Life finds a way

I've dealt more than once here at Skeptophilia with the repeated mass extinctions the Earth has undergone.  Part of this is that I have an admitted fascination with things that are big and powerful and can kill you.  These include:

• tornadoes and hurricanes
• lightning
• earthquakes
• volcanoes
• death asteroids from outer space

The latter is thought to have been the prime mover of the Cretaceous Extinction, which occurred 66 million years ago and killed an estimated 75% of the species on Earth, including all of the large dinosaurs (the exception being the lineage that led to modern birds).  Here's a cool, if terrifying, simulation of what it'd be like if the Earth got hit by an asteroid five hundred kilometers in diameter (the Chicxulub Meteorite, which caused the extinction, is estimated to be about a tenth that diameter, so you can scale down your picture of that event accordingly):

But dwelling on that stuff is a little morbid, even if it's kind of awe-inspiring.  So today, I'd like to look at some recent research that looks at how life recovered after the cataclysm -- discoveries that suggest the encouraging idea that even with a catastrophe, life can bounce back amazingly quickly.

A few years ago, Ian Miller and Tyler Lyson of the Denver Museum of Nature and Science were involved in a fossil dig in Corral Bluffs, Colorado, and made a rather astonishing discovery.  Initially the area seemed to be rather fossil-poor, but it had a great many concretions (roughly spherical blobs of cemented sediment).  When Miller and Lyson split one of these open, they found it was full of skeletal remains.

It turns out Corral Bluffs represent sedimentary layers of rock deposited immediately after the collision, so it provides an incredibly detailed record of the years following.  Large animals and flowering plants (especially trees) were hit the hardest by the extinction; despite the prevailing wisdom that "dinosaurs died and mammals didn't," the more accurate statement is "big species were much more likely to die than little ones."  The bottleneck, in fact, seems to have taken out all the mammals larger than your average rat.  (Miller and Lyson found no evidence of mammals larger than six hundred grams that survived the extinction.)  Miller, who is a paleobotanist, concentrated not on the animal remains but the plants -- especially the 37,000 pollen grains he found fossilized in the sediment layers.  And from this, a picture began to emerge of what things were like in the years following the collision, which was described this week in a fascinating paper in Science.

The largest group of plants to come through the bottleneck were ferns, which thrive in disturbed areas and have spores that are pretty damage-resistant.  Unfortunately for the animals, fern leaves and roots are rather low in nutrients, so for a while, body sizes remained small because there simply wasn't enough food around to support big, or even medium-sized, herbivores.  But within a few thousand years -- a flash, evolutionarily speaking -- Fern World was replaced by Palm World, as proto-monocots (the group that contains not only palms, but grasses, lilies, orchids, irises, and a variety of other familiar plant families) evolved to be more robust.  Palms have oily fruit that are high in sugar, and there's a commensurate jump in mammalian body size, with species showing up that weighed five kilograms.

Palms were superseded by the ancestors of today's walnuts and hickories a hundred or so thousand years after that, and in "Pecan Pie World" (as Miller and Lyson call this era), and the higher nutritional quality of those seeds fueled another jump in body size, with the largest ones reaching thirty kilograms (the size of a large dog).  And after seven hundred thousand years, legumes diversified, and the high protein content of these species triggered another growth spurt, topping out at fifty kilograms -- a hundred times larger than the survivors of the collision, in less than a million years.

Nota bene: the growth in size wasn't done yet.  The Oligocene Epoch, from 34 to 23 million years ago, saw the largest land mammals that have ever existed, including the enormous Baluchitherium, a behemoth that could have converted an African elephant into an African elephant pancake:

[Image licensed under the Creative Commons Waqas-anees2014, Baluchitherium, The Largest Land mammal at Pakistan Museum of Natural History (PMNH), CC BY-SA 3.0]

The Miller and Lyson study offers us a message that is simultaneously reassuring and terrifying.  First, the human-caused "Sixth Extinction" that we are almost certainly undergoing as we speak is not going to eliminate life on Earth, and the species that survive will quickly spring back and diversify once we stop doing whatever we can to make the planet uninhabitable.  But the cautionary tale is that no matter what, it won't be what we had.  The diversity of flora and fauna that existed before the Chicxulub Collision was gone forever, and even though "life found a way" (to borrow a phrase from Jurassic Park), what evolved afterward was dramatically different than what was lost.  And, to put not too fine a point on it, the years immediately following the bottleneck were pretty freakin' horrible for all concerned, with an entire planet laid waste, and the animals that weren't directly killed by the impact itself largely facing habitat loss and rampant starvation.

So we shouldn't be so quick to adopt the Pollyanna-ish "it'll all be fine, nature is resilient" attitude toward our current fossil-fuel-crazy, pollution-blind willfully ignorant behavior.  If anything, we should recognize how fragile it all is -- and how, if we push too hard, we're likely to see a collapse of catastrophic proportions.  While we can pretty much count on evolution eventually producing a whole new set of what Darwin called "endless forms most beautiful and most wonderful," there's more than a passing chance that we won't be around to see them.

