Althouse: "Crystallization is the only place in nature where you see straight lines. Everything else is wobbly, round and wiggly."

September 2, 2019

"Crystallization is the only place in nature where you see straight lines. Everything else is wobbly, round and wiggly."

"I think that we are innately drawn to order and organization in the midst of all this cosmic chaos."

Says a gem dealer, quoted in "What Draws Hundreds to This Lake Bed? Spellbinding Crystals/Welcome to Gem-O-Rama, California’s new gold rush" (NYT)(lots of cool photos at the link).

70 comments:

Josephbleau said...: Of course you see straight lines in radiation. A “natural” example is sunlight shining through openings in clouds. Nature has no onlies.; 9/2/19, 8:59 AM
David Begley said...: Where does Trump and 1619 fit in this story?; 9/2/19, 9:02 AM
Wince said...: Crystallization is the only place in nature where you see straight lines.

Don't tell AOC. She'll question their attractiveness.; 9/2/19, 9:06 AM
rehajm said...: I don't see Diplo or Nina but are we sure that's not Burning Man?; 9/2/19, 9:07 AM
Maillard Reactionary said...: Natural crystals are never perfect when viewed on the nano-scale, but to be fair, you can't see that scale with the unaided eye.

Among the best crystals we have today are the silicon ingots (like huge silvery salamis) that are grown to make semiconductors (they're thinly sliced with a diamond saw into thin wafers the patterning is made on). Impurity levels are 10e-7 or better before doping.

The other exceptionally good crystals are the two-dimensional ones of graphene (hexagonal carbon) and boron nitride that are made by a single lab in Japan. There is some interesting physics that only happens with these materials if they are very pure.; 9/2/19, 9:16 AM
Fernandinande said...: A “natural” example is sunlight shining through openings in clouds.

That's not straight, the light follows an "orbit" in the gravitational field. But it's still straighter than the edges of the crystals.; 9/2/19, 9:18 AM
sinz52 said...: Josephbleau said: "Of course you see straight lines in radiation."

Those are not straight lines, only approximations to straight lines. Einstein established that electromagnetic radiation is bent by a nearby gravitational field. It's just that the Sun and Earth have much smaller gravitational fields than neutron stars or black holes, so the radiation only appears to be straight lines.

The real reason why we are drawn to straight lines is that the geometry can be easily analyzed without advanced mathematics. To analyze general curves, you need calculus. And to analyze those "wiggly" things the guy mentioned, you need fractals.; 9/2/19, 9:27 AM
Josephbleau said...: I bow to the will of Landreu, nothing is straight, it is now unconscionable to use Newtonian approximations in our quantum world. I admit to heresy.; 9/2/19, 9:33 AM
Anonymous said...: Fredrich Mohs knew better; 9/2/19, 9:50 AM
Mr. Forward said...: John Wayne was straight.; 9/2/19, 9:50 AM
Fernandinande said...: John Wayne was straight.

The "straight pride" parade went in a straight line but they're just "normal", not "natural".; 9/2/19, 9:53 AM
Phil 314 said...: Professor,
Do you get a little royalty every time you link to an NYT article (and those annoying, log in and subscribe, messages)?; 9/2/19, 9:54 AM
Narr said...: No thing is straight in nature (except some pride parades, but are those natural?), is the nugget of De Rerum Natura as glossed in "The Swerve" by Greenblatt-- interesting ancient insight that apparently has some modern empirical backing. (I'm no physicist so will defer to those who are--with the reservation that scale is crucial, so there.)

Narr
One of my campus lunch buddies was a physicist doing work with graphene--hired away by a richer school of course; 9/2/19, 9:54 AM
Fernandinande said...: I bow to the will of Landreu, nothing is straight, it is now unconscionable to use Newtonian approximations in our quantum world. I admit to heresy.

Newtonism is an easier religion than Einsteinism.

And IIRC quantum mechanics likes special relativity (speed o' light) a lot more than it likes special relativity (bent space).; 9/2/19, 10:01 AM
Mark said...: Of course, the universe is remarkably ordered and not chaotic. We wouldn't exist if it were not. And if we did, we'd float off into space or disintegrate as atoms and molecules lost their cohesion.

Unfortunately, there are so many people who are pathologically impelled toward seeing chaos in all this order. So much so that they see the human person and human relationships as chaotic, rather than perceiving the objective order in nature. Not to mention objective good being evil and evil being good.; 9/2/19, 10:15 AM
traditionalguy said...: This comment has been removed by the author.; 9/2/19, 10:19 AM
traditionalguy said...: It's the flatness, stupid. Seeing Lines and curves and angles every where is left over from the Euclidean Geometry. But crystals have that Divine flat side.

Remember, Flat Earthers have nothing to fear but sphere itself. See, Flatlands.; 9/2/19, 10:20 AM
JaimeRoberto said...: Since the halite crystals smell bad, I was expecting the Althouse analysis of the connection between halite and halitosis.

I'm glad that something attracts people to Trona at least once a year, because the rest of the year it looks like the set of a zombie movie.; 9/2/19, 10:35 AM
chickelit said...: Metamictization appears like a cancer with every discussion of crystallinity; 9/2/19, 10:41 AM
n.n said...: Chaos ("evolution") is order but incompletely or insufficiently characterized and unwieldy.; 9/2/19, 10:53 AM
Narr said...: I see dread Entropy nodding its head.

Narr
It's everywhere!; 9/2/19, 11:22 AM
Mike (MJB Wolf) said...: Not true. Surface of still water is flat, i.e. proscribing a straight line. So dry lake beds do the same. That both are capable of crystallizing, water and salt, is just a coincidence.; 9/2/19, 11:28 AM
Scott Patton said...: ..."electromagnetic radiation is bent by a nearby gravitational field"...

NAP (not an physicist) but I think that space is bent by gravity and the electromagnetic radiation is still moving in a straight line. Maybe. If so, it may be true to say that it isn't traveling farther than it otherwise would.; 9/2/19, 11:32 AM
Fernandinande said...: Wiki says halite is contaminated table salt, sodium chloride.

"Three previously unknown minerals have been discovered encrusted in the walls of abandoned uranium mines in south Utah."; 9/2/19, 11:34 AM
Fernandinande said...: NAP (not an physicist) but I think that space is bent by gravity and the electromagnetic radiation is still moving in a straight line.

The fact that light (electromagnetic radiation) is bent is the evidence that space itself is bent. The first evidence of it, which Einstein asked astronomers to look for, was that the apparent position of other stars is displaced by the sun's gravity, observable during a "total" solar eclipse.; 9/2/19, 11:43 AM
Fernandinande said...: Surface of still water is flat, i.e. proscribing a straight line.

Wut?; 9/2/19, 11:51 AM
RobinGoodfellow said...: Halite? That’s salt. I want salt crystals I’m driving to Ralph’s.; 9/2/19, 12:00 PM
Otto said...: "I think that we are innately drawn to order and organization in the midst of all this cosmic chaos."
You could have fool the 60s crowd.
Another Ann meme "boring is good" theme.
Amazing this bawdy blogger having this epiphanal moment. It's all about power and 2020.; 9/2/19, 12:07 PM
Mike (MJB Wolf) said...: All a matter of perspective Fernandistein. The closer you get the less perfect the lines, but Nature can lay one straight now and then.; 9/2/19, 12:17 PM
wildswan said...: "Scott Patton said...
..."electromagnetic radiation is bent by a nearby gravitational field"...

NAP (not an physicist) but I think that space is bent by gravity and the electromagnetic radiation is still moving in a straight line. Maybe. If so, it may be true to say that it isn't traveling farther than it otherwise would."

Also NAP but always speculating on plant form, I would say:
Imagine the curve of a circle inside a square as four arcs which we straighten into four straight lines of the same length making the sides of a new square. That square would have longer sides than the square formed by the four diagonals of the original square. Originally the four arcs and the four diagonals formed four sets composed of an arc and a diagonal connecting the same two points on ends of two radii. But now the straightened arcs are connecting points further out than the radii long the same line. So there are always two possible regular and related distances between two points - the shortest distance, a straight line and the path formed by the radius of the square related to the straight line* as that radius turns through 90 degrees. One line, the curve is always 1.1107... units longer than the other, the straight line.

