The Terrors of Sleep Paralysis

Imagine living in medieval times, when weird and unexplained phenomena, especially those related to strange subjective experiences (such as feeling that you're being suffocated by demons in your sleep), were seen as indications and evidence of malevolent spiritual forces at work. In the famous Bull of 1484, for instance, Pope Innocent VIII (don't you love the irony of these names?) declared that:

members of both sexes do not avoid to have intercourse with evil angels, incubi and succubi, and that by their sorceries, and by their incantations, charms and conjurations, they suffocate, extinguish, and cause to perish the births of women [among many other evil things].

As Carl Sagan recounts in his book, The Demon Haunted World, "with this Bull, Innocent initiated the systematic accusation, torture, and execution of countless 'witches' all over Europe." This would lead to the publication of the infamous Malleus Maleficarum (the "Hammer of Witches"), one of the most vile, irrational, fearsome and cruel documents in all of human history. There's a chance even Hitler might have shuddered at it... Yay religion!?

Fortunately, and as usual, science has helped to shed some light on this otherwise dark and obscure phenomenon, saving people from medieval persecution and from forced mental institutionalization by discovering some of the underlying mechanisms at work, as well as their ubiquity because, believe it or not, it happens to most of us...

If you know someone whose life has been affected by the fear that they are being visited by probing aliens or haunted by evil spirits in the middle of the night, you might want to show them this video and assuage those feelings of fear and anguish...

And in case you are not aware of the distinction between an incubus and a succubus, and assuming these demons were not gay, incubi were 'seducers' of women, while succubi were 'seducers' of men, although if they're having their way with you while you're paralyzed, I'm not sure that would really count as 'seduction'...

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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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Open Access Explained, PhD Comics Style

As biological creatures, we are very adaptable. If we notice that some background condition remains relatively stable, we tend to ignore it after a while. On the one hand, this makes perfect sense, since we can't afford to devote all of our energy and attention resources to things that are unlikely to affect us in sudden ways. On the other hand, this makes us very susceptible to the status quo bias (failing to recognize better alternatives; failing to even acknowledge that there could be potentially better methods; perpetuating the current system as the solution to a problem that we often don't realize is the result of the very same system we use to 'fix' it; and even actively working against new possibilities, even while being fully cognizant of the problems and negative consequences associated with the systems currently implemented).

This problem is ubiquitous, and there are entire industries built upon the simple and great idea that for any given situation, there are probably better solutions than those that are currently being implemented. Unfortunately, some of these same industries, once they acquire a certain level of success and financial power, tend to re-affirm their own system instead of the original idea of constantly improving things. And if they have enough power and influence, they can actually become an impediment to improved efficiency. Professional academic journals, for all the wonderful work they do, have also fallen into this self-reinforcing pattern where their financial success has replaced the original idea for which they were created, and maybe it's time we start a dialogue to figure out how to make everyone better off...

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The Punishable Perils of Plagiarism

As we've seen before (in a case in which a professor discovered a massive collective case of cheating), academic dishonesty is a serious and growing problem. What most cheaters don't always realize, however (especially those who engage in plagiarism), is the paradoxical nature of cheating: those who need to do it are usually not clever enough to know how to do it well enough to get away with it, and those who could get away with it are smart enough not to need to do it...

To paraphrase something I read in a fascinating article on anosognosia a couple of years ago: if you're too stupid to cheat, you're probably too stupid to know you're too stupid to cheat... The irony, of course, is that if you think you're clever enough to get away with it, you probably don't belong to the clever category...

Now, while the following video disavows the existence of our agency, those of us who, willingly or unwillingly, work for the Department of Plagiarism Investigation are familiar with lots of different versions and variations of cheating, and the disadvantage of any one cheater is that he/she is competing against the accumulated knowledge our agency has collected since its inception a long, long time ago...

Here is just a small sample of the many ways (both laughable and frustrating) in which students think they can get away with plagiarized work:

Of course, we can't divulge all the methods we have for catching instances of plagiarism, but even if you don't care about education itself or the value of honest work, it's still in your own self-interest not to cheat because if you get caught... well, let's not go there...

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What Is Evolution and Natural Selection?

I don't know if it's by design or circumstance, but (apart from the religious and ideological elements) part of the resistance to evolution has to do with the fact that a number of related but distinct concepts are normally conflated with each other, so that if you disagree with one, you automatically assume that you must disagree with all of them. For instance, many people confuse natural selection with evolution, and think of them as interchangeable concepts, but the former is simply the most famous, and possibly main mechanism driving the fact of the latter.

