The seat of free will

The subject of whether or not humans have free will has been debated ad nauseam for centuries by much wiser heads than my own.  I'm up front about being a generalist (the type of person whose knowledge has been described less flatteringly as "a light year across and an inch deep"), and although there are a few areas I have some small degree of expertise in, philosophy ain't one of them.

So I'm unqualified to discuss whether free will actually exists, but I was still pretty intrigued when I read a paper a few days ago about some neuroscientists who have found the brain regions where activity gives us the sense of having free will.

[Image is in the Public Domain]

The researchers, R. Ryan Darby (of Vanderbilt University), and Juho Joutsa, Matthew J. Burke, and Michael D. Fox (of Beth Israel Deaconess Medical Center, the teaching hospital for Harvard University), looked at people with brain lesions that seemed to interfere with volition.  They investigated two different odd neurological disorders stemming from lesions -- akinetic mutism (which causes people to move their own limbs to accomplish actions without being conscious of it) and alien limb syndrome (in which one or more limbs seems to be under someone else's control).

The authors write:

Our perception of free will is composed of a desire to act (volition) and a sense of responsibility for our actions (agency).  Brain damage can disrupt these processes, but which regions are most important for free will perception remains unclear.  Here, we study focal brain lesions that disrupt volition, causing akinetic mutism (n = 28), or disrupt agency, causing alien limb syndrome (n = 50), to better localize these processes in the human brain.  Lesion locations causing either syndrome were highly heterogeneous, occurring in a variety of different brain locations. 

The scientists reasoned that despite the lesions not seeming to form a pattern of any kind, there had to be some commonality given the similar symptoms of the lesion sufferers.  And they found it:

We next used a recently validated technique termed lesion network mapping to determine whether these heterogeneous lesion locations localized to specific brain networks.  Lesion locations causing akinetic mutism all fell within one network, defined by connectivity to the anterior cingulate cortex.  Lesion locations causing alien limb fell within a separate network, defined by connectivity to the precuneus.  Both findings were specific for these syndromes compared with brain lesions causing similar physical impairments but without disordered free will.  Finally, our lesion-based localization matched network localization for brain stimulation locations that disrupt free will and neuroimaging abnormalities in patients with psychiatric disorders of free will without overt brain lesions.  Collectively, our results demonstrate that lesions in different locations causing disordered volition and agency localize to unique brain networks, lending insight into the neuroanatomical substrate of free will perception.

The final piece came into place when they looked at cases where people who had strange (temporary) side effects from targeted magnetic fields "knocking offline" certain brain regions -- and found that the ones who had akinetic mutism-like symptoms lost activity in brain networks connected to the anterior cingulate cortex, and those describing alien limb syndrome-like symptoms lost activity in ones connected to the precuneus.

What I find most interesting in all of this is how easily our sense of agency can be disrupted.  It seems to be one of our most basic sensations, that we are in control of what we think and do.  The idea that it's this easily altered is a little frightening, and once again brings home what I always tell my neuroscience students -- that in reality you just have one sense organ.  Your brain.  If you alter the electrical impulses coming into or out of your brain, that altered pattern becomes your reality -- even if it's completely at odds with the real world.

So the Darby et al. research doesn't even begin to settle the overall free will question, but it does give us a lens into why we feel like we have free will.  As for me, I think that's about as much philosophy as I can handle.  I'm gonna will myself to get up and get a second cup of coffee.

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This week's Skeptophilia book recommendation is a fun one -- Hugh Ross Williamson's Historical Enigmas.  Williamson takes some of the most baffling unsolved mysteries from British history -- the Princes in the Tower, the identity of Perkin Warbeck, the Man in the Iron Mask, the murder of Amy Robsart -- and applies the tools of logic and scholarship to an analysis of the primary documents, without descending into empty speculation.  The result is an engaging read about some of the most perplexing events that England ever saw.

[If you purchase the book from Amazon using the image/link below, part of the proceeds goes to supporting Skeptophilia!]

Room for exploration

I've discussed the Fermi Paradox here at Skeptophilia before -- and the cheerful idea of the Great Filter as the reason why we haven't heard from alien life.  As I explained in a post last month, the explanation boils down to three possibilities, nicknamed the "Three Fs."

We're first, we're fortunate, or we're fucked.

