Resonant Constellation

Read about his “book” by clicking on this link.

That is all.

I went back to New Mexico for a weekend and a bit, and as per usual during the summer. Also as per usual, I had a fit of allergy attacks. It seems that New Mexico is a breeding ground for every type of pollen that ever bloomed, and then some. Most times, I recover in a couple of days, but I spend those days completely miserable and unable to function. This time was incalculably worse, as my entire six day stay at home was effected this time. At the time of this writing, back in Tucson, I am still entirely miserable. The pilot on my plane flight was none-too skilled with the cabin pressure controls, and as a result, my right ear has completely (and painfully) blocked up. To make it worse, my sinuses are still suffering from extreme spasms. I have resolved that I am never going back to New Mexico during the summer, no matter how much I love the green chile, I am inevitably miserable for a lot longer than I can enjoy the spicy food.

Bleh.

I was supposed to be up on Mt. Bigelow, observing right now. Instead, I am at home, impotently shaking my tiny fists at the sky. Why, you ask? Because of my arch-nemesis, clouds. We still accomplished our most important goal, which was to get certified to operate the telescope on our own. Basically this involves learning how all of the systems work, how they break, and what to do when they do break. Most of the instruction seemed to actually be tips on quirks of the system and ways to get around them. In fact, most of the operating procedures seem to be clever/desperate ways to get around the fact that most of the equipment doesn’t, in the strictest sense, work. There’s a hell of a lot of components that make a big telescope run, and keeping them all straight was a significant task.

As we were driving up, Jared and I heard and saw lightning, which already made us doubtful about our night of observing. While the rain and thunder moved on, the cloud cover refused to lift and with the prediction of thunderstorms in the morning we decided to stow the telescope and take emergency lightning precautions before leaving (this includes airgaping every single electronic device on the premises, which takes about a half an hour to complete). We were back down by 9:30.

Oh well, at least I’ll get some sleep now.

Every once in a while, I entertain myself by learning about random math stuff. A recent example is my foray into Fibonacci sequences which I mentioned in a previous post. This time, my friend Pete mentioned a peculiar number, called Graham’s number. As far as I can tell, this is the largest number to ever be used in a serious mathematical proof.

I know what you math-nerds out there are thinking: larger, even, than a Googol? (), or a Googolplex? (). Yes, my friends, Graham’s number is inconceivably big. It makes a Googolplex look like a mere handful. Interesting note: when I was little, no more than five, I remember writing out a Googol on an etch a sketch and trying to explain it to my grandparents. I was a weird kid.

Graham’s number is so absurdly large that there are not enough particles IN THE UNIVERSE to express it via any standard notation. Think about that-go outside to a high place and look around. Then think that everything you can see is made of inconceivably tiny particles which are so small, they cannot be seen by the human eye, nor any optical magnifier that has ever, or will ever, be made. Look at your hand-there must be millions, perhaps billions of particles in your hand alone. And yet including everything you can see, much less the entire friggin’ universe, there aren’t enough of these unfathomably tiny particles to write out this number, even using a series of exponents. Wow.

So how do you write it down? Well, mathematicians are relatively creative people (if not entirely practical), and they’ve come up with intriguing ways of expressing large numbers. One way is called “Up-arrow notation,” in which the number is expressed by a series of rows including numbers and arrows which signify computational steps to arrive at the number itself. Each higher row is predicated on how many arrows are in the last row. This is the only way to express Graham’s number. To show just how depressingly large this number is, you still can’t even express just the first row of up-arrow notation with all of the particles in the universe. There are 64 total rows.

What I can tell you about it is that it ends in the string “…262464195387″, where the … represents a whole lotta other numbers. So why would anybody in their right mind need such a comically large number? Were these mathematicians perhaps compensating for something (say, the budget differential between their department and a useful department like Astronomy)? From wikipedia:

Graham’s number is connected to the following problem in the branch of mathematics known as Ramsey theory:
Consider an n-dimensional hypercube, and connect each pair of vertices to obtain a complete graph on 2n vertices. Then colour each of the edges of this graph using only the colours red and black. What is the smallest value of n for which every possible such colouring must necessarily contain a single-coloured complete sub-graph with 4 vertices which lie in a plane?
Graham & Rothschild [1971] proved that this problem has a solution, N*, and gave as a bounding estimate 6 ≤ N* ≤ N, with N a particular, explicitly defined, very large number; however, Graham (in unpublished work) revised this upper bound to be a much larger number. Graham’s revised upper bound was later published — and dubbed “Graham’s number” — by Martin Gardner in [Scientific American, "Mathematical Games", November 1977].
The lower bound was later improved by Exoo[2003], who showed the solution to be at least 11, and provided experimental evidence suggesting that it is at least 12. Thus, the best known bounding estimate for the solution N* is 11 ≤ N* ≤ G, where G is Graham’s number.

Wow, that’s so useful (/sarcasm). It must have been a profoundly depressing result: “So, Ronald, how’s that proof you’re working on coming? Did you ever get a result?”
“Yeah, it’s somewhere between 11 and wharrgarbl.”

Even as an astronomer (a field which is known for large numbers, even coining the term ‘astronomical’), I’d probably just call it “effectively infinite for all foreseeable/sane purposes.” No wonder it was published in “Mathematical Games.”

