Forums find GamesWithWords

A number of forums have picked up the WhichEnglish quiz, and have produced some really intelligent and insightful conversation. I recommend in particular this conversation on metafilter. There is also an extensive conversation at hacker news and a somewhat older discussion at reddit. And there is a lot of discussion in Finnish and Hungarian, but I have no idea what they are saying...

Peaky performance

Right now there is a giant spike of traffic to GamesWithWords.org, following Steve Pinker's latest tweet about one of the experiments (The Verb Quiz). I looked back over the five years since I started using Google Analytics, and you can see that in general traffic to the site is incredibly peaky.

The three largest single-day peaks account for over 10% of all the visitors to the site over that time period.

Moral of the story: I need Pinker to tweet my site every day!

Is Dragon Dictate a believer?

I've been using Dictate to take notes on Talmy's Toward a Cognitive Semantics. One of the example sentences is as follows:

I aimed my gun into the living room. (p. 109)

I cannot by any means convince Dictate to print this. It prefers to convert "my gun" to "my God". For example, on my third try, it wrote:

I aim to my God into the living room.

Dictate offers a number of alternatives in case its initial transcription is incorrect. Right now, it is suggesting, as an alternative to "aim to my God":

aimed to my God
aim to my God and
aim to my god
aim to my gun
aimed to my God and
aim to my garden
aimed to my god
aimed to my gun
aim to my guide
aim to my God in
aimed to my God in 

Perhaps Nuance has a religious bent, but I suspect that this is a simple N-gram error. Like many natural language processing systems, Nuance figures out what word you are saying in part by reference to the surrounding words. So in general, it thinks that common bigrams (2-word sequences) are more likely than uncommon bigrams.

According to Google, "my god" appears on the Web 133,000,000 times, whereas "my gun" appears only 8,770,000 times. So "my god" is just much more likely. Similarly, "aim to" is fairly common (215,000,000) hits. So even though "aim to my God" is gibberish, the two components -- "aim to" and "my god" -- are fairly common, whereas the correct phrase -- "aimed my gun" -- is fairly rare (138,000 hits). (The bigram "aimed my" is also infrequent: 474,000 hits).

N-gram systems work better than most everything else, which is why Nuance, Google, and many other companies use them. But examples like this show their deep limitations, in that they make many obvious errors -- obvious to humans, anyway. In this case, because Nuance doesn't know what sentences mean, and doesn't even know basic grammar, it can't tell that "aimed to my god" is both grammatically incorrect and meaningless.

Fair Use & FedEx

And now for something completely different:One private citizen's trials and travails trying to convince FedEx to print posters.

I have wanted a map of Hong Kong on my wall for some time. The Survey & Mapping office of the Hong Kong government helpfully provides some free maps for public use on their website. You will notice how the website helpfully includes a "free maps"logo, along with a copyright notice forbidding only commercial use of the map. Presumably they thought this was a good way of providing some publicity for the Special Administrative District.

They did not take into account FedEx Office. I put this map on a USB stick and went to the FedEx Office at Government Center to have it printed. The manager there refused to print it as I didn't have proof of copyright ownership. I showed him the website (particularly where it says "free maps"). He said the fact that the map is free for public use was irrelevant; he needed a signed document from the copyright owner (the government of Hong Kong) stating that I, personally, had the right to print off the map.

His explanation for his refusal was simple: "I can't get between me and the copyright holder." I pointed out that he was getting between me -- who wants to print the map -- and the copyright owner -- who also wants me to print the map. He repeated that even so, he "can't get between me and the copyright holder." This was just repetition, so I pointed out again that the map is clearly labeled for public use. He said that was just "he said/she said" business; what he needed was a signed document.

I'm curious what he would do with a signed document in Chinese, and whether he would require a notarized translation. I realized as I was leaving that at the beginning when the manager was trying to establish whether I had the right to print the map, he had asked me if I was a member of the organization that made the map -- that is the Hong Kong government. I'm curious what would have happened if I had said yes.