Being an aficionado of all things extraterrestrial, that has never sat well with me.  The idea that we might be all alone in the universe -- for any of the three Fs -- is just not a happy answer.  Yes, I know, I always say that the universe is under no obligation to act in such a way as to make me happy.

But still.  C'mon... Vulcans?  Time Lords?  Ewoks?  G'gugvuntts and Vl'hurgs?  There's got to be something cool out there.  With luck, lots of cool things.  The Dentrassi, Quantum Weather Butterflies, Andorians, the Vashta Nerada...

Okay, maybe not the Vashta Nerada.  But my point stands.

The Andromeda Galaxy [Image licensed under the Creative Commons Adam Evans, Andromeda Galaxy (with h-alpha), CC BY 2.0]

So I was considerably cheered yesterday when I ran into a study out of Pennsylvania State University that attempted to estimate what fraction of the universe we actually have surveyed in any kind of thorough fashion.  The authors, Jason Wright, Shubham Kanodia, and Emily G. Lubar, write:

Many articulations of the Fermi Paradox have as a premise, implicitly or explicitly, that humanity has searched for signs of extraterrestrial radio transmissions and concluded that there are few or no obvious ones to be found.  Tarter et al. (2010) and others have argued strongly to the contrary: bright and obvious radio beacons might be quite common in the sky, but we would not know it yet because our search completeness to date is so low, akin to having searched a drinking glass's worth of seawater for evidence of fish in all of Earth's oceans.  Here, we develop the metaphor of the multidimensional "Cosmic Haystack" through which SETI hunts for alien "needles" into a quantitative, eight-dimensional model and perform an analytic integral to compute the fraction of this haystack that several large radio SETI programs have collectively examined.  Although this model haystack has many qualitative differences from the Tarter et al. (2010) haystack, we conclude that the fraction of it searched to date is also very small: similar to the ratio of the volume of a large hot tub or small swimming pool to that of the Earth's oceans.  With this article we provide a Python script to calculate haystack volumes for future searches and for similar haystacks with different boundaries.  We hope this formalism will aid in the development of a common parameter space for the computation of upper limits and completeness fractions of search programs for radio and other technosignatures.

The actual analogy Wright and his colleagues used is that saying our current surveys show there's no intelligent life in the universe (except for here, which itself seems debatable some days) is comparable to surveying 7,700 liters of seawater out of the total 1.335 billion trillion liters in the world's oceans.

So basing a firm conclusion on this amount of data is kind of ridiculous.  There could be intelligent alien species out there yelling, "Hey!  Earthlings!  Over here!  We're over here!", and all we would have to do is have our radio telescopes pointed a couple of degrees off, or tuned to a different wavelength, and we'd never know it.

Which is pretty cool.  Given the fact that my all-time favorite movie is Contact, I'm hoping like hell that people don't read Wright et al.'s paper and conclude we should give up SETI because it's hopeless to make a thorough survey.  When I think about what poor Ellie Arroway went through trying to convince her fellow scientists that her research was valid and deserved funding... yecch.  And if anything, the current attitudes of the government toward pure research are, if anything, worse than those depicted in the movie.

But despite all that, it's awe-inspiring to know we've got so much room to explore.  Basically... the entire universe.  So my dream when I was a kid, sitting out in my parents' yard with my little telescope, that as I looked at the stars there was some little alien boy in his parents' yard looking back at me through his telescope, may one day prove to be within hailing distance of reality.

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This week's Skeptophilia book recommendation is a fun one -- Hugh Ross Williamson's Historical Enigmas.  Williamson takes some of the most baffling unsolved mysteries from British history -- the Princes in the Tower, the identity of Perkin Warbeck, the Man in the Iron Mask, the murder of Amy Robsart -- and applies the tools of logic and scholarship to an analysis of the primary documents, without descending into empty speculation.  The result is an engaging read about some of the most perplexing events that England ever saw.

[If you purchase the book from Amazon using the image/link below, part of the proceeds goes to supporting Skeptophilia!]

Slap shot

Every time I find what I think must be the stupidest possible alt-med quack "cure," the alt-med crowd says, "Hold my beer."

We've looked at fire cupping.  We've considered quantum downloadable medicines.  We've investigated homeopathic water, bee sting acupuncture, and "rectal insufflation" (also known as blowing ozone gas up your ass).

But this one is the odds-on winner for the 2018 "How Gullible Can You Get?" Award: slapping therapy.

