Orders of magnitude

Our minds tend to boggle when numbers get too large or too small.

It's why we get in trouble talking about things like the national debt.  To a lot of people, a million dollars, a billion dollars, and a trillion dollars all sound pretty much alike; "more money than we're ever likely to see in our lives."  Explaining that a trillion dollars is "the amount of money owned by a million millionaires" helps some, but the fact remains that we can't really wrap our brains around numbers that big.

The same thing happens on the small end.  I remember trying to get my students to grok the difference between the sizes of small things -- say, an amoeba, a virus, a DNA molecule, and an atom.  My analogy for the size of the atom is that if you had as many grains of sand as there are atoms in a typical raindrop, you'd have enough sand to fill a trench a foot deep, a mile wide, stretching from New York City to San Francisco.

It was a good "oh wow" moment, but once again, I'm not sure how much good it did to fight the general trend of our not being able to conceptualize things that are very far outside of the scales we're used to.

The more we find out through science, though, the wider the actual scales of our understanding need to grow.  This is why if you want to have a prayer of getting anywhere in science, you need to understand scientific notation -- a way of notating very large or very small numbers, such as the speed of light, which is 300,000,000 meters per second -- or, as it's put in scientific notation, 3x10^8 meters/sec.  The bigger (or smaller) the numbers get, the more useful scientific notation is; take, for example, the distance to the Andromeda Galaxy, which is 2.4x10^19 kilometers (24 followed by eighteen zeroes).  With something that large, just counting the zeroes to get an idea of what magnitude you're talking about becomes unwieldy.

On the other hand, for unwieldy, you can't beat the English units of measurement. This is a chart of the relationships between the ones for length. The rest of them are just as bad. [Image licensed under the Creative Commons Christoph Päper, English length units graph, CC BY 3.0]

The same thing happens on the other end of the scale.  The width of one of your DNA molecules is about two billionths of a meter; in scientific notation, 2x10^-9 meters.  (The negative sign means the decimal point is moved to the left; this is 0.000000002 meters.)

To obviate the need for such large exponents, there are prefixes used to get rid of some of the zeroes.  Some are familiar -- "kilo-" for a thousand, "milli-" for one-thousandth, "micro-" for one millionth, and so on.  This, in fact, is the reason this comes up; we've plunged so deep into the realms of the very large and the very small that the previous ones have proven insufficient, so they've invented four new ones and tacked them onto the outside of the scale.

It's not like we didn't already have some pretty extreme prefixes.  On the large end, we go up to "yotta-," meaning 10^24.  On the other end, "yocto-" means 10^-24.  But now we have "ronna-" and "quetta-" (10^27 and 10^30, respectively) and "ronto-" and "quecto-" (10^-27 and 10^-30, respectively).  (Abbreviations are, in order, R, Q, r, and q.)  For reference, the Sun has a mass of about two thousand quettagrams; an electron, one rontogram.

The funny thing is, even these won't cover all contingencies.  When you get to galactic masses, you're talking about something that would require scientific notation even if you measured it in quettagrams.  And in the realm of the very small, when you get down to where physicists believe even such quantities as length and time are quantized (made up of chunks that can't be subdivided any further), you're still in the negative exponent range.  These Planck units of length and time are, respectively, 1.6x10^-35 meters (1.6x10^-5 quectometers) and 5.4x10^-44 seconds (5.4x10^-14 quectoseconds).

So we're still not out of the woods.  But I don't mind, because "quectosecond" is fun to say.

I'm not sure if this does anything to help the original problem -- that our brains can't really handle very big and very small numbers.  Anything more than a couple of orders of magnitude outside of what we deal with every day, and we boggle.  Which is why I think, science geek that I am, that I'm going to stick with my friend's favorite large unit of mass, which is the "metric shit tonne."

At least I have a pretty good idea of what that means.

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Reaping the whirlwind

Once again I'm sick at heart because of the news of a mass shooting, this time at a prominent LGBTQ+ club in Colorado Springs called Club Q.  At the time of this writing, five people are dead and another twenty-five wounded.  The suspected shooter, Anderson Aldrich, was subdued by two people at the club and is now in custody, currently being treated for minor injuries.

