Standard Deviations From the Beaten Path

Bad Science writer Ben Goldacre wrote about how “Guns don’t kill people, puppies do,” where he points out some ways in which the probabilities of things can be a bit confusing. An extremely common example, which was messed up by a British newspaper, is the probability of multiple people (siblings in this case) sharing a birthday.

Like he says, the trick is that it doesn’t matter when the first child was born, only that the next two were born on the same day. This is a trivial case in which the binomial coefficient simply cancels out the leading 1/365. In general, though, you can use the binomial coefficient (sometimes called “n choose k”) to calculate probabilities where you can get the same result in multiple ways.

So if you’re guessing the suit of a hidden playing card, you have a 1/4 chance of guessing correctly. If you guess for 10 different cards and get 5 correct, you might be tempted to say your feat was as likely as , and that you might have psychic powers. What you’re missing, though, is the number of ways you could have guessed correctly, , which means the probability of correctly guessing half the cards was 0.058. You could still be psychic, but now it doesn’t seem quite as likely.

Tune in later for a crash-course introduction to P-values and hypothesis testing, so we can conclude with more certainty one way or the other on your psychic abilities.

I have ideas kicking around all the time for things I want to write about, but more often than not they’re derailed because my LaTeX support has again been broken or something else is wrong. So if all goes according to plan, the next line should contain the differential form of Ampere’s Law with Gauss’ correction:

Feel free to see if it works in the comments. I have no idea if it’s even supposed to. Put equations between double $ and proceed as usually if you’re TeX savvy.

I’d be remiss in my duties if I failed to post a link to Jorge Cham’s recent PHD comic about the use of polls and statistics in the news media. He hits the proverbial nail on its proverbial head. Also, if you haven’t read the comic before, it will be an amusing and whimsical dark comedy to those who have not experienced grad school, and a humorously whimsical reflection of the dark, bleak reality that is graduate school for those who have.  Has anyone seen my thesis topic?

Two Wi-Fi (what does that even stand for, anyway?) stories from recently.

1. A device that claims to get power from Wi-Fi.
2. A man who claims his neighbor’s Wi-Fi signal makes him sick.

I doubt the plausibility of both of these claims. A run-of-the-mill household wireless router is rated by the manufacturer as having a total power output of 15 dBmW. This is a logarithmic scale describing the power output of radiative devices in such a way that the same units can be used for very powerful and not so powerful antennas. In good old SI units, this is about 32 mW.

Electromagnetic waves typically propagate isotropically. That is, wavefronts take the form of spheres expanding in every direction from the point of origin at the speed of light. When we talk about the power of a transmitter we’re usually talking about the power obtained by integrating over the size of the wavefront. So the power is the same from any point that is the same distance from the antenna, but constantly decreasing with distance. Because the wavefront is spherical, the rate at which the power density falls off is one over the square of the distance.

An order of magnitude estimate for the power of an FM radio station is 100 kW. How  far away would we have to be from the radio station in order to see the same power density (watts per meter squared) as we would 1m away from the Wi-Fi router? About 1.8 km (1.1 miles). So I might ask, does being near a radio station make the electromagnetically sensitive gentleman ill? One mile isn’t an unreasonable distance to be from a transmitting tower. And if it’s possible to pick up power from a 32 mW signal, why hasn’t it been developed for FM radio earlier? And what’s the efficiency? Is 32 mW (assuming you’re right next to the transmitter) enough to charge a battery, anyway?

Fear not, I have not strayed from the one true path and still adhere to the practices of the Church of Emacs. For the last six years or so, though, I have stuck by the XEmacs fork. I’m at least going to pretend that six years ago it did things that GNU Emacs couldn’t that  I wanted it to do. In the process of setting up my main work computer with Arch Linux, a departure from my longtime Debian/Ubuntu preference, I encountered problems getting my editor buffed into the same shape I’m used to.

So I’ve gone GNU. Read the rest of this entry »

A couple of links for you. These are many years old in Internet Years, but what can you do?

Chili peppers burn your butt. As said in the linked Boing Boing article, what’s not to love about a graph entitled “Effect of chili consumption and placebo on anal burning in the first 7 days after sphincterotomy”.

Big Numbers and Air Travel. Mark lays out how incomprehensible big numbers are to people and relates it to the fantastically huge number of flights that arrive safely at their destination. And might make you scarred of the dentist the next time you need a filling.

I hope everyone had a fantastic solstice season. I spent a week visiting family in Arizona, including a day trip to Sedona, woo-woo capital of the United States. Each visit there I feel like I should really write something about it, and I have a few ideas that will probably require some time I don’t have to do research. What I wanted to say today, though, is on a slightly more serious note. As you almost certainly know by now, Umar Farouk AbdulMutallab attempted to detonate plastic explosives on a Northwest Airlines flight from Amsterdam to Detroit.

The result is that another set of inane restrictions are being placed on innocent American travelers. As Joel Johnson at Gizmodo has pointed out, TSA is providing a line of defense against plans so specific as to be nearly useless in screening. I already have to take my shoes off thanks to the shoe bomber. I can’t take the kind of hair gel I like with me unless I check a bag thanks to the perpetrators of the (completely implausible) 2006 liquid explosives plot. On top of that, I have to take my laptop out of it’s bag thanks to some supposed threat so archaic I honestly have no idea what it was.

