Radiation Chart

There’s a lot of discussion of radiation from the Fukushima plants, along with comparisons to Three Mile Island and Chernobyl. Radiation levels are often described as “<X> times the normal level” or “<Y>% over the legal limit,” which can be pretty confusing.

Ellen, a friend of mine who’s a student at Reed and Senior Reactor Operator at the Reed Research Reactor, has been spending the last few days answering questions about radiation dosage virtually nonstop (I’ve actually seen her interrupt them with “brb, reactor”). She suggested a chart might help put different amounts of radiation into perspective, and so with her help, I put one together. She also made one of her own; it has fewer colors, but contains more information about what radiation exposure consists of and how it affects the body.

I’m not an expert in radiation and I’m sure I’ve got a lot of mistakes in here, but there’s so much wild misinformation out there that I figured a broad comparison of different types of dosages might be good anyway. I don’t include too much about the Fukushima reactor because the situation seems to be changing by the hour, but I hope the chart provides some helpful context.

(Click to view full)

Note that there are different types of ionizing radiation; the “sievert” unit quantifies the degree to which each type (gamma rays, alpha particles, etc) affects the body. You can learn more from my sources list. If you’re looking for expert updates on the nuclear situation, try the MIT NSE Hub. Ellen’s page on radiation is here.

Lastly, remember that while there’s a lot of focus on possible worst-case scenarios involving the nuclear plants, the tsunami was an actual disaster that’s already killed thousands. Hundreds of thousands more, including my best friend from college, are in shelters with limited access to basic supplies and almost no ability to contact the outside world. If you’re not sure how to help, Google’s Japan Crisis Resource page is a good place to start.

Edit: For people who asked about Japanese translations or other types of reprinting: you may republish this image anywhere without any sort of restriction; I place it in the public domain. I just suggest that you make sure to include a clear translation of the disclaimer that the author is not an expert, and that anyone potentially affected by Fukushima should always defer to the directives of regional health authorities.

Parentheses

Every now and then, I stumble on a Wikipedia passage that makes me smile. I don’t usually share them, since calling attention to them almost certainly means they’ll be rewritten or deleted, but in this case I can’t resist. The following is from the Bracket article:

Parentheses may also be nested (with one set (such as this) inside another set). This is not commonly used in formal writing [though sometimes other brackets (especially parentheses) will be used for one or more inner set of parentheses (in other words, secondary {or even tertiary} phrases can be found within the main sentence)].[citation needed]

To the three anonymous editors who together wrote this paragraph, thank you for brightening my day.

Distraction Affliction Correction Extension

Lots of people have asked me for the system I used to implement the restriction in the alt-text of today’s comic.

At various times, I thought of doing it with an X modification, Firefox extension, a Chrome add-on, an irssi script, etc—but none of them worked too well (or involved a lot of sustained undistracted effort, which was sort of a Catch-22).  Then I hit on a much simpler solution:

I made it a rule that as soon as I finished any task, or got bored with it, I had to power off my computer.

I could turn it back on right away—this wasn’t about trying to use the computer less. The rule was just that the moment I finished (or lost interest in) the thing I was doing, and felt like checking Google News et. al., before I had time to think too much, I’d start the shutdown process.  There was no struggle of willpower; I knew that after I hit the button, I could decide to do anything I wanted. But if I decided to look at a website, I’d have to wait through the startup, and once I was done, I’d have to turn it off again before doing anything else. (This works best if your ongoing activities are persistent online—for example, all my IRC chat is through irssi running in screen, so turning off my laptop doesn’t make me sign out.)

Other ‘honor system’ approaches have never worked for me.  Blocking the sites (or keeping the computer off) didn’t work—I could always find a way to argue with myself. I’d decide this day needed to be an exception for some reason, think of a project that required the computer, or just grow frustrated after a few hours and get really curious about something I’d seen a website somewhere.  There’s some interesting research about novelty and dopamine, suggesting (tentatively) that for some people exposure to novelty may activate the same reward system that drug abuse does.  In my case, I felt like my problem was that whenever I was trying to focus on a (rewarding) project, these sites were always in the background offering a quicker and easier rush.  I’d sit down to write code, draw something, build something, or clean, and the moment I hit a little bump—math I wasn’t sure how to handle, a sentence I couldn’t word right, an electronic part I couldn’t find, or a sock without a mate—I’d find myself switching to one of these sites and refreshing.  Reward was briefly unavailable from the project, but constantly available from the internet.  Adding the time-delay removed the promise of instant novelty, and perhaps helped disconnect the action from the reward in my head.  Without that connection dominating my decisions, I could think more clearly about whether the task was really important to me.