The idea here, which comes out of Traditional Chinese Medicine, is that if you're sick, the flow of chi through your meridians is stuck, and what you need is to jar it loose, similar to when you smack the bottom of a ketchup bottle to get the last bit out.

But I'm not talking about a few little love-taps, here.  This is one patient following a "treatment:"

The link I included above, which is to Frank van der Kooy's outstanding blog about scientific charlatans and medical quackery, describes a darker side of this kind of bullshit.  A six-year-old Australian boy with type-one diabetes, Aidan Fenton, was brought by his parents to a "self-healing course" run by Hongchi Xiao, and subjected to slapping therapy.  Xiao charged each participant $1,800, smacked their bare skin, and told them they could not receive ordinary medications during the "therapy" because it would "interfere with the flow of chi."

The boy, deprived of his insulin, went into hyperglycemic shock.  He was rushed to a hospital, but could not be revived.

The only positive note is that Xiao is being charged in the boy's death, and it's possible charges of negligence will be brought against the parents as well.

Let me cut to the chase, here.  There is absolutely no rigorous evidence of "chi" and "meridians," much less that something like a slap could change it somehow with beneficial results for your health.  If you don't take my word for it -- and you shouldn't, as I'm a layperson at best with respect to medical claims -- take a look at this article from way back in 1995 by Peter Huston, who has researched Traditional Chinese Medicine extensively.  It's fair and thoughtful -- and comes to the inevitable conclusion that there is no evidence for it whatsoever.  (This takedown of TCM in The Skeptic's Dictionary is equally unequivocal, and not nearly so gentle.)

So once again, we're faced with the objection of "what's the harm?" having a very specific answer.  The principle of caveat emptor should apply -- if someone who is ill wants to try a crackpot cure, that's their choice -- but when a child's life is at risk, the moral calculus changes.  In this case, it's criminal negligence at the very least.  And quacks like Hongchi Xiao need to be put out of the way for a long, long time.

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This week's Skeptophilia book recommendation is a fun one -- Hugh Ross Williamson's Historical Enigmas.  Williamson takes some of the most baffling unsolved mysteries from British history -- the Princes in the Tower, the identity of Perkin Warbeck, the Man in the Iron Mask, the murder of Amy Robsart -- and applies the tools of logic and scholarship to an analysis of the primary documents, without descending into empty speculation.  The result is an engaging read about some of the most perplexing events that England ever saw.

[If you purchase the book from Amazon using the image/link below, part of the proceeds goes to supporting Skeptophilia!]

Polar opposites

A new study out of Michigan State University has confirmed what a lot of us sensed all along: the polarization between the Right and the Left in the United States is about as bad as it's ever been.

Zachary P. Neal, a professor of psychology at MSU, did a statistical analysis of bill sponsorship and support from members of Congress, from the 1970s to the present:

Claims that the United States Congress is (becoming more) polarized are widespread, but what is polarization?  In this paper, I draw on notions of intergroup relations to distinguish two forms.  Weak polarization occurs when relations between the polarized groups are merely absent, while strong polarization occurs when the relations between the polarized groups are negative.  I apply the Stochastic Degree Sequence Model to data on bill co-sponsorship in both the U.S. House of Representatives and U.S. Senate, from 1973 (93rd session) to 2016 (114th session) to infer a series of signed networks of political relationships among legislators, which I then use to answer two research questions.  First, can the widely reported finding of increasing weak polarization in the U.S. Congress be replicated when using a statistical model to make inferences about when positive political relations exist?  Second, is the (increasing) polarization observed in the U.S. Congress only weak polarization, or is it strong polarization?  I find that both chambers exhibit both weak and strong polarization, that both forms are increasing, and that they are structured by political party affiliation.  However, I also find these trends are unrelated to which party holds the majority in a chamber.

The last sentence is, I think, the most important.  It's easy for liberals to point fingers at conservatives (and vice versa) and lay the entire blame for polarization at the opposition's feet.  The truth, predictably, is more complex than that.  "In truth," Neal said, in a press release from MSU, "the only thing that is bipartisan in Congress is the trend toward greater polarization."

These results are discouraging, to say the least.  "What I’ve found is that polarization has been steadily getting worse since the early 1970s," Neal said.  "Today, we’ve hit the ceiling on polarization.  At these levels, it will be difficult to make any progress on social or economic policies...  We’re seeing lots of animosity in politics.  Although bills do occasionally get passed, they don’t stick around long enough, or never get fully implemented, and therefore don’t have lasting impact.  This kind of partisanship means that our democracy has reached a kind of stalemate."

