s Carnival of Mathematics #60. If you have never been to this blog before I feel that I should give a bit of an introduction to what ACME Science is as a website. We are primarily the home to the two podcasts Combinations and Permutations and Strongly Connected Components. Combinations and Permutations is the original podcast hosted by me, Samuel Hansen, and is a light hearted, once in a while even funny, take on mathematics where we choose a topic, like the Calculus Cage Match or Combinations and Permutations themselves, and riff on the topic and any tangential conversations that it causes to arise. Strongly Connected Components is a much more serious show where I interview mathematicians such as Joshua Cooper or President of the AMS George Andrews. I also post on various things in science and mathematics that I find interesting. I am happy that you are here viewing the site and I hope you find something that interests you here. For updates about when the new episodes of the podcasts are up or new blog posts you can follow me @acmescience on twitter.
From Mathematics
Bayes and Probability
Thanks to the Royal Society’s new Trailblazing site, we can now read Bayes’s original probability paper, which Uta Frith described in this way:
Bayes had an amazing insight that completely changed our reasoning about probabilities. This makes it easier to think about one’s chances in gambling and dealing in insurance. Recently, Bayes’ theorem was used to filter spam e-mail. This paper, published after Bayes’ death, was known by specialists, but now Google shows over 5 million hits if you search for ‘Bayesian’. But what is so groundbreaking about the Reverend Thomas Bayes’ concept? Without it our way of doing science would be much less accurate. Furthermore, understanding probabilities in the Bayesian way probably comes closest to the most fundamental thing that the brain has to do. The Bayesian approach is therefore at the heart of current models about the brain.
If The Story is Good Enough They Will ALL Listen
One of the main reasons I got into podcasting was because I was interested in the stories behind mathematics. I have approached this in a few different ways with the podcasts. With Combinations and Permutations we cover a specific topic and in between the tangential conversational strands and crazy non sequiturs I try to make sure that the story of the topic, be it a mathematician, a problem, or a discipline, comes out. With Strongly Connected Components I am more than anything else there to find out the story of the person I am interviewing , the story of why they do and the story of what they do. The story has been the most important way of making humans understand the world around them for the longest time and I think it may be the way to once again make people engage with the sciences and mathematics, if we can make our story interesting enough people will pay attention again and, not only that, they will want to understand. I am not the only person who thinks this thankfully; Randy Olson, in The Scientist, recently wrote an article entitled Tell Me A Story of Science discussing this very topic. From the article:
But maybe you’ll say, “Storytelling is just for fiction.” Sorry, but that’s not true. This is a shortcoming of today’s science education—the failure to make scientists realize they are storytellers, every bit as much as novelists. They just don’t like to admit it, or really even think about it. They tend to think stories mean Star Wars and Harry Potter. The truth is, stories are as equally important in nonfiction as fiction. They are the way we understand our world.
The Beauty of the Fourier
Thanks to twitter I stumbled upon a beautiful Fast Fourier Transform video, here it is:
Fast Fourier Transform from peter menich on Vimeo.
In case you want to know some more about Fourier Transforms, Larry Hardesty from MIT has a really nice Explained article on them:
In 1811, Joseph Fourier, the 43-year-old prefect of the French district of Isère, entered a competition in heat research sponsored by the French Academy of Sciences. The paper he submitted described a novel analytical technique that we today call the Fourier transform, and it won the competition; but the prize jury declined to publish it, criticizing the sloppiness of Fourier’s reasoning. According to Jean-Pierre Kahane, a French mathematician and current member of the academy, as late as the early 1970s, Fourier’s name still didn’t turn up in the major French encyclopedia the Encyclopædia Universalis.
Now, however, his name is everywhere. The Fourier transform is a way to decompose a signal into its constituent frequencies, and versions of it are used to generate and filter cell-phone and Wi-Fi transmissions, to compress audio, image, and video files so that they take up less bandwidth, and to solve differential equations, among other things. It’s so ubiquitous that “you don’t really study the Fourier transform for what it is,” says Laurent Demanet, an assistant professor of applied mathematics at MIT. “You take a class in signal processing, and there it is. You don’t have any choice.”(Rest of the Article)
Favorite Theorem
There is a very fun conversation going on over at twitter about people’s favorite theorems. Here are some that showed up so far:
@andy_swallow: #favoritetheorem Of course Euclid’s proof of infinitude of primes is a beautiful thing.
@sumidiot: i like the little theorems, like… khinchin’s constant exists#favoritetheorem
@divbyzero: #favoritetheorem? Gotta be Euler’s polyhedron formula: V-E+F=2
@bakhvalov: My vote goes to Banach-Tarski Theorem can it get more counterintuitive? “…doubling the ball can be accomplished with five pieces; fewer than five pieces will not suffice.” #favoritetheorem
@RobertTalbert: Fermat’s Little Theorem: a^p = 1 mod p (p prime).#favoritetheorem
Join in on the conversation and let us know what your favorite theorem is as well as find out what the favorite theorems are for Combinations and Permutations and Strongly Connected Components.