October 11, 2009
All right, here's a fun one. It usually comes as part of a story. The story as told is mostly true, though a few details have been a little fudged by the winds of history. It goes like this: when the young Carl Gauss was a small child in school, his teacher wished to kill some time by making the…
October 8, 2009
ScienceBlogs' Razib is back from the Singularity Summit, with summaries of a good portion of the proceedings and some interesting links. Relatively recently I've written about why the Singularity very well may not happen (at least not the wilder version) - roughly, the growth curve of technology…
October 7, 2009
I shot an arrow into the air,
It fell to earth, I knew not where;
For, so swiftly it flew, the sight
Could not follow it in its flight.
- Henry Wadsworth Longfellow
This is what happens when you don't pay attention in freshman physics. You don't need to see where the arrow goes to find out where…
October 6, 2009
Apologies for the absence. A brand new research project is getting cranked up and I've been pretty short on time. As such the posting schedule may get a bit erratic. I'll do my best.
I'm also working on improving some other things as well. When I started college I somehow managed to avoid the…
October 1, 2009
One of the nice things about energy is that there's many, many different forms of it. There's many, many different ways to convert between those forms.
Yesterday we discussed the problem of turning the energy in sunlight into electricity via the circuitous route of sunlight to electricity (in a…
September 30, 2009
In theory I like solar power a lot. There's a lot to be said for energy that falls from the sky for free for as long as we care to use it. But actually getting that energy to do useful work in an economical way. Solar panels are expensive and not terribly environmentally friendly to produce, and…
September 28, 2009
Sometimes in math we'll understand one aspect of a problem very well, while at the same time we understand another aspect of a problem very poorly. For instance, take the prime numbers. According to the prime number theorem, the number of prime numbers below x is approximately given by:
Where…
September 24, 2009
Astronomers and space exploration enthusiasts around the web are expressing lots of enthusiasm for the discovery of water on the moon by the Indian Chandrayaan-1 orbiter. Long story short (Ethan has a good version of the long story), the probe discovered relatively large quantities of water frozen…
September 23, 2009
Ideas about the nature of light have been around for thousands of years, but until Newton came along in the 17th century most of these attempts were little more than speculation. Newton himself held to the view of light as composed of huge numbers of tiny "corpuscles", or particles, which bounce…
September 22, 2009
Every once in a while it's a good idea to remember that even the simplest-looking physical systems can have completely bonkers behavior. The pendulum is certainly one of those systems. It's so simple that it's a mainstay of freshman classes, for technical and non-technical majors alike, though…
September 21, 2009
Note to the reader: this post is relatively stiff mathematically. For those not mathematically inclined, I think you might enjoy reading it anyway and enjoying it as you would a tour of a widget factory; even if you're not worried about the details of the nuts and bolts, it's fun to see it done.…
September 20, 2009
The vast majority of the functions we've talked about over all these Sundays have been ones that are expressible as a relationship between two numbers x and y. Sometimes the relationship is simple, sometimes it's fairly complicated. Mostly though, we just work according to the function as though…
September 17, 2009
I note an interesting short piece by James Hrynyshyn about a bit of a local controversy in Nova Scotia about the installation of a tower to provide wireless internet to the area. Leading the opposition is a guy worried about the health effects:
"I think over a period of time it will change the DNA…
September 16, 2009
Let's say you've got a water molecule. It doesn't have to be water, but it helps if it's one we can easily picture:
You can imagine water vapor as an ensemble of many of these molecules flying and bouncing around in their container. This translational motion is not the only kind of motion they'…
September 14, 2009
One of my fellow ScienceBloggers, ScienceWoman, has made a few waves by saying the following:
I am against accommodating our full-time worker, part-time graduate student students by moving a significant number of our classes to evening hours. There I said it. I don't want to make life easier for…
September 13, 2009
Anybody heard of the idea of The Singularity? Roughly, it goes like this: technological progress builds on itself, and this self-reinforcing feedback loop is eventually going to come to a head where humanity makes a quantum leap into an unknowable and godlike transhuman technological future -…
September 11, 2009
Eight years ago today a terrorist group attacked and killed more than three thousand people. Nothing I can say can improve on what other have said in the memory of this horror, and nothing I can say will change any opinions about what followed.
I would, however, like to express my bitterness and…
September 10, 2009
All right, time for an actual example of this gravitational force law I've been ruminating on for the last two days. Today we'll look at an alternate version of the gravitational potential that's truly screwy:
The first thing to notice is that it's not finite as r becomes very large. Among other…
September 9, 2009
One of the first great discoveries of modern physics was Newton writing down the equation for the force of gravity between two massive objects. The discovery was monumental not because it was complicated, but because it was profound. You can state the law in plain English very briefly. "The…
September 8, 2009
I'd like to do a little bit of classical mechanics, but the particular thing I want to do is a little hefty for one post. We'll split it in two. Today I'll set the stage and tomorrow we'll use it to solve an interesting problem.
The problem involves the orbit of a planet in a gravitational field…
September 7, 2009
At this rate I should change the name of this feature to Monday Function, but with any luck I can get my weekend schedule back to something approaching normal and break this streak of late SFs. But hey, every day is a good day for math.
This function is one we can define in a piece-by-piece way.…
September 4, 2009
What do we think about nuclear power? Benjamin Cohen of The World's Fair is not a fan. I am.
Modern nuclear power has a lot going for it. In no particular order, here's the reasons that appeal to me.
It's reliable. No worrying about solar or wind availability, and it works anywhere.
It's safe…
September 3, 2009
"Why is the sky blue?"
It's one of those questions that most people don't know the answer to, while others know at least the basic explanation that the atmosphere scatters blue light more strongly than the other visible wavelengths. Ask why that happens and you'll enter the realm of some…
September 2, 2009
Anybody still read newspaper comics these days? I do, but sadly for the newspaper business I read them online. Worse, usually in the context of people making fun of them. On the other hand, there are a few gems out there. Is Spider-Man one of those gems? Uh...
Well, Shakespeare it ain't. But…
August 31, 2009
This guy is Allo Diavolo:
He was a circus daredevil. At the dawn of the 20th century he worked on a number of stunts dressed in his ominous horned outfit. These days a lot of people, including me, have heard of him as an example in the pages of physics textbooks. In my case it was Halliday and…
August 30, 2009
I think we've developed a nice theme over the last few weeks, gradually working our way through a less well-behaved function - the triangle wave - and trying to find various series expansions for it. "Well-behaved" is kind of a term of art, which mathematicians use as shorthand for long strings of…
August 28, 2009
We've seen that it's pretty easy to determine your latitude using the sun as a reference point. All you need is a shadow and chart that was easily available to sailors of previous centuries and you're set. Finding your longitude is another story. The reason for the difference in difficulty is…
August 27, 2009
Holy moly, if you want to see a great post you should read Ethan's post on the solar analemma. If you photograph the sun in the sky at the same time each day, it won't be in the same spot. The orbital motion of the earth, your location on the curve of the earth, and the tilt of the earth's axis…
August 26, 2009
Not much meat here at the Built on Facts table today. Our research group is embarking on a new project with the Office of Naval Research, and today was the official all-day meeting with the officer in charge of coordinating the various projects in his part of the ONR funding structure. We've…
August 25, 2009
Sorry for the two-day delay. The personal business to which I alluded kept me out until yesterday morning, delaying this post until today. I hope it's decent for all that!
This week, the same function as last week. There's nothing so special about the function itself, but it does serve as a nice…
