Pancakes and Waffles

There are many theorems which are really easy to prove after you develop some technical machinery, tricks and shortcuts. This is analogous to waffles: you need the iron and the mix, but once you have them it's just a matter of pour and wait.

On the other hand many of these same theorems have more difficult "direct" proofs, which is analogous to pancakes: the ingredients and tools required are simple, but you have to have skill to apply them properly.

A great example of this is the theorem that you can always find as many primes as you like. A pancake proof would be like Euclid's, assuming very little and deriving the result after a clever argument. A waffle proof would be Furstenberg's version which is short but uses topology, an entire field of mathematics with its own notions and terminology.

This is similar, but distinct, from a notion my physics teacher Ruby Musgrow had about solving problems. She described two different problem solving methods as the Ulysses S. Grant approach and the Robert E. Lee approach. The Grant approach is throwing all your resources at a problem thus overpowering it and arriving at the solution, while the Lee approach is using your resources cleverly and selectively and still resolving the problem.

While we're at it I might as well mention Paul Erdős, a famous mathematician who once said that there was a book with all the best proofs written down, and our attempts at proofs are simply trying to emulate these proofs. He would call a proof "from the book" if it were particularly elegant, powerful and at the same time simple. So now given this discussion one could also call a "proof from the book" a Robert E. Lee Pancake proof.

Sublime Science

Most of the time I eschew space images which are not in the visible spectrum. I like to observe the "visible" universe without (too much) meddling, but I found myself stunned at the beauty of a recent gamma ray survey of the sky. So instead of opining in the Digg comments, I decided to share this with you dear visitor.

This map was made using Fermi (previously known as GLAST), a gamma-ray observatory launched last year. It is the highest resolution picture of its kind ever recorded. The gamma rays used to make this map all had energies higher than 150 million times the energy of a garden variety visible photon.

To the Almighty: Thank you for science.

Newspapers just like me

I'm in the New York Times this time. I'm glad it's for something I did, rather than merely my football affiliation this time.

Way crunk eh? The article in the New York Times. Antbed.com a.k.a. that thing I did.

XSLT

I have this thing for XSLT. I really love doing nifty things with it. You have to respect a language that can convert a stupidly verbose foreign XML format into another foreign, crazily restricted format in only 37 lines. It's like the universal rosetta stone. One day, starship captains may use XSLT in universal translators to communicate with alien species. OK, that might be a bit optimistic, but hey XSLT is Turing Complete so if a computer can do it, so can XSLT.

I would encourage everyone to get their feet wet with XSLT. Find your favorite blog, subscribe to its RSS feed and write a stylesheet that will convert it to a format you like reading it in. It's why Al Gore invented the series of tubes. Don't let the former vice president down, he needs this.

At some point in the past I made a playlist of music that goes well with work, like creating an XSL transformation, which I named xslt. Even more recently, I stored it on my servers so that I could stream it anywhere, including into your speakers. Think of it as a mix-tape ... for XSLT. Enjoy.

Railguns

Who doesn't love a railgun? Perhaps newbs being pwned in unreal tournament, but beyond that, really, who doesn't love a railgun?

  I love railguns.

Why? Well, they're one of the few futuristic weapons that are actually in development. Gravity guns? Cool, but not likely. Photon torpedoes? What does that even mean? On the other hand, a rail gun accelerates basic, metal rounds by electromagnetism to high velocities. This is possible, in production, and coming Navy ships in the next few decades.

The thought of causing explosions from kinetic energy alone is just incredible, no waste, no radiation, just a six pound slug.

We're probably all familiar with the 1.21 GigaWatts and 88 mph needed for time travel. Let's compare that to 32 MegaJoules. We can't make the comparison directly since Joules are energy and Watts are work, but if you consider that level of energy working for one second, you get 32 MegaWatts. That's about a quarter of a million times as powerful your average household lightbulb, yet still less than a quarter of a thousandth of what you need to travel in time. What's that mean? It means that there's some crazy physics behind Mr. Fusion and the flux capacitor and that Doc doesn't work for the navy.

In this video we see a shell labeled 3.52 kg. So then the muzzle velocity for a test with that round at 32 MegaJoules is (naively) given by

and hence is close to 4300 meters per second. The speed of sound is 343 meters per second. That means that if all the energy were transmitted with perfect efficiency to the round, its initial velocity would be over mach ten.

This is fast enough that the round itself doesn't have to explode, it can destroy things with its kinetic energy alone. That's pretty impressive.

Unfortunately, this is being developed as a weapon of war and will probably take the lives of thousands of soldiers and possibly innocents. Why can't we just make stuff like this for fun and shoot clay pigeons with them?

The Famous Mr. Blair

As noted below, the Dallas Morning News quoted me in their story about Stone Creek. This is the most famous I have ever been for doing so little. I can't say that it's a bad thing, because while watching the last playoff game that matters I met people in the bar that claimed they came because of this article. I'm glad they were able to come enjoy the game with fellow fans. That's what I want my life to be, increasing people's ability to do what they wish.

I also heard through the grapevine that I was also on TV. Pretty cool.

