Thursday, December 11, 2025
Burning down the house
Wednesday, December 10, 2025
Coded messages
Did you know that there are illegal numbers?
I didn't, at least not until yesterday. It turns out, of course, that the issue isn't the number itself, but the information it contains (or makes reference to). Numbers by themselves, as simple mathematical symbols, are pretty devoid of meaning -- although to the suspicious-minded, it sometimes doesn't look that way. While physicist Richard Feynman was doing highly classified work at Los Alamos, he repeatedly got in trouble, and was accused of sending encoded information to his wife. He recounts the following experience in his autobiography, Surely You're Joking, Mr. Feynman!:
Anyway, one day I'm piddling around with the computing machine, and I notice something very peculiar. If you take 1 divided by 243 you get .004115226337... It's quite cute. It goes a little cockeyed after 559 when you're carrying but it soon straightens itself out and repeats itself nicely. I thought it was kind of amusing.
Well, I put that in the mail, and it comes back to me. It doesn't go through, and there's a little note: "Look at Paragraph 17B." I look at Paragraph 17B. It says, "Letters are to be written only in English, Russian, Spanish, Portuguese, Latin, German, and so forth. Permission to use any other language must be obtained in writing." And then it said, "No codes."
So I wrote back to the censor a little note included in my letter which said that I feel that of course this cannot be a code, because if you actually do divide 1 by 243, you do, in fact, get all that, and therefore there's no more information in the number .004115226337... than there is in the number 243, which is hardly any information at all. And so forth. I therefore had to ask permission to use Arabic numerals in my letters.
The thing is, Feynman is being a little disingenuous, here. Numbers can mean more than just a bare symbolic representation of a mathematical quantity. After all, using a number in two different ways -- both to represent a quantity, and to encode a meaningful mathematical statement -- is the trick behind the proof of the brilliant Gödel Incompleteness Theorem, something I'm certain Feynman knew.
It's not always that deep, of course. Sometimes what they mean is banal. A good example is the current idiotic "6-7" thing that apparently is rampant amongst teenagers, and which makes me glad I retired from teaching high school when I did.
In any case, it's evident that implicit meaning is just as important to people as the explicit one. To take one infamous example, consider 666, supposedly the "Number of the Beast" in the Book of Revelation. Some people take that one extremely seriously. Ronald and Nancy Reagan lived in a house in Los Angeles, on 666 St. Cloud Road, until they petitioned the city (successfully) to change it to 668. There was a highway named U. S. Route 666 in New Mexico, until in 2003 it was changed to U. S. Route 491 -- prompting a spokesperson to say, "The devil's outta here, and we say goodbye and good riddance." (I bet the priest in The Exorcist wishes he'd known it was that easy.) In 2013, a maintenance worker in a metal manufacturing plant in Clarksville, Tennessee quit his job when he was assigned an ID badge ending in 666, and the company refused to change it. "I cannot accept that number," he told ABC News. "If you accept that number, you sell your soul to the devil."
What's wryly amusing about all this is that some scholars believe the identification of the Number of the Beast as 666 is a scribal or translation error, and the actual Number of the Beast is 616, because if you transliterate "Nero Caesar" into Hebrew and then use the rules of gematria to turn it into a number, you get 616.
Somehow, though, I doubt that's gonna catch on. The biblical literalists seem pretty set on 666.
So forbidden numbers have a long history. These days, they seem mostly to center around one of three things; trade secrets, classified information, and code for suppressed (or oppressive) ideologies. Because you can encode information in a string of digits, that string then becomes more than just the bare mathematical representation. It even goes beyond that, though, because afterward, any pattern can be made to stand for numbers, if only you know the correspondence. There was a legal case centering around a pattern of colors on a flag:
Sometimes, numbers can be labeled as illegal in certain contexts, usually when there's some external meaning that's been attached to them. In 2012, there was a report that internet search engines in China were blocking any searches containing the numbers 4, 6, and 89 -- because the Tiananmen Square Massacre happened on June 4, 1989. The numbers 14 and 88 are associated with white supremacy -- a well-known slogan by white supremacist David Lane has fourteen words, and 88 is code for "Heil Hitler" (H is the eighth letter of the alphabet). 88 regularly shows up in neo-Nazi tattoos -- and far-right Slovak politician Marian Kotleba was criminally charged for donating €1,488 to various charities. He was found guilty of "supporting and propagating a movement whose aim is the repression of human rights and freedoms," and sentenced to six months in prison, although on appeal the sentence was suspended.