There's a lot to unpack, here.  How Aldrich got a gun, despite a previous arrest for a bomb threat.  Where he picked up the hateful and homophobic ideology that impelled him to do such a thing.  It was just revealed that he's the grandson of California Assemblyman and staunch MAGA Republican Randy Voepel, but whether that will turn out to be relevant to Aldrich's horrific act of violence remains to be seen.

The queer community is, understandably, reeling.  Colorado Springs is soundly conservative, and Club Q was one of the only safe havens they had there.  Social media this morning has been full of tearful, terrified individuals who have once again been reminded of how vulnerable they are, and how much unreasoning and vicious hatred still exists in this country.

My horror started turning to anger, though, when I saw the tweet yesterday morning from Representative Lauren Boebert, whose district includes Colorado Springs.  "This morning the victims & their families are in my prayers," she wrote.  "This lawless violence needs to end and end quickly."

With all due respect, Representative Boebert, you can take your thoughts and prayers and shove them up your ass.

Boebert has been a strident voice in the anti-LGBTQ+ right wing, accusing the left of "grooming children" for such actions as pressing educators to honor trans youths' pronouns and including LGBTQ+ representation in school library books.  She warned drag queens to "stay away from Colorado's Third District."  Oh, but when her own hateful ideology comes back to her own district in the form of violence, she wants to -- as AOC succinctly put it -- "thoughts-and-prayers her way out of" any responsibility for what happened.

There's a line from the Bible that covers this kind of thing.  It's Hosea 8:7.  "Who sows the wind, reaps the whirlwind."

Neither I, nor any of the other members of the queer community whom I've spoken with, wants anything to do with the thoughts and prayers of people who after today will go back to doing everything they can to harm us.  No, not just harm us; eradicate us, erase every last one of us from the face of the Earth.

Think I'm exaggerating?  Consider monsters like Pastor Dillon Awes of the Steadfast Baptist Church in Watauga, Texas, who a couple of months ago told a cheering congregation that gay people should be lined up against a wall and shot in the head.  Or Pastor Joe Cammilleri, who saw a boy wearing fingernail polish and said to his congregation, "Oh, I just want to break his fingers."  Or far-right commentator Matt Walsh, who has built his career fighting against trans people's right to be who they are, and just last week crowed about once again being allowed to be as horrible as he wants to on Twitter now that Elon Musk has taken over: "We have made huge strides against the trans agenda.  In just a year we’ve recovered many years worth of ground conservatives had previously surrendered.  The liberation of Twitter couldn’t have come at a more opportune time.  Now we can ramp up our efforts even more."

Anyone in public office who honestly wants to stem the tide of violence against queer people can start by speaking out against these ugly spewers of hatred.  Until such time as Representative Boebert and the others like her will stand up and say to them, "This is morally indefensible.  LGBTQ+ people are deserving of the same rights and protections as anyone else.  No one gets to threaten the life, safety, and happiness of any other human being.  Not on my watch," they can sit down and shut the fuck up.

Actions like that of Anderson Aldrich are meant to terrify.  And yes, I've heard a lot of fear in the people I've talked to and those whose posts on social media I've seen this morning.  But not a single one of them has said, "So I'm just going to go back into hiding."  Queer people know all about the devastating effects of shame and fear; it's what kept me in the closet, literally for decades.  Whatever happens, we're not going back there.

Silence validates hatred.  Acquiescence perpetuates the feeling of being less worthy, less valued, less human.  Once we've mourned the victims of the shooting, innocent people who were just there to dance and laugh and socialize and have fun, we will redouble our efforts to make sure nothing like this ever happens again, and you can bet we will fly the rainbow flag more proudly than ever.

You homophobes think we can be bullied and threatened back into silence?  You ain't seen nothin' yet.  Gives a different twist to the line from the Book of Hosea, doesn't it?

Who sows the wind, reaps the whirlwind.

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A hand and a message

One of the most enduring mysteries, both in history and in linguistics, is the Basque people of northeastern Spain.