The "copyright waiver"


This is not the 1st time that I've had a run-in with the copyright police at FedEx. Last year the Palo Alto FedEx refused to print a poster that I was supposed to present at a conference at Stanford. I study story comprehension in small children, and a common practice is to use stories about familiar characters. In this case, I had stories about Dora the Explorer and a few other cartoon characters. Because my poster showed an example of one of the pictures that we had drawn to go with the stories, FedEx initially refused to print the poster, saying that it violated copyright.

After a long discussion about fair use and noncommercial uses, one of the employees remembered that they have a “copyright release” form that they can use in these circumstances. Unfortunately, they couldn't find any blank copies. One enterprising employee simply wrote the words “copyright release” on a piece of paper and asked me to sign that piece of paper.

I wasn't sure about the wisdom of signing and essentially blank piece of paper (you can see a photo of it on the right), so they came up with another plan, which was to whiteout all the writing on a previously filled out form, which they then copied (not waiting for the whiteout to dry and getting white out all over their copier in the process) and which I signed. Then they printed my poster and I went on to have an otherwise successful conference.

Copyright and FedEx

Clearly somebody has instilled the Fear of the Lord into the  employees at FedEx with regards to copyright infringement. FedEx is understandably concerned about their liability, since unlike me, they have actual assets. I also realize that FedEx may not have the resources to have somebody on staff who has been adequately trained to deal with copyright issues ... but in that case, it suggests that maybe they do not have the resources to run a print shop. After all, it is not like they are not making determinations now. They are just doing it randomly and incorrectly.

Zeno

Many people are familiar with Zeno's paradox, though probably not in the form presented by XKCD:

(If you aren't familiar with it or need a refresher, just follow the link above.)

Perhaps this is widely known, but I only recently discovered what the point of Zeno's paradox was: he was trying to prove that motion is impossible. Nothing ever moves and nothing ever changes.

This probably sounds absurd, but it was the basis of a philosophical school of which Zeno was part. Zeno created a number of paradoxes, all of which were meant to demonstrate that if the idea that nothing ever moves or changes is absurd, well then it is no more absurd than the idea that things do move and do change. If motion was possible, you would end up, for instance, with Zeno's never-ending race.

This is just another demonstration that many famous philosophical ideas are often remembered now for reasons very different from the reason for which they were first put forth.

(Insight gleaned from Anthony Gottlieb's excellent The Dream of Reason).

Ethics

I'm doing my periodic re-certification on research ethics. One of the questions on one of the quizzes is as follows:

TRUE/FALSE: A good alternative to the current peer review process would be web logs (BLOGS) where postings where [sic] papers would be posted and reviewed by those who have an interest in the work.

Apparently, the correct answer is "false". Presumably because we have much better technology for this kind of thing, rather than using a simple blog? 

Nature, Nurture, and Bayes

I generally have very little good to say about the grant application process, but it does force me to catch up on my reading. I just finished several papers by Amy Perfors, who I think does some of the more interesting computational models of language out there.*

A strange sociological fact about language research is that people generally come in two camps: a) those who don't (really) believe language is properly characterized by hierarchical phrase structure and also don't believe in much innate structure but do believe in powerful innate learning mechanisms, and b) those who believe language is properly characterized by *innate* hierarchical phrase structure and who don't put much emphasis on learning mechanisms. But there's no logically necessary connection between being a Nativist and believing in hierarchical phrase structure or being an Empiricist and believing in relatively simple syntactic forms. In the last few years, Perfors has been staking out some of that (largely) unclaimed territory where hierarchical phrase structure and Empiricism meet.

In "The learnability of abstract syntactic principles," she and her colleagues consider the claim by (some) Nativists that children must have an innate expectation that language be something like a hierarchical context-free grammar because there isn't enough data in the input to rule out alternative grammars. (Empiricists often buck the whole question by saying language is no such thing.) Perfors et al. show that, in fact, with some relatively simple assumptions and a powerful (Bayesian) learning device, the learner would conclude that the most likely representation of English is a hierarchical context-free grammar, based on relatively little input (reproducing what happened in linguistics, where linguists came to the same conclusion). You do have to assume that children have the innate capacity to represent such grammars, but you don't need to assume that they prefer such grammars.

