Skeptophilia (skep-to-fil-i-a) (n.) - the love of logical thought, skepticism, and thinking critically. Being an exploration of the applications of skeptical thinking to the world at large, with periodic excursions into linguistics, music, politics, cryptozoology, and why people keep seeing the face of Jesus on grilled cheese sandwiches.
I'm currently working on a trilogy about the fall of civilization that is not, I hasten to state, inspired by current events.
It's actually a story I've been cogitating on since I was in college. How would ordinary people cope with the collapse of the comfortable support network we're all so very used to? The three books of the trilogy are set about five hundred years apart, and center around (respectively) the time when everything fell apart, a period of "Dark Ages" during which a significant chunk of what's left of humanity has lost technology and even literacy, and the time during which things come full circle and people begin to rediscover science and mathematics and all that comes with it. In the second book, The Scattering Winds, there's a sequence when the main character comes across the mostly-intact remnants of a library from before the fall -- and is overwhelmed by the magnitude of what was lost:
"Do these books come from the Before Time?" Kallian asked in a near whisper.
Kasprit Seely nodded, looking around them at the shadowed shelves, laden with dust-covered books. "Before the flood, you mean? I’ve no doubt that many of them do. During the Black Years, with the floods and the plagues, people were trying their hardest just to survive. A lot of them didn’t, of course. From what I’ve read, in the times before, there were a thousandfold more people than there are now, and they had ample food and living space and comfort and could spend their time reading and writing books. But when a hundred years passes with deprivation and famine and death on your doorstep every day, a lot is forgotten. You’ll see in some books there are numbers that I believe were some sort of system of keeping track of the passage of years. But I’ve not been able to decipher how it’s to be read, nor how it relates to the present day. Nowadays we simply track time by the year of the reign of the current king. So this is the twenty-first year of the reign of High King Sweyn VII, long may he live." Kasprit pulled a book off a shelf in the room they’d entered—the cover said The Diversity of Life by E. O. Wilson, and was adorned with a design of a brightly-colored beetle with long antennae. He blew the dust off the top and opened the cover, flipped a couple of pages in, and rested the tip of his long index finger on a line that said, "Copyright 1992."
I thought about this scene when I came upon an article about an archaeological discovery made in 2017 in the center of the German city of Cologne. Cologne is immensely old; it was the main settlement of the Ubii, a Germanic tribe that (unlike many of their neighbors) forged a strong and long-lasting alliance with the Romans. Eventually, the place got so thoroughly Romanized that it was renamed Colonia Claudia Ara Agrippinensium -- "Colony of Claudius and the Altar of the Agrippinians." This proved to be a clumsy appellation, and it was shortened to Colonia, which is where the modern name of Cologne comes from.
Well, it turns out in the center of modern Cologne, a city with a million inhabitants, are the remnants of what used to be the Library of Colonia. At first, it was thought that the foundation was part of a stone-walled fortification, but when the archaeologists began to discover deep niches in the walls, they realized that its purpose was something altogether different.
"It took us some time to match up the parallels – we could see the niches were too small to bear statues inside," said Dirk Schmitz, of the Roman-Germanic Museum of Cologne, who participated in the research. "But what they are are kind of cupboards for the scrolls. They are very particular to libraries – you can see the same ones in the library at Ephesus."
The foundations of the Roman Library of Cologne [Image courtesy of the Romano-Germanic Museum of Cologne]
The library of Cologne in its heyday -- the middle of the second century C.E. -- is thought to have housed around twenty thousand scrolls, of which not a single one survives. All that remains are the spaces they occupied, now inhabited only by the ghosts of long-gone books whose titles we'll never know.
When I read this article, I was struck with same feeling of longing and grief I get whenever I think about the Great Library of Alexandria and the other repositories of human knowledge. It's what I tried to communicate in Kallian Dorn's character in The Scattering Winds; perhaps lost knowledge can be regained, but the creativity, hearts, and voices of the people who wrote these scrolls are gone forever. Impermanence is part of reality, and -- in the words of the band Kansas -- "Nothing lasts forever but the Earth and sky." But seeing the remains of this once-great library makes me mourn for what was housed there, even so.