For many years, it was thought that because they speak Euskara -- a linguistic isolate, certainly not Indo-European and seemingly unrelated to any other known language -- that they were physically unrelated to the rest of Europeans as well.  That's proven to be untrue; their genetics are markedly similar to other western Europeans, including a high prevalence of the R1b-DF27 Y-DNA haplogroup, found throughout Spain and southern France.  While there is some evidence that the Basque people are remnants of a Paleolithic population of western Europe, there's enough similarity with the surrounding population that this question is considered far from settled.

There's no doubt they've been genetically isolated for a long time, though.  One good indicator is their abnormally high frequency of the Rh negative blood type allele.  If you, or one of your parents, is Rh negative, there is a great likelihood that you have ancestry in northern Spain or southwestern France.  (My mom, who was Rh negative, was nearly a hundred percent of French descent, mostly from western France -- I'm quite certain she has some Basque ancestry back there somewhere.)  This has a significant downside; the danger of Rh incompatibility disorder, which occurs when a negative mother conceives a positive fetus (i.e. the father is positive).  When that happens, the mother's immune system can set up a reaction against the baby's blood and destroy it.  It's what killed my sister, Mary Margaret -- when she was born, in 1945, she was premature and severely anemic, and only lived a couple of days.  Between her birth and mine, in 1960, the RhoGAM injection was developed, which suppresses that part of the mother's immune system and prevents the damage.

That injection is why I'm alive today.

In any case, there's no doubt the Basques are a unique people.  The origin of their gene pool, culture, and language are still shrouded in mystery.  But a discovery last year near Pamplona may end up shedding some light on their history.

Called the "Hand of Irulegi," it's a bronze piece thought to be about two thousand years old.  This is cool enough in and of itself, but recent analysis has shown that it has an inscription, seemingly in proto-Basque, the language of the Vascones -- the Iron Age tribe encountered in northeastern Spain by the Romans, and who are thought to be the ancestors of the modern Basques.

It had been thought previously that the Vascones had little in the way of written language -- no traces of it had been found except for occasional one-word inscriptions on coins.  So almost nothing is known about the language they spoke (except, as previously noted, that it was definitely non-Indo European).  The first word in the inscription on the Hand of Irulegi is sorioneku, almost certainly the root word of modern Euskara zorioneko, meaning "luck" or "a good omen."

It's worth being cautious, though.  Unfortunately, such claims have been made before -- and have turned out to be worse than false, actually fraudulent.  Two years ago, two archaeologists were fined and given short jail sentences for faking artifacts and claiming that they were evidence of an early Basque written language.  So following the "once burned, twice shy" rule, the archaeologists and linguists studying the Hand of Irulegi are proceeding carefully.

But if it holds up under scrutiny, it will be a pretty remarkable discovery.  The early history and linguistics of the Basque people have been huge unanswered questions before now, and any pieces we can add to the puzzle will help clarify the origins of what is undoubtedly one of the most fascinating cultures in Europe.

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Dance of life

Dancing is ubiquitous amongst human societies.

Everywhere you go, every culture you look at, there is some form of rhythmic movement, usually to music.  (Sometimes the dancing creates its own music.)  I love to dance; I'm not saying I'm great at it, but starting out the day by putting on some tunes and moving my body just feels good.  And it's much more fun to do daily chores like cooking dinner with my music on, rockin' to the beat while I'm chopping the vegetables.

It's an interesting question why this is.  A shrewd guess is that a lot of it is about social cohesion.  You get a bunch of people together, all moving in the same way to the same rhythm, and it's a strong symbol of unity and common purpose.  

There's some biochemical support for this contention.  A series of studies a few years ago found that dancing releases four of the most important feel-good and bonding hormones -- dopamine, oxytocin, serotonin, and endorphin.

No wonder we feel better after we dance.

[Image licensed under the Creative Commons Ramesh lalwani, Revanta Sarabhai Male Dancer, CC BY-SA 4.0]

For me, one of the most wonderful -- and difficult -- things about dancing is that it requires you to forget about yourself.  To dance fluidly, you need to be immersed in the music and the movement, and overcome the self-consciousness we all seem to carry around with us, to greater or lesser degrees.  I'm plagued with more than my fair share of it, and it's only been fairly recently that I've been willing to dance with other people around.  Which, of course, is missing a good part of the fun of it -- sharing the experience of moving your body in synchrony to the music.

