A Few Thoughts…

I’ve been struggling with this problem from my recent homework set: Prove that the number of triangles t in any triangulation of a fixed point set s is constant. This is something that after trying a few examples and thinking about it makes perfect sense to me. And indeed it is provable. However, everyone who references this says it is obvious and can be proven by induction – yet no one has actually shown the proof.

This is where I have a problem: I’m not so good at writing proofs, which is why I was terrible at algorithms 1. So while something seems obvious to me (at least now that I’ve thought about the problem for a while), and everyone else seems to be able to put down “it’s obvious, go prove it yourself” in their publications, I’m still stuck on getting this proven. Perhaps when I finally get the answer, I’ll post it here so that future me can find it…not that I’ll probably have much use for it in the future.

So, it’s been quite a while since I’ve posted anything – not that my many fans are complaining, I probably talk to the people who read this blog almost everyday anyway! But for those who are a ways away, here’s what I’ve been up to since school has been out!

To start off, I have joined the Cincinnati Astronomical Society. It’s been a good long time since I’ve looked skyward at night and really studied what I saw. There are a few constellations I remember from when I was younger, but I certainly didn’t study any nebulae or other heavenly bodies. They have 4 telescopes at their headquarters, and I’m working on getting checked-out on the 14″ Newtonian. Once I get the key, I can head up whenever I want! And, they’re working on building a radio telescope using gnuradio – which I’ve been wanting to work with for a while now! I also managed to run into an old friend who I never knew was a ham or into radio-astronomy, so that was really cool! It has been a real thrill to start finding things in the night sky again (and meeting some new friends here on the ground)!

I’ve also been doing a bit of reading – quite a bit for me, but others might laugh at what I’ve accomplished in the month and a half of no school reading. I started with C.S. Lewis’s “The Screwtape Letters” and would recommend it to anyone interested in getting a good dose of thought about the subject of temptation.

I then moved on to a book I’ve been wanting to read since the TV show “The Unit” was released (great show by the way). The series is based on a book by command sergeant major (ret) Eric Haney called “Inside Delta Force.” It’s a wonderful look at (some of) the training that the elite forces of our nation, and of some of the monotony of the missions they were tasked with. I wished there was a little more information about some of the “more exciting” missions they were deployed to, but of course, most of those details are probably classified.

Now, I have turned directions once again, and am working on a book entitled “Poincaré’s Prize: The Hundred-Year Quest to Solve One of Math’s Greatest Puzzles” by George G. Szpiro. We were having a discussion at work about the need to have n-1 dimensions to visualize an n-dimensional object (think drawing a cube on a chalkboard) – and applying that to higher dimensional objects. I knew that Poincaré’s Conjecture had something to do with a problem involving higher-dimensional objects, and that triggered a search of the bookstore for more information! I’m about a third of the way through it, and I can’t really say I fully understand the problem yet – but a lot of background knowledge being covered, which is necessary since I’ve never done any formal studies in topology. I tend to like to jump into topics like this and struggle through them – which, I guess, is a good thing since I’m a grad student!

HTG work has been going well – we’re trying to slow down some of the development on our first application and let it ride for a while. We need to get some more clients using it before we invest too much more time in it – not that I have invested a lot of time recently – Tim and Wyatt have been cranking on it hard for the last several months, and they deserve a break. Unfortunately, it’s to a point where I think I am unable to come in a make a contribution to the project feature-wise without a lot of time studying the existing implementation. And there are rumors about rewrites, but that’s another story.

We have a few new apps in the mixing pot, some that might make us some money even! One of the projects is mostly being used to bring us up to speed on a newer development model (Ruby on Rails). There look to be some really promising things with the Rails framework, and hopefully we can leverage the nice things the language provides and develop some awesome products!

Well, I think that’s all for now. We have an HTG dev meeting here in 5 minutes, and I need to get some more coffee and switch mindsets over to ruby before the others show up ready to run. If you’ve made it this far – thanks for sticking with me

Today’s QC is just funny – I like Martin’s idea of taking charge, I know I’ve done that before! Hooray for self-pride in getting food from the store. Our hunter/gatherer ancestors would be proud. I can imagine the world of a bachelor man in those days:

“What do I want to dine on tonight? Boar sounds good, I haven’t had boar in a while.”
[walks to dark area under tree where food is kept, sees nothing]
[Silence except for a few bugs and crickets]
“Hmm….maybe squirrel, that’s a lot less work…”

Squirrel, the earlier human equivalent of soup in a can, or microwaveable dinners….I kinda like equating them to that! Though, I think the college version of the aforementioned problem would have said “BUGS! w00t!” In which case we can probably equate bugs to Ramman noodles (never had them, this is not a commentary on the noodles themselves, though they do look somewhat grub like….).

Oh, and this t-shirt is just cool…

From mathematician and author Marcus du Sautoy comes an article over at Seed magazine about number theory, and the number 42. The 42 is really just a coincidence, but has some big implications in the realm of the Riemann Zeta Moments, which in turn has implications on proving the famed Riemann Hypothesis. du Sautoy’s books are very good reads, if you like math that is, and explain some of the more complex number theory problems in great detail. The article lacks a bit in scientific detail, but I guess it is a magazine article and not a journal paper. Makes me want to read more about Riemann and the primes again, but it seems like ever time I walk into a bookstore and pick up what looks to be an interesting book on the subject, I end up realizing that I’ve already read it…which is pretty disappointing. Anyone out there got a good book on the subject? Something less that a grad-level text book, but more than something for the layman?
Seed: Prime Numbers Get Hitched

Okay, I confess – while being an engineer, I do enjoy the occasional art show/gallery visit. I don’t get into a lot of the modern art stuff, or maybe it’s post-modern art, of which the term never made any sense to me. Anyway, what I do enjoy is digital art, especially art based on mathematical and scientific principles such as projections of 4 dimensional objects onto a 3 dimensional space (2 dimensions loose WAY to much information to make them useful for anything other than text-book material). Anyway, there’s an artist who has done some of this in metal no less: Bathsheba Grossman. There’s some really cool stuff there, go check it out!

The other thing that I enjoy looking at, and working with (though I don’t have the necessary tools or time right now) is completely digital representations of real environments. I’ve always wanted to work on a ray tracer/rendering tool – not to put it to market, but just for personal edification on the techniques of such a system. A company called Next Limit Technologies have come out with some really awesome tools that do much of what I would like to attempt: real-world physics renderers and fluid simulation tools – geared for presentation, not engineering (though they could be used for science). The renders may take longer, but the results from complex materials with internal caustics is simply stunning. Very cool stuff indeed! It’s times like this I know I’m a nerd: “Hey Joe, what would you like to do for fun?” “Why, I’d like to write a rendering engine based on the physics of the real world!” Just go look at the galleries [render] [fluid - click on the gallery button at the top] and you’ll see what I mean!

At least in the early twentieth century it was. According to some of the physics at the time, ice could wipe out large civilizations in the blink of an eye. Obviously, since this didn’t happen they researchers knew something was wrong. Physicists Lord Rayleigh and Sir James Jeans described how light and temperature (and therefore energy) were related. Their equations worked very well for large wavelengths at low energy, but completely blew as the wavelengths got smaller and smaller. Here’s their equation:

It’s pretty easy to see that as the wavelength gets smaller, the fraction gets bigger and bigger. As a wavelength approaches zero, the energy emitted goes to infinity! Any and all objects emit infinite amounts of high-energy radiation! Ice can wipe out civilizations!

I love math….