"Joint acquisition of word order and word reference" presents some interesting data bearing on a number of questions, but following the theme above, she notes that her model does not require very much data to conclude that the typical word-order in English is subject-verb-object. She and her colleagues note: "The fact that word order can be acquired quickly from so [little data] despite the lack of bias [for a particular word order] may suggest no need to hypothesize that children are born with strong innate constraints on word ordering to explain their rapid acquisition."

I'm sympathetic to all these points, and I think they bring an important perspective to the question of language learning (one that is not, I should say, unique to Perfors, but certainly a minority perspective). What I can't help wondering is this: she (and others) show that you could learn the structure of language based on the input without (certain) innate assumptions that the input will be of a particular sort. Fine. But why is the input of that particular sort across (most? all?) languages? One thing the Nativist positions Perfors argues against have going for them is that they give a (more or less) principled explanation. Empiricists (typically) do not. (I am aware that some try to give explanations in terms of optimal information structure. What I have seen of this work has not struck me as overwhelmingly convincing, but I admit I haven't read enough of it and that I am willing to be convinced, though my prior on this line of argumentation is fairly low).


*My quasi-journalistic training always makes me want to disclose when I know personally the people I am writing about. But psycholinguistics is a small world. It would be safe for the reader to assume that I know *all* of the people I write about to one degree or another.

*********
Perfors A, Tenenbaum JB, & Regier T (2010). The learnability of abstract syntactic principles. Cognition PMID: 21186021

Maurits, L., Perfors, A., & Navarro, D. (2009). Joint acquisition of word order and word reference Proceedings o the 31st Annual Conference of the Cognitive Science Society, 1728-1733

New tags

Rather than write a new blog post (or my nearly-due BUCLD proceedings paper), I decided to revamp the post tags on this blog. Their usage has been inconsistent, which is making it harder and harder to find old blog posts that I want to link to.

Hopefully the new and improved tags will also be useful for you, dear reader. Now if you want to find any of my articles on the academic career path, on animal language or on universal grammar -- just to give a few examples -- they are only a mouse click away.

In addition to standard tags, there are also a series of tags beginning with the preposition "on". These appear on most posts now and are more meta-thematic than the others.

Mendeley -- Not quite ready for prime time

Prompted by Prodigal Academic, I decided to give Mendeley a shot. That is, instead of working on a long over-due draft of a paper.

Mendeley is two things. First, it is a PDF library/reader. Second, it is a citation manager.

Currently, I used Papers for the first and Endnote for the second.  Both work well enough -- if not perfectly -- but it is a pain that I have to enter every paper I want to cite into two different programs.

(Don't tell me I could export my Papers citations library to Endnote. First, I'd have to do that every time I update my library, which is annoying. Second, Papers was created by someone who clearly never cites books, book chapters, conference proceedings, etc. So I'd have to fix all of those in Endnote ... every time I export.)

(Also, don't tell me about Zotero. Maybe it's gotten better in the last year since I tried it, but it was seriously feature-deficient and buggy beyond all belief.)

First glance

At first, I was pleasantly surprised. Unlike Papers, Mendeley is free so long as you don't want to use their Cloud functionality much (I don't). Papers is convinced there are people named Marc Hauser, Marc D Hauser, M D Hauser, and M Hauser. Mendeley can be led astray but has some nice options to allow you to collapse two different author records -- or two different keywords.

(On that note, my Papers library has implicit causality, Implicit causality and Implicit Causality all as different keywords. Once Papers has decided the keyword for a paper is, say, Implicit Causality, nothing on G-d's green Earth will convince it to switch to implicit causality. And its searches are case sensitive. Mendeley has none of these "features.")

Also, Mendeley will let you annotate PDFs and export the PDFs with your annotations in a format readable by other PDF viewers (if, for instance, you wanted to share your annotated PDF with someone). That's a nice feature.

These would all be nice additional features if the the core functionality of Mendeley was there. I'm sorry to say that the product just doesn't seem to be ready for prime time.

I typed "prime time" into Flickr, and this is what it gave me. Not sure why.

photo credit here.