What brings all this up is a fascinating study from the University of Tokyo released last week showing that humans aren't the only ones who feel like shakin' their tails when the music comes on.

Rats do it, too.

Rats were fitted out with tiny helmets containing wireless accelerometers, and then exposed to varying types and speeds of music.  Sure enough -- they began to move their heads in time to the beat.

"Rats displayed innate — that is, without any training or prior exposure to music — beat synchronization most distinctly within 120-140 bpm (beats per minute), to which humans also exhibit the clearest beat synchronization," said Hirokazu Takahashi, of the Graduate School of Information Science and Technology, who co-authored the paper.  "The auditory cortex, the region of our brain that processes sound, was also tuned to 120-140 bpm, which we were able to explain using our mathematical model of brain adaptation...  Music exerts a strong appeal to the brain and has profound effects on emotion and cognition.  To utilize music effectively, we need to reveal the neural mechanism underlying this empirical fact."

I find this absolutely astonishing, given that rats don't have music in their natural environments (well, except for the rats that sometimes end up cohabiting with us).  What possible purpose can this serve?  It's interesting, but it seems to me to raise as many questions as it answers.

Which, of course, is the hallmark of good science.

Whatever the reason, it's pretty cool that this impulse to move to the music has a long evolutionary history.  And there's no doubt that it does a body good.  I'll end with a quote from the wonderful writer Dave Barry: "Nobody cares if you can't dance well.  Get out there on the floor and dance anyway."

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A projectile from deep space

Sometimes the most interesting questions to ask in science are the ones about facts so commonplace that we don't usually even think about them.  For example: how did the Earth end up with the composition it has?

The crust of the Earth -- the part that (obviously) we're most familiar with -- is largely made of silicate rocks (especially feldspars), with a good bit of magnesium, aluminum, potassium, and sodium thrown in.  The mantle, the liquid-to-semisolid bit beneath the crust, is also rich in silicates, but as you go deeper the iron and magnesium content increases (minerals with those elements are generally denser than silicates, so the silicates float to the top).  The core is mainly iron and nickel.

The oceans and atmosphere are a thin layer that is insignificant in terms of contribution to the mass of the Earth as a whole.  (Pretty damn significant to life on Earth, of course.)  And the impressive mountains and valleys, not to mention things like the oceanic trenches, aren't as impressive as they seem from our vantage point.  I remember being blown away when one of my geology professors said that the highest mountain ranges and deepest trenches have less topographic relief than you find on a typical billiard ball.

The Earth formed during the early days of the Solar System from accretion of asteroids, dust, and debris that pulled together from what was probably a set of rings around the Sun similar to what still exists around the planet Saturn.  During that phase, the energy of the constant collisions and bombardment heated the nascent Earth to beyond the melting point of the rock that it was made of, rendering the whole mass molten, glowing orange-hot.  (Some of that heat is what still makes the interior of the Earth hot today; the rest comes from the breakdown of radioactive elements in the core and mantle.  It's what keeps the Earth tectonically active, and the liquid metallic outer core is very likely why our planet has a magnetic field.)

But the specific makeup of the particular rocks that came together early in Earth's history determined what we have here today.  That includes the water in our lakes, rivers, and oceans.  The vast majority of our water arrived during the coalescence of our world -- but we just found out a little more about that particular feature from a much more recent arrival.

On the 28th of February, 2021, a football-sized meteorite streaked across the skies of Winchcombe, a town in Gloucestershire, in the southwest of England.  The intense heating from friction in the atmosphere made the rock explode, and a large chunk of it landed in the driveway of Rob and Cathryn Wilcock, who donated it to the Natural History Museum of London.

Rob Wilcock's photograph of what was left of the Winchcombe meteorite after it smashed into his driveway in February of 2021

The meteorite turned out to be a carbonaceous chondrite, a rare sort of meteorite that is carbon and water-rich.  And the first cool thing was that when the scientists measured the hydrogen-to-deuterium ratio of the the water in the meteorite, they found that it was identical to that in the Earth's oceans.

But you want the kicker?  Also present in the Winchcombe meteorite were various amino acids and a slew of other organic compounds -- the biochemical building blocks of life.

