No, Wikipedia’s editors aren’t guilty of bias (this time). It’s the featured article for today! Check it out! Of course if you read talk pages for long enough you will discover that Wikipedia does have a bias towards America, the English language and English-speaking countries, hurricanes (at least one was a tropical storm, though), and antarctic explorers. (Note: tongue planted firmly in cheek.)
I never got far enough learning German to tell you if there are different genders for “intuition” and “logic”, but that’s not what this is about, anyhow. Alex at A Most Curious Planet asks, “Is Science Sexist?” Chad at Uncertain Principles responds with “Huh?” Don’t worry he explains.
To me this is a question that is only slightly more sane than the faux-feminist accusation that science is a man’s way of knowing that suppresses an equal, but unexplainable (and actually fictitious) woman’s way of knowing. In terms of answering practical scientific questions, science is the way of knowing. As Chad points out, intuition isn’t separate from science, which is not strictly logic. Read the rest of this entry »
On this day, July 20th, in the year 1969 humans landed on the moon. This is, in my opinion the coolest thing that has ever happened. Before graduating to the level of adult nerd, as an adolescent nerd I read everything I could about space. There is nothing uncool about space. Cosmic rays come from space, and that has a lot to do with why I’m so excited to be studying them, but the most awesome thing about space is that we landed humans on the moon 41 years ago.
There were no computers, not by modern standards anyway. There were no robots. There was just pure, unadulterated human chutzpah and a whole bunch of really smart people who found a way to make it happen. That’s why I wanted to do science. I wanted to figure out how to make things happen. And I have. Duck tape and cable ties. So take some time today to reflect on how awesome space is. Here’s an article in wired with less snark and more pretty pictures.
I’m right an awful lot of the time. Being right isn’t about being loud, violent, or tenacious. Being right is about being willing to give up when your position becomes less certain. So often times I start out wrong, and only become right when someone points out my error. The challenge of being right that I have the easiest time seeing in myself and others is an unwillingness to give up a position that holds sentimental sway.
When I argued with friends about nuclear power or the population of the planet, I didn’t convince anyone of anything. Not because I was wrong, or because I didn’t have a well constructed argument, but because the people I was arguing with had an emotional investment in the subject. No amount of evidence will satisfy, because the fear of Chernobyl or the guilt of living a consumer-driven developed-world lifestyle makes certain unreasonable choices very appealing emotionally.
Sentimental attachment is a trap anyone can fall into. Sometimes the thought of something being true makes us feel good–whether it’s a supreme being, our immanent salvation by renewable energy, or anything that seems to justify a lifestyle choice we’re just not sure about otherwise. Usually the sign of such an attachment is a very defensive response to any kind of criticism, no matter how level. Instead of arguments structured around evidence, these defenses tend to to betray a feeling that the subject in question must be true no matter what.
I usually walk away. I don’t know if letting the sentimental devotee have the last word just lends them more wood for their fire, but I usually find that I can’t even get a direct response to my critique or a single citation of evidence, so it certainly feels like I’m waisting my time. I do know that when I’ve been the emotionally invested, I usually don’t back down until I get something from somewhere unexpected that makes me reflect on my own position. At least for me, the direct approach never works–so when dealing with others I try to back off when the emotions are running high.
My smug title bar makes it sound simple. How to be right? Don’t get attached to ideas–they can be wrong. It’s a lot easier to say than to do, but I think it might be even harder to know how to handle one’s self when confronted with an intensely emotional defense. For the defender, it’s just a matter of holding their ground against any onslaught. For the critic, it’s about communicating without damaging another person’s well-being and friendship.
This one only just barely slips in on-topic. I think I’ve mentioned before my almost unhealthy obsession with the nuttery of one R. Buckminster Fuller. His ideas are often patently crazy, but simultaneously inspiring, artistic, and utterly fascinating. He invented the geodesic dome and a whole host of other things, now mostly unused. So when my fabulous colleague told me about a book she saw at the store about a kid living with his grandmother who was obsessed with Fuller, I had to find it. Then I read it. And now I want to tell you what I thought about it, The House of Tomorrow by Peter Bognanni.
NPR talks to Dan Myers of Notre Dame University about the shortest possible game of Monopoly he and his son designed. It’s extremely unlikely. One player quickly moves around the board to buy Boarwalk and Park Place, then the other player draws a chance card to go to one of those properties with four houses on it and can’t afford the rent. Two turns per player.
Next project is reported to be finding the shortest possible game of Risk. It kind of makes me want to analyze Settlers of Catan or something.
http://www.npr.org/templates/story/story.php?storyId=127575676
I saw this one go around a bit on Facebook. Not sure how widespread it is.
Of all the humans who’ve ever lived, 6.4 percent are alive today. The sheer number of people is overwhelming natural systems, destroying biodiversity, and challenging efforts to control global warming. Earth’s population is rising at 80 million people per year – roughly the number of unwanted pregnancies. Solving the population problem means making every child a wanted child.
