It’s 8/8/08, and I’m in a symmetrical mood. Enjoy this animation, created by Nobuyuki Kayahara, of a spinning dancer, and ask yourself this question: Is she spinning in a clockwise direction, or a counter-clockwise direction?

I’ll be honest: this picture freaks me out. Sometimes, she’s spinning clockwise; sometimes she’s spinning counter-clockwise. Sometimes her left foot stays on the ground; sometimes, it’s her right.

According to Yami McMoots, this is an example of bistable perception. There’s not enough information in the image to tell for sure which direction she’s really turning. But we can recognize a human when we see one. “When presented with stimuli that have two valid, mutually contradictory interpretations, your brain just picks one. Then, sometimes, it picks the other.”

I thought this was a hoax at first, and that the animation actually spins both ways, but this site set me straight. We can see the dancer as spinning clockwise or counter-clockwise, but our brains won’t allow us to see the ambiguity. Once we see what we identify as a human figure, our brains fill in all of the missing details. That’s why we can make smiley faces with punctuation marks.

It’s also why the effect of this Charlie Chaplin mask (via Mighty Optical Illusions) is so eerie.

The word of the week is smarter.

That links to the word “smart” but I deliberately chose the comparative form. Here it is in context:

Are You Smarter Than A 5th Grader?

Forgetting that the show in question tests knowledge and not intelligence, it may seem at face value to be a very silly question to ask in the first place. I would, however, argue that it is completely nonsensical, based on what we now understand about human intelligence. Making glib statements about who is smarter than whom ignores the wide range of ways that people can be smart.

In 1905, Alfred Binet, a French psychologist, created a diagnostic test to identify students who needed extra help in school. It was the misapplication of this test that led to the highly-flawed concept of IQ. Over the past century, the IQ has been used for purposes that range from merely misguided to downright ugly. For more on that, read The Mismeasure of Man by Stephen Jay Gould.

We really need to get past the idea that intelligence is something that can be ranked in a linear manner. In his landmark 1983 book Frames of Mind, Howard Gardner makes a case for the Theory of Multiple Intelligences, the theory that there are distinct and identifiable areas of intelligence that exist in the human mind, that are “independent of one another, and that … can be fashioned and combined in a multiplicity of adaptive ways by individuals and cultures.” Gardner identifies seven such intelligences, though he allows for the possibility that there may be others, and the conversation surrounding various other possible intelligences continues today. His original seven — Linguistic, Musical, Logical-Mathematical, Spatial, Bodily-Kinesthetic, and the two personal intelligences commonly referred to as Interpersonal and Intrapersonal — have gained wide acceptance among learning theorists and educators in the field.

And yet, as a system, we still judge student achievement solely from test scores in literacy and math, and cling to IQ as a meaningful measurement of a person’s intelligence.

After everything we’ve learned about the human mind, we should be smarter than that.

I invite my readers to take this awareness test and discuss in the comments:

My nephew’s drawing made the local newspaper today.

I’m really impressed by the juxtaposition of the different objects in the picture. This is a kid who likes to make maps, which apparently stimulates spatial thinking, so maybe it shouldn’t be a surprise.

It’s been a while since I’ve really written anything, but I’ve been busy with a number of things, mostly work related. I’ve also been working on a new resource for this website which should be available shortly. Watch this space!

Last weekend, I attended a social studies conference that I’ve been meaning to write about. One of the speakers was Phil Gersmehl, who discussed the latest research in spatial intelligence. It seems that there are now believed to be eight different types of spatial intelligence, each housed in a different section of the brain. He suggested that geography education, at an early age, could help to strengthen these abilities. I say, it’s never too late.

Via The Media Dude, here’s a geography game that will help you practice your map skills. His brother, The Boy Wonder, points us toward an old Nintendo game called Warehouse 18, which is less about dexterity and more about using spatial thinking to solve visual puzzles.

And yeah, I’ve been pretty busy with these, too.

Last night, Ken Jennings of Jeopardy! fame had a book signing event at the Barnes & Noble in Chelsea. There were probably around eighty people there. Ken spoke for a bit and took some questions from the audience. Then he hosted an informal trivia game, giving away a free copy of his new book, Ken Jennings’s Trivia Almanac, to the two winners.