**************************************

In keeping with Monday's post, this week's Skeptophilia book recommendation is about one of the most enigmatic figures in mathematics; the Indian prodigy Srinivasa Ramanujan.  Ramanujan was remarkable not only for his adeptness in handling numbers, but for his insight; one of his most famous moments was the discovery of "taxicab numbers" (I'll leave you to read the book to find out why they're called that), which are numbers that are expressible as the sum of two cubes, two different ways.

For example, 1,729 is the sum of 1 cubed and 12 cubed; it's also the sum of 9 cubed and 10 cubed.

What's fascinating about Ramanujan is that when he discovered this, it just leapt out at him.  He looked at 1,729 and immediately recognized that it had this odd property.  When he shared it with a friend, he was kind of amazed that the friend didn't jump to the same realization.

"How did you know that?" the friend asked.

Ramanujan shrugged.  "It was obvious."

The Man Who Knew Infinity by Robert Kanigel is the story of Ramanujan, whose life ended from tuberculosis at the young age of 32.  It's a brilliant, intriguing, and deeply perplexing book, looking at the mind of a savant -- someone who is so much better than most of us at a particular subject that it's hard even to conceive.  But Kanigel doesn't just hold up Ramanujan as some kind of odd specimen; he looks at the human side of a man whose phenomenal abilities put him in a class by himself.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

Talking to the animals

Language is defined as "arbitrary symbolic communication."  The "symbolic" part is because the word (either spoken or written) for a concept is representative of the concept itself, and "arbitrary" because with the exception of onomatopoeic words like bang and swish there is no logical connection between the word and the concept itself.  (For example, the English word dog and the French word chien both have the same referent, but other than learned association there's nothing especially doggy about either word.)

It's been an argument of long standing whether any other animal species have true language.  A 2006 paper in the Journal of the Acoustical Society of America strongly suggests that whales have one of the most characteristic features of language -- syntax, the way words are put together to form meaningful sentences.  (What whale songs actually mean is still a matter of conjecture.)  A lot of animal sounds, such as bird songs and dogs barking, are dismissed as "non-linguistic vocalization" -- they are communication, but lack the "arbitrary symbolic" part of the definition of language.

Myself, I wonder.  I can tell when I hear my dog barking or growling whether he:

1. is playing;
2. sees a vicious intruder, like the UPS man;
3. sees an even more vicious intruder, like a chipmunk;
4. sees or hears my wife driving up;
5. is excited because he sees me or my wife get the ball and he knows he's going to get to play fetch, which is his most favorite thing ever;
6. is bored; or
7. wants to come inside because it's raining and he doesn't like getting his little toesies wet.  (He's just that tough.)

Each of those different-toned barks is completely distinct, and certainly they're arbitrary in that the connection between the tone and what it's communicating really has no logic to it.  (An exception is that the "excited bark" and "bored bark" are clearly different in volume and energy level, which you could argue isn't arbitrary.)

Even dog lovers will admit, however, that the set of concepts expressed by barking or growling is fairly limited.  So if you want to call it language, it's pretty rudimentary.  The situation becomes blurrier, however, with animals with a rich vocal repertoire, like parrots and dolphins.  And our sense that we're the only ones with true language was dealt another blow by a study released this week from the University of Zurich showing that primates called common marmosets not only speak regional dialects, when individuals are moved to a different region they learn -- and begin to use -- the dialect of the group they've joined.

"We could clearly show that the dialects of common marmosets are learned socially," said anthropologist Yvonne Zürcher, who co-authored the study.  "If their dialects were genetically determined, moving to a new place wouldn’t cause any change in calls.  The changes can’t be explained by differences in the environment, either."

Which seems to meet the characteristic of arbitrariness.

Again, I'm not trying to imply that marmosets have language in the same sense we do; whatever they're saying, it's unlikely that it has the richness and flexibility of human language.  But the black-and-white, "we have language and no one else does" attitude that has been prevalent for as long as the question has been considered may turn out to be as inaccurate as the "human vs. animal" distinction I still hear students voicing.  The truth is, vocal communication -- from the simplest (such as the hissing of a snake) to the most complex known (human language) -- is a continuum, just as are complexity, intelligence, emotional capacity, and anything else you might think separates us from the rest of Kingdom Animalia.

Which I think is pretty cool.

In any case, I better wrap this up, because Guinness is barking.  I know it's time to play ball.  He just told me so.

**************************************

In keeping with Monday's post, this week's Skeptophilia book recommendation is about one of the most enigmatic figures in mathematics; the Indian prodigy Srinivasa Ramanujan.  Ramanujan was remarkable not only for his adeptness in handling numbers, but for his insight; one of his most famous moments was the discovery of "taxicab numbers" (I'll leave you to read the book to find out why they're called that), which are numbers that are expressible as the sum of two cubes, two different ways.

For example, 1,729 is the sum of 1 cubed and 12 cubed; it's also the sum of 9 cubed and 10 cubed.

What's fascinating about Ramanujan is that when he discovered this, it just leapt out at him.  He looked at 1,729 and immediately recognized that it had this odd property.  When he shared it with a friend, he was kind of amazed that the friend didn't jump to the same realization.

"How did you know that?" the friend asked.

Ramanujan shrugged.  "It was obvious."