I suspect I'm not the only one who feels this way. And if time travel is ever invented, I think the Great Libraries of Antiquity tour is going to be sold out indefinitely.
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 usefully, 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.
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.
[Nota bene: it works with any map, not just maps of Scotland. I just happen to like Scotland.]
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:
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:
I've always wondered how our distant ancestors survived during the various ice ages.
After all, we're mostly-hairless primates evolved on the warm, comfy African savanna, and it's hard to imagine how we coped with conditions like you often see depicted in books on early humans:
Le Moustier Neanderthals by Charles Knight (1920) [Image is in the Public Domain]
Despite the bear pelts around their nether regions, I've always wondered how they didn't all freeze to death. When the weather's nice, bare skin is fine; I only wear a shirt during the summer under duress, and can't remember the last time I wore swim trunks when I went swimming in my pond. But when the weather's cold -- which, here in upstate New York, is more often than not -- I'm usually wearing layers, and that's even indoors with our nice modern heating system. Okay, admittedly I'm a wuss about the cold, but the fact remains that we're evolved to dwell in temperate regions. Which, for a significant part of the Pleistocene Epoch, most of the world was not.
In particular, during the Last Glacial Maximum, between twenty-six and twenty thousand years ago, much of the Northern Hemisphere was experiencing a climate that the word "unpleasant" doesn't even begin to describe. The average temperature was 6 C (11 F) colder than it is today, which was enough to cause ice sheets to spread across much of North America and northern Europe (where I currently sit, in fact, was underneath about thirty meters of ice). Much of the non-glaciated land experienced not only dreadful cold, but long periods of drought. The combined result is that the sea level was an estimated 130 meters lower than it is today, and broad dry valleys lay across what are now the bottoms of the Bering Sea, the North Sea and English Channel, and the Gulf of Carpentaria.
These conditions opened up passageways for some people, and closed off living space for others. This was the time that the various pulses of immigrants crossed from Siberia through Beringia and into North America, where they became the ancestors of today's Indigenous Peoples of North and South America. (If you want to read a brilliant account of how this happened, and some of the science behind how we know, you must read Jennifer Raff's wonderful book Origin: A Genetic History of the Americas.) The same sort of thing happened from southeast Asia into what is now Australia.
In Europe, though, things got dicey to the point that it's a wonder anyone survived at all. In fact, what brings this up is a study that appeared in Nature last week by a humongous team led by paleogeneticist Cosimo Posth of the Max Planck Institute of Evolutionary Anthropology. The team did a complete genomic analysis of 356 individuals whose remains range from thirty-five thousand to five thousand years of age -- so right across that awful Last Glacial Maximum period -- to try to figure out how groups moved when the ice started coming in, and afterwards, once it retreated.
What they found was that only one part of Europe showed a consistent human genetic signature throughout the time period: the Iberian Peninsula. What this indicates is that modern Spain and Portugal were a "climate refugium" during the worst of the glaciation, where people came to stay when the climate turned very cold, and pretty much stayed put. Other areas that you might think were possible candidates for comparatively warm hideouts, such as what are now Italy and Greece, show a significant genomic shift across the Last Glacial Maximum, indicating that the people there before the cold set in either migrated or else died out, and were replaced by immigrants who moved in after things warmed and the area once again became more hospitable for humans.
"At that time, the climate warmed up quickly and considerably and forests spread across the European continent," said Johannes Krause, senior author of the study, in an interview with Science Daily. "This may have prompted people from the south to expand their habitat. The previous inhabitants may have migrated to the north as their habitat, the 'mammoth' steppe, dwindled,. It is possible that the migration of early farmers into Europe triggered the retreat of hunter-gatherer populations to the northern edge of Europe. At the same time, these two groups started mixing with each other, and continued to do so for around three thousand years."
Me, I'm curious what happened to these people afterward. As a linguist, not to mention a white guy of western European descent, I've wondered if we're talking about my forebears, here -- and what languages they spoke. My suspicion is that we're looking at the ancestors of today's Basques, who still live in northern Spain; they speak a non-Indo-European language that is usually considered a relic of the earliest languages spoken in Europe. The Indo-European-speaking peoples (therefore the ancestors of the majority of today's Europeans) didn't reach Europe until about four thousand years ago, so long after the heyday of the people who were the subjects of the Posth et al. paper.