[Image is in the Public Domain]

Neal doesn't look at cause (except the fact that the blame can't clearly be assigned to one party).  But I wonder how much of this is exacerbated by the rise of talk radio and partisan news channels.  When the goal becomes getting viewers (or listeners, or clicks), not accuracy and fairness, there's an incentive to play to people's basest motives -- fear, tribalism, resentment, retribution.  If you look at the rhetoric from people like Tucker Carlson (on the Right) and Ted Rall (on the Left) you'll find they do business with the same currency -- whipping up the righteous indignation of the people who already agreed with them.  It no longer depends on looking at the evidence in a dispassionate fashion, it has become instead a contest to see who can be the most outrageous and incendiary.

That, after all, keeps people watching, listening, and clicking, which pays sponsors -- who pay the commentators.

Until there's more of an incentive to report and analyze the news fairly, it's only going to get worse, as each party does what it takes to stay in power, which means keeping the voters convinced that if they don't vote the party line, BAD STUFF WILL HAPPEN.  The result?  We've tended to elect partisan hacks who don't care about anything but their own corporate sponsors, and the whole thing comes full circle.

"The solution could be electing more centrists to Congress," Neal said.  "But that’ll be tough because centrists often don’t appeal to American voters."

So the sad truth is that we're probably in for more of the same, and things getting worse before they get better.  I can only hope that at some point, people realize that the members of the opposition party are their neighbors, coworkers, teachers in their schools, members of their churches, and they can realize that disagreement has a human face.  That, I think, is the only way this will ever change.

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This week's Skeptophilia book recommendation is a fun one -- Hugh Ross Williamson's Historical Enigmas.  Williamson takes some of the most baffling unsolved mysteries from British history -- the Princes in the Tower, the identity of Perkin Warbeck, the Man in the Iron Mask, the murder of Amy Robsart -- and applies the tools of logic and scholarship to an analysis of the primary documents, without descending into empty speculation.  The result is an engaging read about some of the most perplexing events that England ever saw.

[If you purchase the book from Amazon using the image/link below, part of the proceeds goes to supporting Skeptophilia!]

Brain linkage

New from the "Should I Be Scared?" department, we have: the first experimental proof of a successful brain-to-brain interface.

To be sure, the information passed through it was rather rudimentary.  Two "senders" played a game of Tetris, and passed along to a "receiver" the information about whether a particular block had to be rotated or not in order to fit in the grid.  The receiver then recorded what the decision was -- and got it right with an accuracy of 81%.  Furthermore, in a second round where the receiver was given information about the accuracy of their choices, the researchers tried to muddy things up by injecting noise into the transmission from one of the senders.  The result?  The receiver was able to figure out which one of the senders to pay attention to -- which one had the highest accuracy -- and ignore the input from the channel with the noise.

The researchers -- Linxing Jiang, Andrea Stocco, Darby M. Losey, Justin A. Abernethy, Chantel S. Prat, and Rajesh P. N. Rao, of the University of Washington and Carnegie Mellon University -- are unequivocal about where this could lead.  "Our results," they write, "raise the possibility of future brain-to-brain interfaces that enable cooperative problem solving by humans using a 'social network' of connected brains."

Which certainly seems likely.  What worries me, however, is where else it could lead.  The technology is surely going to do nothing but improve, the interfaces working better and faster and more accurately.  At what point would it be possible to use such an interface to read a person's thoughts without their will?  To inject a directive, something like a post-hypnotic suggestion, into their brains?  To suppress or erase a memory of something you would prefer they didn't remember?

Of course, there are a lot of good directions we could go.  I've always thought I'd love to have a Matrix-style plug in the back of my head that would allow me to download information.  

Think of how cool that would be!  Even if (for example) you'd still have to learn the grammatical rules and semantic nuances of a language, you could simply input the dictionary into your brain and you'd never have to memorize the vocabulary (which has always been the sticking point for me, linguistics-wise).  And Jiang et al.'s optimistic prediction of using it as a tool for collaborative problem solving is kind of awesome as well.

But you have to admit, we humans don't exactly have a sterling track record of using scientific discoveries for positive purposes.  Our general approach has usually been "personal gain first, power second" -- and only as an afterthought, "Oh, yeah, we could also use this to benefit humanity."  