They take these things seriously in Slovakia. Not like in another nation I can think of, where being a white supremacist with sketchy tattoos gets you appointed as Secretary of Defense.
So sometimes, numbers can mean a lot more than the seem to at first, and making them illegal -- or at least, illegal in some contexts -- makes better sense than it might appear at first.
I do have to agree with Feynman, though, that pointing out an interesting pattern in the decimal expansion of a fraction is pretty unlikely to be a way of giving away the nation's nuclear codes. Doubt that'd work even if you made a flag out of it.
Tuesday, December 9, 2025
Repulsive
Back in 2006, some people in Hong Kong noticed that despite its facing out over the warm waters of the South China Sea, it seldom gets hit by typhoons. In fact, sometimes the typhoons seem to go out of their way to avoid hitting Hong Kong. For example, here's the path of Typhoon Lionrock in 2010:
If you don't know your Asian geography, Hong Kong is basically right in the middle of the loop of the question mark.
There's at least a tentative scientific explanation for this; cyclones of all sorts are moved by upper atmosphere steering currents, which are created -- like all winds -- by air pressure gradients. There is a stable-ish high pressure zone near Hong Kong, and that causes an outflow of air that acts like a repulsive force on any storms heading that way. It's not permanent; like all air masses, it moves. Hong Kong has experienced typhoons, just fewer than you might expect based on its location.
But when the pattern was noticed, a business tycoon named Li Ka-Sheng started telling everyone that he had created a repellent force field, and that was keeping Hong Kong safe. Because, after all, if there's a major typhoon it would cause businesses to close, and we can't have that. Everyone still talks about "Li's field," and it comes up every year during typhoon season. "Well, it's typhoon season again," people in Hong Kong will say. "At least we have Li's field protecting us."
Here's the thing, though. Li, and just about everyone who talks about Li's field, are joking. It's satire, and everyone knew it right from the get-go.
Over here in the United States, though, we're hearing something similar, and the sad thing is I don't think the people making the claim are trying to be funny.
Homeland Security Secretary Kristi Noem, taking a break from her usual jobs of killing dogs and doing Border Patrol cosplay, attended a cabinet meeting in which the topic of this year's hurricane season came up. Despite there being thirteen named storms, four of which reached category 4, none of them hit the continental United States. (The last time this happened was 2015.) And guess who got praised for this?
"Sir, you made it through hurricane season without a hurricane," Noem gushed. "Even you kept the hurricanes away. We appreciate that."Monday, December 8, 2025
Genetic walkabout
The topic comes up because not only did I discover the fifth (and it probably won't be the last) unexpected cousin just a couple of days ago, but almost simultaneously I received a link to a paper illustrating how even geographically separated populations are connected. The researchers used mtDNA from two-millennium-old teeth in Syria to show that Mesopotamia deserves its moniker "the Cradle of Civilization;" that same mtDNA signature shows up today as far away as Tibet.
Mitochondrial (mt) DNA is unique in that it always inherits through the matrilineal ancestry. In other words, you contain the same mtDNA as your mother's mother's mother's etc., as far back as you like to go. This takes out the role of recombination in your genetic makeup -- the random scrambling of the chromosomes in the nucleus every time they're passed on makes it damn near impossible that the same two parents could produce two genetically identical (non-twin) children. But with mtDNA, the only differences occur from mutations, which are infrequent -- so this allows us to determine the relationships between different human populations, and track their movements back into prehistory.