As the Gizmodo article quoted, the two biggest factors keeping us safe are the reinforcement of cockpit doors and passengers identifying and taking out threats on their own. So these new rules that forbid having anything in our laps and having to hold it in for the last hour on international flights are, in my opinion, only slightly less idiotic than requiring that a brave Dutch man be on every international flight since it was Dutch passenger Jasper Schuringa who tackled the perpetrator on flight 253. If my dime-store science fiction paperback book is a threat, arrest me when we’re all safely on the ground.

CDMS stands for Cold Dark Matter Search. The experiments objectives are to find evidence for the existence of dark matter–matter that we have so far only been able to see due to its gravitational interaction–that is low in kinetic energy, as opposed to “hot” dark matter like neutrinos. The most compelling form of dark matter are Weakly Interacting Massive Particles, or WIMPs. They’ve just released their 2007-2008 results, which you can find here, straight from the source: http://cdms.berkeley.edu/

So what have they seen? One strong point of CDMS is a very intense understanding of their background, that is, events that look like they could be coming from WIMPs, but probably aren’t for a variety of reasons. So after all is said and done and they’ve isolated the WIMP signal they are left with two events. But this still doesn’t mean they’ve discovered dark matter! In their arXiv paper they go on to say that there is a 23% probability of background creating two or more events in the region that would get past their filters. So there’s about one out of four chances that it was missed background, so as they say, “These expectations indicate that the result of this analysis cannot be interpreted as significant evidence for WIMP interactions, but we cannot reject either event as signal.”

And hopefully your excitement is not oscillating too rapidly, but in case your disappointed by the news that no especially compelling evidence for WIMP interactions has been found, they will be able to set some awesome upper limits on the WIMP-nucleon cross-section.

Some people will have you think that we atheists are out to fight a war against the most Christian of Christian holidays: Christmas. See that? Christ is right in the title. If we face the facts, though, it becomes obvious that one thing sitting at the very heart of the problem is that everyone has a solstice holiday. Many of these are described as a “festival of lights”. Proceeding with great sarcasm, there could not possibly be a common thread linking them, could there?

Before I continue I’ll let you know that I’m going to pull quotations from the King James Version unless otherwise specified. My motivation for doing so is because it is an available (if not always accessible) translation, and is also popular enough that many people will have some familiarity with it. If you’re one of the odd ones like me who doesn’t have a pulp copy of a translation you prefer, there are others available on the web. I know of NET Bible, and will use it when a different perspective is necessary.

Christmas Trees — Well as it turns out a religious rite practiced in the bible is quite similar to what we now call the Christmas tree. It was a pagan thing and in Jeremiah 10:2-5 God tells the Israelites not to do it:

Thus saith the LORD, Learn not the way of the heathen, and be not dismayed at the signs of heaven; for the heathen are dismayed at them.

For the customs of the people are vain: for one cutteth a tree out of a forest, the work of the hands of the workman, with the axe.

They deck it with silver and with gold; they fasten it with nails and with hammers, that it move not.

They are upright as the palm tree, but speak not: they must needs be
borne, because they cannot go. Be not afraid of them; for they cannot do
evil, neither also is it in them to do good.

So there you have it. Don’t be afraid of decorated trees used in a religious way, but they won’t save you, either (kind of like the supposed narrator, actually). Alright, so if one mention is insufficient for the idea to gain traction, I’ll also point you toward Isaiah 40:19-20, and 44:14-16 in which we are warned further of graven images in the form of trees and other worshipful acts associated with these.
Read the rest of this entry »

Are you in a warm, dry environment? If so, go open your refrigerator door, stand there for a few seconds and get something out if you’d like. Wait a short while, another few seconds or so. Maybe long enough to pour a glass of water if you’re the kind of person who keeps that in your refrigerator. Now try to open the door to your refrigerator again. Feel that? It’s hard, or at least harder to open!

For those of you who are either not living in a desert or pretty much anywhere in the northern hemisphere at the moment this will probably not do much of anything, so  I guess you’ll just have to take my word for it. But what you would be experiencing is the creation of a pressure difference between your kitchen and your refrigerator. The why isn’t particularly hard to understand, although it is a little unintuitive.

So, let’s start with a refrigerator, shall we?

The air inside is cold(er) and the air outside is warm(er), and dry. After opening the door, warm air is introduced to the interior, mostly by way of the closing door itself. Once the door is closed, the warm dry air cools rapidly. Cool air takes up less space than warm air (the same reason hot air balloons can fly), so what you wind up with is a rather surprising pressure difference between the inside of the refrigerator and the rest of the kitchen.

You might be wondering. Why dry air. Water takes up way less space than water vapor, so wouldn’t you get a stronger vacuum that way? Well, yes and no. If you had a really tight seal on your ‘fridge that could work. The problem is that the phase transition has an overhead so you’d need a bigger temperature difference to achieve the same effect and is also slower. The dry air is so effective because it can cool down and “shrink” rapidly compared to the rate at which pressure is exchanged  by the seal on the door.

This was an incredible source of amusement while I was in Argentina for a couple of weeks. Someone would open the refrigerator to extract the bottle of water, say, pour a glass, then walk back with the bottle in hand to return it. Except the pressure difference was so great, it took two hands to open the door. An entire evening was passed trying to explain this physically, so I figured I had to share.