If we take another step back and look at how that number has changed over time we’ll see that it was over 2% for most of the 1960-70s and has been on the decrease ever since. Saying a large figure like 80 million people per year triggers panic, not because that’s bad, but because it’s a really big number and we’re not sure how to handle that information. It sounds bad, right? So I think this is just a scare tactic to convince people we need to put the hand brake on global population growth by making careful, sane family planning the norm (something we should do, just not for this reason) because Earth’s population is screaming out of control… when it’s not. Read the rest of this entry »
Remember those circular metal pieces you used to do your laundry back in college or graduate school? They had easily distinguished sides so that you could toss them in the air and let them land in one of two configurations, known for reasons now increasingly obscure due to a face lift on the American penny as “heads” or “tails”. Naturally, there is a 
chance of either outcome–or as I mentioned earlier, over the course of an infinite number of measurements you’ll get an even 50/50 split.
What I want to do next, is add another coin. Each coin can be heads or tails so we have a total of four possible configurations, HH, TT, HT, or TH, with 
probability of each. You can continue to add more coins, resulting in an ever increasing number of unique outcomes, increasing like 
for 
coins tossed. Let’s say, though, that you don’t really care in which order the events occur, only how many coins land heads up. In this case, you’re concerned with the number of possible combinations, as opposed to the number of permutations. We can find the number of combinations by first finding the number of permutations and dividing this by the degeneracy.
So if we’re interested in tossing coins and getting 
heads, we start with a choice of coins for our first flip, then 
for our second and so on until we have 
coins for the final of our heads. While there might be some initial despair, this can be easily summed up with the factorial as 
. As I mentioned, if we don’t care in what order the coins were flipped, we need to divide by the degeneracy. For heads, there are 
possible orderings, so the number of combinations of items sampled ax a time is given by 
, which is frequently called “n choose x”.
Probability: We can get probability from this quite simply. We know the probability of an individual event occurring, 1/2 in this case, and we know how many ways in which it can happen, so we combine these to get 
, where 
. The name “binomial distribution” arises from the binomial theorem, which tells us that the sum over all possible values of for 
must be one.
Mean: I’ll spare the mathematical justification for the mean and standard deviation, as these are not straightforward. We can, however, get these correctly with a bit of intuition. In the case of the coin tossing experiment in which 
, we expect to get half heads and half tails. So for trials, we expect 
of our outcome of interest leading to 
.
Standard Deviation: The intuitive tack to this one is a little less, well, intuitive. We can exploit a trick called “expectation of the square minus square of the expectation” to get the variance, 
. For a single coin flip, the mean of the square is just just 
. Conveniently, the square of the mean is 
. So we can calculate 
. For trials, it’s a simple sum so we can get the standard deviation for the binomial distribution 
.
Naturally, we don’t need a 
coin flip. It could work just as well for rolling dice where the probability of a particular outcome on one die is 1/6. If you’re sufficiently nerdy to have ever played the game Settlers of Catan, you might recall the dots under each number on the game board. These represent combinations on two dice that will yield that result. So really, any game in which you roll dice can be partially characterized by the binomial distribution. Next, we can take the limit as the probability becomes very small and arrive at the Poisson distribution, which is extremely useful for understanding the results of surveys and polls, so stay tuned for that.
On some level, statistics is the process of describing distributions, which help us describe the probability of an event given a certain set of circumstances. I’ll get into the particulars of a few different types of statistical distributions like the binomial, Poisson, and Gaussian distributions which are commonly used to describe scientific data. Before we get into that, though, I wanted to just talk a bit about the statistical distribution as a concept, particularly the idea of a parent distribution and a sample distribution.
A lot of physics boils down to trying to characterize a random processes. The ubiquitous, quintessential example is a coin flip. If you want to test the fairness of a coin you might flip it many times and count the number of heads. What you would have collected is a sample distribution from the parent distribution of the coin describing the randomness of the coin. If you attempt this experiment with a real coin, you will likely get something very close to the canonical distribution for a coin flip, the binomial distribution, because for a probability close to 0.5 the sample tends to lie very close to the parent.
For other distributions the important distinction becomes much more apparent. I threw together a little python script you can play with yourself that generates 100 numbers from a randomly seeded pseudo-random number generator. It’ll then plot these data on the same axis as the probability density function of the parent distribution. Potential results might look like this. The values of the mean and standard deviation for a Gaussian distribution are listed in the legend, as well as the calculated values for a sample of 100 “measurements”. A common convention is to refer to the statistics of the parent distribution by the Greek letters 
and 
and the sample statistics by the roman letters 
and 
(or 
for the deviance).
May 16th is recognized as the anniversary of the laser. Lasers are pretty cool–I’ve had the opportunity to work on the back-end to some laser systems for studying atmospheric aerosols. Which is a bit like saying I’ve had the chance to live in the same state with John Mellencamp, except I like lasers way more than I like John Mellencamp. Anyway. On with the list of cool laser links: