As pointed out by a commenter, there are some really surprising places where fractal patterns can
appear. For example, there was a recent post on the Wolfram mathematica blog by the engineer who writes
the unlimited precision integer arithmetic code.
The year before our first kid was born, my wife and I went on vacation in Budapest. It was a beautiful city, and the food was wonderful – I particularly loved the chicken paprikash that they seemed to server everywhere. When I got home, I started looking for recipes to reproduce it. This is the closest I’ve been able to come.
The most important thing for this recipe is the paprika. Get good hungarian paprika. American paprika is pretty much just powdered red food coloring. Hungarian paprika is a richly flavorful spice which is the heart of this dish.
Via YouTube, I came across this little gem. Who would have thought that you could create a beautiful fugue from a Britney Spears song?
Fugues are one of my favorite musical forms. There’s something magical (and something mathematical) about the way it sounds when a theme counterpoints itself. Anyway – here it is, the Danny Pi video “How to Write a Fugue”, featuring the “Oops, I did it again fugue”, from a theme by Britney Spears.
Now that you’ve heard the “Oops I did it again” fugue, here’s a better example of the form, by the great master himself, Johann Sebastian Bach. A little slice of musical perfection to brighten your day. The video is a bit heavy on clever tricks (it’s the “Wedge Fugue”, so naturally, they use a bunch of wedge effects), but the music is stunning.
As of 2/24/2008, Sewell has just responded to this, pretending that he just noticed it. To make discussions easier to follow, I have responded with a new post here, and I would appreciate it if comments could be posted there, to keep it all in one place.
My SciBling Mark Hofnagle over at the Denialist blog wanted me to take a look at the pseudo-mathematical ramblings of Granville Sewell. It actually connects with some of the comments in the thread about the paper by Dembski and Marks – Sewell uses part of the article to make the same kind of quantum nonsense claims that showed up here.
Sewell claims to have written a simulator which simulates the Universe, and is complaining that his supposed simulation didn’t produce things like computers or aircraft carriers. I say claims because I’m pretty convinced that he did no such thing. Actually programming a simulator like the simplest of the several he claims to have done, which produces the results that he claims it produced, would be an absolutely astonishing feat of programming, involving a quantity of data that’s more on the scale of Google than on the scale of Granville Sewell’s laptop.
In the course of the series of posts I’ve been writing on fractals, several people have either emailed or commented, saying something along the lines of “Yeah, that fractal stuff is cool – but what is it good for? Does it do anything other than make pretty pictures?”
That’s a very good question. So today, I’m going to show you an example of a real fractal that
has meaningful applications as a model of real phenomena. It’s called the logistic map.
Yet another example of how graphs can be used as models to solve real problems comes from the world of project management. I tend to cringe at anything that involves management; as a former IBMer, I’ve dealt with my share of paper-pushing pinheaded project managers. But used well, this demonstrates using graphs as a model for a valuable planning tool, and a really good example of how to apply math to real-world problems.
Project managers often define something called PERT charts for planning and scheduling a project and its milestones. A PERT chart is nothing but a labeled, directed graph. I’m going to talk about the simplest form of PERT, which considers only time, but not resources. More advanced versions of PERT exist that also include things like required resources, equipment, etc.
I don’t remember where I found this, but it’s really amazing. The 2005
conference on electron/ion microscopy gave awards for the best bizarre or art-like images produced using electron or ion microscopy. The images range from beautiful,
like the C60 crystalline lattice to the right, to extremely bizzare like the nano-meter scale toilet image to the left.
Since the friday pathological programming died out, I’ve been looking for something else to
do for special friday posts. A while back, I posted a bunch of recipes for a mutant meme, and
it seemed a lot of people really liked it. So I’ve decided to do an off-topic friday thing: friday random recipes.
For today, a special chinese dish: braised salmon in meat sauce. This dish would traditionally
be done using pork for the meat in the sauce, but since I don’t eat pork, I use ground chicken thighs. Whatever meet you use, you need to make sure it’s not too lean – the sauce does need a bit of fat in it; not a huge amount, but in needs some. Ground chicken breasts are too dry. I like to do this with wild alaskan salmon. If you don’t like or can’t get salmon, it would work with other strong-flavored firm fish – this would probably be very good using swordfish, or mahi-mahi.
There’s a kind of graph which is very commonly used by people like me for analysis applications, called a lattice. A lattice is a graph with special properties that make it
extremely useful for representing information in an analysis system.
Both in comments, and via email, I’ve received numerous requests to take a look at
the work of Dembski and Marks, published through Professor Marks’s website. The site is
called the “Evolutionary Informatics Laboratory”. Before getting to the paper, it’s worth
taking just a moment to understand its provenance – there’s something deeply fishy about
the “laboratory” that published this work. It’s not a lab – it’s a website; it was funded
under very peculiar circumstances, and hired Dembski as a “post-doc”, despite his being a full-time professor at a different university. Marks claims that his work for
the EIL is all done on his own time, and has nothing to do with his faculty position at the university. It’s all quite bizarre. For details, see here.
On to the work. Marks and Dembski have submitted three papers. They’re all
in a very similar vein (as one would expect for three papers written in a short period
of time by collaborators – there’s nothing at all peculiar about the similarity). The
basic idea behind all of them is to look at search in the context of evolutionary
algorithms, and to analyze it using an information theoretic approach. I’ve
picked out the first one listed on their site: Conservation of Information in Search: Measuring the Cost of Success