The Man Who Knew Infinity by Robert Kanigel is the story of Ramanujan, whose life ended from tuberculosis at the young age of 32.  It's a brilliant, intriguing, and deeply perplexing book, looking at the mind of a savant -- someone who is so much better than most of us at a particular subject that it's hard even to conceive.  But Kanigel doesn't just hold up Ramanujan as some kind of odd specimen; he looks at the human side of a man whose phenomenal abilities put him in a class by himself.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

Hello Dolly

Despite my tendency to fall into the "dubious" column with respect to most paranormal claims, I'm always appreciative of anyone who is more of a believer who nevertheless wants to see any evidence analyzed the right way.

That's my impression of The Anomalist, a website I check regularly for news of the weird.  It acts as a sort of clearinghouse for recent stories of odd or unexplained phenomena, but is really good about presenting all sides of the story -- and for calling out bogus claims as such.

Take, for example, some recent stories that appeared there, having to do with the alleged phenomenon of "haunted dolls."

For a lot of us, dolls are right up there with clowns in the "oh, hell no" department.  Their still, unresponsive faces and fixed expressions land right in the middle of the uncanny valley -- we tend to perceive a face that is human-like, but not quite human enough, as being more frightening or repellant than a face that has fewer distinctly human features.  (Think of a doll's face as compared to a teddy bear's.)  So we're already in scary territory for a good many folks.

Add to that the possibility of the doll being possessed, and you're looking at "scream like a little child and run away."

[Image licensed under the Creative Commons Eric Skiff from New York City, Creepy kid with a piano (194351881), CC BY-SA 2.0]

The first example is a World War II-era ventriloquist's dummy head called "Mr. Fritz" kept in a glass cabinet by its owner.  The owner started getting suspicious when he'd get up in the morning to find the cabinet door open, so he set up a camera to film it when he wasn't around.

The result, even if you're suspicious it's a fake, is pretty fucking creepy.  The glass door swings open, and then Mr. Fritz's eyes pop open -- and then his mouth moves.

After this, the owner apparently took the doll head out of the case and put it in a cabinet "secured by heavy chains." Why this was necessary, given all that happens is the door opens and the face moves, I don't know.  It's not like it had arms and legs and was walking about unassisted, or anything.

Still, I understand the apprehension.  Skeptic though I am, I don't think I'd want to sleep in the same room as that thing, heavy chains or no.

Then we have a British doll named Scarlet, who has been recorded using an "Electronic Voice Phenomena" (EVP) recorder -- and what she supposedly says indicates she should have her prim little porcelain mouth washed out with soap.

In a video of the doll, we get to hear playback of the alleged EVP.  Not only does she say her owner's name (Linzi), she says such things as "fuck off," "you're fucked," "shut the fuck up," and "fuck this."

So apparently Scarlet is even more fond of the f-word than I am, and that's saying something.

Anyhow, I listened to the recording several times -- and I'm just not hearing it.  I could barely make out "Linzi," but all of the alleged obscenities just sounded like white noise to me.  And that's the problem; as is pointed out in The Anomalist, there's a good explanation for a great many alleged EVP claims, and that's apophenia.  The human mind is a pattern-finding machine, which means that sometimes we'll see patterns when there's nothing there but chaos.  (You can think of our tendency to see faces -- pareidolia -- as a special case of apophenia.)

With Scarlet, people are already primed to hear something meaningful, so the static pops, clicks, and hums the EVP recorder plays back are interpreted with this bias.  Especially when we already know what the doll allegedly said -- all of which are listed right there in the article.

Put simply, you can't miss it when I tell you what's there.

The Anomalist provides a link to an article in The Skeptical Inquirer about this very tendency -- looking at particular cases of EVP claims and analyzing why they're probably nothing more than our tendency to impose order on chaos.

So unlike a lot of sensationalized sites about alleged paranormal phenomena, I can hold up The Anomalist as a place that has the exact right approach.  I'm probably still a bit more dubious than the site owners are, but by and large, we both have the same touchstone for accepting a claim -- logic and evidence.

And a bit of healthy skepticism about humanity's capacity both for getting things wrong... and for engaging in fakery.

**************************************

In keeping with Monday's post, this week's Skeptophilia book recommendation is about one of the most enigmatic figures in mathematics; the Indian prodigy Srinivasa Ramanujan.  Ramanujan was remarkable not only for his adeptness in handling numbers, but for his insight; one of his most famous moments was the discovery of "taxicab numbers" (I'll leave you to read the book to find out why they're called that), which are numbers that are expressible as the sum of two cubes, two different ways.

For example, 1,729 is the sum of 1 cubed and 12 cubed; it's also the sum of 9 cubed and 10 cubed.

What's fascinating about Ramanujan is that when he discovered this, it just leapt out at him.  He looked at 1,729 and immediately recognized that it had this odd property.  When he shared it with a friend, he was kind of amazed that the friend didn't jump to the same realization.

"How did you know that?" the friend asked.

Ramanujan shrugged.  "It was obvious."

The Man Who Knew Infinity by Robert Kanigel is the story of Ramanujan, whose life ended from tuberculosis at the young age of 32.  It's a brilliant, intriguing, and deeply perplexing book, looking at the mind of a savant -- someone who is so much better than most of us at a particular subject that it's hard even to conceive.  But Kanigel doesn't just hold up Ramanujan as some kind of odd specimen; he looks at the human side of a man whose phenomenal abilities put him in a class by himself.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

A chat at the pub

When I'm out in a crowded bar, I struggle with something that I think a lot of us do -- trying to isolate the voice of the person I'm talking to from all of the background noise.

