In The Cuckoo's Egg Cliff Stoll recounts an episode from the oral defense of his astrophysics PhD thesis. A bunch of people ask questions but one prof holds back until...
"""
“I’ve got just one question, Cliff,” he says, carving his way through the Eberhard-Faber. “Why is the sky blue?”
My mind is absolutely, profoundly blank. I have no idea. I look out the window at the sky with the primitive, uncomprehending wonder of a Neanderthal contemplating fire. I force myself to say something—anything. “Scattered light,” I reply. “Uh, yeah, scattered sunlight.”
“Could you be more specific?”
Well, words came from somewhere, out of some deep instinct of self-preservation. I babbled about the spectrum of sunlight, the upper atmosphere, and how light interacts with molecules of air.
“Could you be more specific?”
I’m describing how air molecules have dipole moments, the wave-particle duality of light, scribbling equations on the blackboard, and . . .
“Could you be more specific?”
An hour later, I’m sweating hard. His simple question—a five-year-old’s question—has drawn together oscillator theory, electricity and magnetism, thermodynamics, even quantum mechanics. Even in my miserable writhing, I admired the guy…
"""
"Could you be more specific" is a great question to find out more what the person knows and how they thing. You give an answer that, just due to the nature of knowledge and the limitation of language, has some black boxes. And "could you be more specific" is basically asking to go through the black boxes.
Its like asking how does Java work or something like that? You can go from "The JVM interprets java byte code" to quite a lot of depth on how various parts work if you have enough knowledge.
> “Scattering” is the scientific term of art for molecules deflecting photons. Linguistically, it’s used somewhat inconsistently. You’ll hear both “blue light scatters more” (the subject is the light) and “atmospheric molecules scatter blue light more” (the subject is the molecule). In any case, they means the same thing
There's nothing ambiguous or inconsistent about this. In English a verb is transitive if it takes one or more objects in addition to the subject. In "Anna carries a book", "carries" is transitive. A verb is intransivite if it takes no object as with "jumps" in "The frog jumps.".
Many verbs in English are "ambitransitive" where they can either take an object or not, and the meaning often shifts depending on how it's used. There is a whole category of verbs called "labile verbs" where the subject of the intransitive form becomes the object of the transitive form:
* Intransitive: The bell rang.
* Transitive: John rang the bell.
"Scatter" is simply a labile verb:
* Intransitive: Blue light scatters.
* Transitive: Atmospheric molecules scatter blue light more.
Interesting here is: Actually, for most blue butterflies, it’s not even a pigment-it’s just a trick of the light.
Since blue is so rare in the biological world (hardly any plants or animals can produce real blue chemicals), they evolved structural colors.
Their wings have these microscopic ridges that reflect blue light while canceling out other colors.
It’s basically the same reason the sky looks blue, just built into a wing. If you were to look at the wings from a different angle or get them wet, the blue often disappears because you're messing with that physical structure
Not just butterflies, birds too! But what selection pressure drove the evolution of these structural colors? Presumably signaling, the opposite of muted, camouflaging colors.
Also, as many might know, blue eyes are the result of a lack of pigment (eumelanin). The iris is translucent, but Rayleigh scattering preferentially backscatters blue photons. Green eyes have some pigment, making them a mix of brown and blue.
I have a related but deeper question about sun and colors:
Sunlight in space is considered white. When it reaches earth surface, it's considered a warmer color. Why human eyes that never (during evolution) saw sunlight without the atmosphere, consider it true white, and not colder color?
It's also not just why the setting or rising sun is red, but why it's yellow when high in the sky. The sun doesn't look yellow when viewed from outside the atmospheric veil.
Some of the demonstrations are not working correctly, at least on my machine (Windows + MS Edge). Any demo with a "reference image" is not correctly updating the reference.
Your intuition isn’t far off; there is an angle where the weight of green relative to the sum over wavelengths sees a local maximum. But it doesn’t dominate. In that transition zone, there is still an overlapping, transitioning abundance of redder and bluer wavelengths, adding with the green. Consequently, you see red, going into a red+green transition (== oranges, yellows), go into into a green+blue transition (== cyan), which already has few photons relative to the red and yellow zones, so it’s a dark/weak cyan, before it blends into the darker blue of the night sky.
Because the color of the sky is determined by a shifting mixture of wavelengths, not a single shifting wavelength.