So you have to wonder who the descendants of these very early Europeans are. "Not me" is my general assessment, considering my general cold-hardiness. Drop me into an ice age where I had to live in a cave, hike on glaciers, hunt mammoth, and fend off cave bears, and I'd last maybe three days, tops. I'm highly impressed by the ability of these ancient humans to survive, but given a choice I'll stick with my warm house, indoor plumbing, electric stove, and coffee maker.
When I was in Ecuador in 2019, I was blown away by its natural beauty. The cloud forests of the mid-altitude Andes are, far and away, the most beautiful place I've ever been, and I've been lucky enough to see a lot of beautiful places. Combine that with the lovely climate and the friendliness of the people, and it puts the highlands of Ecuador on the very short list of places I'd happily move to permanently.
What brought me there were the birds. It's a tiny country, but is home to 1,656 species of birds -- about one-sixth of the ten-thousand-odd species found worldwide. Most strikingly, it has 132 different species of hummingbirds. Where I live, in upstate New York, we have only one -- the Ruby-throated Hummingbird (Archilochus colubris) -- but there, they have an incredible diversity within that one group. Because each species is dependent on particular flowers for their food source, some of them have extremely restricted ranges, often narrow bands of terrain at exactly the right climate and altitude to support the growth of that specific plant. You go a few hundred meters up or downhill, and you've moved out of the range where that species lives -- and into the range of an entirely different one.
The most striking thing about the hummingbirds is their iridescence. My favorite one, and in the top five coolest birds I've ever seen, is the Violet-tailed Sylph (Aglaiocercus coelestis):
What's most fascinating about birds like this one is that the feathers' stunning colors aren't only due to pigments. A pigment is a chemical that appears colored to our eyes because its molecular structure allows it to absorb some frequencies of light and reflect others; the chlorophyll in plants, for example, looks green because it preferentially absorbs light in the red and blue-violet regions of the spectrum, and reflects the green light back to our eyes. Hummingbirds have some true pigments, but a lot of their most striking colors are produced by interference -- on close analysis, you find that the fibers of the feathers are actually transparent, but when light strikes them they act a bit like a prism, breaking up white light into its constituent colors. Because of the spacing of the fibers, some of those wavelengths interfere destructively (the wavelengths cancel each other out) and some interfere constructively (they superpose and are reinforced). The spacing of the fibers determines what color the feathers appear to be. This is why if you look at the electric blue/purple tail of the Violet-tailed Sylph from the side, it looks jet black -- your eyes are at the wrong angle to see the refracted and reflected light. Look at it face-on, and suddenly the iridescent colors shine out.
So the overall color of the bird comes from an interplay between whatever true pigments it has in its feathers, and the kind of interference you get from the spacing of the transparent fibers. This is why when you recombine these features through hybridization, you can get interesting and unexpected results -- as some scientists from Chicago's Field Museum found out recently.
Working in Peru's Cordillera Azul National Park, on the eastern slopes of the Andes, ornithologist John Bates discovered what he'd thought was a new species in the genus Heliodoxa, one with a glittering gold throat. He was in for a shock, though, when the team found out through genetic analysis that it was a hybrid of two different Heliodoxa species -- H. branickii and H. gularis -- both of which have bright pink throats.
"It's a little like cooking: if you mix salt and water, you kind of know what you're gonna get, but mixing two complex recipes together might give more unpredictable results," said Chad Eliason, who co-authored the study. "This hybrid is a mix of two complex recipes for a feather from its two parent species... There's more than one way to make magenta with iridescence. The parent species each have their own way of making magenta, which is, I think, why you can have this nonlinear or surprising outcome when you mix together those two recipes for producing a feather color."
The gold-throated bird apparently isn't a one-off, as more in-depth study found that it didn't have an even split of genes from H. branickii and H. gularis. It seems like one of its ancestors was a true half-and-half hybrid, but that hybrid bird then "back-crossed" to H. branickii at least once, leaving it with more H. branickii genes. All of which once again calls into question our standard model of species being little cubbyholes with impermeable walls. The textbook definition of species -- "a morphologically-distinct population which can interbreed and produce fertile offspring" -- is unquestionably the most flimsy definition in all of biology, and admits of hundreds of exceptions (either morphologically-identical individuals which cannot interbreed, or morphologically-distinct ones that hybridize easily, like the Heliodoxa hummingbirds just discovered in Peru).