My earliest-known matrilineal ancestor, Marie-Renée Brault, had the mtDNA haplotype H13a1a. This places her origin in western Europe (which we already knew); the "H clade" to which she belongs is in fact the commonest mtDNA in Europe. So no big surprises there.
That bit of DNA had a long walkabout to get to me, though. Marie-Renée was born in 1616 in the Loire Valley of western France. Her specific haplogroup, H13a1a, according to Eupedia, goes back a very long way -- it's been traced to populations living in eastern Anatolia and the Caucasus, and from there spread through the mountains of Greece, across the Alps, and all the way to western France where my maternal great-great (etc.) grandmother lived.
I also know about the mtDNA signatures of a few of my other ancestors, based on their matrilineal descendants. My two known Native American ancestors, both from the Abenaki tribe of Nova Scotia, were proven as such by their matrilineal descendants having a characteristic "A clade" mtDNA signature, which clearly demonstrates their ethnic heritage -- and their ultimate connection to other A-clade members in Siberia, Korea, and Japan.
The research that got me started on all this is not new, but was new to me; I was sent a link by a friend and loyal reader of Skeptophilia to a paper in PLOS-ONE called, "mtDNA from the Early Bronze Age to the Roman Period Suggests a Genetic Link between the Indian Subcontinent and Mesopotamian Cradle of Civilization," by Henryk W. Witas, Krystyna Jędrychowska-Dańska, and Tomasz Płoszaj (of the University of Łódź), Jacek Tomczyk (of Cardinal Stefan Wyszyński University), and Gyaneshwer Chaubey (of the Biocenter of Estonia). And in this paper, we find out that an mtDNA type -- haplogroup M4 and M6, which currently are found only in India -- apparently are older than anyone realized, and came from what is now Syria:
Ancient DNA methodology was applied to analyse sequences extracted from freshly unearthed remains (teeth) of 4 individuals deeply deposited in slightly alkaline soil of the Tell Ashara (ancient Terqa) and Tell Masaikh (ancient Kar-Assurnasirpal) Syrian archaeological sites, both in the middle Euphrates valley. Dated to the period between 2.5 Kyrs BC and 0.5 Kyrs AD the studied individuals carried mtDNA haplotypes corresponding to the M4b1, M49 and/or M61 haplogroups, which are believed to have arisen in the area of the Indian subcontinent during the Upper Paleolithic and are absent in people living today in Syria. However, they are present in people inhabiting today’s Tibet, Himalayas, India and Pakistan. We anticipate that the analysed remains from Mesopotamia belonged to people with genetic affinity to the Indian subcontinent since the distribution of identified ancient haplotypes indicates solid link with populations from the region of South Asia-Tibet (Trans-Himalaya).The amazing part of this isn't so much in the details, but the method. Mitochondrial DNA extraction from fossilized teeth can give us information about the movement of people back into prehistory. These ancestors of ours, about whom we know virtually nothing -- not their names, their faces, their professions, their cultures -- tell us about their travels by the genetic information carried in their bodies.
Which I find absolutely fascinating. It's kind of mind-boggling that I carry a bit of DNA in my cells (lots of bits of it, in fact) that originated in the Middle East twenty-thousand-odd years ago, was carried from mother to daughter as these people moved through the Caucasus and Anatolia into eastern Europe, crossing the Alps into France, and thence across the Atlantic Ocean to Nova Scotia for over a hundred years -- then back to France after they lost the French and Indian War and got kicked out -- and finally crossed the Atlantic again in 1785 to settle in southeastern Louisiana.
And each of you carry in your own cells pieces of DNA that have equally long, convoluted, and unexpected histories.
Makes you realize that we're all connected, down to the very instructions that built us, and are far more alike than we are different.
Saturday, December 6, 2025
The cosmic Tilt-O-Whirl

I've shown a bunch of people, and I've gotten answers from an electron micrograph of a sponge to a close-up of a block of ramen to the electric circuit diagram of the Borg Cube. But the truth is almost as astonishing:
It's a map of the fine structure of the entire known universe.