Second glance

The first disappointment is that Mendeley does not have smart collections. Like smart playlists in iTunes, smart collections are collections of papers defined by various search terms. If you have a smart collection that indexes all articles with the keywords "implicit causality," "psych verbs" and "to read", then whenever you add a new paper with those keywords, they automatically go into the smart collection. This is very handy, and it's an excellent feature of Papers (except that, as mentioned above, my smart folder for implicit causality searches for the keywords "implicit causality," "Implicit causality" OR "Implicit Causality").

I suspect Mendeley doesn't have smart collections because it doesn't have a serious search function. You can search for papers written by a given author or with a given keyword, but if you want to search for papers written by the conjunction of two authors or any paper on "implicit causality" written by Roger Brown, you're out of luck. Rather, it'll perform the search. It just won't find the right papers.

Third glance

That might be forgivable if the citation function in Mendeley was usable. The idea is that as you write a manuscript, when you want to cite, say, my paper on over-regularization (18 citations and counting!), you would click on a little button that takes you to Mendeley. You find my paper in your PDF library, click another button, and (Hartshorne & Ullman, 2006) appears in your Word document (or NeoOffice or whatever) and the full bibliographic reference appears in your manuscript's bibliography. You can even choose what citation style you're using (e.g., APA).


Sort of. Let's say you want to cite two different papers by Roger Brown and Deborah Fish, both published in 1983 (which, in fact, I did want to do). Here's what it looks like:

Implicit causality effects are found in both English (Brown﹠Fish, 1983) and Mandarin (Brown﹠Fish, 1983)

At least in APA style, those two papers should be listed as (Brown﹠Fish, 1983a) and (Brown﹠Fish, 1983b), because obviously otherwise nobody has any idea which paper you are citing.

This gets worse. Suppose you wrote:

Implicit causality effects have been found in multiple languages (Brown﹠Fish, 1983; Brown﹠Fish, 1983).

Correct APA 5th Ed. style is, I believe, (Brown﹠Fish, 1983a, 1983b). Actually, I'm not sure what exactly the correct style is, because Endnote always takes care of it for me.

There are other issues. Mendeley doesn't have a mechanism for suppressing the author. So you end up with:

As reported by Brown and Fish (Brown﹠Fish, 1983; Brown﹠Fish, 1983), verbs have causality implicit in their meaning.

instead of

 As reported by Brown and Fish (1983a, 1983b), verbs have causality implicit in their meaning.

Nor does Mendeley know about et al:

Hauser, Chomsky and Fitch (Hauser, Chomsky﹠Fitch, 2001) put forward a new proposal....blah blah blah...as has been reported several times in the literature (Hauser, Chomsky﹠Fish, 2001; Brown﹠Fish, 1983; Brown﹠Fish, 1983).

That is, the second time you cite a paper with more than 2 authors, it doesn't contract to (Hauser et al. 2001). Unfortunately, there is no work-around for any of these problems. In theory, you can edit the citations to make them match APA style. Within a few seconds, a friendly dialog box pops up and asks you if you really want to keep your edited citation. You can click "OK" or click "cancel," but either way it just changes your carefully-edited citation back to its default -- at least it does on my Mac (the forums suggest that this works for some people).

It's possible that people who don't use APA won't have as many of these problems. Numbered citations, for instance, probably work fine. I've never submitted a paper anywhere that used numbered citations, though. So I either need to switch professions or continue using Endnote to write my papers.

Hopefully

One can hope that Mendeley will solve some of these issues. I found discussions on their "suggested features" forum going back many months for each of the problems discussed above, which suggests I may be waiting a while for these fixes. I do understand that Mendeley is technically in beta testing. But it's been in beta testing for over two years, so that's not really an excuse at this point.

Alternatively, maybe Papers will add a good citation feature (and discover books). Or maybe Zotero will confront its own demons. I'm going to have to wait and see.

It makes one appreciate Endnote. Yes, it's a dinosaur. No, it hasn't added any really useable features since I started using it in 2000. But it worked then, and it still works now. There's something to be said for that.

Your age

Who participates in Web-based experiments? I recently analyzed preliminary results from about 4,500 participants in Keeping Things In Mind, an experiment I'm running in collaboration with a colleague and friend at TestMyBrain.org.

One of the things we're interested in is the age of people who participate. Here is the breakdown:

Not surprisingly, the bulk are college age (particularly freshmen). There are still a sizable number in their 30s, 40s and early 50s, but by the 60s it drops off considerably.