Obviously I'm bummed that the Cowboys are not going to get the chance to play the Patriots in Phoenix, but there is one good thing about it. I was anticipating Cowboys participating in XLII hence forcing me to choose between my eight and a half foot television and Stone Creek. Now I don't have that problem. Therefore, I'm going to be throwing one heck of a party on February 3rd. You're invited. Just be sure to RSVP first. =)

In other news, this fine lady has quite a musical selection on her blog. What does that have to do with the price of snuff in Texas you ask? Well, as far as that particular question is concerned, probably nothing. On the other hand, I have recently discovered SeeqPod and now you can see what I mean when I say the 1970s was the best decade of music ever.

Two words. Holy. Crap.

Um.. Yeah... So, I'm above the fold on the Dallas Morning News' website.

More details after I regain consciousness and get off the floor.

The coolest thing I have ever done

I did the coolest thing I have ever done in my life the other night (20071028).

It was just after 3 AM. We were on the L train headed to Brooklyn. It was going slllllooowwwww. This happens, NYC does night/weekend construction to inconvenience the least amount of people possible. Unfortunately in a town with 8 Megapeople, that's still going to be a lot. Luckily for me it inconvenienced more than 30 people in my immediate area that night.

I had just sat down next to a Cuban-American guy dressed as a wiseguy. There were at least two other Cubans sitting near us. When I first saw them, I assumed they all spoke English as well as the one doing most of the talking which was not well. So when 'mugsy', as I referred to him in my head, said something, I meant to ask him if he dressed as 'mugsy,' but I think I accidentally introduced myself as such. In any case, he had grown up in New York so there was no problem with his English.

He looked rather young, but the ladies didn't believe that he was 36. So they checked his drivers license and found out, yes he was 36, but not only that his birthday was only 2 days away from one of the girls'. That's when the nerd moment began.

In mathematical parlance there's something called the 'Birthday Problem' in which the probability of two people in a group sharing a birthday is calculated. As it turns out it only takes 23 people to have greater than even odds that some pair in the group share birthdays.

There were far more than 23 people on that train car.

Then I turned him and said, "It is likely that two people on this train car share a birthday." He didn't believe me.

That was all the excuse I needed to walk up to the middle of the train car and yell out, "Ok, everyone we're going to do an experiment about birthdays!" I then started asking people to raise their hand if they had a birthday in January, February, etc.

Unfortunately for this type of interaction, the subway is not the ideal place because socially it's a lot like an elevator. That is, people aren't big on interacting with people they don't know in a subway car. The platform is a different story, but on a subway car (for me at least) it's not socially easy to start a conversation with the whole car. Because of this I didn't get a very enthusiastic response. I eventually got to November and thought that it was going to fail, but a bit of fortune was on my side!

As it turns out, two people sharing July 24th as a birthday were sitting across from each other! I assume that when I asked about July either one of them raised their hand and answered and at that point the other person thought, "That's my birthday, should I speak up? What's this crazy short dude going to do next???"

Thankfully they told me and I brought the Cuban guy back and showed him and he was quite impressed. As was I.

Mathematics. Ladies and gentlemen, it works.

The Incredible Planetoid Frank

The Cassini-Huygens mission to Saturn is one of my all-time favorite space exploration missions. It has produced a massive amount of really exciting astronomy, both for scientists and the public as well. This is our closest and most comprehensive look at the planet Galileo examined through his telescope. It is one of the first nuclear powered space missions which caused a lot of controversy at the time of its launch. Realistically, however, if we wish to explore the vast reaches of our own solar system we will need to continue utilizing nuclear energy unless someone comes up with warp drive in the next few years.

And so recently it discovered the sixtieth known moon of Saturn, and for now scientists are calling it

Frank.

Frank is a good friend of mine and it is fitting that he should have a planetoid named after him. "So what," you say, not knowing the man, the myth, the Frank. Well let me tell you what, he has a belly button and won't deny it to anyone. When something needs to be pushed? Frank can handle it. Why, that shyster Frank of perennial Subway and library employment, he even fended off the advances of that infamous coquette 'Heidi S'. All in all he's a great guy, and very deserving of the honor of planetoid. Therefore I suggest whenever you see Frank, on the street, in the gym, in space or in 'Meatball Sub,' invite him to lunch. He's likely to respond, "I could eat."

A Revelation

As I was studying for my finals I noticed something that I have to reveal to everyone. If you have seen Back to the Future, you will know what I am talking about. I have discovered a striking analogy between this movie and complex analysis. Remember the line “The flux capacitor is what makes time travel possible.” Now in just about any complex analysis class, you'll come across a slough of theorems and results due to Augustin Louis Cauchy. So the analogy is, the flux capacitor is to time travel as the Cauchy-Goursat Theorem is to complex analysis. Goursat was a later mathematician who proved the theorem as it is presented today. (Although I doubt either discovered it after hitting his head on a toilet.) In other words, The Cauchy-Goursat Theorem is what makes complex analysis possible. It's true, just go ahead and try to do something in complex analysis which does not either depend on this theorem or is motivated by it. If you find something, let me know. So now this is the second mathematical result involving Cauchy that I have found that relates directly to American cinema. What is the other one you ask? “You make all my Cauchy sequences converge.”