It's discoveries like this that that make me even more certain there's life out there in the cosmos.  Intelligent life is another matter; we still have yet to explain the Fermi paradox (Enrico Fermi's comment that if extraterrestrial life is common, then "where is everybody?" -- a topic about which I wrote in some detail a while back).  But non-technological life?  I'd bet a significant amount of money that it'll turn out to be abundant.  Think of what we could learn from a biology that was entirely separate from us, that had no ancestral connection to anything on Earth.

The mind boggles.

Studies like the one just done on the Winchcombe meteorite give us a perspective not only on how our planet formed, but what else might be out there waiting for us to find.  To quote Carl Sagan: "The universe is a pretty big place.  If it's just us, it seems like an awful waste of space."

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A black hole's warm glow

Once again I was sent a link by my buddy Andrew Butters, of the wonderful Potato Chip Math, who is not only a great writer but has a keen eye for a cool science article.

The link was to a story in Science Alert, and was titled, "Scientists Created a Black Hole in the Lab, and Then It Started To Glow," by Michelle Starr.  But before I tell you what the gist is, I have to bring up a peevish complaint about the headline (which may not have been Starr's fault; many times the headlines aren't written by the journalist herself, so I'm not jumping to blaming her for it).  The researchers, as you will see, did not "create a black hole;" what they did was create something that models some of the behavior of a black hole.  Which is cool enough, but doesn't have the cachet that black holes have, so Science Alert apparently thought they needed to jazz things up.  The headline is wildly misleading; no massive stars were destroyed in the course of this experiment.

Of course, this is not going to stop people from reading only the headline and then posting hysterical screeds about how those Mad Scientists Are Trying To Destroy Us All and undoubtedly tying in CERN, HAARP, the Illuminati, and Reptilian Aliens From Zeta Reticuli.

You know how it goes.

Anyhow, back to reality.  What the scientists really did was pretty amazing, and may give us some inroads into figuring out one of the biggest puzzles in physics; why theoretical physicists have been unable to reconcile the equations of quantum mechanics and those of relativity.  When they attempt to accommodate gravitational effects on the scale of the very small, the equations "blow up" -- they result in infinities -- usually a sign that something is very wrong about our understanding.

The reason black holes play into this question is that in the extraordinary gravitational field at the event horizon (the "point of no return," where the space is so strongly curved that even light can't escape), there is a quantum effect that becomes important on the macroscopic scale.  It's called Hawking radiation, after Stephen Hawking (who first proposed it), and deserves some closer attention.

 To start with, empty space isn't empty.  There is an inherent energy in space called zero-point energy or vacuum energy, and it is possible for this energy to be "borrowed" to produce particle-antiparticle pairs (such as an electron and a positron).  There's a catch, though; the pairs always recollide (in a minuscule amount of time, the upper limit of which is determined by the uncertainty principle).  So the pairs pop into existence and right out again, creating continuous tiny, extremely short-lived ripples in the fabric of space.  Not enough for anyone even to notice.

Well, unless you're near the event horizon of a black hole.

[Image is in the Public Domain]

The huge gravitational field at the event horizon means that vacuum energy is much higher, and pair production happens at a much greater rate.  And because of that boundary, sometimes one member of a pair falls into the event horizon, while the other one doesn't.  At that point, the survivor radiates out into space -- taking a little of the black hole's mass/energy along with it.

That's the Hawking radiation.  What it implies is that black holes don't last forever -- eventually they evaporate, finally exploding in a burst of gamma rays.

The problem has been that the Hawking radiation is impossible to study experimentally; we're (fortunately) not near any black holes, at least so far as we know, and the faint signature of the radiation would be lost in the general white noise of the universe.  But now -- and this is where we get to the current research -- a team led by Lotte Mertens of the University of Amsterdam has developed a model that simulates this behavior, and found that just like the real thing, it emits radiation exactly the way Hawking predicted (this is the "it started to glow" in the headline).

What they did was to lock together a chain of atoms that provided a path for electrons to move, and by fine-tuning the rate at which this happened, they created a simulated event horizon that caused some of the electrons' wave-like behavior to vanish completely.  The result was an increase in thermal radiation that matched the Hawking model precisely.