Beyond that one rule, I put no other restrictions on myself.  Want to go read a 17-part Cracked article?  Fine!  Think you might have an important email?  Go check.  Feel like looking at Reddit for the 20th time today?  Go for it; you might find something interesting (hey, it’s where I found that dopamine article).  Want to play Manufactoria until your eyes bubble?  Absolutely.  The only catch is that you have to stare at a startup screen for 30-60 seconds first. (If you have one of those instant-boot laptops, you’re out of luck.)

It was remarkable how quickly the urges to constantly check those sites vanished. Also remarkable was that for the first time in years, I was keeping my room clean. Since the computer was no longer an instant novelty dispenser, when I got antsy or bored I’d look around my room for a distraction, and wind up picking up a random object and putting it away.

I’ve since relaxed this restriction; the family health situation I mentioned a while back has meant that I’ve had less free time lately, and when I do, mindless distractions have been welcome (thank you again to everyone who sent in games!). But just following this system for a short time was enough to break most of my distracting website habits completely, and when things return to normal around here I’ll probably start using it again.

There’s still a place for a browser extension, though.  A lot of peoples’ jobs require them to be on a computer running something all the time, or can’t shut down for other reasons, so my quick turning-the-computer-off trick won’t work for them.  None of my abortive attempts are worth building on, but if someone’s looking for a quick project, building an extension like this might be a good one.  It could let you impose a delay like this on loading a new page, or a page outside the current domain, or refreshing a page you’re already on (and no, just running the browser under Vista on a Pentium-133 doesn’t count).  If anyone makes a good one, I’d be happy to share it here .  Just post a link in the comments!

Trochee Chart

Here’s something I made as I drew today’s comic.  It’s a chart of Google results for “X Y” (in quotes) where X and Y are words from the first panel of the strip.  The first word is on the top, the second down the side (the opposite of the intuitive way, of course).

"Doctor Doctor" and "Jesus Jesus" are highest. The highest non-repeating combo is "Pirate Captain", followed by "Robot Monkey" and "Penguin Zombie".

I generated this using a Google API variable search tool developed by Eviltwin on #xkcd (I’m not linking to the tool so as to avoid potentially getting his API key revoked) Edit: He now offers the source and says it can be run without a key, and is happy to let people use it until Google does something. Not only is the API helpful in making these kinds of charts (which I spend more time doing than I care to admit), it also gives a roughly accurate count of results—in contrast to the Google search page.

The “number of results” count that Google gives when you search is clearly fabricated.  This is clear for a few reasons.  When Google says this:

Excellent!  That's a lot!

You can tell that it’s wrong first by scrolling to the end of the results.  When you get to page 32, it suddenly becomes:

I learned in AP Calculus that 316 is WAY less than 190,000.

This doesn’t usually matter, since nobody looks much past the first few pages of results, but it’s annoying if you’re trying to use the number of results as a measure of something.  When I was making the Numbers comic, I didn’t use the API, and there were a few graphs I had to throw out, crop, or put on an unnecessary log scale; otherwise, Google’s clumsy number-fudging made the graphs look nonsensical.  I can’t find a good example now (perhaps they’ve smoothed it out a bit) but when searching for things like “I was born in <X>”, the results for successive years would look something like this:

… 150 : 200 : 250 : 300 : 350 : 117,000 : 450 : 251,000 : 500 : 550 : 312,000 : 320,000 : 390,000 : 425,000 …

If you scrolled to the last page for each, you’d find that the smaller counts were roughly accurate, but the counts in the hundreds of thousands had no more actual results than their neighbors.

I suppose it’s remotely possible that these numbers are correct, there are no years with an in-between number of hits, and for some reason they’re just not showing you most of the promised pages when you try to flip through them.  But making this even less likely is the fact that the search API (which is apparently being deprecated and replaced right now) doesn’t return these bad numbers—it gives reasonable-looking results which seem to be roughly consistent with the number you come up with by navigating to the last search page.

So it really looks like there’s a certain threshold of result volume beyond which Google apparently says “screw it” and throws out a gigantic number.  I imagine this is probably due to incompetence rather than intentional deception; I’m sure it’s hard to generate pages quickly from many sources, and maybe for searches with a lot of results they don’t have time to get it all synced up.  So they fudge the numbers.  The fact that this makes it look like they have way more results than they do is presumably just an unintended bonus.

