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The Color of Infinite Temperature (johncarlosbaez.wordpress.com)
332 points by c1ccccc1 on Jan 17, 2022 | hide | past | favorite | 132 comments



The generalization of this is the Planckian locus:

https://en.wikipedia.org/wiki/Planckian_locus

That's the image of the temperature range (0,∞), mapped to the corresponding blackbody color in chromaticity space. The limit T -> ∞ is a point discontinuity near the center of CIE space.


FWIW, that article's top graphic[1] is currently malformed[2]. Hmm, and the text incorrect[3].

Wikipedia's coverage of this topic has regrettably been unstable over the years. Broken chromaticity diagrams are so common, each time the graphic is swapped, it's a toss up whether it's a correct one. And then edits reflect that, and common misconceptions. Perhaps if WP had not just Article and conversational Talk pages, but also something like a writer's notebook, it might serve as memory, as immune system, as a place to caution "make sure when editing that you don't ...". Perhaps it will stabilize some day - the Sun[4] page seems to have at long last settled on a white-not-yellow Sun. Yay. That's more than several of the most used intro astronomy college textbooks have managed. Science education content is... something we struggle to do well.

[1] https://en.wikipedia.org/wiki/File:PlanckianLocus.png https://commons.wikimedia.org/wiki/File:PlanckianLocus.png (13:38, 3 January 2012) [2] Obvious errors: the blackbody curve shown doesn't go through white, and does go through yellow. Incorrect white-point math is a recurring cause. [3] "It goes from deep red at low temperatures through orange, yellowish white, white, and finally bluish white at very high temperatures." (emphasis added) [4] https://en.wikipedia.org/wiki/Sun


After twenty years of using wikipedia, my conclusion is this: in order to keep a single article in decent shape, you need both:

1) Constant vigilance, to monitor the article and revert drive-by edits putting up random nonsense.

2) Solid political backup from other long-time wikipedia editors, to fight off constant AFDs and DRN attempts to destroy whatever you've done.

If at any point you slack off, the article will be gutted and replaced with garbage. This resembles any other human endeavor, in that you're valiantly resisting entropy while everyone in the world calls you a moron for even bothering.

As a disclaimer, I suppose I don't see any way this could be technically "fixed", short of replacing humanity with something else.


When I edit an article, it is automatically added to my watchlist, which currently has about 800 articles in it (most of which I don't care about; I should do some weeding). On an average day, maybe 20 of those articles are edited.

Most of those edits are minor. Most vandalism has already been reverted before I see it. A substantial wrong edit needs my attention maybe once a week.

When you speak of "valiantly resisting entropy", it sounds like a battle against the forces of Mordor. For me it's more like weeding the garden; a fairly pleasant activity, that's easiest if you do a little every day. You're still working against entropy, of course, but as you note that is like every other human endeavour.

There are articles I care about that I don't edit. These are mostly articles that some person or group reckons they "own". I don't edit anything to do with the Middle East, for example, nor any article about nationalist politics. Life's too short. I agreee there's no technical fix for that problem. There doesn't seem to be a social fix either; such articles are presumably just going to remain unreliable. Perhaps Wikipedia just isn't suitable as a repository for certain kinds of information.

Incidentally, articles on food seem to get nationalists going. The article on Biryani, for example is the subject of constant drive-bys, constantly flipping back and forth between India, Persia and Pakistan.


> constant AFDs and DRN attempts

what does this mean?

I think the edit history is quite harmless on this article at least.


Well, the biggest error for me is that the tongue-shaped region is completely filled with color! On any three-color device like an LCD display, the gamut of producible colors will cover a triangular region inside that tongue. Any chromaticity diagram that is filled completely is a lie.


It's hard to call that an error. Do you want it to show garbled static? Every point on the diagram shows the closest available color based on the format.



Out of curiosity...what background do you have to make such a wonderful highly technical comment in a casual way...I'm so interested in the field of your expertise that you know so much about that this stuff, that something so technical is familiar to you, that you can come up with this brilliant analogy straight away and do it so casually. Do you work in "color technology" for a media company or something? I have no idea. I'm so interested what part of the world people who know these things do work in.

