mspringer | October 20, 2008
There's famously dozens of ways to measure the height of a building with a barometer. If you're sufficiently clever, you can think of many, many more ways to measure temperature with just about anything.
One of the most visually impressive ways to measure temperature is the Galilean thermometer, which is also sometimes called the Galileo thermometer. It consists of little fluid-filled glass bulbs immersed in another liquid. The suspending liquid is itself encased in a long glass tube. Hanging from each of the glass bulbs is a marker with a temperature label. Look at the temperature on…
mspringer | October 19, 2008Time for a vacation! Grab a globe of the earth and pick a random number between 0 and 180 degrees for your latitude and between 0 and 360 for your longitude and set off on your vacation. It's exciting! You're bound for anywhere on earth, and every obscure location has the same probability of being chosen!
"Not so fast," the stern voice of vector calculus intones. "In fact not every location is equally probable. You're most likely to be visiting one of the polar regions if you pick a location using your method."
Why is this? Picture abstractly a globe of the earth with a latidude and…
mspringer | October 18, 2008The standard Saturday random observations:
Via Adventures in Ethics and Science, a quote from Revere of Effect Measure:
A wag once commented (and I have quoted here often) that to expect a scientist to understand the philosophy of science is like expecting a fish to understand hydrodynamics.
I disagree. Expecting a scientist to understand the philosophy of science is like expecting a professional quarterback to understand the hot dog vendor.
Here's an interesting article from Inside Higher Ed on the economic contraction and college growth. Among its conclusions is that colleges may have to…
mspringer | October 17, 2008Let's say you have a thousand of your friends in a large field, and every one of them has exactly two coins - one penny and one dime - in his pocket. Or her pocket, as the case may be. No exceptions, they all have those and only those two coins. Now imagine nearly the same situation with a thousand friends, but this time five hundred of them have two pennies and five hundred of them have two dimes. You don't know which ones have which, but you do know for a fact that any given person has two of the same coin.
If you take a random sampling of people and ask them to randomly select exactly…
mspringer | October 16, 2008I follow cheerfully; and, did I not,
Wicked and wretched, I must follow still
Whoever yields properly to Fate, is deemed
Wise among men, and knows the laws of heaven.
- Euripides
Wise advice as quoted in the Enchiridion of Epictetus. With that in mind, let those of us to the right of center contemplate the coming abyss with calm composure. Some things are in our control and others not, Epictetus tells us. This election is in the latter category. In the absence of a truly shocking and unexpected surprise, senator Obama is the next president of the United States.
We would like to have…
mspringer | October 15, 2008This week I'm teaching rotational motion to my students. Here's an easy problem from their textbook, which comes from the idea of using a flywheel to store energy. I'm modifying it from problem 9.41 in Young and Geller:
Suppose we want to built a flywheel in the shape of a solid cylinder or radius 1.00m using concrete of density 2.2 x 103 kilograms per cubic meter. What must its length be to store 2.5 MJ of energy in its rotational motion, if for stability its speed is limited to 1.75 seconds for each revolution?
That seems a little slow - I bet some decent engineering could get it a lot…
mspringer | October 14, 2008Mark C. Chu-Carroll at Good Math, Bad Math has an excellent post in which he mercilessly dispatches the misbegotten idea that infinity is a number. It's not.
How do we know? He explains it very well, but the fundamental thing to remember is that number is a word, and like all words it has a specific meaning. The words we use in mathematics and science have to be very carefully defined to make sure we're all talking about the same thing, and the definition of infinity is simply not even remotely compatible with the definition of number.
To take an extreme example, if you define dragon as "A…
mspringer | October 13, 2008The Feynman Lectures are the bible of physics.
Because it's the definitive and authoritative sacred text? Nope. Because everyone has it but not many people have actually read it. This is too bad. The lectures are a fantastic way to learn about physics.
Richard Feynman was a brilliant physicist, one of the true titans of modern science. Unlike most great scientists, he was also tremendously charismatic, a ladies man, musician, adventurer, and a skilled popular writer. Sometimes science snobs look down on the cult of Feynman popularity, but this is just sour grapes. The man really was…
mspringer | October 12, 2008Quick! Add up all the numbers between 1 and one trillion, inclusive!
The story goes that the great Carl Friedrich Gauss in his days as a little kid in late-18th-century German primary school was told with the rest of his class to add up the numbers from one to one hundred. The teacher was probably tired of the little squirts and wanted to keep them busy for a while. Gauss is in solid contention for the title of Smartest Man Who Ever Lived, so it took him a few seconds. Not because he was a arithmetic savant - most mathematicians are not unusually good with actual numbers - but because he…
mspringer | October 11, 2008This post is skimpy, that is. No scantily-clad women, though I bet it would drive up traffic!
The post is skimpy because yesterday I spend several hours grading exams and six more driving to Louisiana. No time to write a good post and do the usual Saturday random observations and links. But usually everything on my blogroll is very good, and I can assure you that you'll enjoy your time spent around the physics blogosphere.