And then there are the few jokers who claim to be 3 or 100.

This is pretty similar to the breakdown I usually see at GamesWithWords.org, except that I usually have fewer tweens and more people in their 60s. But the mode is usually 18.

What this means for the experiment is that people in their 50s on up are woefully underrepresented. We're continuing to run the experiment in the hopes that more will participate.

How to win at baseball (Do managers really matter?)

It's a standard observation that when a team does poorly, the coach -- or in the case of baseball, the manager -- is fired, even though it wasn't the manager dropping balls, throwing the wrong direction or striking out.

Of course, there are purported examples of team leaders that seem to produce teams better than the sum of the parts that make them up. Bill Belichick seems to be one, even modulo the cheating scandals. Cito Gaston is credited with transforming the Blue Jays from a sub-.500 team into a powerhouse not once but twice, his best claim to excellence being this season, in which he took over halfway through the year.

But what is it they do that matters?

Even if one accepts that managers matter, the question remains: how do they matter? They don't actually play the game. Perhaps some give very good pep talks, but one would hope that the world's best players would already be trying their hardest pep talk or no.

In baseball, one thing the manager controls is the lineup: who plays, and the order in which they bat. While managers have their own different strategies, most lineups follow a basic pattern, the core of which is to put one's best players first.

There are two reasons I can think of for doing this. First, players at the top of the lineup tend to bat more times during a game, so it makes sense to have your best players there. The other reason is to string hits together.

The downside of this strategy is that innings in which the bottom of the lineup bats tend to be very boring. Wouldn't it make sense to spread out the best hitters so that in any given inning, there was a decent chance of getting some hits.

How can we answer this question?

To answer this question, I put together a simple model. I created a team of four .300 hitters and five .250 hitters. At every at-bat, a player's chance of reaching base was exactly their batting average (a .300 hitter reached base 30% of the time). All hits were singles. Base-runners always moved up two bases on a hit.

I tested two lineups: one with the best players at the top, and one with them alternating between the poorer hitters.

This model ignores many issues, such as base-stealing, double-plays, walks, etc. It also ignores the obvious fact that you'd rather have your best power-hitting bat behind people who get on base, making those home-runs count for more. But I think if batting order has a strong effect on team performance, it would still show up in the model.

Question Answered

I ran the model on each of the line-ups for twenty full 162-game seasons. The results surprised me. The lineup with the best players interspersed scored nearly as many runs in the average season (302 1/4) as the lineup with the best players stacked at the top of the order (309 1/2). Some may note that the traditional lineup did score on average 7 more runs per game, but the difference was not actually statistically significant, meaning that the two lineups were in a statistical tie.

Thus, it doesn't appear that stringing hits together is any better than spacing them out.

One prediction did come true, however. Putting your best hitters at the front of the lineup is better than putting them at the end (291 1/2 runs per season), presumably because the front end of the lineup bats more times in a season. Although the difference was statistically significant, it still amounted to only 1 run every 9 games, which is less than I would have guessed.

Thus, the decisions a manager makes about the lineup do matter, but perhaps not very much.

Parting thoughts

This was a rather simple model. I'm considering putting together one that does incorporate walks, steals and extra-base hits in time for the World Series in order to pick the best lineup for the Red Sox (still not sure how to handle sacrifice flies or double-plays, though). This brings up an obvious question: do real managers rely on instinct, or do they hire consultants to program models like the one I used here?

In the pre-Billy Beane/Bill James world, I would have said "no chance." But these days management is getting much more sophisticated.

It appears I am in the right field

You Should Get a PhD in Science (like chemistry, math, or engineering)

You're both smart and innovative when it comes to ideas. Maybe you'll find a cure for cancer - or develop the latest underground drug.

What Advanced Degree Should You Get?

Why is losing $10 worse than winning $10 is good?

Losses loom larger than gains.

This useful mnemonic describes an odd experimental finding: if you have people rate on a scale of 1 to 10 how unhappy they would be to lose $100, that rating will be higher than if you ask them how happy they would be to win $100. Similarly, people tend to be reluctant to gamble when the odds are even (50% chance of winning $100, 50% chance of losing $100). Generally, if odds are even, people aren't likely to bet unless the potential prize is greater than the potential loss.

