Olber's Paradox - Why Is the Sky Dark at Night?

I know that may seem like a silly question at first glance, but there is a long history of seemingly silly questions that end up producing some mind-blowing and really counter-intuitive results that really get us to question our most basic presuppositions about the nature of reality, and in many cases redefine our understanding of the universe. This case is no exception.

So back to the question, sure, the sun is hiding on the other side of the planet, but there are stars in literally every possible direction, so photons are hitting us all the time from every possible direction. But if this is the case, shouldn't the night sky look bright from all these stars?

Well, as the following simple animation brilliantly demonstrates, the sky really is bright from all those stars... we just can't see all that light, not with our eyes anyway, but it is there, and what that tells us about cosmology and the universe is absolutely fascinating!

Bet you didn't see that coming, huh? No pun intended, actually. I was just blown away by the connections. This stuff is awesome :)

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The Prisoner's Dilemma

One of the interesting aspects of social interactions is that our interests are not always aligned with those of other agents, and when the result of an interaction is a function of your choice and that of someone else whose motives may be different from your own, you face a dilemma... what to do?

Well, you kind of know what you'd like to do, but you also know what he'd like to do, and you know that he knows what you'd like to do, and so you think about what he's going to think you're going to do, so you try to anticipate that by doing something else, except that he probably realizes you're going to try to cheat him, so he's going to try to get you before you get him, lather, rinse, repeat ad infinitum and you're not one step closer to figuring out what to do.

One of the fascinating and paradoxical implications of trying to rationally maximize your own utility function is that, when confronted with certain scenarios, such as the famous prisoner's dilemma, and by virtue of pursuing your own individual interests, you end up screwing yourself more than if you simply decided to cooperate. Oh, but it's never that simple. Anyway, here's a basic introduction to the idea of the prisoner's dilemma:

Now, you may think that because you now understand how this dilemma works, you could beat it if you were to find yourself in such a scenario, but as Dilbert shows, that's not quite right (which is exactly why such scenarios are so interesting and why so many academics in all sorts of disciplines have devoted so much of their time to think about and research such cases):

In political philosophy, one of the most famous instances of a philosopher recognizing the nature of these interactions was Thomas Hobbes, who argued (a few centuries before game theory was actually invented... isn't it awesome how philosophy is so often way ahead of its time?) that the way to solve these problems is to make sure there is some sort of mechanism to enforce cooperation.

Hobbes' particular solution was that all rights should be transferred to a sovereign who would have a monopoly on power (and the violence that could be inflicted on defectors), but as the following absolutely brilliant and gripping game-show example demonstrates, there can be other ways to ensure cooperation:

Was that brilliant or what?!?

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Romney to Travel Back in Time to Kill Liberal Version of Himself

If you are a Republican, you're probably not all that thrilled with your presidential candidate Mitt Romney, what with more flip-flopping on political issues than a patient with multiple-personality disorder on meth. It looks like this guy will say anything for votes.

But if you're concerned about all the inconsistencies, fear not. The Onion reports that Conservative Romney plans to travel back in time to kill younger Liberal Romney and finally escape from the liberal precedents that have been haunting him for the past few years. And if you're concerned with a grandfather paradox type of scenario (in which current Romney would cease to exist were he to kill a younger version of himself), it looks as though that will not actually be quite the problem you might have thought :)

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To Infinity and Beyond

Apparently the title of this documentary also has something to do with Toy Story? Well, I haven't seen that movie, but I can tell you what this documentary is about... Infinity. The most obvious way to start thinking about infinity is through numbers: take any number, and you'll soon realize that there is no such thing as the biggest number because you can always add 1. No, a googol won't do it, nor even a googolplex or Graham's number. Yes, these numbers contain more zeros than there are atoms in the observable universe, but they still fall short, infinitely short, in fact, of infinity.

But the strangeness doesn't end there because infinity may not only be a mathematical conceptual idea: infinity raises all kinds of interesting scientific and philosophical questions and paradoxes (what Immanuel Kant called antinomies of reason) about the physical universe that even modern cosmology doesn't quite know what to do with: is space infinite? If not, what's beyond its edge? Infinite empty space? What about time? If it is, and the amount of matter in the universe is finite, then everything that could logically happen has happened, and will continue to happen, an infinite number of times... And hey, are there an infinite amount of universes? And as you'll see in this fascinating documentary, this is just the beginning of the weirdness:

For a fascinating treatment of the problems of infinity, check out the documentary Dangerous Knowledge.