To hold you over until tomorrow's Sunday Function, here's the inimitable genius Richard Feynman discussing just exactly what physics is. Enjoy, and have a great weekend…
mspringer | October 10, 2008I see that bailout is working wonderfully. Of course if it hadn't passed and the stock market had behaved identically, we be hearing that we were fools not to pass the bailout. And they would be wrong. Yes, I know God Emperor Paulson hasn't actually used any of his trillion dollar blank check yet. It won't make a difference. Give a cowboy all the expensive equipment in the world and he still won't be able to herd clouds. C'est la vie.
There's nothing to be done about that though so let's talk about gravity. The force due to gravity between objects with masses M and m is given by the…
mspringer | October 9, 2008#6 - Ernest Rutherford
The New Zealand physicist Ernest Rutherford was an incubator of genius, and a genius himself. His position on this list is probably a little unorthodox as he wasn't a very flashy scientist and he wasn't a theoretical wizard. He just happened to be a surpassingly great physicist anyway.
When Rutherford started his work in the late 1800s, modern physics was still quite new. Classical mechanics had been fleshed out reasonably well, but relativity and quantum mechanics didn't exist, and the world of the microscopic was very poorly understood. The very concept that…
mspringer | October 8, 2008Physicists like to name things after their discoverers. Sometimes if there's a unit of measurement that doesn't have someone's name attached to it, they'll grab the name of somebody who worked in that field and use it. Let's take a look at some units, first a few examples not named after people:
Length - meter
Mass - kilogram
Time - second
There's a couple more slightly obscure units not named after people, but most units are named after somebody. Sometimes repeatedly:
Temperature - Kelvin, Celsius
Current - Ampere
Electric Potential - Volt (the guy's name was Volta, but close enough)…
mspringer | October 7, 2008How'd the test go? Eh, ok I think. In particular I vapor-locked on a pretty easy question involving transforming E & B fields to another reference frame. There was another question where you had to prove that the energy-momentum tensor was Lorentz invariant, and I didn't get that one either. The rest were pretty good as far as I can tell.
Momentum happens to be what's currently being taught in Physics 201, which of course I'm a TA for this semester. Having done force and energy already, momentum's not too hard to describe. Momentum is just mass times velocity. Unlike forces, there'…
mspringer | October 6, 2008Today is Judgment Day number 1 of 3. "Why today, and why are there three of them?" you ask.
Well ok, I exaggerated. It's just the first of three exams in my electromagnetic theory class. Let's see what's on the test... "special relativity, Lorentz covariance of Maxwell's equations, scalar and vector potentials, gauge invariance, relativistic motion of charged particles, action principle for electromagnetism, energy momentum tensor"
It's not as bad as it sounds. The test does have to be doable in two hours, despite containing eight or so problems. I'm not super-comfortable with all this…
mspringer | October 5, 2008As we get closer to Halloween, let's take a look at one of the few functions that might cause a stir in Salem. I give you the Witch of Agnesi, for several values of its free parameter a:
The Witch is a geometric construction involving triangles that's easier to show than describe:
(Both images are from the Wikipedia article)
Geometric construction though it is, you can also write it in closed form as a standard old function of x:
Why did this seemingly mundane function merit such a creepy name? It was originally named by the Italian mathematician Maria Gaetana Agnesi, who called it la…
mspringer | October 4, 2008
This is of course from the 1939 World's Fair. It represents the era of perhaps the most optimistic vision of science held by the public, from back when Progress was spelled with a P. The war put things on hold for a few years, and then we had a decade or so of glorious Streamline Moderne before the public image of science fell apart and science became just another occupation; thought about fairly rarely and with a volatile combination of appreciation and suspicion. But it was nice while it lasted.
I assume it was. The era was over two decades before I existed. I've always had a taste for…
mspringer | October 3, 2008Thursdays I'm not a fan of, because I teach two classes back to back. Since both classes are associated with a lab, that's six continuous hours in front of a chalkboard. Teaching I like, but six hours without a stopping leaves me pretty beat.
That's probably why in high school and below the teacher teaches for some smaller amount of time and then has the students do work on their own. In college there's just too much that has to be said, so such a strategy would be impossible even were it not a waste of student and professor time.
This week more tiring than most. I'm teaching the 201…
mspringer | October 2, 2008A quick aside: via professor Bernstein at Volokh Conspiracy comes this delightful quote, regarding the reason for the specific $700,000,000,000 figure in the bailout bill:
"It's not based on any particular data point," a Treasury spokeswoman told Forbes.com Tuesday. "We just wanted to choose a really large number."
Sigh.
Now back to your regularly scheduled program.
You know about electric and magnetic fields. You experience them in daily life: electric fields push current through all the electrical devices you encounter in your day, as well as sticking lint to your clothes and shocking you…
mspringer | October 1, 2008
We talk about the earth rotating on its axis. We say the same thing about tops, and spinning basketballs, and gyroscopes, and car tires, and pretty much everything else that spins. Rotations happen around an axis.
Well, except that they actually don't.
No, I'm serious. Rotations happen in a plane, and the fact that a plane happens to correspond to a unique perpendicular axis is just a lucky coincidence that occurs in three dimensional space and nowhere else. The earth rotates in the plane of its equator. If you want to make a rotation in 4-d or higher space, you'll actually need to…