In all honesty, stuff like this is probably good for the math departments-it will keep them at their desks during the inter-departmental war. I for one know that the physics department has long desired to vaporize the chemistry department with a large laser array. The mathematicians will likely be too busy coming up with crazy stuff like Graham’s number to be bothered by such events.

Last minute note:
I have just discovered that there is a larger named number, called TREE(3). It is part of a sequence of numbers: TREE(1)=1, TREE(2)=3, TREE(3)=Makes the word big seem hackneyed. Apparently, Graham’s number is “unnoticeable” next to a lower bound to TREE(3), which is itself unnoticeable next to TREE(3). I hear TREE(3), will anybody go to TREE(4)? Sold to the man in the straightjacket.

There are even bigger numbers yet, obviously, including “Totally Indescribable Cardinals,” (yes, that is the formal name), Transfinite numbers, and all sorts of made up names (Bajillion, Frumptillion, etcetera). For an incredibly humorous article on made up, unspecified numbers, look here.

Of course, infinity puts all of these so-called large numbers to shame. Compared to infinity, they might as well be 0. Maybe you should be careful next time you use the word “infinite” in casual conversation. You probably doesn’t mean that many.

Well, it’s finally over, and aside from a slight headache and severe sleep deprivation, I’m not too much worse for the wear. Just before the semester ended, however, fun things began to occur. The first was that my name is now on a submitted paper, which you can find here. It is not yet accepted to the journal, and we’re still waiting on referee’s notes.

Also on the research front, I have a new job, researching the stellar population around the light-echo source V838 Monocerotis. This is a really interesting star, and my research is aimed at determining if it is part of a young or old population. This could tell us a lot about how the outburst event occurred, and even what it was.

This weekend, I have been in Phoenix at the invite of my friend Pete (you can find his website to the right in my links) attending a blog bash and the NRA Convention. I went to this event as a member of the media and as such, felt obligated to take pictures, investigate things, and write interesting things down. In all honesty, I did feel a bit out of place at this convention (Star Trek conventions are much more my speed). There were quite a few people there, and the overwhelming majority of them live by the de-facto catchphrase of the convention: “Guns, Family, and God.” This is obviously not the usual crowd that I hang out with, hence the slight uncomfortableness, but we did meet up with several other bloggers who are anything but stereotypical NRA members. In fact, I believe I was the only non-member in that group. I channeled my inner journalism nerd (high-school paper) and wrote down many fascinating observations. I’m still mulling over these, but expect to see my reaction here within a couple of days.

Tomorrow, before leaving Phoenix, we plan to visit Luthier Walt Kuthman of Gypsy mandolins. I’ve been in contact with Walt about the possibility of him building me a custom Bouzouki. At the moment, this seems unlikely due to financial concerns, but I’m still hopeful about the future. Also musically, I just got a new CD by 2Duos, which includes Claire Mann and Aaron Jones, whose album I reviewed in one of the first posts for this blog. I may post a review of this new album here when I get home.

Every summer, I have a project-this is a tradition I have going back at least…well, about three years. This project invariably involves building something. For example, last summer one of my projects (there were two) was building and painstakingly painting a model of the U.S.S. Reliant, Khan’s ship from Star Trek II: The Wrath of Khan. My other was constructing a custom prop-lightsaber. These were very entertaining. At the moment, I am considering several things for this summer’s project (or projects). First, I have designed a system for focusing many laser rays into a single beam. This would involve wiring the lasers to power supplies, and making or otherwise obtaining an optics system. So far, this is my best idea, but if anybody out there has any suggestions, I’d be glad to hear them.

The best thing, of course, is that I survived another year, becoming one of the approximately 6 astronomy majors out of 100 beginning in our freshman class to make it to senior year on schedule. 6% made it. I’m going to need this summer to recuperate a bit.

I saw Star Trek last night. Wow. I don’t want to provide any spoilers, but let me say this: I always enjoy movies when I am watching them in a theater, but I have never before wanted to stay and watch it again directly afterwards. As the movie was drawing to a close, I found myself wishing it wouldn’t end.

The action was mind-blowing, the plot was solid, it looked absolutely beautiful, but Sci-Fi is character driven, and this movie came through in spades on that department. Chris Pine played the perfect brawling, womanizing, brilliant Kirk. Zachary Quinto not only looked spot on Spock, the writers did a great job portraying his internal conflict between Human and Vulcan identities. Look, I could go on, but all the actors did an incredible job. Simon Pegg deserves special mention, as he played a perfect Scotty-a brilliant engineer and physicist with a touch of humor.

Okay, so it wasn’t a perfect movie-the science behind most of it was at best shaky (a supernova threatens to destroy the universe, everything they did with black holes), but having read the prequel comic, I found I was able to suspend my disbelief rather readily. Several people around me complained that the movie was about half made of lens flares, and that anytime there was a window, the light became blinding. I noticed this, but it didn’t bother me as much as it did others.

So, really, I urge you to go see this movie, even if you don’t like Star Trek. Hell, you should go even if you DO like Star Trek.

Hello everybody out there. It is finals time, which means that there is a multitude of tests, papers, and miscellaneous assignments for me to complete. I’ll be on hiatus here until all of this insanity is over in a week or two. See you then.