And talking about facts, people also tend to confuse the fact of evolution with the theory of evolution. Evolution, the change in (gene) allele frequency in populations over the span of multiple generations, is a fact that even the most hard-core creationists can't deny with a straight face (after all, you are not identical to either of your parents, nor to your own children). The theory of evolution is a scientific model (and by far the most successful account so far) to explain, understand and make sense of the fact of evolution (why it happens). And to bring it all full-circle, the theory makes use of various mechanisms, most notably, though not exclusively, natural selection. So yeah, I can understand why some people might get a little confused...

But if that seems needlessly abstract, here's a little animation to clarify what evolution is:

Having established that, the next point to touch on is the consequences of evolution and what it implies about us and our place in the grand scheme of things. Many people tend to disagree with evolution, not because it's not supported by more evidence than we know what to do with or because it doesn't make sense but because, as a kind of universal acid, it tends to undermine our inflated egos.

We like to think of ourselves as fallen angels, ignited by a kind of divine spark, but it may be more accurate to say that we are risen apes, and that we can trace our inglorious genealogical lineage all the way back to pond scum. Then again, how is that any worse than thinking we come from dust?

But before we consider the logical implications of this idea, here's a little lesson, again clearly articulated, explaining the basic logic behind the mechanism of natural selection:

And here's why the idea of 'intelligent design' is undermined by our observation of fossils and the massive number of extinct species: evolution is a 'blind watchmaker,' a tinkerer (not a designer) whose success is acquired by the death and destruction of all those experiments that ended up failing.

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Dogs vs. Hyenas - Chew On This!

I've never been one to like hyenas. I don't know if I find it ignoble to rely on great numbers to bring down a great beast, or if it's guilt by association, since usually where there's vultures there's probably hyenas (or is it the other way around?), or if their preposterously high levels of testosterone (especially in the females) feels somehow emasculating, or if they're just ugly as all hell... but either way I find them repulsive.

That's not to say, however, that one can't also find them interesting, indeed fascinating. For instance, did you know that hyenas are evolutionarily closer to cats than to dogs? Me either. So what else about these social animals might you not know but could learn in about two minutes?

The idea of convergent evolution could have been stated with even more strength if they had also compared dogs and hyenas to certain marsupials that hit upon the same basic adaptations, quite independently, as things usually happen, Down Under in Australia.

And if you want, there's also a poster:

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What Is Zeno's Dichotomy Paradox?

When I first introduce my students to the weirdness of philosophy and how even our most deeply-entrenched beliefs might be subject to serious questioning, I usually like to begin by posing to them Zeno's attempt to refute the idea that motion is possible (here's a fun little animation to get you started), and then continue to defend him against the objections raised by the students.

This has the dual benefit of being both a nice introduction to questioning dogmas and a nice exercise in critical thinking: since the students are convinced beyond a shadow of a doubt that Zeno is wrong, they concoct all kinds of arguments to refute him. The problem, of course, is that it's notoriously difficult to explain why exactly he's wrong, where he's made some kind of mistake.

Now, I get the idea of a limit in calculus, and I get the idea of the sum of a series as opposed to the sum of the individual members of a series, but I have noticed that we seem to have such an aversion to Zeno's conclusions that even professional philosophers and mathematicians tend to engage in a kind of prestidigitation in which they explain a mathematical method for solving the paradox that ends up being more smoke and mirrors than a genuine solution. The problem, and the following animation is an example of this, is that they tend to frame the paradox in a way that's question-begging, one in which they assume motion in order to prove motion.

In the following animation, it seems clear how you can refute Zeno once you grant him motion to the first halfway point, but for Zeno, he wasn't willing to concede actually having crossed that halfway point. For him, the challenge is that BEFORE you reach that halfway point, you must reach the halfway point of that halfway point, and before you can do that, you must reach that other halfway point, lather, rinse, repeat ad infinitum, and Zeno's conclusion is that you NEVER actually get to leave the starting point: you haven't gone anywhere.

As you can see, if you don't grant any motion at all to begin with, the above explanation, nice as it is, doesn't quite do the trick, does it?

When trying to refute someone, you should always ask how that person might respond to your objections, and if you're charitable, right or wrong, that will give you a better sense of the real strength of your own arguments. When it comes to Zeno, I tend to think that if you were to explain to him the asymptotic concept of a limit in calculus, he could just apply his paradox to that and be right back in business with his own paradox, now fortified with steroids...

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"To This Day" ... for the Bullied and Beautiful

The saying goes that sticks and stones may break my bones, but words will never hurt me... I've broken my bones before, a couple of ribs, but there are forms of pain that are orders of magnitude worse, and which leave scars that last much longer, but that no one can see because they are not branded in your body; they are branded in your memory and soul...

Despite the amazing things that we have in this world, and despite the amazing things people do to help and inspire each other, there is still a very large amount of cruelty inflicted on people, especially the ones least able to cope with it. And even when we're not directly cruel, we are often indifferent, apathetic, and we blind ourselves to the cries of help that people who are drowning are barely able to make audible.

