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Mark ChangiziRSS Feed of this column.

Mark Changizi is Director of Human Cognition at 2AI, and the author of The Vision Revolution (Benbella 2009) and Harnessed: How Language and Music Mimicked Nature and Transformed... Read More »

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Here’s my vote for the best illusion ever. It was created by B. Pinna, G.J. Brelstaff / Vision Research 40 (2000) 2091–2096.

Loom your head toward, and away, from the center point. Print it out and bring to a bar, and it is even more impressive -- the paper appears to be twisting in your hands.

 
Some other time I'll tell you my speculation for why it works. (It is a
perceiving-the-present explanation
.)

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There aren’t many cyclopses in nature, and those that exist don’t live up to expectation. They tend to be crustaceans like water fleas and another aptly named “cyclops” (see left photo below) or early invertebrate fish-like ancestors of ours like lancelets.

Getting these animals tipsy and stabbing them through the eye with a stake turns out to be much less impressive than when Odysseus did it.
A word is vague if it has borderline cases. Yul Brynner (the lead in "The King and I") is definitely bald, I am (at the time of this writing) definitely not, and there are many people who seem to be neither. These people are in the “borderline region” of ‘bald’, and this phenomenon is central to vagueness.

Nearly every word in natural language is vague, from ‘person’and ‘coercion’ in ethics, ‘object’ and ‘red’ in physical science, ‘dog’ and ‘male’ in biology, to ‘chair’ and ‘plaid’ in interior decorating.
Vagueness is the rule, not the exception. Pick any natural language word you like, and you will almost surely be able to concoct a case -- perhaps an imaginary case -- where it is unclear to you whether or not the word applies.
This week a computer science researcher named Vinay Deolalikar claimed to have a proof that P is not equal to NP.

Let’s set aside what this means for another day, lest I get distracted.  The important thing now is that this is big. Huge, even!

If, that is, he’s correct.

But correct or not, that’s the kind of thing one expects to see in academia. Tenure gives professors job security and research freedom, exactly the conditions needed to enable them to make the non-incremental breakthroughs that fundamentally alter the intellectual landscape. (And in the case of P not equal to NP, to acquire fame and fortune.)
“John is a man. All men are mortal. Therefore, John is mortal.” This argument from two premises to the conclusion is a deductive argument. The conclusion logically follows from the premises; equivalently, it is logically impossible for the conclusion not to be true if the premises are true. Mathematics is the primary domain of deductive argument, but our everyday lives and scientific lives are filled mostly with another kind of argument.

Not all arguments are deductive, and ‘inductive’ is the adjective labeling any non-deductive argument. Induction is the kind of argument in which we typically engage.

I believe that music sounds like people, moving. Yes, the idea may sound a bit crazy, but it’s an old idea, much discussed in the 20th century, and going all the way back to the Greeks. There are lots of things going for the theory, including that it helps us explain (1) why our brains are so good at absorbing music (…because we evolved to possess human-movement-detecting auditory mechanisms), (2) why music emotionally moves us (…because human movement is often expressive of the mover’s mood or state), and (3) why music gets us moving (…because we’re a social species prone to social contagion).