I can do it, but it's a struggle.  When I'm tired, or have had one too many pints of beer, I find that my ability to hear what my friend is saying suddenly disappears, as if someone had flipped off a switch.  His voice is swallowed up by a cacophony of random noise in which I literally can't isolate a single word.

Usually my indication that it's time to call it a night.

[Image is in the Public Domain]

It's an interesting question, though, how we manage to do this at all.  Think about it; the person you're listening to is probably closer to you than the other people in the pub, but the others might well be louder.  Add to that the cacophony of glasses clinking and music blaring and whatever else might be going on around you, and the likelihood is that your friend's overall vocal volume is probably about the same as anyone or anything else picked up by your ears.

Yet most of us can isolate that one voice and hear it distinctly, and tune out all of the other voices and ambient noise.  So how do you do this?

Scientists at Columbia University got a glimpse of how our brains might accomplish this amazing task in a set of experiments described in a paper that appeared in the journal Neuron this week.  In "Hierarchical Encoding of Attended Auditory Objects in Multi-talker Speech Perception," by James O’Sullivan, Jose Herrero, Elliot Smith, Catherine Schevon, Guy M. McKhann, Sameer A. Sheth, Ashesh D. Mehta, and Nima Mesgarani, we find out that one part of the brain -- the superior temporal gyrus (STG) -- seems to be capable of boosting the gain of a sound we want to pay attention to, and to do so virtually instantaneously.

The auditory input we receive is a complex combination of acoustic vibrations in the air received all at the same time, so sorting them out is no mean feat.  (Witness how long it's taken to develop good vocal transcription software -- which, even now, is fairly slow and inaccurate.)  Yet your brain can do it flawlessly (well, for most of us, most of the time).  What O'Sullivan et al. found was that once received by the auditory cortex, the neural signals are passed through two regions -- first the Heschl's gyrus (HG), and then the STG.  The HG seems to create a multi-dimensional neural representation of what you're hearing, but doesn't really pick out one set of sounds as being more important than another.  The STG, though, is able to sort through that tapestry of electrical signals and amplify the ones it decides are more important.

"We’ve long known that areas of auditory cortex are arranged in a hierarchy, with increasingly complex decoding occurring at each stage, but we haven’t observed how the voice of a particular speaker is processed along this path," said study lead author James O’Sullivan in a press release.  "To understand this process, we needed to record the neural activity from the brain directly...  We found that that it’s possible to amplify one speaker’s voice or the other by correctly weighting the output signal coming from HG.  Based on our recordings, it’s plausible that the STG region performs that weighting."

The research has a lot of potential applications, not only for computerized vocal recognition, but for guiding the creation of devices to help the hearing impaired.  It's long been an issue that traditional hearing aids amplify everything equally, so a hearing-impaired individual in a noisy environment has to turn up the volume to hear what (s)he wants to listen to, but this can make the ambient background noise deafeningly loud.  If software can be developed that emulates what the STG does, it might create a much more natural-sounding and comfortable experience.

All of which is fascinating, isn't it?  The more we learn about our own brains, the more astonishing they seem.  Abilities we take entirely for granted are being accomplished by incredibly complex arrays and responses in that 1.3-kilogram "meat machine" sitting inside our skulls, often using mechanisms that still amaze me even after thirty-odd years of studying neuroscience.  

And it leaves me wondering what we'll find out about our own nervous systems in the next thirty years.

**************************************

In keeping with Monday's post, this week's Skeptophilia book recommendation is about one of the most enigmatic figures in mathematics; the Indian prodigy Srinivasa Ramanujan.  Ramanujan was remarkable not only for his adeptness in handling numbers, but for his insight; one of his most famous moments was the discovery of "taxicab numbers" (I'll leave you to read the book to find out why they're called that), which are numbers that are expressible as the sum of two cubes, two different ways.

For example, 1,729 is the sum of 1 cubed and 12 cubed; it's also the sum of 9 cubed and 10 cubed.

What's fascinating about Ramanujan is that when he discovered this, it just leapt out at him.  He looked at 1,729 and immediately recognized that it had this odd property.  When he shared it with a friend, he was kind of amazed that the friend didn't jump to the same realization.

"How did you know that?" the friend asked.

Ramanujan shrugged.  "It was obvious."

The Man Who Knew Infinity by Robert Kanigel is the story of Ramanujan, whose life ended from tuberculosis at the young age of 32.  It's a brilliant, intriguing, and deeply perplexing book, looking at the mind of a savant -- someone who is so much better than most of us at a particular subject that it's hard even to conceive.  But Kanigel doesn't just hold up Ramanujan as some kind of odd specimen; he looks at the human side of a man whose phenomenal abilities put him in a class by himself.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

A window into the distant past

I love a good mystery, and mysteries abound regarding human prehistory.

