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Sometimes simple words can be the hardest to define accurately.
For example, in physics, what do we mean by the word structure? The easiest way to conceptualize it is that it's a material object for which whatever force is holding it together outcompetes any other forces that might be involved. For example, a brick could be considered a structure, because the chemical bonds in the fired clay are stronger than the forces trying to pull it apart. The sand on a beach, however, doesn't form a single structure, because the forces between the sand grains aren't strong enough to hold them together against the power of the wind and water.
Simple enough, it'd seem, but once you get out into space, it gets a little more difficult.
In astronomy, a structure is something that is bound together by gravity so that on some scale, it acts as a single unit. The Solar System is a cosmic structure; within it, the gravitational pull of the Sun overwhelms all other forces. The Milky Way is a cosmic structure by the same definition. But how big can you get and still call it a single structure? The question gives astronomers fits, because (to abide by the definition) you have to show that the pieces of the structure are bound together in such a way that the mutual gravitational attraction is higher than the other forces they experience -- and given that a lot of these things are very far away, any such determination is bound to rest on some fairly thin ice.
The largest generally accepted cosmic structure is the Hercules-Corona Borealis Great Wall, a galactic filament that (from our perspective) is in the night sky in the Northern Hemisphere in spring and early summer. It's ten billion light years in length -- making it a little over a tenth as long as the entire observable universe!
In the above image, each one of the tiny dots of light is an entire galaxy containing billions of stars; the brighter blobs are galaxy clusters, each made up of millions of galaxies.
And the whole thing is bound together by gravity.
What's kind of overwhelming about this is that because there are these enormous cosmic structures, there are also gaps between them, called supervoids. One of the largest is the Boötes Void. This thing is 330 million light years across, and contains almost no matter at all; any given cubic meter of space inside the void might have a couple of hydrogen atoms, and that's about it. To put it in perspective; if the Earth was sitting in the center of the Boötes Void, there wouldn't be a single star visible. It wouldn't have been until the 1960s that we'd have had telescopes powerful enough to detect the nearest stars.
That, my friend, is a whole lot of nothing.
What's coolest about all this is where these structures (and the spaces between them) came from. On the order of 10^-32 seconds (that's 0.00000000000000000000000000000001 seconds) after the Big Bang, the bizarre phenomenon of cosmic inflation had not only blown the universe up by an amount that beggars belief (estimates are that in that first fraction of a second, it expanded from the size of a proton to about the size of a galaxy), it also smoothed out any lumpy bits (what the cosmologists call anisotropies). This is why the universe today is pretty smooth and homogeneous -- if you look out into space, you see on average the same number of galaxies no matter which way you look.
But there are some pretty damn big anisotropies, like the Hercules-Corona Borealis Great Wall and the Boötes Void. So where did those come from?
The current model is that as inflation ended, an interaction between regular matter and dark matter triggered a shock wave through the plasma blob that at that point was the entire universe. This shock wave -- a ripple, a pressure wave much like a sound wave propagating through the air -- pushed some bits of the regular matter closer together and pulled some bits apart, turning what had been a homogeneous plasma into a web of filaments, sheets... and voids.
These baryon acoustic oscillations, that occurred so soon after the Big Bang it's hard to even wrap my brain around a number that small, are why we now have cosmic structures millions, or billions, of light years across.
So that's our mindblowing science for today. Gravitationally-linked structures that span one-tenth of the size of the observable universe, and spaces in between containing damn near nothing at all, all because of a ripple that passed through the universe when it was way under one second old.
If that doesn't make you realize that all of our trials and tribulations here on Earth are insignificant, nothing will.
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Here are the answers to the puzzles from yesterday's post. If you haven't finished thinking about them on your own, scroll no further!