After the event, he was signing books. He signed my free copy of the Trivia Almanac “To Bill — The Chelsea Barnes & Noble Trivia Champ!”

I mentioned that I was a regular reader of his blog and poster to his message board. He didn’t recognize the name, understandably, but when I said “Shakespeare Teacher” he lit up. He told me that he had been to the blog and was in admiration of the 3-D Pic Tac Toe puzzles. He told me “I wouldn’t have thought that was possible.” I had a good comeback. “I wouldn’t have thought it was possible to win 74 consecutive games of Jeopardy!”

I asked if he would sign my copy of his first book, Braniac, and he signed it “To Bill — My Pic Tac Toe Guru!” which absolutely made my day.

In person, Ken turns out to be exactly the nice down-to-earth guy you’d expect him to be from his public persona. It was a great pleasure to meet him.

Scott Malia of The Shakespeare Blog poses a question:

While Shakespeare appreciation might be near universal among writers, it begs the question of comparison. Who among today’s writers is what might be considered the twenty first century answer to him?

Malia goes on to make a compelling case for Aaron Sorkin. Look, Shakespeare is so much of a product of time and place, as well as genius, that there never really can be another. However, the same genius can manifest itself distinctly within any particular culture. Virginia Woolf wrote a famous essay about what would have happened if Shakespeare had had a sister with equal gifts to his. Can we imagine a Shakespeare born in our time? What would he do? Who would he be? I posted my own response:

I’m a huge fan of Aaron Sorkin, but I would instead nominate David Mamet. Writing for both stage and screen, Mamet has elevated the art of the dramatist to create a body of work that simulaneously embodies and trandscends his contemporary culture. His use of language has the natural credibility of truth, while at the same time making use of the subtle artifice of poetry. His subject matter ranges from insightful cultural criticism to the basest elements of humanity. If anyone from our time qualifies as today’s Shakespeare, I vote for David Mamet.

Anyone else have an opinion?

Who is today’s Shakespeare?

A game is considered to be “solved” when all of the possible moves have been mapped out in a mathematical tree and thus the perfect set of moves can be determined regardless of an opponent’s play.

Tic-Tac-Toe is a pretty easy one. You solved this as a kid. There are three opening moves - corner, edge, center. And then you work from there.

Connect Four was solved in 1988. That’s because those new-fangled computer thingies were starting to get some real power behind them. If you want to play Connect Four against the best opponent you’ve ever played in your life, check out the applet on John’s Connect Four Playground which is programmed to play flawlessly, based on a database of pre-determined best moves. But if you go first, and play just as flawlessly, you can beat it.

Checkers was solved this past April by researchers from the University of Alberta. You can play against Chinook, which will play flawlessly, but the best you can hope for is a draw. It doesn’t matter how amazingly good you are at checkers. You will never win. For me, there’s something a little disturbing about that.

Could chess be next? There are an incredibly large number of possible games, but it must be finite. And if it’s finite, then the tree must conceptually exist even if nobody has been able to come close to mapping it yet. Some see chess playing ability as intutive and creative, and not merely a number cruching process. But if number crunching continues to get better, it might evolve to the point where we get a chess-playing program as unbeatable as Chinook.

To be clear, we’re not talking about a really, really good chess-playing program. We have that now. We’re talking about a program that can access an exhaustive database of pre-determined best moves in order to ensure the most favorable outcome possible.

What do you think?

Will computers ever solve chess?

Ro has a thought-provoking post about the relationship between learning something and knowing it. Before I address that question, it might be worth taking a moment to consider what it means to know something.

What do we mean when we say we know something? For the individual, it might be the same as saying we unequivocally believe it. But is that enough? If Iago believes his wife has been unfaithful, and he has no evidence to support his belief, does that count as knowledge? Probably not.

Socrates argued that a belief must be justified to be considered knowledge. Othello might say that he knows his wife Desdemona has been faithful, because he has reason to believe in her love and trustworthiness. His belief is justified. But that doesn’t necessarily make it true, and so that probably doesn’t count as knowledge either. Knowledge must be both true and justified.