*Every straight line is always the singular possible diagonal of a singular possible square.; 9/2/19, 12:20 PM
Scott Patton said...: Wildswan. I agree with everything you wrote with the given that all measurements are taken within the same shaped space. Consider, an inch of curved space is still an inch (measured internally). Things traveling through that inch of curved space are only traveling an inch. In curved space, the shortest distance between two points would appear curved to an external observer in un-curved (less curved or differently curved) space.; 9/2/19, 12:43 PM
YoungHegelian said...: If you're into crystals, be sure to check out the Museum of Natural History's Gems & Minerals Exhibit at the Smithsonian in DC.

It is, pun intended, a hidden gem among the Smithsonian collection.; 9/2/19, 12:47 PM
TML said...: My mom was born in Trona.; 9/2/19, 12:50 PM
Guildofcannonballs said...: My cock (erect) is an extreme example of nature being ultro-straight.; 9/2/19, 1:14 PM
D 2 said...: Robber: Let me be straight: you give me your phone or I shoot you.
Guy: well, actually, in nature, ....
Robber: Goddamn pedants! It's people like you that have made this world gone all to hell! Fine, sit there, I'm done arguing.; 9/2/19, 1:26 PM
Narayanan said...: Blogger sinz52 said...
Josephbleau said: "Of course you see straight lines in radiation

Those are not straight lines, only approximations to straight lines. Einstein established that electromagnetic radiation is bent by a nearby gravitational field.
_______
What is bending mean for light coming at Earth, vs that flowing around Earth; 9/2/19, 1:31 PM
wildswan said...: "Scott Patton said...
Wildswan. I agree with everything you wrote with the given that all measurements are taken within the same shaped space. Consider, an inch of curved space is still an inch (measured internally). Things traveling through that inch of curved space are only traveling an inch. In curved space, the shortest distance between two points would appear curved to an external observer in un-curved (less curved or differently curved) space."

My Quest Among the Flowers: An Homage to Darcy Wentworth Thompson.
What I am trying to say is that there are two possible regular paths from two points. One is what we call "straight" and its length is the shortest length between the two points. And one is 1/4 of the curve of a circle going between the same two points. That length will always be 1.1107... longer than the straight line. This works in plane geometry but I think maybe you are asking about solid forms - what if the "straight line" is going over a shallow hill such as a highway going across Nebraska toward Colorado. Then the measured straight line, as you say, would really be a measured curve. As I see it if that hill were a perfect circle curve, a part of a sphere, and if we were not deceived by appearances and we knew it was a perfect circle curve, there would be no problem. We could just tunnel between the two points because the four arcs and the four diagonals of a square or cube and its internal circle or sphere are related in regular ways and we can find these numbers. Heinlein liked such thoughts. But if the curve were part of an ellipse then there would be trouble which would be trebled if we were talking about a solid since no one has figured out how to determine the circumference of an ellipse. I believe that light rays are bent by an elliptical field. So what can we do?

But, wait, plants increase in diameter and volume in an elliptical form also. But, as you can see on the surface of a pineapple where two lines meet and form a corner, the pineapple maintains a constant ratio because it maintains a constant corner. Therefore somewhere there is a constant or, dare I say an elliptical absolute, which pineapples, pinecones, sunflowers and even lowly daisies know more about than we do. Perhaps. If we found that constant and how it works we would know more than we do about plant form. Perhaps.; 9/2/19, 1:33 PM
wildswan said...: "the pineapple maintains a constant ratio because it maintains a constant corner."

the pineapple maintains a constant ratio because it maintains a constant corner as it grows larger and the ellipse flattens.; 9/2/19, 1:36 PM
Ingachuck'stoothlessARM said...: ""Straight enough" is a high standard" as far as Nature goes.; 9/2/19, 1:42 PM
hstad said...: A "straight line" is an abstract mathematical model. But in nature, everything is spacetime perturbations jiggling and oscillating and quivering in probabilistic clouds and waves and so forth - there are no rigid, stable “objects”.