Most everyone knows that the stars are clustered into galaxies, and that there are huge spaces in between one star and the next, but far bigger ones between one galaxy and the next. Even the original Star Trek got that right, despite their playing fast and loose with physics every episode. (Notwithstanding Scotty's continual insistence that you canna change the laws thereof.) There was an episode called "By Any Other Name" in which some evil aliens hijack the Enterprise so it will bring them back to their home in the Andromeda Galaxy, a trip that will take three hundred years at Warp Factor Ten. (And it's mentioned that even that is way faster than a Federation starship could ordinarily go.)
So the intergalactic spaces are so huge that they're a bit beyond our imagining. But if you really want to have your mind blown, consider that the filaments of the above diagram are not streamers of stars but streamers of galaxies. Billions of them. On the scale shown above, the Milky Way and the Andromeda Galaxy are so close as to be right on top of each other.
What is kind of fascinating about this diagram -- which, by the way, is courtesy of NASA/JPL -- is not only the filaments, but the spaces in between them. These "voids" are ridiculously huge. The best-studied is the Boötes Void, which is centered seven hundred million light years away from us. It is so big that if the Earth were at the center of it, we wouldn't have had telescopes powerful enough to see the nearest stars until the 1960s, and the skies every night would be a uniform pitch black.
That, my friends, is a whole lot of nothing.
Friday, December 5, 2025
Excusing the past
How should we as readers deal with fiction in which there is evidence of reprehensible attitudes like racism, sexism, and homophobia?
I'm not referring here to stories where the bigotry is depicted in order to show how bad bigotry is; the viciously racist characters in the Doctor Who episode "Rosa," for example, are there to illustrate in no uncertain terms what it was like for People of Color in the Civil Rights era American South. Nor, on the other end of the spectrum, am I really considering awful stories where the bigotry is presented in a positive light, and is kind of the point. (A particularly egregious example is the H. P. Lovecraft short story "The White Ape," which is repellent from the get-go.)
I'm more interested in the gray area; stories where there is evidence of a bigoted attitude, but the bigotry doesn't form an essential part of the story. The topic comes up because I've been re-reading the murder mysteries written in the 1930s by Dorothy Sayers, whose name is right up there with Agatha Christie and Erle Stanley Gardner and Ngaio Marsh and the other greats of classic mystery literature.
The bigotry in Sayers's work doesn't smack you over the head. The main characters are (very) upper-crust British nobility in the early twentieth century, so there's no doubt the attitudes she portrays were prevalent at the time. And there are some things she does pretty well, even to modern eyes. Her detective, Lord Peter Wimsey, clearly treats his wife Harriet Vane as a complete equal, and in fact in the book where they finally marry (Busman's Honeymoon) Harriet asks him if he will expect her to give up her career as a novelist, and he reacts with surprise that she would even consider such a thing.
The racism, however, is there, and in more than one place. There's one book (Unnatural Death) where part of the twist of the story is that in the family tree of the victim, one of the great-uncles had been a sketchy sort, had gone to the West Indies, and married a Black woman; their children and grandchildren remained in that culture, accepting their place as People of Color.
So far, so good, I guess. But when one of their descendants returns to England, he's very much looked at as an aberration. The Englishman who was the progenitor of that branch of the family is more than once referred to as having done something immoral and offensive by engaging in an interracial marriage; the great-great grandson who shows up in white English society isn't really portrayed negatively, but there's no doubt he's played for laughs (starting with the fact that his name is Reverend Hallelujah Dawson).
Even worse is her repeated low-level anti-Semitism. There are Jewish characters here and there, and one and all they are the "of course he's money-conscious, he's Jewish" stereotype. In Whose Body?, Sayers kind of goes out of her way to present the character of Reuben Levy as a nice and honorable guy, but there's something about it that reeks of, "I'm not racist, I have a Black friend."