Basically, the scattering process that "remove" blue from the spectrum also removes green, albeit to a lesser extent. There are some greenish and yellowish wavelengths in the sunset sky, but they're dominated by red, so the overall color appears red or orange.
In order for the sky to look noticeably green, there would have to be something that scattered reds and blues, without significantly absorbing green.
If you try to interpolate between sky-blue and orange using graphics software, the result depends on what "color space" you're using. If your software interpolates based on hue, you might see green (or purple) in the middle. But that's not physically realistic.
A realistic model is to interpolate each wavelength of the continuous spectrum separately. Interpolating in RGB color space is a crude approximation to this. And if you try the experiment, you'll see that the midpoint between sky-blue and orange is a kind of muddy brown, not green.
You won't get a green sky, but at least there is a meteorological optical phenomenon called the green flash around sunset. To see it, I think, you have to know what you're looking for - and you need good conditions.
Great article! I have to admit I had also heard of "Rayleigh scattering", but didn't really know more than that, until today.
Actually, I liked it so much that I went to the homepage of the blog, only to find out that this is the only article. Oh well... I hope there will be more to come!
In terms of "qualia", its the other way round probably? Like the way we see colours would have evolved (within the available environment of wavelengths and scatterings and the possibilities with rods and cones) so that the things we want to see are more likely to stand out. So we see the sky as blue because leaves are green and berries are red.
Funniest memory re: Rayleigh scattering: in anime show Aldnoah Zero, the uber-genius protagonist mansplains about it to a high profile girl, basically completely out of blue. An impostor of the girl later appears on an in-universe pirate broadcast, making an agitating environmentalism talking point using a technically incorrect explanation of the phenomenon that isn't consistent with the fact. The ever-right protagonist immediately notices it, having enlightened the girl previously on that exact topic, and it leads to actions.
Like, dude, as if anyone would care about such a highly technical point, like eg some React framework quirk or race condition mitigation for specific generation of Intel procesdor or a semi-well known edge cases with btrfs inode behavior, even if I had been on that exact camp.
Let's be real. The sky is blue because God thought it was a pretty color, simple as. All this stuff about wavelengths and resonant frequencies and human color perception got retconned into the physics engine at some point in the past millennium, that's why all these epicycles are needed.
Back in my youth, after the Internet became common but before Wikipedia, I tried to discover the answer to this and came away disappointed again and again. Every article I could find simply stated "because light scattering", and barely much more.
How does scattering work? Why does light scatter? _What does scattering even mean in the context of light?_
Air molecules are much smaller than the wavelength of visible light, by several orders of magnitude. This is why you can't resolve individual molecules in an optical microscope, and why photolithography with visible light doesn't go down to molecular feature sizes.
Fs is the frequency at which whatever your measuring is most efficient at vibrating
So it’s a combination of the composition of the thing and the environmental coupling with other vibrating things
Size and material composition are the primary factors
So for this case, the photon spectrum interact with nitrogen-oxygen mixture most efficiently at the frequency that reflects blue
I mostly studied sound frequency mixing with static objects (matching or cancelling the fs of room/space with the fs of a driver) but the principles of resonance hold across media
Going to be that guy, even though I think this is a really nice work overall...
But the winking and "cool guy" emojis are so grating. In general, technical explanations that apologize for themselves with constant reassurances like "don't worry" and "it's actually simple" undermine their own aim.
Your job -- if you're making content for people with double digit ages -- is to make the explanation as clear as you can, not to patronize and emotionally hand-hold the reader.
No, your job is to help your reader get to the end of the text. That means writing in a way that most of your audience finds compelling, readable, and not intimidating.
Not all readers are the same, so you will fail at your job for some readers.
But few readers are emotionless automatons that need nothing but dry technical content, unless it’s a topic they are very motivated to understand.
> That means writing in a way that most of your audience finds compelling, readable, and not intimidating.
I would agree with that. And I think emojis and unnecessary reassurances subvert that goal. It's fluff, it's more to read, and if the writing isn't already clear, they don't fix the problem.
> But few readers are emotionless automatons that need nothing but dry technical content
Nothing in my post argues for dry technical content.
Bartosz Ciechanowski's superb work, which may have inspired the author, gets the balance just right without any hand-holding asides:
The "Rayleigh Scattering" comic is really spot on.
