Flatland - Exploring Other Dimensions

Plato's myth of the cave is an allegory that tries to make the point that there may be more to reality than meets the eye, that our experience is simply of a very limited and lowly aspect of reality. Given the knowledge and technology of the time, Plato's use of puppets and shadows in his ancient writing is brilliant in conveying the difference between the real and the apparent, but in the 1800's, Edwin Abbott took this idea much further, and in a way more rigorously and convincingly, as he was able to tell it through a creative exploration of mathematical space:

Compare the experience of a creature from three-dimensional space against one from a two-dimensional world. Easy, and completely reasonable to understand why the two-dimensional figure was skeptical of "more" dimensions, even if it was wrong, right? Well, apply the same reasoning to the difference between four-dimensional space and the three-dimensional space we're all used to. Wouldn't the reasoning you applied in the first case also apply to this one? And just like that time we were introduced to these ideas by the irreplaceable Carl Sagan, when he tried to show us the projection of a tesseract, here's a fun little animation to inspire your imagination and help you explore the beauty of mathematical space that can be understood by the mind even if it cannot be always perceived by the senses :)

Now, are there 'really' more dimensions than the three spatial ones we're used to or is this just a fancy mathematical abstraction? That's a topic for another discussion :p

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How to (and Why) Prove a Mathematical Theory

When it comes to the world of our sensory experience, the idea of "proof" is somewhat misplaced, since there is always the possibility of new evidence contradicting something we previously had every good reason to believe, not to mention the fact it could all be a dream or a simulation in The Matrix!

But in the world of abstract ideas, especially numbers, the kind of reasoning used there does lend itself to proofs because you get to specify exactly what you mean by a certain concept, and then all you have to do is follow a few rules of inference to deduce the logical consequences of your idea.

And we owe a debt of gratitude for the whole idea of theory and proof to the ancient Greeks, people like Pythagoras, Plato and Archimedes. But today we get to learn a little bit about the man who is widely considered the father of geometry, a title appropriate to the scope and importance of his work: he formalized the rules of geometry that mathematicians have relied upon for over two thousand years. That man was Euclid.

QED

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When Aliens Read the Socratic Dialogues

Apparently they get a different satisfaction from reading Plato:

Of course, that might either mean that they are intellectually superior to us, or that maybe they're semi-autistic engineers. Oh snap! :)

To be fair, at least two humans, Kierkegaard and Nietzsche, got the joke, except Nietzsche didn't find it very funny...

Via Saturday Morning Breakfast Cereal

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Woody Allen reads "My (Socratic) Apologies"

If you follow me on Google+, you may have noticed that there was recently a new trial for Socrates in which the previous verdict of guilty was overturned (by an impressively small margin). Philosophy was just barely vindicated by the new ruling. And people say we don't make progress :)

If that's too much seriousness, however, you may enjoy the following short story, written and read by none other than that philosophically-minded comic, Woody Allen, about certain dreams he's been having recently:

Hat tip to Tony!

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Christopher Hitchens - Philosophy and Booze

If you're familiar with the late Christopher Hitchens, you probably know that besides being a prolific writer, social commentator, public intellectual, fierce debater and a master rhetorician, the man loved his booze and his smokes.

In the following clip, and true to form, Hitch decides to give an impromptu performance of Monty Python's famous philosophers' song, which he sings/recites by heart.

Since my own memory sucks big time, that's really impressive :)

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Damon Horowitz - Philosophy in Prison

As you probably already know from this blog, TEDTalks are awesome: bring in some of the greatest minds in the world, working on the greatest and most interesting questions, with the best and most creative ideas, give them 18 minutes, and they will awe and wow you.

Well, when they brought in philosopher Damon Horowitz, he only needed about three minutes to inspire a standing ovation and blow everyone out of the water in what can only be described as one of the best TEDTalks of all time...

But you don't have to be in prison to study philosophy and be free. There are plenty of other practical reasons for deciding to study this mother of all intellectual disciplines.

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Philosophy Jam

I'm too busy to post any thoughtful entries at the time, so I'll just leave each of you to ponder what the hell the following philosophy jam is all about...

Warning: before you know it, this is going to be stuck in your head for days :)

And don't ask me what the footage had to do with the audio... I have no clue.
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