The problem is, once the cat's out of the bag, you can't exactly stuff it back inside.  As soon as someone shows proof of concept -- which Jiang et al. clearly have -- the next step will inevitably be refinement.  It's like the line from Ian Malcolm in Jurassic Park: "Your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should."

I'm not saying we should halt this kind of research, but some caution seems advisable, especially since we're crossing the line into infringement on that most sacred and private realm -- one's own mind.  So I would urge anyone involved in this endeavor to move slowly, and take care to assure as best we can that this discovery won't be used as one more assault on free thought.

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This week's Skeptophilia book recommendation is a fun one -- Hugh Ross Williamson's Historical Enigmas.  Williamson takes some of the most baffling unsolved mysteries from British history -- the Princes in the Tower, the identity of Perkin Warbeck, the Man in the Iron Mask, the murder of Amy Robsart -- and applies the tools of logic and scholarship to an analysis of the primary documents, without descending into empty speculation.  The result is an engaging read about some of the most perplexing events that England ever saw.

[If you purchase the book from Amazon using the image/link below, part of the proceeds goes to supporting Skeptophilia!]

Nostalgia

I was talking with a friend this past weekend, and the subject of children's television came up.

"It all sucks," he lamented.  "There's nothing around any more that's the quality of what we had when we were growing up."

I certainly see what he was talking about.  In my opinion, Bugs Bunny and Daffy Duck are up there in the top ten funniest comedy writing ever (not to mention brilliant animation, incredible voice-overs, and impeccable comic timing).

Classic episodes like "Duck Amuck" and "The Rabbit of Seville" and "Bully for Bugs" still make me howl with laughter even though I've seen them dozens of times.

Another winner was Bullwinkle, which combined completely offbeat, goofy humor with sharp political satire. 

The problem is, this kind of nostalgia only works if you've got a really selective memory.  There were some truly horrid children's shows when I was growing up.  One that sticks in my memory, because it not only was terrible but was, to put it bluntly, really fucking weird, was H. R. Pufnstuf.

If you've never seen this show, it's the adventures of an odious little twerp named Jimmy who has a magic talking flute, and somehow ends up in a land where the mayor is a green dinosaur with a Tennessee accent, and most of the characters are wearing full-body costumes supposed to be people, animals, or... pieces of furniture.  Oh, yeah, and the villain -- I shit you not -- is named "Witchiepoo."  It also had a really creepy fake laugh-track, so you knew when something funny had happened, because heaven knows there was no other way to tell.  To get a sense of the overall effect, imagine what would have happened if J. R. R. Tolkien wrote a script for Barney and Friends while tripping on acid.

Don't believe me?  Take a look at this little excerpt:

The whole thing was dreamed up by Sid and Marty Kroft, who also came up with The Banana Splits, which was similar not only in its frenetic, seizure-inducing pacing, but in its psychedelic content:

So I'm not quite buying the "things were so much better back then" argument.  We naturally tend to look at our own past in a sentimental fashion, so a lot of our memories are colored by that.  (Although I do wonder how much of my own sense that the world is a weird and chaotic place was generated by watching shows like H. R. Pufnstuf when I was eight years old.)

On a more serious note, isn't this the same thing that drives the whole MAGA phenomenon?  "Make America Great Again," by returning to... when?  When was America so great that we'd jump in a time machine and head back there?  The prosperous Fifties -- when minorities could be legally denied their rights as citizens?  The Roaring Twenties -- with its class stratification and reckless economic policy that led directly to the Great Depression?

Even earlier?  No matter where you look, it was all a mixed bag -- as it is now.  There has never been a time that was unalloyed good, and there have been plenty of times in the past when it has been significantly worse than it is now.  Consider, for example, what it was like for your typical feudal peasant.  When we think of medieval times, we tend to picture lords and ladies in fancy dress dancing the galliard, but fail to consider that this represented maybe five percent of the population -- and the other ninety-five percent spent their lives in backbreaking labor and lived in squalor.

So if I was offered a one-way trip in a time machine, I'd stay put, thank you very much.  If I were forced to choose, my criteria would be practical ones -- some time after the invention of indoor plumbing and general anesthesia.  Call me a stick in the mud, but I'm just fine right here.

And now, I need to take advantage of another wonderful modern invention, which is recorded music. Because if I don't do something to get that stupid damn "Oranges Poranges" song out of my head, I'm going to lose my marbles.