Of course, that's kind of self-evident, given that it's pre-history.  Anything we know is based on inference, from looking at artifacts and other traces left behind for us to find.  And like fossils, we have to keep in mind that what we're seeing is a small percentage -- no one knows how small -- of what was originally out there.  (One of my biology professors said that trying to reconstruct the Tree of Life from the existing fossil record is analogous to reconstructing the entire History of Art from a dozen paintings or sculptures chosen at random from the tens of thousands that have been created by humanity.  This was before the use of genetic evidence for determining phylogeny, so the situation has improved -- but we're still working from inference and very incomplete evidence.)

So that's pretty much where we are with our knowledge of human prehistory.  Which is why when there are eye-opening new discoveries in that field, it always makes me sit up and take notice.

Today we're going to look at three new archeological finds that have given us a new lens into our distant ancestors' lives, and all of which were published in the last week.

First, some new artifacts from Scotland have provided information about one of the least-known European cultures -- the Picts.

The Picts were a collection of (probably) Celtic-speaking tribes that inhabited Scotland prior to its invasion first by the Irish Dál Riata and then by the Vikings.  We know next to nothing about them or their culture.  Even the name of the group isn't native to them -- it comes from the Latin pictus ("painted"), from their habit of going into battle naked, covered with paint.

Which, I have to admit, is pretty damn badass.

But we don't know much else about them, because they left no written records at all.  We assume they spoke a Celtic language, but don't really know for sure; and any suggestion of root words in Gaelic that may have come from Pictish are guesses (such as the claim that place names starting with Pit-, Lhan-, and Aber- come from Pictish words).

So any artifacts that are unequivocally Pictish in origin are pretty amazing.  Like the ones discovered earlier this year by Anne MacInnes of the North of Scotland Archaeological Society.

The face of the stone in the photograph not only has designs and a pretty cool-looking mythical beast, it has an inscription -- in Latin letters -- that may well be a Latin transliteration of the Pictish language.  Which makes it a rarity indeed.

"The two massive beasts that flank and surmount the cross are quite unlike anything found on any other Pictish stone," said John Borland, of Historic Environment Scotland and the Pictish Arts Society.  "These two unique creatures serve to remind us that Pictish sculptors had a remarkable capacity for creativity and individuality.  Careful assessment of this remarkable monument will be able to tell us much about the production of Pictish sculpture that we could never have guessed at."


Then, there's the discovery that was made near the Tollense River, on the Baltic coast of Germany, that indicates the existence of mercenary soldiers -- three thousand years ago.

On a historic -- well, prehistoric -- battleground, a team from the Lower Saxony State Agency for Cultural Heritage discovered, alongside skeletal remains showing war-related injuries, a toolkit brought in by one of the soldiers.  It contains a chisel, a knife, an awl, and a small sword, along with fasteners that seem to indicate its origin in southern Germany -- a distance of about five hundred miles.

"It was a surprise to find a battlefield site.  It was a second surprise to see a battlefield site of this dimension with so many warriors involved, and now it's a big surprise that we are dealing with a conflict of a European scale," says Thomas Terberger, co-author of the study.  "We had before speculated that some of these people might have come from the south.  Now we have, from our point of view, a quite convincing indication that people from southern Central Europe were involved in this conflict."

Suggesting that the man who carried the bag may have been a mercenary, although that is (of course) an inference.  So right around the time King David ruled the Israelites, there were professional soldiers waging war upon either other in northern Europe.

Last, we have a study showing that the Greek islands have been occupied for longer than we'd realized...

... a lot longer.

When most people in North America and Western Europe think of an "old civilization," they come up with Greece, Rome, Egypt, Sumer, China, India, the Inca, the Mayans...  but all of those (venerable and fascinating though they are) only date back a few thousand years.  The Great Pyramid at Giza, for example, was built around 3,500 years ago -- which seems like a lot.

But this new discovery shows that the island of Naxos was inhabited by our ancestors (and/or near relatives) two hundred thousand years ago.

At that point, they weren't exactly human, or at least not what we usually consider to be modern humanity.  These inhabitants of Naxos were Neanderthals, and had crossed into what is now an island during a time when the sea level was considerably lower because a lot of the water was locked up in glacial ice.

"Until now, the earliest known location on Naxos was the Cave of Zas, dated to 7,000 years ago," said project director Tristan Carter, an anthropologist at Ontario’s McMaster University.  "We have extended the history of the island by 193,000 years...  It was believed widely that hominin dispersals were restricted to terrestrial routes until the later Pleistocene, but recent discoveries are requiring scholars to revisit these hypotheses."

The word "Neanderthal" has, in common parlance, become synonymous with "uncultured cave man," and that characterization misses the mark by a mile.  They had culture -- they buried their dead, apparently made music, and may have even had spoken language (DNA studies show that they had the FOX-P2 gene, which is one of the genetic underpinnings of language in humans).  They made artifacts not only of utility but of great beauty:

A Neanderthal Acheulean hand-axe from about 50,000 years ago

Some of the archaeologists associated with the Naxos study even think the Neanderthal inhabitants of the island may not have walked there when the sea level was low -- they may actually have arrived there by boat.

Pretty smart folks, the Neanderthals.

It's also uncertain that they actually represent a different species from us.  Most of us carry Neanderthal genetic markers -- apparently I have three-hundred-odd of them, making me in the sixtieth percentile, cave-man-wise -- so there was definitely interbreeding between them and modern humans.  So they might be more correctly considered a subspecies -- although, as I've mentioned before, the concept of species is one of the wonkiest definitions in biology, and all attempts to refine it have resulted in more exceptions and contradictions than ever.