All in all, this isn’t a big deal and I don’t think there’s anything particularly evil about it. It does make it hard to use Google hits as an accurate gauge of anything, but I suppose if you’re trying to study something by seriously analyzing Google result counts, you have bigger methodological problems to worry about.

Edit: As Mankoff observes, it looks like the API sometimes *underestimates* the number of results, too.  For example, it still reports 0 results for “narwhal zombie”, when a regular search shows quite a few. Now, I notice, scrolling through them, that most either have some minor character/text in between the two words, or are related to the comic I just posted.  But at least one seems to date back to last year.

Submarines

I’m going through a rough period right now. There’s an illness in my family and I’m having a hard time focusing on anything but worrying and trying to take care of health stuff. Everyone is going to be okay, but it’s going to be a difficult four or five months, and I really appreciate your patience and understanding. I’m going to keep putting up comics, but I don’t how much else I’ll be able to work on.

To anyone I’ve been corresponding with, I’m sorry that I may be even more tardy than usual. While davean (the xkcd sysadmin/business manager) monitors the press@xkcd.com address, I know he only forwards to me a fraction of the huge flood of mail that goes there. If you’re trying to reach me personally about something, you can write to me directly at xkcd@xkcd.com, but I’m afraid I won’t able to reply to most of it right now.

I know there haven’t been any posts here in a while. Since most of my projects are on hold right now, I thought I’d share some pictures from one that’s almost done: an underwater ROV. Exploring lakes and oceans has always fascinated me, and while I’ve spent a lot of time snorkeling and free diving, in the end I’m more interested in sending robots than going myself.

I tried to build a couple of ROVs in high school out of scavenged R/C cars and spare parts, but none of them ever worked very well. Last summer, I got interested again and picked up an Inventivity ROV-in-a-Box:

Inventivity ROVIAB

It’s a very basic kit designed to use off-the-shelf parts as much as possible, to encourage people to play with the design or expand on it. I’ve gotten a lot of help and some cool ideas from the company founder, Dr. Karen Suhm, who coaches robotics teams in ROV-building competitions and generally knows everything about ROVs. The kit comes with a good set of underwater motors and a sensitive camera, and this summer I started modifying it to use an Arduino and joystick control, running the whole thing over Cat-5 cable (which significantly lightened the tether). This will also let me add other equipment, like a still camera, depth gauge, compass, and sonar.

It’s very close to being finished—I just have a couple wires to reroute and a leak to seal—but for now, here are some pictures from construction and testing:

Hello.

I made a coupler so the tether could be detached, and added a chamber to hold the Arduino, Ethernet shield, and motor control board. A Python script on the surface translates joystick values into motor speeds, and the Arduino has some code to listen to commands via the Ethernet and control the motors using three TLE-5206 H-bridges. The 5206s offer more protection than some other H-bridges—I initially used some smaller chips, and managed to blow out a couple. (Thank you to mpanetta of #sparkfun for hooking me up with the 5206s.)

A note to anyone who wants to build something like this: the Arduino isn’t actually capable of processing video, so you’ll need to either put an Ethernet camera and hub on the rover, or—if your camera isn’t digital—do what I did and divert two of the Cat-5′s twisted pairs to carry RCA video, running the Ethernet solely on the other half.

This canoe (and everything else in the shot) travels through time.

My friend Mike loaned his canoe for depth testing in Walden Pond, which is (according to data from the 1940s) the deepest lake in Massachusetts

It's about 90 feet down from here.

At the bottom of Walden, there are close to three extra atmospheres of pressure.

In this shot, read left to right.

The zip ties double as binary depth markers. This one is 14 meters.

Shlooooop.

This is the vacuum pump for sealing up wires passing into the sub (it’s sitting atop a draft of the online communities map). If you open up the exterior/water side of a cable and submerse it in a pool of marine epoxy, then apply suction to the dry interior of the sub, it sucks the epoxy through the cable, plugging it up completely. You can also use it to suck all the air out of a wine bottle with random objects inside. It’s fun to see how different materials react to a near-vacuum—particularly if you’ve just drunk a bottle of wine. I didn’t get much more done that day.

Lastly, here’s a clip of the bottom of Walden Pond, about 80 feet below the surface.  This was an unpowered pressure test—the sub was just dangling on a rope—so it’s not very exciting, but it was the only test where I could record the video feed:

The Walden lakebed is pretty dead—the material you’re seeing is flakes of debris stirred up by the sub. In other lakes, we’ve found cooler stuff.  In Seymour Pond on Cape Cod, we had huge catfish fish swim up to the camera and look at it, and we explored a sunken fishing boat on the bottom of Sheep Pond.  I’ve also learned that deck chairs apparently fall off docks all the time—the lakebed 20 feet below the dock on one lake was absolutely littered with them.  When I get a chance to send it to some more interesting places, I’ll be sure to share footage.