For instance: You can think of a photon’s path as a “line,” but you are generating a conceptual abstraction. The photon itself does not have a stable shape, and doesn’t leave a straight trail behind it - that trail you imagine in your mind is purely in your mind.; 9/2/19, 1:45 PM
Rick.T. said...: Speaking of crystals my rock hound grandfather gave me a large (12” diameter) geode he collected on a trip about 40 years ago. Theoretically it could have a beautiful colored crystalline interior....or maybe nothing. I was going to have it cut and polished for my 65th but didn’t do it. I don’t know that I ever will do it.; 9/2/19, 2:02 PM
Ingachuck'stoothlessARM said...: @Rick T
you are postponing joy-- crack that mofo!!

He would have wanted it that way.; 9/2/19, 2:10 PM
Jaq said...: ""I think that we are innately drawn to order and organization in the midst of all this cosmic chaos.”

NYT looking for a “strong man” to free us from Trump. Well, more likely a stern, fearsome woman.; 9/2/19, 2:22 PM
stephen cooper said...: "How the Tiger Lost his Stripes" ?

"The Melancholy view of a fecund Meteor shower on a clear dark winter night in the old Mid-West, far from any city lights"

"Are Asian women with straight hair naturally more attractive than Eurasian women with curly hair" ?

Prime numbers are part of nature and as we observe them at greater and greater volume we see they form (that is, in their multitudes they can be plotted out on) a straight line on an x/y axis which is subtly connected to the Riemann Hypothesis, we hope.
For further info, John Derbyshire wrote a whole book about this.

A CIRCULAR OBJECT SUCH AS A WEDDING RING EXTRAPOLATED TO A TWO DEGREE PLANE FORMS A STRAIGHT LINE

and seriously, there are a lot of people you see every day who can think of no material object more worthy of HAPPY AND GRATEFUL THOUGHTS than the wedding ring they wear.

When the angel Gabriel left Heaven to tell Mary the good news of salvation, Gabriel followed a straight line to her quite home in the Holy Land
THAT IS NATURAL HISTORY too

Ascension Sunday (read poor Larkin's poem on Whitsuntide Weddings for the sequel) and several other Biblical stories that really happened --- the angels leaving Heaven to sing to the shepherds, as Berlioz immortalized in "l'adieu aux burgers", is one example --- and another good example is
the straight line between Stephen, the first martyr, and the first glimpse of Heaven as it actually is that any mortal living in this wonderful Christian world ever had while still mortal, an event we Christians celebrate on December 26 ......; 9/2/19, 2:39 PM
Tina Trent said...: Stephen Cooper: the crystal hunters pictured in the article, ecstatic in their massive mom jeans, made me think of the opposite of straight lines.

More like Hopkins' dappled things:

Glory be to God for dappled things ... rose-moles all in stipple upon trout that swim ... things counter, original, spare, strange ... fickle, freckled ... swift, slow; sweet, sour; adazzle, dim ...

Etcetera.; 9/2/19, 3:33 PM
Fernandinande said...: Lileks sez:
"Nothing today, Bleat-wise, but please enjoy this unprovoked update to the Google Street View page, where mostly unpopulated urban vistas masquerade as "art." Twenty pages! I was saving it for something like a hiatus, but it's time to start burning off these excess updates."

The google camera car takes some pretty swell photos, maybe it should get a scholarship to art school.; 9/2/19, 3:33 PM
Tina Trent said...: the google camera car would be better off getting a STEM degree; 9/2/19, 3:35 PM
wildswan said...: Mathematics is based on analyzing imaginary objects with perfect forms - with an infinite number of points between any two points and between any two points of those infinite points. But all the same if we could find a mathematical model for plant form it would be a big advance in botany.

And it would have implications for the theory of evolution as we know it. In that theory the mechanism is natural selection. But what if plants could be shown to be building on a basic form just as atoms build on the hydrogen atom? Then evolution would remain but the mechanism would not be natural selection but a natural progression. This wold completely undercut eugenics which is based on applying natural selection to social problems on the theory that it is scientific to do so because biology is based on progress by natural selection and we are biological beings and for eugenicists, nothing more.; 9/2/19, 3:40 PM
Mark said...: Something ain't straight when out of 39 people on board at the time of a boating accident, the only five survivors are crew members.; 9/2/19, 4:03 PM
stephen cooper said...: Tina - good catch ...

almost anyone who has been through law school in the last 30 years knows that there was a guy named Chirelstein ( a professor at Columbia Law ) who wrote the major "handbooks" on first year contract law and on USA income tax law ----

his real love in life was the poetry of Hopkins.
and I am sure he was the sort of guy who would seem to be wearing mom jeans .... God bless his heart .....

and ..... one of my favorite excerpts from a book ever is the portion of that book where I.A. Richards discusses teaching the Hopkins poem "Margaret Grieving" to his students who really wanted to know if they could read the poem better than they read it the first time .....