In any case, the discovery of this hybrid is fascinating. You have to wonder how many more of them there are out there. The fact that its discovery ties together the physics of light, genetics, and evolution is kind of amazing. Just further emphasizes that if you're interested in science, you will never, ever be bored.
It's fascinating to consider what our distant forebears actually looked like.
Realistic paintings are a relatively recent innovation. The marble statues at the height of classical Greek and Roman civilization were amazingly detailed, in some cases showing almost photographic realism; but it bears keeping in mind that since the people being depicted were often the rich and powerful, portraying them as they actually looked might not have been in the sculptor's best interest if the subject wasn't very attractive. Any art historians in the audience could comment with far greater authority on the topic, but suffice it to say that in picturing what a great many historical figures looked like, we have little to go on.
Recent advances in reconstruction of faces from skulls has given us some idea of the appearance of our (very) distant ancestors; most notably, the stunning work of my friend John Gurche in creating lifelike models of early hominins has appeared in Smithsonian Magazine, National Geographic, and museums around the world. This kind of work not only requires incredible artistic ability, but a deep understanding of how the morphology of the human skull, and the arrangement of layers of muscle on top of it, creates the contours of the face -- i.e., a comprehensive understanding of human anatomy.
The reason all this comes up is an article link sent to me by a friend and loyal reader of Skeptophilia about the reconstruction of a face from a skull found in the ancient city of Jericho. The site of Jericho -- now part of the West Bank -- has been inhabited for a very long time. The first certain settlement there was eleven thousand years ago, and it's been occupied pretty much continuously ever since. (If you're curious, the famous biblical Battle of Jericho, in which Joshua of the Israelites allegedly had his men blow trumpets and thereby flattened the walls of Jericho, almost certainly never happened, and that's not even counting the whole magical music thing; the city had already been seriously damaged during a well-documented invasion from Egypt in the fifteenth century B.C.E., and there's no archaeological evidence whatsoever of a later destruction by the Israelites. The whole Joshua story, said archaeologist and Old Testament scholar William Dever, was "invented out of whole cloth" to bolster the Israelites' "God is on our side" narrative.)
Be that as it may, the city of Jericho does have a very long history, and has laid claim to being the oldest continuously inhabited city in the world. So it was with a great deal of interest that I read the article sent by my friend, which describes the reconstruction of a nine-thousand-year-old skull from Jericho -- and gives us an idea of how its owner might have appeared.
Without further ado, here's what this inhabitant of Jericho, circa 7000 B.C.E., may have looked like:
[Image courtesy of Cicero Moraes, Thiago Beaini and Moacir Santos, and the British Museum]
"With the data we have, which [is] basically structural, we have a good idea of what … this living person’s face would look like," said Cicero Moraes, who led the research. "But details like the shape of the hair, the color of the hair and eyes are very difficult to do precisely."
Still, the reconstruction brings to life the face of someone who has been dead for ninety centuries, and that's a remarkable achievement. Even if some of the details aren't quite right, it's closer than anything we've had before. Looking at his expression makes me wonder who he was, what he was like, how he lived, how he died -- and it connects me to this ancient man who lived in another time and place. Even if we never find out anything more about him, it links us all across the ages to our shared humanity, and that, I think, is wonderful.
A couple of days ago, I was talking with my son about the Standard Model of Particle Physics (as one does).
The Standard Model is a theoretical framework that explains what is known about the (extremely) submicroscopic world, including three of the four fundamental forces (electromagnetism, the weak nuclear force, and the strong nuclear force), and classifies all known subatomic particles.
Many particle physicists, however, are strongly of the opinion that the model is flawed. One issue is that one of the four fundamental forces -- gravitation -- has never been successfully incorporated into the model, despite eighty years of the best minds in science trying to do that. The discovery of dark matter and dark energy -- or at least the effects thereof -- is also unaccounted for by the model. Neither does it explain baryon asymmetry, the fact that there is so much more matter than antimatter in the observable universe. Worst of all is that it leaves a lot of the quantities involved -- such as particle masses, relative strengths of forces, and so on -- as empirically-determined rather than proceeding organically from the theoretical underpinnings.