P.S. A belated thank-you to the NYC Makerbotters; after I posted comic #743, they fabricated and mailed to me an actual tiny open-source violin.

Miscellaneous

Color Survey

People have made some fun things with the color survey data already.  Howard Yeend did a 3D visualization, Gissehel made some maps out of the raw data, and Rune Grimstad made a color picker tool.  Also, Jacob Rus nerd sniped me with this, which is not related to the color survey but I’m sharing it anyway.

School-Building

Breadpig, the publisher of the xkcd book, is holding a survey to see where people want Room to Read to invest their remaining profits from the book.  If you want to vote, it closes at noon EST on Monday.

xkcd: Mobile Version

If you read xkcd on your phone, or you just prefer simple pages without a lot of clutter, check out m.xkcd.com.  It has a nice, clean design and should be capable of showing the alt-text in any browser (even Lynx, which can’t even show the comic). Report any problems with the site to mobile@xkcd.com.  Thanks!

Sex and Gender

I’ve gotten a few emails and /msgs about this so I really wanted to post a clarification.

When I put the color survey together, I was mostly interested in making maps and tables of color names; the opening survey was almost an afterthought. Elizabeth added a question about chromosomal sex, since it’s closely correlated with colorblindness (she’s one of the rare colorblind women).

We debated for a long time to find a wording of the question that would be answerable unambiguously by everyone, regardless of gender identification or any other issues.  In response to a friend who was suggesting we were overcomplicating things, she said, “I *refuse* to word the question in a way that doesn’t have a good, clear answer available for transsexuals, intersex people, and people who already know they have chromosomal anomalies.”  I felt the same way, and at the same time I didn’t want to assume everyone remembers what the hell chromosomes are. After hours of debate, everyone was happy with this:

Do you have a Y chromosome?

If unsure, select “Yes” if you are physically male and “No” if you are physically female. If you have had SRS, please respond for your sex at birth. This question is relevant to the genetics of colorblindness.

We didn’t add a question about gender identification, in part because I wasn’t really planning to do anything with the survey data beyond basic calibration and didn’t want to hassle people with more questions, and in part because gender is really complicated.  We recently programmed Bucket, the IRC chat bot in #xkcd, to allow people set their gender so he can use pronouns for them.  This ended up taking hundreds of lines of code, three pages of documentation, and six different sets of pronouns and variables, just to cover all the basic ways people in the channel with different gender identifications wanted to be referred to (even without invented pronouns like “xe”, which we vetoed).  And that’s just to cover the pronouns.  The role of gender in society is the most complicated thing I’ve ever spent a lot of time learning about, and I’ve spent a lot of time learning about quantum mechanics.

So when I wrote the survey, I really didn’t have anything in mind for the data. After it went up, I saw the DoghouseDiaries comic, and immediately wanted to investigate.  I was really amazed by the results, particularly the top-five list of colors, which came as a complete surprise.  Everyone agreed it was the most interesting of my results (at some point, my friends were sick of hearing me talk about hues and saturations) and I couldn’t resist publishing it somehow.

Originally, my post had a big wall of text discussing how all I had was chromosomal data, and that what the comic talked about was gender identification.  I rewrote this post a bunch of times, and ended up with roughly the wording that’s there now:

[...] realized I could test it (as far as chromosomal sex goes, anyway, which we asked about because it’s tied to colorblindness).

I didn’t want to spend a long time boring people about sex and gender (I’ll talk forever if you let me), but I also wanted to clarify that this was something I cared about and was trying to pay proper attention to.  I ran it by some friends before posting, and they approved; one specifically thanked me for adding that note.  So I figured I’d found a good balance.

But a number of people were still offended or upset by my use of the chromosomal data in a conversation about gender. Now, there are always going to be people upset about anything; as Ford Prefect said, “Fuck ‘em. You can’t care about every damn thing.” But this is an issue I really do care about, and one I spend a lot of time trying to get right—and I genuinely appreciate the guidance. If people were offended or feel I didn’t handle this right, I’m sorry, and it’s my fault. But it wasn’t for lack of caring.

And to anyone writing software that handles gender or sex information, it’s a good reminder that these questions are not always straightforward for everyone, and a little courtesy can do a lot to make someone feel respected.