So probably best just to say that they're part of the family.

In any case, we've got three papers in one week that give us some very impressive new data on prehistory.  Until we invent time travel, this kind of evidence is about all we can rely on to create a picture of what life was like back then.  Which, even with the new information, leaves lots of room for refinement -- and imagination.

**************************************

In keeping with Monday's post, this week's Skeptophilia book recommendation is about one of the most enigmatic figures in mathematics; the Indian prodigy Srinivasa Ramanujan.  Ramanujan was remarkable not only for his adeptness in handling numbers, but for his insight; one of his most famous moments was the discovery of "taxicab numbers" (I'll leave you to read the book to find out why they're called that), which are numbers that are expressible as the sum of two cubes, two different ways.

For example, 1,729 is the sum of 1 cubed and 12 cubed; it's also the sum of 9 cubed and 10 cubed.

What's fascinating about Ramanujan is that when he discovered this, it just leapt out at him.  He looked at 1,729 and immediately recognized that it had this odd property.  When he shared it with a friend, he was kind of amazed that the friend didn't jump to the same realization.

"How did you know that?" the friend asked.

Ramanujan shrugged.  "It was obvious."

The Man Who Knew Infinity by Robert Kanigel is the story of Ramanujan, whose life ended from tuberculosis at the young age of 32.  It's a brilliant, intriguing, and deeply perplexing book, looking at the mind of a savant -- someone who is so much better than most of us at a particular subject that it's hard even to conceive.  But Kanigel doesn't just hold up Ramanujan as some kind of odd specimen; he looks at the human side of a man whose phenomenal abilities put him in a class by himself.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

Weird math

When I was in Calculus II, my professor, Dr. Harvey Pousson, blew all our minds.

You wouldn't think there'd be anything in a calculus class that would have that effect on a bunch of restless college sophomores at eight in the morning.  But this did, especially in the deft hands of Dr. Pousson, who remains amongst the top three best teachers I've ever had.  He explained this with his usual insight, skill, and subtle wit, watching us with an impish grin as he saw the implications sink in.

The problem had to do with volumes and surface areas.  Without getting too technical, Dr. Pousson asked us the following question.  If you take the graph of y = 1/x:

And rotate it around the y-axis (the vertical bold line), you get a pair of funnel-shapes.  Not too hard to visualize.  The question is: what are the volume and surface area of the funnels?

Well, calculating volumes and surface areas is pretty much the point of integral calculus, so it's not such a hard problem.  One issue, though, is that the tapered end of the funnel goes on forever; the red curves never strike either the x or y-axis (something mathematicians call "asymptotic").  But calc students never let a little thing like infinity stand in the way, and in any case, the formulas involved can handle that with no problem, so we started crunching through the math to find the answer.

And one by one, each of us stopped, frowning and staring at our papers, thinking, "Wait..."

Because the shapes end up having an infinite surface area (not so surprising given that the tapered end gets narrower and narrower, but goes on forever) -- but they have a finite volume.

I blurted out, "So you could fill it with paint but you couldn't paint its surface?"

Dr. Pousson grinned and said, "That's right."

We forthwith nicknamed the thing "Pousson's Paint Can."  I only found out much later that the bizarre paradox of this shape was noted hundreds of years ago, and it was christened "Gabriel's Horn" by seventeenth-century Italian physicist and mathematician Evangelista Torricelli, who figured it was a good shape for the horn blown by the Archangel Gabriel on Judgment Day.

There are a lot of math-phobes out there, which is a shame, because you find out some weird and wonderful stuff studying mathematics.  I largely blame the educational system for this -- I was lucky enough to have a string of fantastic, gifted elementary and middle school math teachers who encouraged us to play with numbers and figure out how it all worked, and I came out loving math and appreciating the cool and unexpected bits of the subject.  It's a pity, though, that a lot of people have the opposite experience.  Which, unfortunately, is what happened with me in my elementary and middle school social studies and English classes -- with predictable results.

So math has its cool bits, even if you weren't lucky enough to learn about 'em in school.  Here are some short versions of other odd mathematical twists that your math teachers may not have told you about.  Even you math-phobes -- try these on for size.


1.  Fractals

A fractal is a shape that is "self-similar;" if you take a small piece of it, and magnify it, it looks just like the original shape did.  One of the first fractals I ran into was the Koch Snowflake, invented by Swedish mathematician Helge von Koch, which came from playing around with triangles.  You take an equilateral triangle, divide each of its sides into three equal pieces, then take the middle one and convert it into a (smaller) equilateral triangle.  Repeat.  Here's a diagram with the first four levels:

And with Koch's Snowflake -- similar to Pousson's Paint Can, but for different reasons -- we end up with a shape that has an infinite perimeter but a finite area.

Fractals also result in some really unexpected patterns coming out of perfectly ordinary processes.  If you have eight minutes and want your mind completely blown, check out how what seems like a completely random dice-throwing protocol generates a bizarre fractal shape called the Sierpinski Triangle.  (And no, I don't know why this works, so don't ask.  Or, more accurately, ask an actual mathematician, who won't just give you what I would, which is a silly grin and a shrug of the shoulders.)