This poem, by Shane Koyczan, is dedicated to those people:

Sometimes, when the pain is too much, people jump off the cliff... but sometimes they fall because they've been brought to the brink and got pushed off by cruelty and indifference...

Do your part to bring light and laughter to people's lives...

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Wealth Inequality in America

If you consider the difference between what people think is the distribution of wealth in America vs what they consider the ideal distribution vs the actual distribution... you'd be flabbergasted...

The Occupy Wall Street movement tried to raise awareness about the fact that the bottom 99% of Americans have to live under the oppression, greed and corruption of the top 1%.

If you need to visualize these ratios in order to get a better sense of what's going on in the US, the following animation will be an eye-opener.

Go share...

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An Illustrated Interview with Maurice Sendak

You may remember from last year a two-part interview that Stephen Colbert did with author Maurice Sendak. Unfortunately, soon after the interview, Sendak shed his mortal coil and went the way of the dodo.

But it seems that recently someone illustrated an interview Sendak did with NPR's Fresh Air hostess, Terry Gross. Now, I'm not her biggest fan... her questions tend to bore and frustrate me, but it seems that Sendak liked her a lot, and the next excerpt is enough to break your heart...

If you don't have knots in your throat, you're probably not human...

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Dan Ariely - The Truth about Dishonesty

If I were to ask you if you are an honest person, chances are that you'd say yes. Yet, if we look at the details of your everyday behavior with a magnifying glass, we'd most likely discover all sorts of ways in which you lie, cheat and steal, on a regular basis! Notice the irony? In answering a question about your own honesty, you behave dishonestly! Well, it's not quite that straightforward. It's not so much that you'd be lying to me; it's more that you'd be lying to yourself, and then to the rest of us as a consequence.

Our minds have an incredible capacity for compartmentalization: we separate into distinct groups instances of what ought to be logically identical situations, such as when you create the double standard that it's okay for you to take home some office supplies from work, but that it's not okay to steal an equivalent amount of money from the petty cash box. The other thing we're really good at in this context is rationalization: when confronted with our dishonesty, we are masters at justifying our behavior and turning it around to sound heroic: "it's okay for me to illegally download music because that means I'm standing up for freedom and fighting the corruption of multi-billion dollar music label companies, so if you think about it, I'm kind of a moral hero."

Well, in the following RSA animated presentation, Dan Ariely shares some of the fascinating findings of how everyday people like you and me cheat all the time, and what might be some useful mechanisms we can use to decrease our own corruption.

If you liked that, you might also like to check our our selection of TED Talk presentations.

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Propositional Logic - Using Truth Tables to Evaluate the Validity of Complex Arguments

In our previous lesson on propositional logic, we learned that we can take arguments in natural language (English, Spanish, German, whatever) and translate them into symbolic form through the use of variables to represent statements, and connectives to represent relationships between statements. This helps us set aside irrelevant considerations such as the content of an argument (what the argument is about), or the language used to express that content, and focus instead simply on its formal aspects to evaluate its validity (whether the conclusion follows necessarily from its premises).

The claim was that these basic concepts can be applied to a wide range of arguments, including indefinitely complex ones, and that logicians have developed systematic methods for evaluating the validity of such arguments in a systematic way: it's not just a matter of personal opinion or subjective point of view but of objectively demonstrative rationality.

So, let's take a look at one example of a complex argument, and go through these systematic steps to figure out whether it makes logical sense or not.

For more related posts, check out our logic tag.

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Election Results in a Beautiful Animation

I don't know if you heard, but here in the ol' U.S. of A. we just had an election this Tuesday. You know, just trying to choose who the most powerful man in the world would be...

Well, as it turned out, President Barack Obama was re-elected, beating his conservative-liberal-tea-party-ultra-conservative-liberal-conservative opponent Mitt Romney.

If you haven't been paying attention, or don't quite understand how things break down, the following animation should clarify all sorts of questions you may have about this election:

Marihuana, porn and gay marriage... wow, that's what it's come to? :)

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Substance Dualism

Although most philosophers of mind are probably physicalists, there is still a live debate about the ontological status of mind: is it physical or immaterial?

On one side of the debate are those who argue that thoughts are not physical, and therefore cannot be generated by something physical. Apart from obvious religious and soteriological reasons, one of the more popular lines of argument goes roughly as follows: when we have a complete physical description of the brain (and of that which is perceived by the brain), there is still something about the qualitative nature of first-person subjective experiences (or qualia) that is not accounted for, so there must be something non-physical to explain this. In other words, the physicalist account leaves something rather important out of the picture, namely subjectivity and intentionality (or the 'aboutness' of mental experience), and that needs to be explained.