Color Survey Results

Who in the rainbow can draw the line where the violet tint ends and the orange tint begins? Distinctly we see the difference of the colors, but where exactly does the one first blendingly enter into the other? So with sanity and insanity.
—Herman Melville, Billy Budd

Orange, red? I don’t know what to believe anymore!
—Anonymous, Color Survey

I WILL EAT YOUR HEART WITH A FUCKING SPOON IF YOU AKS ANY MORE QUESTIONS ABOUT COLORS
—Anonymous, Color Survey

Thank you so much for all the help on the color survey.  Over five million colors were named across 222,500 user sessions.  If you never got around to taking it, it’s too late to contribute any data, but if you want you can see how it worked and take it for fun here.

First, a few basic discoveries:

  • If you ask people to name colors long enough, they go totally crazy.
  • “Puke” and “vomit” are totally real colors.
  • Colorblind people are more likely than non-colorblind people to type “fuck this” (or some variant) and quit in frustration.
  • Indigo was totally just added to the rainbow so it would have 7 colors and make that “ROY G. BIV” acronym work, just like you always suspected. It should really be ROY GBP, with maybe a C or T thrown in there between G and B depending on how the spectrum was converted to RGB.
  • A couple dozen people embedded SQL ‘drop table’ statements in the color names. Nice try, kids.
  • Nobody can spell “fuchsia”.

Overall, the results were really cool and a lot of fun to analyze.  There are some basic limitations of this survey, which are discussed toward the bottom of this post.  But the sheer amount of data here is cool.

Sex

By a strange coincidence, the same night I first made the color survey public, the webcomic Doghouse Diaries put up this comic (which I altered slightly to fit in this blog, click for original):

It was funny, but I realized I could test whether it was accurate (as far as chromosomal sex goes, anyway, which we asked about because it’s tied to colorblindness) [Note: For more on this distinction, see my follow-up post]. After the survey closed, I generated a version of the Doghouse Diaries comic with actual data, using the most frequent color name for the handful of colors in the survey closest to the ones in the comic:

Basically, women were slightly more liberal with the modifiers, but otherwise they generally agreed (and some of the differences may be sampling noise).  The results were similar across the survey—men and women tended on average to call colors the same names.

So I was feeling pretty good about equality.  Then I decided to calculate the ‘most masculine’ and ‘most feminine’ colors.  I was looking for the color names most disproportionately popular among each group; that is, the names that the most women came up with compared to the fewest men (or vice versa).

Here are the color names most disproportionately popular among women:

  1. Dusty Teal
  2. Blush Pink
  3. Dusty Lavender
  4. Butter Yellow
  5. Dusky Rose

Okay, pretty flowery, certainly.  Kind of an incense-bomb-set-off-in-a-Bed-Bath-&-Beyond vibe.  Well, let’s take a look at the other list.

Here are the color names most disproportionately popular among men:

  1. Penis
  2. Gay
  3. WTF
  4. Dunno
  5. Baige

I … that’s not my typo in #5—the only actual color in the list really is a misspelling of “beige”.  And keep in mind, this is based on the number of unique people who answered the color, not the number of times they typed it.  This isn’t just the effect of a couple spammers. In fact, this is after the spamfilter.

I weep for my gender.  But, on to:

RGB Values

Here are RGB values for the first 48 out of about a thousand colors whose RGB values (across the average monitor, shown on a white background) I was able to pin down with a fairly high degree of precision:

The full table of 954 colors is here, also available as a text file here (I have no opinion about whether it should be used to build a new X11 rgb.txt except that seems like the transition would be a huge headache.)

The RGB value for a name is based on the location in the RGB color space where there was the highest frequency of responses choosing that name.  This was tricky to calculate.  I tried simple geometric means (conceptually flawed), a brute force survey of all potential center points (too slow), and fitting kernel density functions (math is hard). In the end, I used the average of a bunch of runs of a stochastic hillclimbing algorithm.  For mostly boring notes on my data handling for this list, see the comments at the bottom of the xkcd.com/color/rgb/ page.

Spelling and Spam

Spelling was an issue for a lot of users:

Now, you may notice that the correct spelling is missing.  This is because I can’t spell it either, and when running the analysis, used Google’s suggestion feature as a spellchecker:

A friend pointed out that to spell it right, you can think of it as “fuck-sia” (“fuch-sia”).