1. The census taker puzzle
The first clue is that the product of the daughters' ages is equal to 36. There are eight possible trios of numbers that multiply to 36: (1, 1, 36), (1, 2, 18), (1, 3, 12), (1, 4, 9), (1, 6, 6), (2, 2, 9), (2, 3, 6), and (3, 3, 4). Clue #2 is that the ages sum to equal the house number across the street, so the next step is to figure out what the house number could be. Respectively: 38, 21, 16, 14, 13, 13, 11, and 10.
The key here is that when the census taker looks at the house number across the street, he still can't figure it out. So it can't be (1, 4, 9), for example -- because if it was, as soon as he saw that the house number was 14, he'd know that was the only possible answer. The fact that even after seeing the house number, he still doesn't know the answer, means it has to be one of the two trios of numbers that sums to the same thing -- 13. So it either has to be (1, 6, 6) or (2, 2, 9).
Then, clue #3 is that the man's oldest daughter has red hair. In the first possibility, there is no oldest daughter -- the oldest children are twins. So his daughters have to be a nine-year-old and a pair of two-year-old twins.
2. The St. Ives riddle
The answer is one. "As I was going to St. Ives..." -- it doesn't say a thing about where the other people he met were going, if anywhere.
3. The bear
It's a white bear. The only place on Earth you could walk a mile south, a mile east, and a mile north and end up back where you started is if your starting place was the North Pole.
4. A curious sequence
The pattern is that it's the names of the single digit numbers in English, in alphabetical order. So the next one in the sequence is 3.
5. Classifying the letters
The letters are classified by their symmetry. (The capital letters only, of course.) Group 1 is symmetrical around a vertical line, Group 2 around a horizontal line, Group 3 is around either a horizontal or a vertical line, Group 4 has no line symmetry but is symmetrical through a 180-degree rotation around their central point, and Group 5 are asymmetrical.
6. The light bulb puzzle
Turn on switch one, and leave it on. Turn on switch two for ten minutes, then turn it off. Leave switch three off. Go up to the tenth floor. The bulb operated by switch one will be on; the one operated by switch two will be dark, but hot; and the one operated by switch three will be dark and cold.
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One of the biggest impediments to clear thinking is the fact that it's so hard for us to keep in mind that we could be wrong.
As journalist Kathryn Schulz put it:
I asked you how it felt to be wrong, and you had answers like humiliating, frustrating, embarrassing, devastating. And those are great answers. But they're answers to a different question. Those are answers to the question, "How does it feel to find out you're wrong?" But being wrong? Being wrong doesn't feel like anything... You remember those characters on Saturday morning cartoons, the Coyote and the Roadrunner? The Coyote was always doing things like running off a cliff, and when he'd do that, he'd run along for a while, not seeing that he was already over the edge. It was only when he noticed it that he'd start to fall. That's what being wrong is like before you've realized it. You're already wrong, you're already in trouble... So I should amend what I said earlier. Being wrong does feel like something.
It feels like being right.
We cling desperately to the sense that we have it all figured out, that we're right about everything. Oh, in theoretical terms we realize we're fallible; all of us can remember times we've been wrong. But right here, right now? It's like my college friend's quip, "I used to be conceited, but now I'm perfect."
The trouble with all this is that it blinds us to the errors that we do make, because if you don't keep at least trying to question your own answers, you won't see your own blunders. It's why lateral thinking puzzles are so difficult, but so important; they force you to set aside the usual conventions of how puzzles are solved, and to question your own methods and intuitions at every step. This was the subject of a study by Andrew Meyer (of the Chinese University of Hong Kong) and Shane Frederick (of Yale University) that appeared in the journal Cognition last week. They looked at a standard lateral thinking puzzle, and tried to figure out how to get people to avoid falling into thinking their (usually incorrect) first intuition was right.
The puzzle was a simple computation problem:
A bat and a ball together cost $1.10. The bat costs $1.00 more than the ball. How much does the ball cost?
