February 15, 2009
On the surface it's one of the most boring possible functions. Two straight horizontal lines: the Heaviside step function.
Usually denoted θ(x), it's equal to 0 if x is less than zero, and it's equal to one if x is greater than zero. At x = 0 exactly it doesn't really matter what it is for…
February 14, 2009
News from around the world of physics:
Near and dear to my heart is any clever experiment involving lasers. And via Swans on Tea, this one's a doozy. It's paddleball, but instead of a rubber ball you have a single atom. And instead of a paddle you have a beam of laser pulses. No string, so it's…
February 13, 2009
There was, if I am not mistaken, an episode of I Love Lucy wherein Lucy manages to get her head stuck in a metal teakettle. Ethel jokingly (I hope!) suggests that she put her head in the oven to heat up the metal so it will expand and she can fit her head out. A clever idea, not counting the fact…
February 12, 2009
In full early-90s nostalgia mode, you skate down the street in your roller blades. Your thrill at the excitement of the open road distracts you, and one foot goes off the pavement into the soggy soil beside the road. That foot immediately slows down due to the drag and as a result of the…
February 11, 2009
Every section of Physics 218 I've taught this semester has asked me about this question. Really it's less of a physics question than it is a math question, but either way it gives people fits. It's not all that surprising. While it seems like it should be simple, to most beginning students it's…
February 10, 2009
A little off the beaten path today, I'd like to present two poems by two physicists who were both on my Ten Greatest list. They're very different, one contemplative and loose in form, the other playful but more rigorous. It's an interesting comparison.
Untitled
Richard Feynman
There are the…
February 9, 2009
This one's from Young and Freedman, and I pick it out because it's both from the chapter I'm teaching and it's a great conceptual problem as well. (I've modified it slightly.)
A shotgun fires a large number of pellets upward, with some pellets traveling vertically and some as much a 1 degree from…
February 8, 2009
Continuing my series of basic concepts with middle school math will be tricky when we're doing a Sunday Function. But let's give it a shot, and see if we can keep it to that beginning level.
This function is pretty simple. You add reciprocals until you get reach whatever number n you've picked,…
February 7, 2009
And when he had opened the third seal, I heard the third beast say, Come and see. And I beheld, and lo a black horse; and he that sat on him had a pair of balances in his hand.
- Revelation 6:5
Well if everyone's going to talk about the financial crisis like it's the end of the world we might as…
February 6, 2009
Continuing our "basic concepts with no math" series, here's one of the most important for quantum mechanics and statistical mechanics.
To start, imagine a billiards table. It has an assortment of billiard balls, each numbered and colored differently. You can imagine randomly knocking them around…
February 5, 2009
Ok, so yesterday wasn't quite as basic as I planned on shooting for in this week or two of working on non-mathematical concepts. But the idea was too cool to resist. This isn't exactly a mathematically elementary subject either, but the concept can be grasped without needing to see the actual…
February 4, 2009
Standing on the edge of Niagra Falls you can watch the water pour over. Falling down the gravity of the earth, it exchanges its potential energy for kinetic energy by picking up speed. Some of that energy is extracted by turbines and lights the homes and businesses of Yankees and Canucks alike.…
February 3, 2009
As a graduate student, you're an adult on your own. You have to find a place to live, food to eat, and a way to get around. Like most of the necessities of life, these things cost money. Where to get it?
There's three major options.
1. Teaching Assistantships. You are hired by the department in…
February 2, 2009
Whew! Long weekend. Unfortunately, due to work/procrastination the post I wanted to write still isn't ready. But today I'm also teaching 1d accelerated motion to my Physics 218 students, and that's interesting of itself.
One of the things I try to do is give problems that help build instinct…
February 1, 2009
First, a very quick and simple introduction to recursion. Here's an example. Pick a positive whole number n. The factorial function in the product of all the integers between 1 and n. For some reason it's denoted by an exclamation point.