On the other side, the idea of an immaterial soul seems perhaps even more mysterious than the problems with physicalism: how can a non-physical substance interact causally with the physical body? What is it about this non-physical stuff that allows it to think and have first-person subjective experiences in the first place, without just being defined into having it? How can we possibly verify its existence (without arguing in a circle)? In fact, the evidence that we do have when we study the brain, especially when it suffers damage that affects very specific cognitive capacities, seems to indicate that even though we may not know the exact mechanism through which brain processes produce consciousness, that's nevertheless what happens.

But why listen to me when we have a beautiful and nicely organized animation that will take you through the steps to analyze this debate?

Did I say a beautiful animation? I meant two :)

Isn't it amazing how many problems fade away when you organize your thoughts? :)

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Samuel Jackson, Wake the F**k Up! - A Rebuttal

You may remember from a few days ago that video reminiscent of the children's story Go the F**k to Sleep, in which Samuel Jackson highlighted the importance of civil and political involvement, and complained about voter apathy by inciting voters to Wake the F**k Up! Of course, of the two main candidates running, Obama is clearly the better choice over Mitt Romney, but the least of two evils is still not the best state of affairs.

So, the folk over at Reason.com decided to play Jackson's game... and sort of kick his ass :)

Ouch!

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60 Seconds Adventures in Economics - The Invisible Hand

If you thought the Open University's 60 Second Adventures in Thought were over, think again! Yes, they may be done with paradoxes and strange thought puzzles (for now), but there's plenty of other fascinating things to explore, and they have decided to devote some attention to the field of economics.

Of course, no introduction to economics would be complete without Adam Smith's concept of the "invisible hand," that self-directed mechanism through which markets regulate themselves for the collective benefit of both consumers and producers.

Oddly enough, at least here in America, many of those people who deny the self-directed and amoral process of evolution through natural selection are perfectly comfortable with the equally blind and amoral self-directed market, and some, such as objectivists, actually argue that a completely free, unregulated market is the ultimate expression of a moral society.  Oh yeah, we've got it all...

And if you need a refresher on modern economics, you might want to check out the Hayek vs. Keynes rap.

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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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Electric Vocabulary

Why do we call electricity "electricity"? Why do we talk about its "charge"? Or talk about whether that charge is "positive" or "negative"? And why do we refer to a device to store electricity as a "battery"?

One great way to find out about the fascinating history of this strange phenomenon, and the one I would recommend, is to watch the excellent documentary series Shock and Awe: The Story of Electricity, narrated by Jim Al-Khalili.

But if you don't have the time to watch that right now, here's a simple and short introduction to get you started with at least the etymology of these words:

But seriously, go watch Shock and Awe...

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Is Pluto a Planet?

A few days ago we saw that Joe the Plumber (representing the view of thousands or millions of Americans) prefers the Bible to science books because science books go through constant revisions while the Bible contains eternal, unchanging truth.

Of course, Joe the Plumber and company probably don't realize that, over the last few thousands of years, the Bible has gone through countless revisions, additions, omissions, translations, translations of translations, etc. And many of these, of course, are based on either innocent human error at best or ideological manipulation at worst.

When genuine science books come up with revisions, on the other hand, the reason is that new evidence has been shown to challenge some of our former ideas, and there is no sense in holding on to ideas that have been empirically shown to be deficient or at least inconsistent with other things we have evidence to believe are true.

Today we have a simple example of this idea: why Pluto got "demoted" from the status of planet to the master of the Kuiper Belt:

And if you want a more detailed explanation of our changing views of Pluto (and the reasons why), NASA has a nice video. And if Neil deGrasse Tyson is more your style, you can check him out talking about the whole Pluto debacle, including all the hate mail he's been getting from second graders, or you can check out his NOVA documentary The Pluto Files.

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Getting to Mars - Curiosity's Seven Minutes of Terror

On their own right, the semi-autonomic rovers that explore the surface of Mars for us are great feats of engineering. The fact that they do what they do (from such a long distance away it's virtually impossible for us to really wrap our heads around) ought to be enough to impress anyone, but have you wondered how it is that they get there in the first place?

As you may recall from memory or a little history, landing on Mars is no easy feat. Its gravity is relatively similar to our own, but its atmosphere is too thin and light, so even if you get the angle of entry right (and that's a huge challenge in its own right), you still have to contest with the fact that you're falling at vertiginous speeds without much to slow you down sufficiently for a smooth touchdown.

So, how do you do it without smashing to smithereens all the equipment you want to use? Once it hits the atmosphere, the rover has an infamous seven minutes of terror to deploy a number of very delicate and specifically programmed functions about which you'll learn in the following pretty dramatic animation:

How would you do it?

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