This bothers the absolute hell out of a lot of particle physicists. They have come up with modification after modification to try to introduce new symmetries that would make it seem not quite so... well, arbitrary. It just seems like the most fundamental theory of everything should be a lot more elegant than it is, and that there should be some underlying beautiful mathematical logic to it all. The truth is, the Standard Model is messy.
Every one of those efforts to create a more beautiful and elegant model has failed. Physicist Sabine Hossenfelder, in a brilliant but stinging takedown of the current approach that you really should watch in its entirety, puts it this way: "If you follow news about particle physics, then you know that it comes in three types. It's either that they haven't found that thing they were looking for, or they've come up with something new to look for which they'll later report not having found, or it's something so boring you don't even finish reading the headline." Her opinion is that the entire driving force behind it -- research to try to find a theory based on beautiful mathematics -- is misguided. Maybe the actual universe simply is messy. Maybe a lot of the parameters of physics, such as particle masses and the values of constants, truly are arbitrary (i.e., they don't arise from any deeper theoretical reason; they simply are what they're measured to be, and that's that). In her wonderful book Lost in Math: How Beauty Leads Physics Astray, she describes how this century-long quest to unify physics with some ultra-elegant model has generated very close to nothing in the way of results, and maybe we should accept that the untidy Standard Model is just the way things are.
Because there's one thing that's undeniable: the Standard Model works. In fact, what generated this post (besides the conversation with my science-loving son) is a paper that appeared last week in Physical Review Letters about a set of experiments showing that the most recent tests of the Standard Model passed with a precision that beggars belief -- in this case, a measurement of the electron's magnetic moment which agreed with the predicted value to within 0.1 billionths of a percent.
This puts the Standard Model in the category of being one of the most thoroughly-tested and stunningly accurate models not only in all of physics, but in all of science. As mind-blowingly bizarre as quantum mechanics is, there's no doubt that it has passed enough tests that in just about any other field, the experimenters and the theoreticians would be high-fiving each other and heading off to the pub for a celebratory pint of beer. Instead, they keep at it, because so many of them feel that despite the unqualified successes of the Standard Model, there's something deeply unsatisfactory about it. Hossenfelder explains that this is a completely wrong-headed approach; that real discoveries in the field were made when there was some necessary modification of the model that needed to be made, not just because you think the model isn't pretty enough:
If you look at past predictions in the foundations of physics which turned out to be correct, and which did not simply confirm an existing theory, you find it was those that made a necessary change to the theory. The Higgs boson, for example, is necessary to make the Standard Model work. Antiparticles, predicted by Dirac, are necessary to make quantum mechanics compatible with special relativity. Neutrinos were necessary to explain observation [of beta radioactive decay]. Three generations of quarks were necessary to explain C-P violation. And so on... A good strategy is to focus on those changes that resolve an inconsistency with data, or an internal inconsistency.
And the truth is, when the model you already have is predicting with an accuracy of 0.1 billionths of a percent, there just aren't a lot of inconsistencies there to resolve.
I have to admit that I get the particle physicists' yearning for something deeper. John Keats's famous line, "Beauty is truth, and truth beauty; that is all ye know on Earth, and all ye need to know" has a real resonance for me. But at the same time, it's hard to argue Hossenfelder's logic.
Maybe the cosmos really is kind of a mess, with lots of arbitrary parameters and empirically-determined constants. We may not like it, but as I've observed before, the universe is under no obligation to be structured in such a way as to make us comfortable. Or, as my grandma put it -- more simply, but no less accurately -- "I've found that wishin' don't make it so."
Seems like I've featured a lot of research about astrophysics here at Skeptophilia lately, and that's not only because I'm really interested in it, but because the astrophysicists keep discovering stuff that is downright amazing.
Consider two papers last week highlighting different bizarre behaviors of one of the weirdest beasts in the cosmic zoo -- black holes.
