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.

They say a picture is worth a thousand words. But what if you only have room for 650? Enter “Content Aware Image Resizing” or the retargeting of images:

This is truly amazing, another step in the ongoing campaign to make images as dynamic as text in the XML Internet.

It does raise some questions about the medium of photography, though. This isn’t the first time images have been digitally altered to be sure, but there does seem to be a difference here. To begin with, a photograph should not be mistaken for reality. Photographers make choices, and a photograph is a selective representation of the world. A resized photograph, I would argue, is basically the same photograph. A cropped photograph is not, but it can be considered another photograph, as it is a different selective representation of the real world. A digitally altered photograph can no longer be considered a photograph in the same way, but it remains a visual representation of an imagined world.

What, then, is a retargeted image? It is a new concept for a new world. Take the example of the image of the two figures on the beach (about 46 seconds into the video). Resizing the image would make it hard to see the figures. Cropping the image would lose one of the figures. Retargeting the image keeps both figures in their current size, and loses only the beach between them. This may seem like an ideal solution, but what is lost is the distance between the two figures. That is a major element of this photograph. It was deleted, not for artistic or functional purposes, but for practical purposes, to help it fit better on the page. The thousand words represented by a picture can now be cut down to just the verbs and nouns. And one imagines this being one day automated, even built into Web browsers of the future – a future where everything is as adjustable as Quick Text Shakespeare, and with similiar nuance.

Even the phrase “Content Aware Image Resizing” gives me the willies in the same way that the term “content provider” seems to imply that the content is just one of many elements that make up a deliverable product. Under this system, Shakespeare was a content provider. And the process described in the video is not aware of content. For that, you still need a human.

I know I’ve blogged favorably about the changes the Internet is bringing to society, and many of them are inevitable, but others are not, and we have a responsibility to keep up with the changing definition of information literacy. Now we have one more question to ask ourselves when we see a photograph online.

I was originally posting this because I thought it was way cool. But I don’t want us to be so dazzled by the new technologies that come out that we stop asking the critical questions.

This spectacular “blue marble” image is the most detailed true-color image of the entire Earth to date. Using a collection of satellite-based observations, scientists and visualizers stitched together months of observations of the land surface, oceans, sea ice, and clouds into a seamless, true-color mosaic of every square kilometer (.386 square mile) of our planet. These images are freely available to educators, scientists, museums, and the public. This record includes preview images and links to full resolution versions up to 21,600 pixels across.

You can view the high-resolution image and more on the NASA website.

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 solve 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.

How long do you think it will be before science is able to develop a computer sophisticated enough to emulate the complexity of the human mind, and what would be the ramifications of such a computer?

Discuss.

I had wanted to post this clip from the Republican debate earlier, but didn’t want to ruin this week’s Headline Game. Giuliani was asked to respond to a harsh quote from a Catholic bishop about his stand on abortion. As he tried to answer, lightning began to play havoc with the sound system. The audience laughed as the candidates on either side of him, Romney and McCain, began to back away, and Guiliani made a joke about it.

Politics aside, it’s pretty funny. Check it out:

If you watch the rest of the clip, you can see Mike Huckabee’s defense of his earlier stance against evolution. He spins it hard, but then he ends with a quote that leaves little doubt about his position on the matter:

If anybody wants to believe that they are the descendants of a primate, they are certainly welcome to do it.

McCain and Giuliani seemed amused by that. We’ll see how it plays with the Republican base.

I don’t know. Let’s ask Fox News.

Seriously, I don’t know why I bother with Fox News. Every time I think I can walk away, I just keep getting sucked right back in. Maybe it’s because I’m concerned that so many people watch it uncritically that it’s actually doing great damage to our country.

The best we can do is to teach information literacy skills to our students. Are we doing that well?

How do they calculate the digits of pi?

I mean, they’ve calculated the number out to billions of places. When they get a billion digits out, how do they know they’re right? Just think about how incredibly precise that is. A quark’s diameter can be described in 18 decimal places, so surely a billion places is far beyond the realm of any practical scientific purpose or authentic human experience.

From a purely mathematical standpoint, pi is defined as the ratio between a circle’s circumference and its diameter. But the only way we have of measuring such things mathematically is by using pi.

Wikipedia has this article on the subject, but I doubt you’ll be suprised when I tell you it is not helpful to me. We could ask Daniel Tammet but he’d probably just tell us what the algorithm tastes like.

Anyway, if all this math stuff is boring to you, check out this discussion thread putting a more philosophical spin on the digits of pi:

“Somewhere inside the digits of pi is a representation for all of us — the atomic coordinates of all our atoms, our genetic code, all our thoughts, all our memories. Given this fact, all of us are alive, and hopefully happy, in pi. Pi makes us live forever. We all lead virtual lives in pi. We are immortal.” – Cliff Pickover

This means that we exist in pi, as if in a Matrix. This means that romance is never dead. Somewhere you are running through fields of wheat, holding hands with someone you love, as the sun sets — all in the digits of pi. You are happy. You will live forever.

Silly, perhaps, but technically true. And somewhere in the digits of pi, there’s a version of the Shakespeare Teacher who understands how they calculate the digits of pi.