This is a well-known phenomenon in psychology and economics. It is particularly surprising, because simple statistical analysis would suggest that losses and gains should be treated equally. That is, if you have a 50% chance of winning $100 and a 50% chance of losing $100, on average you will break even. So why not gamble?

(Yes, it is true that people play slot machines or buy lottery tickets, in which, on average, you lose money. That's a different phenomenon that I don't completely understand. When/if I do, I'll write about it.)

A question that came up recently in a conversation is: why aren't people more rational? Why don't they just go with the statistics?

I imagine there have been papers written on the subject, and I'd love to get some comments referring me to them. Unfortunately, nobody involved in this conversation knew of said papers, so I actually did some quick-and-dirty simulations to investigate this problem.

Here is how the simulation works: each "creature" in my simulation is going to play a series of games in which they have a 50% chance of winning food and a 50% chance of losing food. If they run out of food, they die. The size of the gain and the size of the loss are each chosen randomly. If the ratio of gain to loss is large enough, the creature will play.

For some of the creatures, losses loom larger than gains. That is, they won't play unless the gain is more than 1.5 times larger than the loss (50% chance of winning 15.1 units of food, 50% chance of losing 10). Some of the creatures treat gains and losses roughly equally, meaning they will play as long as the gain is at least a sliver larger than the loss (50% chance of winning 10.1 units of food, 50% chance of losing 10). Some of the creatures weigh gains higher than losses and will accept any gamble as long as the gain is at least half the size of the loss (50% chance of winning 5.1 unites of food, 50% chance of losing 10).

(Careful observers will note that all these creatures are biased in favor of gains. That is, there is always some bet that is so bad the creature won't take it. There are never any bets so good that the creature refuses. They just differ in how biased they are.)

Each creature plays the game 1000 times, and there are 1000 creatures. They all start with 100 units of food.

In the first simulation, the losses and gains were capped at 10 units of food, or 10% of the creature's starting endowment, with an average of 5 units. Here's how the creatures faired:

Losses loom larger than gains:

0% died.

807 = average amount of food at end of simulation.

Losses roughly equal to gains:

0% died.

926 = average amount of food at end of simulation.

Gains loom larger than losses:

2% died.

707 = average amount of food at end of simulation.

So this actually suggests that the best strategy in this scenario would be to treat losses and gains similarly (that is, act like a statistician -- something humans don't do). However, the average loss and gain was only 5 units of food (5% of the starting endowment), and the maximum was 10 units of food. So none of these gambles were particularly risky, and maybe that has something to do with it. So I ran a second simulation with losses and gains capped at 25 units of food, or 25% of the starting endowment:

Losses loom larger than gains:

0% died

1920 = average amount of food at end of simulation

Losses roughly equal to gains:

1% died

2171 = average amount of food at end of simulation

Gains loom larger than losses:

14% died

1459 = average amount of food at end of simulation

Now, we see that the statistician's approach still leads to more food on average, but there is some chance of starving to death, making weighing losses greater than gains seem like the safest option. You might not get as rich, but you won't die, either.

This is even more apparent if you up the potential losses and gains to a maximum of 50 units of food each (50% of the starting endowment), and an average of 25 units:

Losses loom larger than gains:

1% died.

3711 = average amount of food at end of simulation

Losses equal to gains

9% died

3941 = average amount of food at end of simulation

Gains loom larger than losses

35% died.

2205 = average amount of food at end of simulation

Now, weighing losses greater than gains really seems like the best strategy. Playing the statistician will net you 6% more food on average, but it also increases your chance of dying by 9! (The reason that the statistician ends up with more food on average is probably because the conservative losses-loom-larger-than-gains creatures don't take as many gambles and thus have less opportunity to win.)

So what does this simulation suggest? It suggests that when the stakes are high, it is better to be conservative and measure what you might win by what you might lose. If the stakes are low, this is less necessary. Given that humans tend to value losses higher than gains, this suggests that we evolved mainly to think about risks with high stakes.

Of course, that's all according to what is a very, very rough simulation. I'm sure there are better ones in the literature, but it was useful to play around with the parameters myself.