Air is blue. The reason air is blue is blah blah blah physics, see the article we're all commenting on, but at the end of the day air is blue. We don't demand the same elaborate physics questions for why a ripe banana peel is yellow.
Not really. If the explanation was "air is blue" then the naive expectation would be that sun would appear blue against blackish background, basically the image of sun is being filtered through the atmosphere; if sun is white and air is blue then white filtered through blue should be blue? But sun appears yellowish against blue background. So clearly something different is going on.
HN is in fact quite receptive to humorous comments. The bar on what's considered humorous is just higher than on Reddit. It's about the signal/noise ratio.
In The Cuckoo's Egg Cliff Stoll recounts an episode from the oral defense of his astrophysics PhD thesis. A bunch of people ask questions but one prof holds back until...
""" “I’ve got just one question, Cliff,” he says, carving his way through the Eberhard-Faber. “Why is the sky blue?”
My mind is absolutely, profoundly blank. I have no idea. I look out the window at the sky with the primitive, uncomprehending wonder of a Neanderthal contemplating fire. I force myself to say something—anything. “Scattered light,” I reply. “Uh, yeah, scattered sunlight.”
“Could you be more specific?”
Well, words came from somewhere, out of some deep instinct of self-preservation. I babbled about the spectrum of sunlight, the upper atmosphere, and how light interacts with molecules of air.
“Could you be more specific?”
I’m describing how air molecules have dipole moments, the wave-particle duality of light, scribbling equations on the blackboard, and . . .
“Could you be more specific?”
An hour later, I’m sweating hard. His simple question—a five-year-old’s question—has drawn together oscillator theory, electricity and magnetism, thermodynamics, even quantum mechanics. Even in my miserable writhing, I admired the guy… """
"Could you be more specific" is a great question to find out more what the person knows and how they thing. You give an answer that, just due to the nature of knowledge and the limitation of language, has some black boxes. And "could you be more specific" is basically asking to go through the black boxes.
Its like asking how does Java work or something like that? You can go from "The JVM interprets java byte code" to quite a lot of depth on how various parts work if you have enough knowledge.
Really cool article! Tangential:
> “Scattering” is the scientific term of art for molecules deflecting photons. Linguistically, it’s used somewhat inconsistently. You’ll hear both “blue light scatters more” (the subject is the light) and “atmospheric molecules scatter blue light more” (the subject is the molecule). In any case, they means the same thing
There's nothing ambiguous or inconsistent about this. In English a verb is transitive if it takes one or more objects in addition to the subject. In "Anna carries a book", "carries" is transitive. A verb is intransivite if it takes no object as with "jumps" in "The frog jumps.".
Many verbs in English are "ambitransitive" where they can either take an object or not, and the meaning often shifts depending on how it's used. There is a whole category of verbs called "labile verbs" where the subject of the intransitive form becomes the object of the transitive form:
* Intransitive: The bell rang.
* Transitive: John rang the bell.
"Scatter" is simply a labile verb:
* Intransitive: Blue light scatters.
* Transitive: Atmospheric molecules scatter blue light more.
[delayed]
TIL!
Debates whether to update the sidenote with an explainer on ambitransitive and labile verbs
Interesting here is: Actually, for most blue butterflies, it’s not even a pigment-it’s just a trick of the light. Since blue is so rare in the biological world (hardly any plants or animals can produce real blue chemicals), they evolved structural colors. Their wings have these microscopic ridges that reflect blue light while canceling out other colors.
It’s basically the same reason the sky looks blue, just built into a wing. If you were to look at the wings from a different angle or get them wet, the blue often disappears because you're messing with that physical structure
Not just butterflies, birds too! But what selection pressure drove the evolution of these structural colors? Presumably signaling, the opposite of muted, camouflaging colors.
Also, as many might know, blue eyes are the result of a lack of pigment (eumelanin). The iris is translucent, but Rayleigh scattering preferentially backscatters blue photons. Green eyes have some pigment, making them a mix of brown and blue.
Also the blood veins that you see as bluish through the skin are blue for the same reason, due to light scattered in their walls.
It's also the trick employed by Iridigm, which Qualcomm acquired in late 2004 (i was there then).
https://en.wikipedia.org/wiki/Interferometric_modulator_disp...
I have a related but deeper question about sun and colors:
Sunlight in space is considered white. When it reaches earth surface, it's considered a warmer color. Why human eyes that never (during evolution) saw sunlight without the atmosphere, consider it true white, and not colder color?