Strangely, I'm struggling to write this comment in a way that doesn't sound trolling...sorry, I don't mean trolling at all. If you could see my facial expression it would be easier...


I think we should normalize expressions of awe and curiosity about other people. It's hard to do without sounding ridiculous. A model that helps me is, "I like the state that that person's brain is in. I'll let them know. If I'm lucky, my communication of appreciation might shake out some generalizable knowledge that I have not encountered before."

A good set of people to practice this on is doctors, teachers and Twitter users you admire.


I'm not the parent you're asking, but figure you might be interested anyways since I could've likely made the same comment:

I work on displays within an OS team. Having some basic understanding of colour theory is critical for a significant number of modern display projects, particularly for the high end. For example, enabling colour accurate rendering (games, photos, etc), shipping wide-gamut displays (how do you render existing content on a WCG display?), etc. More specifically to the planckian locus, it generally comes up when deciding which white point to calibrate a given display to at the factory (e.g. iPhone is 6470K, S20 is 7020K in Vivid)[1][2] and if you're doing any sort of chromatic white point adaptation, like Apple's True Tone[1][2].

My background before joining the team was a degree in math, but I really enjoyed doing low level projects in my spare time, so ended up on an OS team. We also have colour scientists who study this full time and have a _significantly_ better understanding of it all than I do :)

[1]: https://www.displaymate.com/iPhone_13Pro_ShootOut_1M.htm#Whi... [2]: https://www.displaymate.com/Galaxy_S20_ShootOut_1U.htm#White... [3]: https://support.apple.com/en-gb/HT208909 [4]: http://yuhaozhu.com/blog/chromatic-adaptation.html


I'd wager bachelor's degree+ in applied math or pure math or maybe physics.


Someone should implement a Planckian locus color space.


Ye olde incandescent bulbs had this built-in, of course you needed a dimmer...


I turned mine up to infinity and they had to build a new Earth. (These kids with their 11!)



Most programmable home LED lighting (e.g. Hue) provides a one dimensional color temperature color space.


I have just computed the colour and find slightly different value, i.e. computed [154, 181, 255] vs article [148, 177, 255]. Here is a Google Colab Notebook that has the colour for 10^200 along with comparisons with a blackbody:

https://colab.research.google.com/drive/1Oyn913zkXYB8Uf8k1hi...


David Madore answered on Twitter : https://twitter.com/gro_tsen/status/1483054395524796421, the discrepancy is likely due to you using Python's colourscience package SPECTRAL_SHAPE_DEFAULT which is based on ASTM E308-15 based on CIE and him using better color conversion functions from http://cvrl.ioo.ucl.ac.uk/index.htm


Hi,

Yes, and as discussed on Twitter, sRGB is defined for the CIE 1931 2 Degree Standard Observer, not other observers. It is not defined spectrally but as a set of chromaticity coordinates (in the CIE 1931 Chromaticity Diagram). Thus, strictly speaking, sRGB values can only be computed for the CIE 1931 2 Degree Standard Observer. I tried four different observers, using strict integration:

  - CIE 1931 2 Degree Standard Observer: [ 153.9026317 ,  180.75617631,  255.        ]
  - CIE 1964 10 Degree Standard Observer: [ 150.32288938,  184.67113624,  255.        ]
  - CIE 2012 2 Degree Standard Observer: [ 145.14899585,  180.69807338,  255.        ]
  - CIE 2012 10 Degree Standard Observer: [ 148.44893332,  185.66849549,  255.        ]
  - Article: (148,177,255)


> strictly speaking

Perhaps think of it as two steps? One of physics and biology, using minimally-flawed spectra, CMFs, and math, to get a plausible chromaticity. And a separate step of communication, using standards of sRGB and image ICC tags (rendering intent), to get browsers to convey that chromaticity to the user as a minimally-misleading (for the use case) color.

Thus the 10 vs 2 deg CMF choice might depend on the physical angular size of the emitting area. And before browsers supported rendering intent, for use cases where users were eyeball comparing the color with screen white, one might calculate using a very non-standard D58 white-point, as the blue-ish D65 would make white chromaticity render as a pink color, with users misled to think the chromaticity was pink.