Hopefully we all one day will see that most humble of straight lines, Jacob's ladder, in a way that makes us happy.; 9/2/19, 4:13 PM
chickelit said...: Skylark said...NYT looking for a “strong man” to free us from Trump. Well, more likely a stern, fearsome woman.

Is there analogy in mythology? Any Greek goddesses?

The word "goddess" is surely as loathsome as the word "actress."; 9/2/19, 4:28 PM
chickelit said...: Mark said...Something ain't straight when out of 39 people on board at the time of a boating accident, the only five survivors are crew members.

And the captain knew "they couldn't get out."; 9/2/19, 4:30 PM
effinayright said...: Mark said...
Something ain't straight when out of 39 people on board at the time of a boating accident, the only five survivors are crew members.
****************
Unless crew sleep on the bridge or first deck below, while passengers have to go down a single companionway to get to their berths, two levels down. In that case they would not be abandoning passengers they can't save in any case. BUT---

The drawing at the Daily Mirror shows only one stairway from the berth deck to the galley above.

https://www.dailymail.co.uk/news/article-7419423/Many-feared-dead-boat-bursts-flames-California-30-people-rescued.html

The article doesn't show a full view of any of the decks, and accompanying photos of the boat leave unclear whether there was a bow exit from the galley. According to the Mirror article:

"In a chilling recording of the mayday call, the Conception captain can be heard telling a Coast Guard dispatcher that all of his passengers are trapped below deck 'with no escape hatch'.

So...Fire below decks blocks the passengers' single way out, and continually exploding O2 diving tanks seal their fate.

Just speculation on my part. One would think safety would demand at least two exits from below deck.

It's pretty clear someone's gonna burn for this.....; 9/2/19, 4:52 PM
ga6 said...: Crystal Blue Persuasion

https://www.youtube.com/watch?v=Dn5Pbug5nRw; 9/2/19, 4:53 PM
effinayright said...: chickelit said...
The word "goddess" is surely as loathsome as the word "actress."
*******

Do you equally object to the "la" and "le" of French? Or the Der, Die and Das of German?

Are such gender distinctions also "loathsome" to you, Oh Arbiter of All that is to be Approved or Loathed"?

STFU and FOAD.; 9/2/19, 4:56 PM
stephen cooper said...: chickelit - well, the 5 crew members were the ones most at risk of being washed overboard, which is these days the most likely way to die while sailing the ocean ----- there is no indication the ones who survived did anything wrong, none at all ---- this was just tragic --- death from fire on the ocean - as long as one is not in a submarine. where smoke inhalation has been a constant danger - is fairly rare, and, from everything I have read, I am sure the crew members who survived were not guilty at all of trying to stay safe while others were at risk ..... just one of those tragedies where chemistry and physics do what they are going to do.; 9/2/19, 4:58 PM
Scott Patton said...: Wildswan. I agree again with everything you've written. I don't believe it applies to the path of light around a massive object. The light is not following a bent path such as an arc. It is the space itself that is distorted (from an external perspective). A hypothetical straight edge would not provide a reference to show the curve of the light and a ruler would not measure it traveling farther than it would appear to travel on an (externally viewed) straight line. Both the straight edge and the ruler would be affected the same as the radiation (or nearly so).
In this case, the tunnel analogy is the basis for much sci-fi faster than light travel, usually with an artificially produced field or with the aid of a black hole/singularity/worm hole. Disclaimers apply... This is my NAP understanding if it.; 9/2/19, 5:02 PM
stephen cooper said...: That being said, it sounds like this boat was designed like a military submarine, and that is not good design strategy for peacetime vessels; 9/2/19, 5:02 PM
chickelit said...: It's pretty clear someone's gonna burn for this.....