2.  The Four-Color-Map Theorem

In 1852, a man named Francis Guthrie was coloring in a map of the counties of England, and noticed that he could do the entire map, leaving no two adjacent counties the same color, using only four different colors.  Guthrie wondered if that was true of all maps.

Turns out it is -- something that wasn't proven for sure until 1976.

Oh, but if you're talking about a map printed onto a Möbius Strip, it takes six colors.  A map printed on a torus (donut) would take seven.

Once again, I don't have the first clue why.  Probably explaining how it took almost a hundred years to prove.  But it's still pretty freakin' cool.


3.  Brouwer's Fixed-Point Theorem

In the 1950s, Dutch mathematician Luitzen Brouwer came up with an idea that -- as bizarre as it is -- has been proven true.  Take two identical maps of Scotland.  Deform one any way you want to -- shrink it, expand it, rotate it, crumple it, whatever -- and then drop it on top of the other one.

Brouwer said that there will be one point on the deformed copy of the map that is exactly on top of the corresponding point on the other map.

It even works on three dimensions.  If I stir my cup of coffee, at any given time there will be at least one coffee molecule that is in exactly the same position it was in before I stirred the cup.

Speaking of which, all this is turning my brain to mush.  I think I need to get more coffee before I go on to...


4.  The types of infinity

You might think that infinite is infinite.  If something goes on forever, it just... does.

Turns out that's not true.  There are countable infinities, and uncountable infinities, and the latter is much bigger than the former.

Infinitely bigger, in fact.

Let's define "countable" first.  It's simple enough; if I can uniquely assign a natural number (1, 2, 3, 4...) to the members of a set, it's a countable set.  It may go on forever, but if I took long enough I could assign each member a unique number, and leave none out.

So, the set of natural numbers is itself a countable set.  Hopefully obviously.

So is the set of odd numbers.  But here's where the weirdness starts.  It turns out that the number of natural numbers is exactly the same as the number of odd numbers.  You may be thinking, "Wait... that can't be right, there has to be twice as many natural numbers as odd numbers!"  But no, because you can put them in a one-to-one correspondence and leave none out:

1-1
2-3
3-5
4-7
5-9
6-11
7-13
etc.

So there are exactly the same number in both sets.

Now, what about real numbers?  The real numbers are all the numbers on the number line -- i.e. all the natural numbers plus all of the possible decimals in between.  Are there the same number of real and natural numbers?

Nope.  Both are infinite, but they're different kinds of infinite.

Suppose you tried to come up with a countable list of real numbers between zero and one, the same as we came up with a countable list of odd numbers above.  (Let's not worry about the whole number line, even.  Just the ones between zero and one.)  As I mentioned above, if you can do a one-to-one correspondence between the natural numbers and the members of that list, without leaving any out, then you've got a countable infinity.  So here are a few members of that list:

0.1010101010101010...
0.3333333333333333...
0.1213141516171819...
0.9283743929178394...
0.1010010001000010...
0.13579111315171921...

And so forth.  You get the idea.

German mathematician Georg Cantor showed that no matter what you do, your list will always leave some out.  In what's called the diagonal proof, he said to take your list, and create a new number -- by adding one to the first digit of the first number, to the second digit of the second number, to the third digit of the third number, and so on.  So using the short list above, the first six decimal places will be:

0.242413...

This number can't be anywhere on the list.  Why?  Because its first digit is different from the first number on the list, the second digit is different from the second number on the list, the third digit is different from the third number of the list, and so forth.  And even if you just artificially add that new number to the end of the list, it doesn't help you, because you can just do the whole process again and generate a new number that isn't anywhere on the list.

So there are more numbers between zero and one on the number line than there are natural numbers.  Infinitely more.


5.  Russell's Paradox

I'm going to end with one I'm still trying to wrap my brain around.  This one is courtesy of British mathematician Bertrand Russell, and is called Russell's Paradox in his honor.

First, let's define two kind of sets:

• A set is normal if it doesn't contain itself. For example, the "set of all trees on Earth" is normal, because the set itself is not a tree, so it doesn't contain itself.
• A set is abnormal if it contains itself. The "set of everything that is not a tree" is abnormal, because the set itself is not a tree.

Russell came up with a simple idea: he looked at "the set of all possible normal sets."  Let's call that set R.  Now here's the question:

Is R normal or abnormal?

Thanks, I'll show myself out.

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In keeping with Monday's post, this week's Skeptophilia book recommendation is about one of the most enigmatic figures in mathematics; the Indian prodigy Srinivasa Ramanujan.  Ramanujan was remarkable not only for his adeptness in handling numbers, but for his insight; one of his most famous moments was the discovery of "taxicab numbers" (I'll leave you to read the book to find out why they're called that), which are numbers that are expressible as the sum of two cubes, two different ways.

For example, 1,729 is the sum of 1 cubed and 12 cubed; it's also the sum of 9 cubed and 10 cubed.

What's fascinating about Ramanujan is that when he discovered this, it just leapt out at him.  He looked at 1,729 and immediately recognized that it had this odd property.  When he shared it with a friend, he was kind of amazed that the friend didn't jump to the same realization.