It boils down to how much slack we should give to authors who were "people of their times," whose attitudes simply reflect the majority opinion of the society they lived in. In Sayers's early-twentieth-century wealthy British culture, there was a tacit assumption of white British superiority; the racism is almost by default. The characters don't set out to demean or mistreat people of other races, it's more that the message is, "Of course we're superior, but that doesn't mean we'll be nasty to you -- as long as you know your place."
Christie herself is not a lot better. One of her most famous novels (and the first of hers I ever read) is And Then There Were None, which has to be one of the most perfectly-crafted mysteries ever written. But the original title of the book was a different line from the nursery rhyme that is the unifying theme of the entire plot -- Ten Little Indians. Worse still, when it was first released, it went by an earlier and even more offensive version of the rhyme -- Ten Little Niggers.
At least she had the good sense to change it. But that doesn't alter the pervasive white wealthy British superiority that runs through all her work.
Even authors who you'd think would be more enlightened sometimes include stuff that is mighty sketchy. One of my earliest favorite books was Madeleine L'Engle's classic A Wrinkle in Time. The third book in the Murry family series, A Swiftly Tilting Planet, has a neat theme -- riding through time and trying to prevent a catastrophe by altering timelines in selected places -- but the "blue-eyed Indian = good, brown-eyed Indian = bad" trope that skims along right beneath the surface gets cringier the longer you look at it. (Especially since the "blue-eyed Indians" have blue eyes because they have European ancestry. Which makes them... better? Eek.)
I wish I had some black-and-white answer for this. I'm certainly not trying to excuse anyone for morally repulsive stances, but it seems to me that considering only overtly racist writing such as "The White Ape" ignores the fact that there's way more gray area here than you might think at first.
I'd love to hear how you approach this as a reader. I can see having students read and study books with problematic attitudes, because (1) that's how they learn that those attitudes exist, and (2) it gives a skilled teacher an opportunity to analyze those beliefs and demonstrate how horrible they actually were. But what about reading solely for pleasure? I loathe the words "woke" and "politically correct" -- they all too often become synonyms for "stuff I don't like" -- but don't they embody the attitude of someone who refuses to read anything that doesn't reflect our current cultural standards?
Even if those standards are laudable?
I honestly don't know the answer to that. I'm not intending on giving up reading, and for the most part enjoying, Sayers and Christie. I can't deny that even Lovecraft -- at least his stories where race doesn't come into it, even subtly and implicitly ("At the Mountains of Madness" comes to mind) -- have been major positive influences on my own work. As for Gaiman and Card, well, I don't want my money supporting people with attitudes and actions I find repulsive, so I won't purchase their work. But it's a way more complex, and less clear-cut, topic than it appears.
What do you think? Is there merit to the "(s)he was a person of the times" argument, or are we giving tacit acceptance of repulsive attitudes just because the work is old -- or because we like it otherwise?
Thursday, December 4, 2025
Descent into chaos
Here's a simple example. If you take a deep bowl, and drop a marble into it, it doesn't take any great intelligence or insight to predict what the end state will be. Marble on the bottom of the bowl. It doesn't matter how high you drop it from or where exactly it hits the sides first. After a bit of rolling around, the marble will stop moving at the bottom.
Now, do the same thing -- but with the bowl flipped over. Where will the marble end up?
Impossible to say, because it is an inherently chaotic system. You could do it a hundred times and the marble will end up in a different place each time, because its final location depends on exactly the speed and angle of its path, where it hits the curved edge of the bowl, even whether the marble is spinning a little or not. A system like this is said to be "sensitive to initial conditions" -- therefore unpredictable. Perturb it a little by altering it in a tiny way, and you get a completely different outcome.
Here's a much cooler example, that I stumbled across in doing research for this post. It's called a double compound pendulum. Take two rigid rods, and suspend one so it's free to swing. Then tie the second rod to the bottom of the first. Start with the rods pulled horizontal, then let it go. Can you predict how the whole system will move?