Why this is significant is that it could provide a way to study the quantum effects of gravity in the lab, something that has been impossible before now.  It's not like we can hop a spacecraft and fly to a black hole (which would be inadvisable anyhow).  So this fascinating experiment might be the first step toward one of the prime goals of physicists -- finding a way to unify the quantum and gravitational models.

So even if they didn't "create a black hole in the lab," the whole thing is still pretty freakin' cool.

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Broken tools

Since 2016, one of the most persistent puzzles to me has been the unflagging support of evangelical Christians for Donald Trump, a man whose main claim to fame seems to be embodying all Seven Deadly Sins in one individual.

I get why people with far-right ideology support him; that, at least, is consistent.  Trump has the same pro-corporate capitalist, xenophobic, anti-immigration, authoritarian views they do.  But the very religious have continued to idolize the man despite his openly admitting affairs while married, multiple credible allegations of fraud, and so many outright lies that it's impossible even to keep up with them.  They even go so far as to consider him anointed by God -- I heard one person, with no apparent sense of irony, call Trump "Jesus's Right-Hand Man."

When I've inquired (cautiously) into how "Jesus's Right-Hand Man" can be so dramatically and thoroughly flawed, I've heard comments like "God can work with a broken tool."  Which seems to me to be a puzzling stance for a group of people who ostensibly believe that the Bible should be followed to the letter, and anyone who doesn't do so is destined for the fires of hell.

[Image licensed under the Creative Commons Gerbilo, Christianity symbols, CC BY 3.0]

A fascinating study that appeared last week in Politics and Religion may have figured out the answer.  It's not that they think Trump is religious himself; they don't.  In fact, only 37% of the white evangelical Christians in the study said they thought Trump was religious.  (Surprisingly, Biden scored slightly higher.)  Despite this, they overwhelmingly voted for Trump -- because, the study found, Trump repeatedly emphasized that evangelical Christians were a threatened minority, and promised to protect them.

The perception, apparently, was that it didn't matter if Trump was religious, or even moral, himself; his election was "part of God's plan" to bolster up the evangelical community against perceived external threats.  Trump's strategy was to play into that fear -- and it worked.

"This finding suggests that Trump is a unique case when it comes to white evangelical evaluations of the religiosity of elites," said Jack Thompson of the University of Exeter, who authored the study, in an interview with PsyPost.  "Instead of projecting their beliefs onto Trump, and thereby supporting him because of his perceived religiosity, white evangelicals support him despite his lack of religiosity...  The findings concerning the salience of identity threats on conditioning white evangelical beliefs also provide an additional explanation for why evaluations on Trump’s religiosity might not have mattered when it came to their vote choice in 2016.  Namely, because Trump’s invocation of the decline of white Christian America proved effective in activating religious identity threat in a way that led to white evangelicals to coalesce around his candidacy.  In this way, Trump’s ability to articulate white evangelicals’ fears about the declining influence of Christianity likely overrode any lingering concerns about his religiosity."

So "God can work with a broken tool" turns out to be pretty spot on, as does the observation by a friend of mine that "the Religious Right loves Trump because he hates the same people they do."  

The whole thing makes some twisted kind of sense.  If you're convinced that "God has a plan" -- and that, importantly, you know what that plan is -- then it doesn't make a difference who contributes to the working out of that plan.  It could be the most evil human being alive, committing atrocities, and as long as that moves God's plan forward -- well, that's what needs to happen.

Mighty convenient, that.

One has to wonder how this will continue to play out, because there's no doubt that evangelical Christianity is declining.  A study in 2021 found that between 2006 and 2020, the number of self-identified evangelicals in the United States dropped by 37%.  (In the same period, the number of Roman Catholics also dropped by 27%.)  What that suggests is that the fears of decreasing influence are well-founded.  At some point, the mobilization of the remaining evangelicals because of fear will inevitably be overcome by the fact that they're simply too few in numbers to make a difference in national elections.

At least, I hope so.  I'm not religious myself but have no problem with people who are, as long as they stay in their lane and don't attempt to force belief down my throat.  On the other hand, any group who could support a moral degenerate like Donald Trump can't be allowed to swing the direction of our entire nation.

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