Arbiter mocked fry; 9/2/19, 5:26 PM
rhhardin said...: Endeavour season 3 episode 3 starts with Bach Mass in B Minor, some countertenor; Morse likes classical music, a plus for the series; labelled by the subtitles as "opera music playing."

It's crystalized for them.; 9/2/19, 5:37 PM
Ingachuck'stoothlessARM said...: @Stephn Cooper
Isaiah 40:3; 9/2/19, 5:44 PM
Mr. Forward said...: An ornery mathematician
Was told where he could go
It only made him giggly
Because this is what he knows.
“It’s always round and wiggly
There is no path that’s straight
So as to your suggestion
You know I can’t relate.”; 9/2/19, 5:57 PM
stephen cooper said...: Isaiah 40:3 is a great verse, and something we should think of when we wonder about the beauty in straight lines (and crooked lines).

I spend little time thinking about beauty, I mostly reflect on the gift of life I have been given, a life that has not been graced with much worldly beauty, trust me, and I reflect on whether I have wasted my opportunities at happiness ....

and reflecting thereon, I take comfort in the lines of the prophet Joel, quoting the Lord:

"I will restore the years the locusts have eaten"

There has not been a single moment in any of our lives where God was not there, ready to restore any moment of suffering or worldly boredom to us in Heaven,
one day.
No matter how much of a loser we are right now, or may have been earlier in our lives.
"God writes straight with crooked lines" said the poet, and God said this:

"Before you were formed in the womb" you were beloved

None of us are not loved with the supreme love that God, from before the first day of creation, planned us to be the beneficiaries of.; 9/2/19, 6:15 PM
gilbar said...: Fernandistein said...about ..A “natural” example is sunlight shining through openings in clouds
That's not straight, the light follows an "orbit" in the gravitational field. But it's still straighter than the edges of the crystals.

partial list of things in nature that seem Really straight because you're not very close to them
the horizon
TREES!
meteor trails
comet tail
particle trails in a bubble chamber
rock strata
snowfall strata
a blade of grass

Of course, In "Reality" NOTHING is anything Like straight.
Quantum Mechanics Tells us that Even an atomic particle's course, aside from being curved; is REALLY a dotted line, as the particle hops in and out of existence

Things only look straight or solid, from a distance; 9/2/19, 6:35 PM
Ingachuck'stoothlessARM said...: @Mr Forward
Damn! Hell of a ditty, as usual!; 9/2/19, 7:08 PM
wildswan said...: "Scott Patton said...
... I don't believe it applies to the path of light around a massive object. The light is not following a bent path such as an arc."

I have been told that it is as if the light were an ant moving on the surface of a balloon from one point to another. But the ant can't go inside the balloon so there's only one kind of line: "straight" over short distances, actually "curved" over long distances and over long distances you see that it is curved. Perhaps it's just that I'm not talking about a physical system, or rather, not the physical system of the planets and their orbits and how light travels in that system. But I ask how a dandelion begins as a cylindrical bud, and becomes a round flat surface, then a round slightly domed surface, then closes into the cylindrical bud shape, then reopens into a spherical puffball. One shape keeps changing but maintains its proportional relationships. Consequently I'm always asking how two lines maintain a proportional relationship. So one of my thoughts is: Any straight line is related to an arc of a circle and I suppose vice versa, i.e., If you have a an arc of a circle curve, there is a straight line which is proportionally related and which is shorter by a definite amount. So if light is bending in a curve there is a related straight line which it is not following.

In short, the real truth is that, as you correctly sense, I have never been able to accept that you can't get off the surface of that damn balloon.; 9/2/19, 7:22 PM
MadisonMan said...: Large hail follows a straight line down to Earth.; 9/2/19, 7:27 PM
rcocean said...: The real question is why did the boat "Burst into flames"? Fire is a great hazard at sea in wooden boats, so why weren't fire extinguishers used?

And why did all the crew escape and no one else? on the surface, it would appear that 99% of their effort went to saving their own skins, and 1% to saving the passengers and fighting the fire.; 9/2/19, 7:52 PM
chickelit said...: The crew were all close to the deck; passengers were down in steerage. I can imagine this will lead to some safety reevaluations.; 9/2/19, 9:13 PM
AdultBilisim3434 said...: This comment has been removed by a blog administrator.; 1/9/23, 10:02 AM