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Schrödinger’s Cat... in 60 Seconds

We've seen in previous episodes of this 60-second Adventures in Thought series, all sorts of philosophical, logical, mathematical and scientific paradoxes and all-around weirdness. To remind you, we've seen Zeno's paradox concerning motion, the grandfather paradox concerning backward travel through time, John Searle's chinese room thought experiment concerning thought and computation, Hilbert's infinite hotel concerning different size infinities, Einstein's twin paradox concerning special relativity.

And finally, today we have Schrödinger’s Cat, that poor kitty whose bivalent fate rests upon the superposition of subatomic particles...

For a more serious treatment of Schrödinger’s Cat, check out Jim Al-Khalili's documentary Atoms: The Illusion of Reality.

And for more on infinities, you'll do your brain a favor by watching the excellent documentary Dangerous Knowledge.

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Hilbert's Infinite Hotel

If you study subjects like philosophy, cosmology or mathematics, it won't be long until you find yourself deep in the contemplation of the nasty little business of infinity.

Zeno's paradoxes of motion represent some of the earliest attempts to confront this beast, and although modern tools like calculus or the idea of an infinite sum seems to resolve the problem, I can't say that we've really solved it. It's more like we've brushed it aside and agreed to pretend it's been dealt with. Although I find myself on a small minority here, I still sympathize with Zeno.

One thought-experiment I've never been able to swallow, however, is Hilbert's Infinite Hotel. From the very beginning, it seems to want to assume premises that I would not want to grant... but this is not about me. It's about you, dear reader, and it's about exposing you to interesting ideas that will be worth your while to think about, so here's a short introduction:

And if you want more, check out the Grandfather paradox or the Chinese Room thought experiment.

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Time Travel and the Grandfather Paradox

Nothing beats boredom quite like philosophy. You start with almost any seemingly simple question, you do some heavy thinking, and before you know it, like when we were first introduced to Zeno of Elea (or even his mentor, Parmenides), it turns out motion may just be an optical illusion.

Now we get to explore the grandfather paradox. It's pretty obvious that if you wanted to kill your grandpa, a simple piece of technology like a pillow could get the job done. But what if you've suffered a lifetime of bad jokes, anachronistic war references, patronizing judgments for being 'metrosexual', and countless stories about how easy you have it now compared to a hundred years ago, when he had to walk five miles naked and barefoot through the snow so they could make it to school?

How could you get rid of the old geezer? Could you be so annoyed that you just get into your time machine and travel back to a time before he even met grandma and kill him right there and then? That would solve all the future annoying moments you've suffered for years... but wait, if you kill him before he meets your grandma, he can't knock her up with your dad, and if your dad is never born, then he obviously could not get your mom preggers with you, but then you would not be born, and if you're not born, how could you possibly travel back in time to kill gramps? Oy vay!

Ask the right questions, and a universe of fascinating opportunities opens up to you, or at least you get to kill boredom for a while. Either way it's a win-win.

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The Impossibility of Motion - Achilles and the Tortoise

There are many things most of us just take for granted as obvious or just plain common sense, and therefore as not worth wasting our time on. Philosophers, however, nit-picking bunch that we are, are insatiably curious, and in our search for some coherent grand theory of everything, usually mange to find trouble instead, of the conceptual kind, although there is also a respectable history of weird philosophers' deaths, which you may find interesting.

When you question what others take as self-evident, you may come to realize that what we take to be real may be anything but. If you can spare 60 seconds, the following animation demonstrates one of Zeno's famous paradoxes of motion proposed to support his mentor Parmenides' thesis that "all is one" and that change is impossible.

According to this paradox,if you think that it is possible for something to move from point A to point B, you've got to be kidding... and you haven't actually "thought" anything...

And for a more comprehensive introduction to, and analysis of, Zeno's paradoxes, check out the article on the Stanford Encyclopedia of Philosophy.

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