When we say someone else knows something, that might mean that they believe it and we believe it too. If Iago uses manufactured evidence to manipulate Othello into believing that Desdemona has been having an affair with Cassio, Othello can say that he knows that Desdemona has been unfaithful, because his belief is justified by evidence that has been presented to him. But we would not say that Othello knows it. He still believes it, but we do not.

Which brings us to the Gettier problem. Imagine that while Othello is being manipulated by Iago, Desdemona has been secretly having an affair with the Duke. Othello makes the statement that he knows Desdemona has been unfaithful. Does he know it? This time, his belief is both true and justified. And yet Gettier would not count this as knowledge, because Othello’s belief, while true and justified, is based on false evidence. He has no knowledge of the actual affair. Robert Nozick would point out that if the statement weren’t true, Othello would still believe it.

Now let’s go back and look at the question originally posed by Ro, which has to do with the relationship between knowledge and learning. If I say I learned something, that means I know it, which means I believe it. If I say you learned something, that means you believe it and I believe it. For example, President Bush got into a bit of trouble for including the following in the 2003 State of the Union address:

The British government has learned that Saddam Hussein recently sought significant quantities of uranium from Africa.

By citing the British government, Bush’s speechwriters sought to insulate the administration from claims they already knew were false. But by using the word “learned” they implied the word “knew” which means that Bush was essentially saying that he also believed that the statement was true. It was later discovered that the statement was not true, and that the Bush administration was aware it was not true at the time the speech was written. Saying “The British government has learned” did not provide the out they were hoping it would.

Ro’s other question was whether knowing something implies that one has learned it. A strict empiricist might say yes, but even John Locke allowed for some a priori knowledge gained through reason alone. The classic example is from René Descartes: Cogito ergo sum. I think, therefore I am. Is this knowledge? Was it learned?

Finally, I can also attest that it is possible to have learned something and not know it. I demonstrate this condition several times every day.

The Center on Education Policy released a disturbing new study this week, measuring the effects of No Child Left Behind:

The report finds that approximately 62% of school districts increased the amount of time spent in elementary schools on English language arts and or math, while 44% of districts cut time on science, social studies, art and music, physical education, lunch or recess.

Now, I’m pretty much appalled by all of the cutbacks, but I’ll leave the bulk of it to ScienceTeacher.com, SocialStudiesTeacher.com, and LunchTeacher.com. I’m ShakespeareTeacher.com, so I want to talk about arts education.

(And let’s make no mistake - the extra time being spent on ELA isn’t being spent on literature. It’s being spent on test prep, and more test prep.)

Arts education is absolutely essential for students preparing for the world that we’re currently living in. With the image continuing to gain dominance over the written word, people who can demonstrate artistic ability are highly marketable in today’s economy. From graphic designers to documentary filmmakers, those who can master today’s tools of communication are able to command a wider audience and expand their range of communication. In the connected world, this is real currency.

And even if all of that weren’t true, the arts teach us how to identify problems and sovle them with creativity and discipline. Those skills help us in any endeavor.

I came across a website for an artist named Jen Stark, who creates sculptures from construction paper that won’t help anyone pass a reading test any time soon. But they bring beauty into the world, which is worth at least a link from my blog. Take a look at her work, and tell me she didn’t have to develop some pretty sophisticated math skills along the way.

Or take French artist Huber Duprat, who recruited caddis fly larvae, who typically create protective shells out of silk and their surrounding materials, and placed them in an environment of gold flakes and precious gems. The result is a combination of art and science that boggles the mind. Click the picture below to see the video.

Or take a look at the Universcale by Nikon, an application of the mathematics of scale to allow human comprehension of the natural universe, and tell me your appreciation of it isn’t primarily aesthetic.

I wonder what Leonardo DaVinci would have thought about eliminating arts education to teach math. What would Shakespeare have thought about eliminating arts education to teach literacy? What would Descartes say about eliminating science to teach math? What would Hemmingway think of eliminating social studies to teach literacy?

Reading and math are important skills. But even if an educational system were somehow able to acheive 100 percent literacy and numeracy, and nothing else, it would still be a failure.