Now if you compute 5!, you don't need to repeat the…
January 31, 2009
[I'm foregoing the usual Saturday miscellany for a Very Special Built on Facts. It's important!]
Imagine a basketball sitting on the top of a hill. The slope of the hill is pretty gentle, and so you can roll the ball around a bit without the risk of it rolling away. But hit it too hard and it's…
January 30, 2009
Yesterday I spend a tremendous amount of time in a very snazzy lab shooting lasers through pyridine. Cool stuff, tempered by the fact that pyridine smells like what Dr. Frankenstein's lab would have smelled like if Dr. Frankenstein used organic chemistry instead of electricity, and also the thing…
January 29, 2009
The Second Law of Thermodynamics probably produces more confusion in the general public than most other physical laws that have percolated themselves into the collective consciousness. Not the least of these are all the seemingly disconnected ways of saying it, which vary in accuracy. Disorder…
January 28, 2009
Consider the turntable of an old record player. Or equivalently, a CD affixed to a player so that it may spin freely. We'll pretend there's no friction, though as always reality will manage to generate some. Now stretch your imagination a bit further and imagine that you shrink yourself down to…
January 27, 2009
In the comments of yesterday's post about the output of the sun, Carl Brannen brought up a good point:
By the way, in comparing your audience to cows and compost heaps is there some sort of message here? It's been 25 years or so but I recall that there was a certain time of year around which I'd…
January 26, 2009
The power output of the sun is often talked about in awe-inspiring terms. You'll be told that it's like a continuous thermonuclear blast, or that a tiny fraction of the tiny fraction of power that happens to hit the earth would support humanity's energy needs. It's all true. The light and heat…
January 25, 2009
There's some math here, I'd rate it at Calc 2 difficulty. If you don't know calculus, that's fine! The details will be obscure but I think you'll still appreciate the abstract beauty of the method.
Ok, pick a rapidly oscillating function. It doesn't really matter which, so as an example I'll…
January 24, 2009
Today I'm going to soapbox about something utterly inconsequential and only tangentially related to science. Apologies all around. It's the weekend though, so I trust you'll forgive a bit of a deviation from the usual!
The nominations for the Oscars are out, and generally it's a pretty mundane…
January 23, 2009
In the United States generally and to a much lesser extent in the UK and a few other countries you'll see some very old-school units of measurements. Miles, yards, pounds, fortnights, pints, gallons, and numerous others. Most of the rest of the world uses metric units, the primary variant of…
January 22, 2009
Thermodynamics and statistical mechanics hold a bit of an odd place in the heart and mind of a physics student. On one hand it's one of the few subjects with truly universal applicability. No matter if you work in galaxy clusters, nuclear theory, experimental solid state, or anything else the…
January 21, 2009
Reader Mike writes in with an interesting problem to work out. It runs thus:
You're in your car parked on the side of the road when you see your friend a distance d away, driving toward you at velocity v. You want to talk to him through your window, so what constant acceleration should you pick…
January 19, 2009
I think personally he is a good man who loves his family and loves his country. And I think he made the best decisions that he could at times under some very difficult circumstances.
- Barack Obama on George W. Bush, 1/16/09
There's no shortage of shortcomings in the administration of the forty-…
January 19, 2009
There's an interesting post over at Sentient Developments about the simulation argument.
The SA essentially states that, given the potential for posthumans to create a vast number of ancestor simulations, we should probabilistically conclude that we are in a simulation rather than the deepest…
January 18, 2009
One of the most important mathematical concepts in physics and pure mathematics is continuity. There's a formal definition for it which for the moment isn't too relevant, but for our purposes we can think of it in terms of smoothness. Put your finger at a point on the graph, and if the function…
January 17, 2009
When I was a young kid growing up in south Louisiana, my family would sometimes make day trips out to John C. Stennis Space Center. Located just over the border in Mississippi, it's a huge rocket testing facility in the middle of absolutely nowhere. It has to be. Rockets are LOUD. Isolated…