The most common error is simply to subtract the two, and to come up with ten cents as the cost of the ball. But a quick check of the answer should show this can't be right. If the bat costs a dollar and the ball costs ten cents, then the bat costs ninety cents more than the ball, not a dollar more (as the problem states). The correct answer is that the ball costs $0.05 and the bat costs $1.05 -- the sum is $1.10, and the difference is an even dollar.
Meyer and Frederick tried different strategies for improving people's success. Bolding the words "more than the ball" in the problem, to call attention to the salient point, had almost no effect at all. Then they tried three different levels of warnings:
All of these improved success, but not by as much as you might think. The number of people who got the correct answer went up by only about ten percent, no matter which warning was used.
Then the researchers decided to be about as blatant as you can get, and put in a bolded statement, "HINT: The answer is NOT ten cents!" This had the best improvement rate of all, but amazingly, still didn't eliminate all of the wrong answers. Some people were so certain their intuition was right that they stuck to their guns -- apparently assuming that the researchers were deliberately trying to mislead them!
If you find this tendency a little unsettling... well, you should. It's one thing to stick to a demonstrably wrong answer in some silly hypothetical bat-and-ball problem; it's another thing entirely to cling to incorrect intuition or erroneous understanding when it affects how you live, how you act, how you vote.
It's why learning how to suspend judgment is so critical. To be able to hold a question in your mind and not immediately jump to what seems like the "obvious answer" is one of the most important things there is. I used to assign lateral thinking puzzles to my Critical Thinking students every so often -- I told them, "Think of these as mental calisthenics. They're a way to exercise your problem-solving ability and look at problems from angles you might not think of right away. Don't rush to find an answer; keep considering them until you're sure you're on the right track."
So I thought I'd throw a few of the more entertaining puzzles at you. None of them involve much in the way of math (nothing past adding, subtracting, multiplying, and dividing), but all of them take an insight that requires pushing aside your first impression of how problems are solved. Enjoy! (I'll include the answers at the end of tomorrow's post, if any of them stump you.)
1. The census taker problem
A census taker goes to a man's house, and asks for the ages of the man's three daughters.
"The product of their ages is 36," the man says.
The census taker replies, "That's not enough information to figure it out."
The man says, "Okay, well, the sum of their ages is equal to the house number across the street."
The census taker looks out of the window at the house across the street, and says, "I'm sorry, that's still not enough information to figure it out."
The man says, "Okay... my oldest daughter has red hair."
The census taker says, "Thank you," and writes down the ages.
How old are the three daughters?
2. The St. Ives riddle
The St. Ives riddle is a famous puzzle that goes back to (at least) the seventeenth century:
As I was going to St. Ives,
I met a man with seven wives.
Each wife had seven kids,
Each kid had seven cats,
Each cat had seven kits.
Kits, cats, kids, and wives, how many were going to St. Ives?
3. The bear
A man goes for a walk. He walks a mile south, a mile east, and a mile north, and after that is back where he started. At that point, he sees a large bear rambling around. What color is the bear?
4. A curious sequence
What is the next number in this sequence: 8, 5, 4, 9, 1, 7, 6...
5. Classifying the letters
You can classify the letters in the English alphabet as follows:
Group 1: A, M, T, U, V, W, Y
Group 2: B, C, D, E, K
Group 3: H, I, O, X
Group 4: N, S, Z
Group 5: F, G, J, L, P, Q, R
What's the reason for grouping them this way?
6. The light bulb puzzle
At the top of a ten-story building are three ordinary incandescent light bulbs screwed into electrical sockets. On the first floor are three switches, one for each bulb, but you don't know which switch turns on which bulb, and you can't see the bulbs (or their light) from the place where the switches are located. How can you determine which switch operates which bulb... and only take a single trip from the first floor up to the tenth?
Have fun!
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After the warmest fall I can remember, we here in upstate New York finally are seeing cooler weather. I greet this with mixed feelings. As I've pointed out here many times, the abnormally warm temperatures we've had in the last few years are not good news. On the other hand, being a transplanted southerner, I can't say I'm fond of the cold, even after forty years of living in higher latitudes.