Simple answer: no. It's a chaotic system.
A little mesmerizing to watch, isn't it?
The reason this comes up is because there's decent evidence that the intersection between the Earth's climate and human society is a chaotic system that has at least some degree of sensitive dependence to initial conditions. If you perturb it, it may not respond the way you expect -- and sometimes small changes in one location can lead to big ones somewhere else. (This concept was made famous as "the butterfly effect.")
As an example of this, take the research from Proceedings of the National Academy of Sciences, the link to which was sent to me by a friend and loyal reader of Skeptophilia yesterday. In "Extreme Climate After Massive Eruption of Alaska’s Okmok Volcano in 43 BCE and Effects on the Late Roman Republic and Ptolemaic Kingdom," by a team led by Joseph R. McConnell of the University of Cambridge, we find out about an Alaskan volcanic eruption that may have been one of the significant factors leading to the collapse of the Roman Republic, and its consolidation as an empire -- events that radically changed the course of history in Europe and North Africa.
Geologists on the team identified tephra (volcanic ash) in ice cores from the Arctic that were fingerprinted chemically and shown to come from the volcano named Okmok in the Aleutian Islands. The dating of the tephra deposit shows that the eruption happened in 43 B.C.E. -- right after the assassination of Julius Caesar, during a time when Rome was in chaos as various political factions were duking it out for control. The eruption of this volcano halfway around the world is also correlated with the coldest year Europe had for centuries, possibly longer. Snow fell in summer, crops failed, there were famines and repeated uprisings by desperate and starving citizens.
This sudden drop in temperature was one of the factors that contributed to the realignment of the Roman government as someone emerged who said he knew what to do to fix the situation -- Octavian (later known as Augustus), Julius Caesar's great-nephew. And he did it, establishing the Pax Romana, quelling the revolts and ushering in two centuries of relative peace and prosperity for Roman citizens (and wreaking havoc on the Gauls, Celts, Teutons, and whatever other tribes happened to be in the way of the Roman Legions).
It helped, of course, that once the volcanic tephra from Okmok settled out, the temperature rebounded, and the first years of Augustus's reign were noted for a beneficent climate and rich crop yields. Not all of the good bits of the Pax Romana were due to Augustus's skill as an emperor; he got lucky because of conditions he had no control over and could not have predicted, just as the last leaders of the Republic got unlucky for the same reasons.
The point here is that we should be wary of perturbing chaotic systems, which is exactly what we're doing by our rampant dumping of carbon dioxide into the atmosphere. And what we're seeing over the last decades is exactly the sort of unpredictable response -- some areas experiencing droughts, others floods; deadly heat waves and trapped polar vortexes that drop areas into the deep freeze for weeks; increased hurricanes, tornadoes, and bomb cyclones. One of the frustrations felt by the people who understand climate systems is that the average layperson doesn't see this kind of unpredictability as precisely what you'd expect from pushing on an inherently chaotic system. If you can't make predictions to pinpoint accuracy -- "okay, because the climate is changing, you can expect it to be 95 F in Omaha on July 19" -- it's nothing to be concerned about.
"The scientists don't even know what's going on," you'll hear them say. "Why should we believe it's a problem if they can't tell us what the outcome is going to be?"
But that's exactly why we shouldn't be messing with it. Systems that have sensitive dependence to initial conditions are dramatically unpredictable, and get pushed out of equilibrium quickly and sometimes with catastrophic results.
As the leaders in the final years of the Roman Republic found out.
I feel like another figure from the Classical world -- Cassandra -- for even bringing this up. Cassandra, you may recall, is the woman who was cursed by the gods to having accurate foresight and knowledge of the future, but with the difficulty that whatever she says, no one believes. The climatologists have been sounding the alarm about this for decades, to little effect. If you can't accurately predict the outcome, to most politicians, it doesn't exist.
Which makes me wonder if before we try to get our leaders to get on board with addressing anthropogenic climate change, we should require they sit through some lectures on chaos theory.