Misspellings aside, a lot of people spammed the database, but there were some decent filters in place.  I dropped out people who gave too many answers which weren’t colors used by many other people.  I also looked at the variation in hue; if people gave the same answer repeatedly for colors of wildly varying hue, I threw out all their results.  This mainly caught people who typed the same thing over and over.  Some were obviously using scripts; based on the filter’s certainty, the #1 spammer in the database was someone who named 2,400 colors—all with the same racial slur.

Map

Here’s a map of color boundaries for a particular part of the RGB cube.  The data here comes from a portion of the survey (1.5 million results) which sampled only this region and showed the colors against both black and white backgrounds.

The data for this chart is here (3.6 MB text file with each RGB triplet named).  Despite some requests, I’m not planning to make a poster of any of this, since it seems wrong to take advantage of all this volunteer effort for a profit; I just wanted to see what the results looked like.  You’re welcome to print one up yourself (huge copy here), but keep in mind that print color spaces are different from monitor ones.

Basic Issues

Of course, there are basic issues with this color survey.  People are primed by the colors they saw previously, which adds overall noise and some biases to the data (although it all seemed to even out in the end).  Moreover, monitors vary; RGB is not an absolute color space.  Fortunately, what I’m really interested in is what colors will look like on a typical monitors, so most of this data is across the sample of all non-colorblind users on all types of monitors (>90% LCD, roughly 6% CRT).

Color is a really fascinating topic, especially since we’re taught so many different and often contradictory ideas about rainbows, different primary colors, and frequencies of light. If you want to understand it better, you might try the neat introduction in Chapter 35 ofThe Feynman Lectures on Physics (Vol. 1), read Charles Poynton’s Color FAQ, or just peruse links from the Wikipedia article on color.  For the purposes of this survey, we’re working inside the RGB space of the average monitor, so this data is useful for picking and naming screen colors. And really, if you’re reading this blog, odds are you probably—like me—spend more time looking at a monitor than at the outdoors anyway.

Miscellaneous

Lastly, here are some assorted things people came up with while labeling colors:

Thank you so much to relsqui for writing the survey frontend, and to everyone else who sacrificed their eyeballs for this project.  If you have ideas and want to analyze these results further, I’ve posted the raw data as an SQLite dump here (84 MB .tar.gz file). It’s been anonymized, with IPs, URLs, and emails removed.  I also have GeoIP information; if you’d like to do geocorrelation of some kind, I’ll be providing a version of the data with basic region-level lat/long information (limited to protect privacy) sometime in the next few days. Note: The ColorDB data is the main survey.  The SatOnly data is the supplementary survey covering only the RGB faces in the map, and was presented on a half-black half-white background.)

And, of course, if you do anything fun with this data, I’d love to see the results—let me know at xkcd@xkcd.com.

Color Name Survey

I’d like your help for a color name survey!  The survey shows you colors, and you type a name (word or phrase) you might use for that color.  The names can be as broad or specific as you want.  The survey is here:

http://aram.xkcd.com/color/

My friend Elizabeth (relsqui on #xkcd) wrote the frontend. I’m doing the analysis, though I won’t go too deeply into the details or purpose (to the extent that it has one) for now so as not to bias peoples’ answers.  Of course, RGB is a small and relative color space which varies depending on the device displaying it, so this survey has its limits, but it’s produced some cool data so far.

If any of  you want to help, you can fill out a few quick questions (don’t worry if you don’t know the answers—they’re highly optional and just help with calibration) and then come up with color names.  There’s no end to the survey; the more you answer, the better the data.  Thanks!

P.S. I’ve added a few much-requested prints and two new posters (Movie Narrative Charts and Gravity Wells) in the xkcd store.  The prints of Comic #150 (Grownups) are marked backordered right now while I replace a batch that was printed wrong, but they should be shipping again within a week.

Math Puzzle

This cool puzzle (and solution) comes from my friend Mike.

Alice secretly picks two different real numbers by an unknown process and puts them in two (abstract) envelopes.  Bob chooses one of the two envelopes randomly (with a fair coin toss), and shows you the number in that envelope.  You must now guess whether the number in the other, closed envelope is larger or smaller than the one you’ve seen.

Is there a strategy which gives you a better than 50% chance of guessing correctly, no matter what procedure Alice used to pick her numbers?

I initially thought there wasn’t, or that the problem was paradoxically defined, but it turns out that it’s perfectly valid and the answer is “Yes.”  See my first comment for an example of one such winning strategy.

This puzzle is similar to, but not the same as, the two envelopes paradox.  For more time-devouring reading, see Wikipedia’s List of Paradoxes.