Our chilly winters, though, are nothing compared to a lot of other places. My Canadian friends, even the ones who live in the southern parts of that vast country, see cold temperatures the likes of which I've never had to deal with. The Rocky Mountain region, from Colorado up into Alberta, drops down to dangerous lows, often coupled with howling winds and snow. Scandinavia, Siberia, Greenland... there are a lot of places on Earth where the cold season is actively trying to kill you. The lowest temperature ever recorded on the surface of the Earth was -89.2 C, at Vostok Station, Antarctica, cold enough to freeze carbon dioxide into dry ice.
Makes our current 2 C seems like a gentle spring zephyr.
But I wonder if you've ever considered how much colder it can get?
Temperature is a measure of the average molecular motion of a substance. It is connected to, but not the same as, the heat energy; to prove that to yourself, put a pot of water on the stove and bring it to boil, and set your oven to 212 F/100C, and then decide which one would be less fun to stick your hand into. The water and the air in the stove are exactly the same temperature -- i.e., the molecules are moving at the same average speed -- but the water has a great deal more heat energy, because water molecules are so much harder to get moving than air molecules are.
So logically, there's a minimum temperature; absolute zero, where all molecular motion stops. This would occur at -273.15 C (0 on the Kelvin scale), but practically speaking, it's impossible to get there. Even if you could somehow extract all the heat energy from a substance, there's still the kinetic energy of the ground states of the atoms that can't be removed. Still, the scientists have gotten pretty damn close. The CUORE laboratory in Italy set a record in 2014, reaching a temperature of 0.006 K, but recently that's been broken on extremely small scales -- two years ago scientists working with an exotic form of matter called a Bose-Einstein condensate got it down to 38 picokelvin -- that's 0.000000000038 degrees above absolute zero.
But that, of course, is all done in a lab setting. What's the lowest naturally-occurring temperature ever measured?
You might think it's somewhere in deep space, but it's not. The temperature in deep space varies all over the place; recall that what matters is the average velocity of the atoms in an area, not how much heat energy the region contains. (The solar corona, for example, can reach temperatures of a million K, which is way higher than the Sun's surface -- there aren't many atoms out there, but the ones there are move like a bat out of hell.)
The coldest known place in the universe, outside of labs down here on Earth, is the Boomerang Nebula, a planetary nebula in the constellation of Centaurus, which has measured temperatures of around 1 K. The reason why is weird and fascinating.
A planetary nebula forms when a red giant star runs out of fuel, and the collapse of the core raises the temperatures to a ridiculously high one million degrees kelvin. This sudden flare-up blows away the outer atmosphere of the star, dissipating it out into space, and leaves the exposed core as a white-hot white dwarf star, which will then slowly cool over billions of years.
So how could a flare-up of something that hot trigger temperatures that cold? What's amazing is that it's the same process that heated up the core, but in reverse -- adiabatic heating and cooling.
Way back in 1780, French scientist Jacques Charles discovered that when you compress a gas (reduce its volume), it heats up, and when you allow a gas to expand (increase its volume), it cools. Volume and temperature turned out to be inversely proportional to each other, something we now call Charles's Law in his honor. If you've ever noticed that a bicycle pump heats up when you inflate your tire, you've seen Charles's Law in action.
This all happens because upon compression, the mechanical work of reducing the volume adds kinetic energy to the gas (increasing its temperature); when a gas expands, the opposite occurs, and the temperature falls. This is how compressors in air conditioners and refrigerators work -- the compression of the coolant gas increases its temperature, and the warmed gas is passed through coils where the heat dissipates. Then it's allowed to expand suddenly, reducing its temperature enough to cool the interior of a freezer compartment to below zero C.