The DaVinci stereogram

A few posts ago, I described how to make stereograms. At the end of the post, I showed a second type of stereogram, in which an illusionary white box appears to float in front of a background of Xs, and I promised to explain how that one was done.

This type of stereogram, discovered by Nakayama and colleagues, is called a "DaVinci stereogram" in honor of the famous artist/engineer who worked out the logic centuries ago (though he didn't, to my knowledge, consider building any stereograms).

The idea works like this: Look at an object (such as your computer monitor). Your left eye can
"see around" the left side of the object a bit more than can your right eye, while your right eye can see more of what is behind the object than can your left eye. It turns out that this information alone is sufficient to induce a perception of depth.









Consider that final stereogram (reproduced here). In both images, there is a white box in the center. However, the left image (the one presented to the right eye, if you use the divergence method) has four extra Xs on the right side of the box, while the right image (the one presented to the left eye) has two extra Xs on the left side of the box. This results in the perception of a white box floating above the background.

Try this at home: Make your own stereogram

Have you ever wanted to make your own 3D movie? Your own Magic Eye Stereogram? This post will teach you to create (and see) your own 3D images.

Magic Eye Stereograms are a relatively new technology, but they grew out of the classic stereograms created in 1838 by Charles Wheatstone. For those of you who don't know what a stereogram is, the word broadly refers to a 3D-like image produced by presenting different images to each eye.

The theory is pretty straight-forward. Focus on some object in your room (such as your computer). Now close one eye, then the other. The objects in your field of vision should shift relative to one another. The closer or father from you they are (relative to the object you are focusing on), the more they should shift.

When you look at a normal photograph (or the text on this screen), this difference is largely lost. The objects in the picture are in the same position relative to one another regardless of which eye you are looking through. However, if a clever engineer rigs up a device so as to show different images to each eye in a way that mimics what happens when you look at natural scenes, you will see the illusion of depth.

For instance, she might present the drawing below on the left to your right eye, and the drawing on the right to your left eye:










If the device is set up so that each picture is lined up perfectly with the other (for instance, if each is in the center of the field of vision of the appropriate eye), you would see the colored Xs in the center at different depths relative to one another. Why? The green X shifts the most between the two images, so you know it is either the closest or the farthest away. Importantly, because it's farther to the left in the image shown to the right eye, it must be closer than the blue or red Xs.

You can demonstrate this to yourself using a pencil. Hold a pencil perfectly vertical a foot or two in front of your face. It should still look vertical even if you look with only one eye. Now, tilt the pencil so that the bottom part points towards your chest (at about a 45 degree angle from the floor). Close your right eye and move the pencil to the right or the left until the pencil appears to be perfectly vertical. Now look at the pencil with your right eye instead. It should appear to slope down diagonally to the left. That is exactly what is happening in the pictures above.

A device that would fuse these two images for you isn't hard to make, but it's even easier to learn how to fuse them simply by crossing your eyes. There are two ways of crossing your eyes -- making them point inwards towards your nose, and making them point outwards. One way will make the green X closer; one will make it farther away. I'll describe how to use the first method, because it's the own I typically use.

Look at the two images and cross your eyes towards your nose. This should cause each of the images to double. What you want to do is turn those four images into three by causing the middle two to overlap. This takes some practice. Try focusing on the Xs that form the rectangular frames of the images. Make each of those Xs line up exactly with the corresponding X from the frame of the other image. If you do this, eventually the two images should fuse into a single image, and you will see the colored Xs in depth. One tip: I find this harder to do on a computer screen than in print, so you might try printing this out.

That is the basic technique. You should be able to make your own and play around with it to see what you can do. For instance, this example has a bar pointing up out of the page, but you can also make a bar point into the page. You also might try creating more complicated objects. If you want, you can send me any images you make (coglanglab_AT_gmail_DOT_com), and I will post them (you can try including them as comments, but that is tricky).

One final tip -- you'll need to use a font that has uniform spacing. Courier will work. Times will not.

Finally, here's another stereogram that uses a completely different principle. If you can fuse these images, you should see an illusory white box floating in front of a background of Xs. In a future post, I'll explain how to make these.