Since the first serious proposal of their existence, by German physicist Karl Schwarzschild in 1916, they've captivated the imagination. Not only are they created in supernovas -- surely the most spectacular events in the universe -- their intense gravitational warping of space makes it impossible for anything, even light, to escape. If you were falling into one (not recommended), time would slow down, at least as perceived by someone watching you from a safe distance. From your perspective, though, your own watch would continue to run normally, until it (and you) succumbed to spaghettification -- yes, that's actually what the astrophysicists call it -- the point where the tidal forces across even such a short distance as the one between your head and your feet became sufficient to stretch you into the universe's most horrifying pasta.
As strange and terrifying as they are, they were thought for a long time to be physically quite simple; physicist John Archibald Wheeler said that "black holes have no hair," by which he meant that they have no arbitrary differences between each other that cannot be accounted for by three externally-observable parameters: their mass, angular momentum, and electric charge. It took no less a luminary than Stephen Hawking to demonstrate that this wasn't true. In 1974 he showed that (contrary to the picture of a black hole as a one-way-only object) they slowly evaporate through a phenomenon now called Hawking radiation in his honor. The general idea here is that the extremely warped space near the event horizon generates sufficient energy to facilitate significant pair production -- creation of particle/antiparticle pairs. Almost always, those pairs recombine and mutually annihilate in a fraction of a second after creation, so they're called "virtual particles" that have a measurable effect on ordinary matter but no long-term reality. However, in the vicinity of a black hole, things are different. Because of the extraordinary gravitational field at the event horizon, sometimes there's enough time for the two particles in the pair to separate sufficiently that one of them crosses the event horizon and the other doesn't. At that point, the one that's fallen in is doomed; the other one just keeps moving away -- and that's the Hawking radiation.
But what this does is robs a small bit of the mass/energy from the black hole, so its volume decreases. What Hawking showed is that black holes actually evaporate. It's on a huge time scale; a massive black hole has a life span many times longer than the current age of the universe. But it suggests that everything -- even something as seemingly permanent as a black hole -- has a finite life span.
[Image is in the Public Domain courtesy of NASA/JPL]
Even that, though, doesn't begin to plumb the depths of the weirdness of these things. Take for example the two papers I referenced earlier, each of which shows an only partially-explained behavior of black holes.
In the first, that appeared in The Astrophysical Journal, researchers looked at the odd behavior of an object called X-7 that is close to Sagittarius A*, the massive black hole at the center of the Milky Way galaxy. X-7 is a cloud of gas and dust about fifty times the mass of the Earth, and is so close to Sagittarius A* that it orbits it once every 170 years. The tidal forces are spaghettifying X-7 -- fast enough to observe in real time.
"No other object in this region has shown such an extreme evolution," said Anna Ciurlo of UCLA, who is the paper’s lead author. "It started off comet-shaped and people thought maybe it got that shape from stellar winds or jets of particles from the black hole. But as we followed it for twenty years we saw it becoming more elongated. Something must have put this cloud on its particular path with its particular orientation."
From its current trajectory, the researchers think that it will get close enough to the black hole by 2036 that it will be torn apart completely.
If X-7 is being chewed up, there's another place in the universe where a black hole has been spat out. The galaxy RCP 28, 7.5 billion light years from Earth, appears to be undergoing something cataclysmic; its central black hole, with an estimated mass of twenty million times that of the Sun, has been ejected from the middle and is moving away at a speed of 5.6 million kilometers per hour, pulling along a streamer of stars behind it like the tail of a comet.
What could possibly slingshot an object that massive at such high velocities remains to be seen; the researchers think it was in some kind of unstable orbit with two or more massive bodies. (As I described in a post a couple of years ago, the three-body problem -- the mathematics of three or more objects of similar masses orbiting a common center of gravity -- is one of the most famous unsolved problems in classical mechanics, and models show that most of the time, these sorts of configurations are unstable.) But the authors are clear that more study is needed to confirm the analysis, and then, to come up with an explanation for what exactly is going on.
In any case, what's obvious is that we've only scratched the surface of these strange objects. Every time we look up into the star-spangled sky, we find new and amazing things to wonder at. The astrophysicists, I think, are in for a long and exciting ride.
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