This is what's happening in the Boomerang Nebula, but on a much larger scale. The outer atmosphere of the star is expanding so fast its temperature has dropped to just one degree above absolute zero -- making this peculiar nebula five thousand light years away the coldest spot in the known universe.
So that's our tour of places you wouldn't want to vacation. Top of the list: the Boomerang Nebula. Might be pretty to look at, but from a long way away, and preferably while warmly dressed.
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In my post a couple of days ago about the unstable geology of the Greek island of Thera, I stated that this is far from the only place in the world where lots of people live in harm's way from the vagaries of plate tectonics. I mentioned the Cascadia Subduction Zone, off the coast of the Pacific Northwest, and included a link to the rather desultory post I'd made a while back about what's going on over there. A loyal reader of Skeptophilia wondered if I might write a more thorough piece about the terrifying situation looming in that beautiful part of the world, so here I am to elaborate, and probably to scare the absolute shit out of anyone living in coastal British Columbia, Washington, Oregon, and northern California.
Even after the general acceptance of plate tectonics by geologists in the 1960s and 1970s, it took a long time for them to see what was happening in the northeastern Pacific. The presence of a ridge (divergent zone) meant that the seafloor was spreading on both sides; the fact that the small Explorer, Juan de Fuca, and Gorda Plates were being shoved eastward meant that there had to be a trench somewhere between the ridge and continental North America. But the earliest sounding techniques couldn't find one. It turned out that it was buried -- submerged under hundreds of meters of muck, silt and sand washed out of the region's numerous rivers.
This, and the fact that there hadn't been a big earthquake in the Northwest since settlement by people of European descent, led a lot of geologists to the conclusion that the trench was "aseismic." Either the small plates east of the ridge weren't moving, or they were slipping underneath the North American Plate so smoothly that there were no measurable earthquakes.
This wasn't just a little bit wrong. This was stunningly wrong. This was wrong with whipped cream and a cherry on top.
The Explorer, Juan de Fuca, and Gorda Ridges are very much active spreading centers, and the fact that there haven't been any recent big earthquakes along the trench -- the Cascadia Subduction Zone, denoted on the map by the line with black triangles -- is not good news. The entire coastline of the Pacific Northwest is compressing as the three small plates get shoved under North America, just like trying to slide something underneath a throw rug makes it rumple and hump up. In fact, surveys measuring the positions of the peaks in the Cascade Range and on Vancouver Island have found that the whole terrain is being squished west-to-east, so entire mountains are being pushed toward each other.
Imagine the power required to do that.
Further, the fact that the trench is filled with mud doesn't mean the subduction zone is aseismic; quite the opposite. It turns out that a large part of the mud deposits there are turbidites -- the result of colossal underwater landslides.
Such as might occur during an enormous earthquake.
More of the mechanism was elucidated in 2003, when researchers found that the whole region was experiencing a phenomenon called episodic tremor and slip, where deeper parts of the conjoined plates -- the bits that are hotter and more plastic -- slip against each other, causing barely a rumble. This slip/tremor happens like clockwork every fourteen months. While this may sound like a good thing, it's actually the opposite. Releasing stress that has built up in the deep parts of the fault merely passes that stress upward to the colder, shallower parts that are still locked together, each ETS episode dialing up the energy like the clicking of another tooth in a ratchet.
So along the subduction zone, the two opposing sides of the plates are stuck together, building up more and more tension -- tension that will one day be released as the faultline unzips, and the whole northwest coast of the continent springs back toward the west.
To say the result will be catastrophic is understatement of the year.
It's happened before. In fact, geologists taking cores of the aforementioned turbidite sediments off the coast of Washington found evidence that in the past ten thousand years it's happened nineteen times. The spacing between megathrust earthquakes -- as these are called -- varies between three hundred and nine hundred years, with the average being around five. And the last one happened a little over 323 years ago.