This was great as it went farther than Rayleigh scattering. On this topic you have to watch this fantastic undergrad physics lecture demonstration: https://www.youtube.com/watch?v=sJG-rXBbmCc&t=1674s
It's also not just why the setting or rising sun is red, but why it's yellow when high in the sky. The sun doesn't look yellow when viewed from outside the atmospheric veil.
Some of the demonstrations are not working correctly, at least on my machine (Windows + MS Edge). Any demo with a "reference image" is not correctly updating the reference.
For the sunset example then, a natural question (for me) is then why isn't the sky green in the transition from blue sky to red sunset sky?
Your intuition isn’t far off; there is an angle where the weight of green relative to the sum over wavelengths sees a local maximum. But it doesn’t dominate. In that transition zone, there is still an overlapping, transitioning abundance of redder and bluer wavelengths, adding with the green. Consequently, you see red, going into a red+green transition (== oranges, yellows), go into into a green+blue transition (== cyan), which already has few photons relative to the red and yellow zones, so it’s a dark/weak cyan, before it blends into the darker blue of the night sky.
Because the color of the sky is determined by a shifting mixture of wavelengths, not a single shifting wavelength.
Basically, the scattering process that "remove" blue from the spectrum also removes green, albeit to a lesser extent. There are some greenish and yellowish wavelengths in the sunset sky, but they're dominated by red, so the overall color appears red or orange.
In order for the sky to look noticeably green, there would have to be something that scattered reds and blues, without significantly absorbing green.
If you try to interpolate between sky-blue and orange using graphics software, the result depends on what "color space" you're using. If your software interpolates based on hue, you might see green (or purple) in the middle. But that's not physically realistic.
A realistic model is to interpolate each wavelength of the continuous spectrum separately. Interpolating in RGB color space is a crude approximation to this. And if you try the experiment, you'll see that the midpoint between sky-blue and orange is a kind of muddy brown, not green.
You won't get a green sky, but at least there is a meteorological optical phenomenon called the green flash around sunset. To see it, I think, you have to know what you're looking for - and you need good conditions.
It can be - https://en.wikipedia.org/wiki/Green_flash
That's refraction not scattering though.
Great article! I have to admit I had also heard of "Rayleigh scattering", but didn't really know more than that, until today.
Actually, I liked it so much that I went to the homepage of the blog, only to find out that this is the only article. Oh well... I hope there will be more to come!
There will be! Requests welcome!
(I will almost certainly do one on quantum mechanics, but that's such a big explanation that I want to do some simpler ones first)
In terms of "qualia", its the other way round probably? Like the way we see colours would have evolved (within the available environment of wavelengths and scatterings and the possibilities with rods and cones) so that the things we want to see are more likely to stand out. So we see the sky as blue because leaves are green and berries are red.
https://www.youtube.com/watch?v=yV-KiTAAcrY
The same reason it's polarized.
Nitrogen.
Brilliant, thank you
Very well explained. I love the in-depthness of the article.
Anyone else immediately think of this commercial?
https://www.youtube.com/watch?v=PbKsC4GCT5k
*Since blue is the shortest wave length...*
Funniest memory re: Rayleigh scattering: in anime show Aldnoah Zero, the uber-genius protagonist mansplains about it to a high profile girl, basically completely out of blue. An impostor of the girl later appears on an in-universe pirate broadcast, making an agitating environmentalism talking point using a technically incorrect explanation of the phenomenon that isn't consistent with the fact. The ever-right protagonist immediately notices it, having enlightened the girl previously on that exact topic, and it leads to actions.
Like, dude, as if anyone would care about such a highly technical point, like eg some React framework quirk or race condition mitigation for specific generation of Intel procesdor or a semi-well known edge cases with btrfs inode behavior, even if I had been on that exact camp.
Brilliant explanation and beautifully presented. I wish I had a technical writer who could write up our business case this well!
I'm the writer of the article, and happy to chat. Email is my username at gmail.
Your blog layout, particularly on desktop, is brilliant.
My day job is UI design, so I especially appreciate this
(Is there something in particular you're referring to? I feel like sticky nav and sidenotes aren't particularly unusual?)
to piss me off, goddammit
Let's be real. The sky is blue because God thought it was a pretty color, simple as. All this stuff about wavelengths and resonant frequencies and human color perception got retconned into the physics engine at some point in the past millennium, that's why all these epicycles are needed.