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This week's Skeptophilia book recommendation is a fun one -- Hugh Ross Williamson's Historical Enigmas.  Williamson takes some of the most baffling unsolved mysteries from British history -- the Princes in the Tower, the identity of Perkin Warbeck, the Man in the Iron Mask, the murder of Amy Robsart -- and applies the tools of logic and scholarship to an analysis of the primary documents, without descending into empty speculation.  The result is an engaging read about some of the most perplexing events that England ever saw.

[If you purchase the book from Amazon using the image/link below, part of the proceeds goes to supporting Skeptophilia!]

Quote miners

Quote mining is a particularly maddening way of misrepresenting a person's position.

This practice involves sifting through the writings of an opponent or opponents, and lifting quotes that, taken out of context, sound like they support the opposite viewpoint.  Here's a famous example, from Ken Ham's site Answers in Genesis, wherein he presents the following quote from Darwin's Origin of Species:

To suppose that the eye with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest degree.

Sounds like old Charlie was doubting his own theory to the point of throwing his hands up in despair, doesn't it?  But only if you stop there, and don't read the very next paragraph:

Yet reason tells me, that if numerous gradations from a perfect and complex eye to one very imperfect and simple, each grade being useful to its possessor, can be shown to exist… then the difficulty of believing that a perfect and complex eye could be formed by natural selection, though insuperable by our imagination, can hardly be considered real.

Much in the same vein, consider the crowing over a new analysis of paleontological evidence I saw on more than one anti-evolution website, accompanied by comments like "the evolutionists admit there's no way evolution can be correct!"  Here's the excerpted quotes:

How do the large-scale patterns we observe in evolution arise?  A new paper in the journal Evolution by researchers at Uppsala University and University of Leeds argues that many of them are a type of statistical artefact caused by our unavoidably recent viewpoint looking back into the past.  As a result, it might not be possible to draw any conclusions about what caused the enormous changes in diversity we see through time...   Because the resulting patterns are an inevitable feature of the sorts of groups available for us to study, Budd and Mann argue, it follows that we cannot perceive any particular cause of them: they simply arise from statistical fluctuation.

Well, one of the sites made the mistake of linking to the actual press release about the study, on Science Daily, so I went and read it for myself.   Needless to say, there's nothing about the study that calls into question evolutionary theory; what it's saying is that using available fossil evidence to estimate changes in the rate of evolution may not be accurate.

[Image licensed under the Creative Commons Ghedoghedo, Meganeura fossil, CC BY-SA 3.0]

But that's not how it's being cast.  The creationists are portraying this as the evolutionists waving a white flag and admitting that they've been wrong all along.  Which is disingenuous at best, and an outright lie at worst.

Quote mining -- and its statistical close cousin, cherry-picking -- smack of desperation, don't they?  It's almost as if they realize, deep down, that they have no legitimate, logical, evidence-based argument for their own stance, so they have to fall back on misrepresenting the opposing view.

The most frustrating part, though, is how confirmation bias enters into this.  Because my sense is that the people who are true believers never question whether the way the research is being portrayed is accurate.  I'd like to know how many of them, even when provided with a link, actually went and read the press release (much less the original, peer-reviewed paper).

I guess if you start out from the stance that your conclusion is true no matter what, you don't need to do any research, or (heaven forfend) reconsider your claim.

So that was my exercise in futility for the day.  And really, what Budd and Mann are doing is how science progresses; by people taking nothing for granted, questioning our base assumptions, asking the hard and controversial questions, and -- this is the most important part -- going where the evidence demands.

Which is the only honest way to approach understanding.

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This week's recommendation is a classic.

When I was a junior in college, I took a class called Seminar, which had a new focus/topic each semester.  That semester's course was a survey of the Book Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter.  Hofstadter does a masterful job of tying together three disparate realms -- number theory, the art of M. C. Escher, and the contrapuntal music of J. S. Bach.

It makes for a fascinating journey.  I'll warn you that the sections in the last third of the book that are about number theory and the work of mathematician Kurt Gödel get to be some rough going, and despite my pretty solid background in math, I found them a struggle to understand in places.  But the difficulties are well worth it.  Pick up a copy of what my classmates and I came to refer to lovingly as GEB, and fasten your seatbelt for a hell of a ride.

[If you purchase the book from Amazon using the image/link below, part of the proceeds goes to supporting Skeptophilia!]