We actually know down to the hour when it happened -- about 9 PM local time, January 26, 1700. Indigenous tribes in the area have a long tradition that many years ago, there was a terrible earthquake one midwinter night, during which the seashore dropped and salt water flooded in, killing many people. Evidence from tree rings in "ghost forests" -- the trunks of hundreds of western red cedars that had all been killed simultaneously by an influx of salt -- showed that some time in the 1690s or early 1700s there had been a massive flood from the ocean as the coastline suddenly dropped by several meters. The exact date was determined from records across the Pacific, where Japanese scribes describe what they called an "orphan tsunami" (a huge wave that, from their perspective at least, was not preceded by an earthquake) striking coastal Japan. Knowing the speed with which such waves travel across the ocean, geologists were able to determine exactly when the fault last unzipped from end to end.
The earthquake that resulted is estimated to have been somewhere between 8.7 and 9.2 on the Richter Scale, and to have resulted in land movement averaging around twenty meters.
Not pleasant to consider how that would play out if it happened today.
The worst part, for coastal communities today, is how close the Cascadia Subduction Zone is to shore. At its closest approaches -- near the west coast of Vancouver Island, and from central Oregon south to Cape Mendocino -- it's estimated that the lag time between the ground shaking and the first of the tsunami waves striking the shore will be around eight minutes. That's eight minutes between being thrown all over the place by an enormous earthquake, and somehow getting yourself to high ground before you're hit by a giant wall of salt water.
I remember when I first heard in detail about the dangers of the Cascadia Subduction Zone -- in 2015, from Kathryn Schulz's brilliant analysis in The New Yorker called "The Really Big One." It impressed me so much I actually used the fault as a plot point in my novel In the Midst of Lions, where the story is bracketed by earthquakes (one of them massive). But when I was a Seattle resident in the 1980s, I had no idea. I still dearly love the Northwest; not only does it have the ideal climate for a fanatical gardener like myself, it has amazing spots for hiking and camping. During my time there I spent many happy days on the coast of the Olympic Peninsula -- never realizing that a monster lurked offshore.
So while I miss many things about the Northwest, I know I could never live there again.
It may be that the fault won't rupture for another two hundred years; on the other hand, it could happen tomorrow. While our ability to analyze plate tectonics is light years beyond what it was even thirty years ago, when the situation in the Northwest first began to come clear, we still don't have any way to determine when the earthquake will happen with any kind of precision. At the moment, all we know is that it will rupture, sooner or later.
And I don't want to be anywhere near it when it does.
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The skies were almost always moist and cloudy, and sometimes I would witness tremendous rains. Once in a while, though, there would be glimpses of the Sun -- which looked abnormally large -- and the Moon, whose markings held a touch of difference from the normal that I could never fathom. When -- very rarely -- the night sky was clear to any extent, I beheld constellations which were nearly beyond recognition. Known outlines were sometimes approximated, but seldom duplicated; and from the position of the few groups I could recognize, I felt I must be in the Earth's southern hemisphere, near the Tropic of Capricorn.
The far horizon was always steamy and indistinct, but I could see that great jungles of unknown tree ferns, Calamites, Lepidodendron, and Sigillaria lay outside the city, their fantastic fronds waving mockingly in the shifting vapors... I saw constructions of black or iridescent stone in glades and clearings where perpetual twilight reigned, and traversed long causeways over swamps so dark I could tell but little of their towering, moist vegetation.Lovecraft's prescience was shown when plate tectonics was discovered, twenty years after the author's death. Antarctica wasn't always centered at the South Pole, and in fact had drifted in that direction from somewhere far nearer to the equator. Since Lovecraft's time, fossils of temperate-climate organisms have been found in abundance, indicating that the climate had shifted dramatically, just as he'd said.
There rolls the deep where grew the tree.O Earth, what changes hast thou seen?There, where the long road roarsHas been the stillness of the central sea.
The hills are shadows, and they flowFrom form to form, and nothing stands,They melt like mists, the solid lands,Like clouds, they shape themselves and go.
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