Our lord Zeus always thinks of everything
His noodly appendage touches all.
> thought it was a pretty color
So was blue intrinsically pretty and thus made into the sky, or considered pretty and thus imprinted in the minds of humans that way?
Back in my youth, after the Internet became common but before Wikipedia, I tried to discover the answer to this and came away disappointed again and again. Every article I could find simply stated "because light scattering", and barely much more.
How does scattering work? Why does light scatter? _What does scattering even mean in the context of light?_
Yes! This is exactly why I wrote this article :)
Any other questions give you the same disappointment?
didn’t cv raman prove just that via his raman-effect for which he got the noble prize ?
Here is a wonderful lecture with real-world demonstrations of the effect:
https://www.youtube.com/watch?v=4a0FbQdH3dY
https://en.wikipedia.org/wiki/Rayleigh_scattering
I do have a question though.
The article says:
> blue and violet have the closest frequencies to a “resonant frequency” of nitrogen and oxygen molecules’s electron clouds
I thought it was more to do with the photon frequency matching the physical size of the air molecules? Or is that the same as its resonant frequency?
Air molecules are much smaller than the wavelength of visible light, by several orders of magnitude. This is why you can't resolve individual molecules in an optical microscope, and why photolithography with visible light doesn't go down to molecular feature sizes.
https://www.youtube.com/watch?v=4a0FbQdH3dY&t=2038
Direct link to timestamp 33:56
Fs is the frequency at which whatever your measuring is most efficient at vibrating
So it’s a combination of the composition of the thing and the environmental coupling with other vibrating things
Size and material composition are the primary factors
So for this case, the photon spectrum interact with nitrogen-oxygen mixture most efficiently at the frequency that reflects blue
I mostly studied sound frequency mixing with static objects (matching or cancelling the fs of room/space with the fs of a driver) but the principles of resonance hold across media
Not discussed but should be:
Prior to the great oxygenation event, Earth's sky was not blue; it was likely red-orange, carbon dioxide and methane being primary components.
Air is mostly nitrogen. Nitrogen gas is blue.
There.
Go watch a video of nitrogen gas evaporating from liquid nitrogen ... tell me what colour you see?
Going to be that guy, even though I think this is a really nice work overall...
But the winking and "cool guy" emojis are so grating. In general, technical explanations that apologize for themselves with constant reassurances like "don't worry" and "it's actually simple" undermine their own aim.
Your job -- if you're making content for people with double digit ages -- is to make the explanation as clear as you can, not to patronize and emotionally hand-hold the reader.
No, your job is to help your reader get to the end of the text. That means writing in a way that most of your audience finds compelling, readable, and not intimidating.
Not all readers are the same, so you will fail at your job for some readers.
But few readers are emotionless automatons that need nothing but dry technical content, unless it’s a topic they are very motivated to understand.
> That means writing in a way that most of your audience finds compelling, readable, and not intimidating.
I would agree with that. And I think emojis and unnecessary reassurances subvert that goal. It's fluff, it's more to read, and if the writing isn't already clear, they don't fix the problem.
> But few readers are emotionless automatons that need nothing but dry technical content
Nothing in my post argues for dry technical content.
Bartosz Ciechanowski's superb work, which may have inspired the author, gets the balance just right without any hand-holding asides:
https://ciechanow.ski/mechanical-watch/
Obligatory xkcd: "Sky Color" https://m.xkcd.com/1145/
Obligatory xkcd[2]: "Rayleigh Scattering" https://m.xkcd.com/1818/
Others?
The "Rayleigh Scattering" comic is really spot on.
Air is blue. The reason air is blue is blah blah blah physics, see the article we're all commenting on, but at the end of the day air is blue. We don't demand the same elaborate physics questions for why a ripe banana peel is yellow.
Not really. If the explanation was "air is blue" then the naive expectation would be that sun would appear blue against blackish background, basically the image of sun is being filtered through the atmosphere; if sun is white and air is blue then white filtered through blue should be blue? But sun appears yellowish against blue background. So clearly something different is going on.
It’s not. It’s raining here.
Wow 3 down votes. Sorry for making a joke. This place is joyful.
HN is in fact quite receptive to humorous comments. The bar on what's considered humorous is just higher than on Reddit. It's about the signal/noise ratio.
complaining in a self reply makes me downvote more