"How did you know that?" the friend asked.

Ramanujan shrugged.  "It was obvious."

The Man Who Knew Infinity by Robert Kanigel is the story of Ramanujan, whose life ended from tuberculosis at the young age of 32.  It's a brilliant, intriguing, and deeply perplexing book, looking at the mind of a savant -- someone who is so much better than most of us at a particular subject that it's hard even to conceive.  But Kanigel doesn't just hold up Ramanujan as some kind of odd specimen; he looks at the human side of a man whose phenomenal abilities put him in a class by himself.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

Truth, lies, and Facebook

There's been a whole lot of buzz lately on the subject of free speech and social media.

The maelstrom has centered around the controversial figure of Mark Zuckerberg, CEO of Facebook, whose rather lax policies about truth in political advertisements is said by many to have contributed to Donald Trump's nomination and eventual electoral win.  As we enter another presidential election season (lord help us all), the whole issue has come up again -- with Zuckerberg defending his position on allowing ads even if they contain factual inaccuracy.

I.e., "Fake News."  Oh, how I've come to loathe that phrase, which gets lobbed every time someone hears a piece of news unfavorable to their preferred politician.  Call it "Fake News," and you can forthwith stop thinking about it.

It's been a remarkably efficient strategy -- and is largely to blame for the current political mess we're in.

In any case, Zuckerberg isn't backing down.  He said:

While I certainly worry about the erosion of truth, I don’t think most people want to live in a world where you can only post things that tech companies judge to be 100% true...  We’re seeing people across the spectrum try to define more speech as dangerous because it may lead to political outcomes they see as unacceptable.  Some hold the view that since the stakes are now so high, they can no longer trust their fellow citizens with the power to communicate and decide what to believe for themselves.  I personally believe that this is more dangerous for democracy over the long term than almost any speech.

Which, to me, misses the point entirely.

Free speech covers opinions like, "I think Donald Trump has been a great president."  I have no right to censor that, whether or not I agree with it.  However, saying "Donald Trump eats live babies for breakfast" is not covered under free speech, because it's a false statement intended to discredit.

Which the law refers to as "libel."

[Image licensed under the Creative Commons Ibrahim.ID, Socialmedia-pm, CC BY-SA 4.0]

So allowing political ads is one thing.  You can craft a political ad that steers clear of libel even if it's highly critical of the candidate you're running against.   But when you post factual inaccuracies (better known as "lies") about someone, with the intent to cause harm to their reputation or electability, that's no longer a matter of free speech.

And as such, yes, Mark, you have an obligation to block such advertisements.

Elizabeth Warren responded to Zuckerberg's stance by putting together an ad claiming that Zuckerberg is a Trump supporter (which he claims is untrue).  But the salvo evidently didn't really strike the target.  Zuckerberg is still unapologetic for his position:

Do we ban ads about health care or immigration or women’s empowerment?  And if you’re not going to ban those, does it really make sense to give everyone a voice in the political debates except for the candidates themselves?  I believe when it’s not absolutely clear what to do, we should err on the side of greater expression.

Well, actually, you have banned ads about health care.  Earlier this year, Facebook (rightly) decided to block ads promoting the talking points of the anti-vaxxers.  Why?  Because what they were saying was false and harmful.  That's the acid test, you know?  (1) Is it false? and (2) is it harmful or damaging to the person or persons targeted?

If the answer to those two questions is "yes," then social media has an obligation to say no to the advertisement.

Hard to see how anything about "women's empowerment" would fall under those guidelines.

So what Zuckerberg is engaging in is a false equivalency -- and I believe he's perfectly well aware of it.  Those ads bring in millions of dollars of revenue, so he has a vested interest in turning a blind eye, regardless of the political or societal outcome.  As usual, it's all about the bottom line.

At present, I still have a Facebook.  For one thing, it's my primary way of keeping in touch with people who live far away and whom I rarely see.  For another, it's the main social media platform used by my publishing company, so I'd be cutting myself off from them pretty thoroughly if I deleted my profile.

So I'm sticking -- for the time being.  I'd love to see enough pressure put on Zuckerberg that he changes his stance, and at least pledges to stop advertisements that engage in spreading demonstrably false statements.  That's all we're asking, really -- not to take sides, but to stop all sides from lying for their own gain.

It's not a difficult concept.  And hard to see how you'd craft an argument that increasing the amount of truth in all kinds of media is a bad thing.

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This week's Skeptophilia book-of-the-week is from an author who has been a polarizing figure for quite some time; the British evolutionary biologist Richard Dawkins.  Dawkins has long been an unapologetic critic of religion, and in fact some years ago wrote a book called The God Delusion that caused thermonuclear-level rage amongst the Religious Right.

But the fact remains that he is a passionate, lucid, and articulate exponent of the theory of evolution, independent of any of his other views.  This week's book recommendation is his wonderful The Greatest Show on Earth, which lays out the evidence for biological evolution in a methodical fashion, in terminology accessible to a layperson, in such a way that I can't conceive how you'd argue against it.  Wherever you fall on the spectrum of attitudes toward evolution (and whatever else you might think of Dawkins), you should read this book.  It's brilliant -- and there's something eye-opening on every page.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]