After a great discussion on Twitter, it comes down to normalisation: I normalised the final EOTF-1 sRGB encoded values while the author normalised the intermediate linear sRGB values and did the EOTF-1 encoding after. We used the same Standard Observer.


Is there reason to believe either of these is more correct? (Very very naively, I would have believed normalizing an intermediate value would be "wrong", but I don't actually know anything about this ;P.)


Well, 10^200K isn't quite infinity yet.

Have you checked if the values change if you increase the temperature even further? Looks like their color is bluer than yours at least..


Yes, it is minimal.


I swear it's Periwinkle like the flower.

https://images.app.goo.gl/8Qs5FARoBhEwYG2N8


weird, several years ago i had a dream i had entered some kind of device that started to accelerate me towards the speed of light, and at the end of it i came to a point where it reached 'infinity' and it was like the most electric intense thing i had ever experienced, and i made a webpage to try and recreate and document what i remembered, and the color is almost exactly the same (strobe / flashing gif warning) http://jollo.org/LNT/public/dream.html


I once had a near death out of body experience and that gif reminds me of it like nothing else I've seen.


My out of body was from hallucinogens rather than near death, but it was very similar as well. The strobing is fascinating, going from a place of undifferentiated light back to the material world and back at a specific frequency.


Ah jeez that's a very flashy GIF at the end of the page there. Might want to throw a sensory warning on that link as a courtesy


I can't help being reminded of the passage in the book of Revelation where John describes the throne room of God, and he notes "a rainbow round about the throne, in sight like unto an emerald".

That's a little hard to imagine, because a rainbow contains a full spectrum of colours, whereas an emerald usually has a single colour, so some translations interpret the rainbow as being like the shine/gleam/glow of an emerald. But the idea that at infinite energy a spectrum might be perceived to human eyes as a single bluish hue is a nice thought, like the coincidence(?) that this colour happens to look like a clear summer's sky.

Anyway, for comparison, here's an image from Wikipedia of a synthetic emerald:

https://en.wikipedia.org/wiki/File:SyntEmerald_0302.jpg


The Greek term here is "ἶρις κυκλόθεν"[1]. According to Liddell-Scott "ἶρις" ("iris") may not only mean specifically the rainbow, but "any bright-coloured circle surrounding another body"[2]. So the emphasis is not on the spectrum, but on the shape. A better translation would be: "and the throne was completely surrounded by an emerald circle."

[1] https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext...

[2] https://www.perseus.tufts.edu/hopper/morph?l=i%29%3Dris&la=g...


I am wondering how many other "theories" of the Bible are similarly ill-informed.


Probably many, but my understanding is that the prophets "visions" aren't really meant to be taken literally: god is supposed to be this thing outside of reason and perception (not a "thing" actually), the visions are what the prophet's human mind makes up: throne, gold, rainbows and stuff aren't what the divine _actually_ is, it's just how the prophet's human mind visualises it. Also sometimes descriptions of visions are symbolic, which means these descriptions are as far from the vision as the vision is far from "actual" god.

(History of God is an interesting book, even/especially for atheists)


It's a nice thought, but describing the color in the OP as emerald seems like it would be a fairly poor attempt at describing your vision. It's more of a cornflower blue, or even as you say (and something easily accessible to the ancients): the color of a clear summer sky.

For example if I was John and I saw the color of infinite temperature around God's throne, I would probably say something more like:

> and there emanated from the throne an incredibly bright blue halo, as if a clear summer sky was shooting forth from God's throne.


It looks as though the colour in Greek is emerald rather than a generic green or blue.

σμαραγδίνῳ smaragdinō - https://biblehub.com/greek/4664.htm smaragdinos: made of emerald, emerald-green from σμάραγδος smaragdos: an emerald.

https://biblehub.com/lexicon/revelation/4-3.htm


The color blue hadn't been invented yet.


It used to be lumped in with green, fwiw; or rather green was more a cyan or sealike color and they binned everything "cool" together.


How in the world do you have a concept of color and not distinguish between the color of the sky and the color of grass and leaves.

And regardless, my point was more that "emerald" is clearly a worse analogue than "sky" for this particular color.


Different cultures distinguish colours into different classes. You can do an experiment where you give a person sheet of randomly colored pages and ask them to divide them into named stacks.

A western civilisation member might do something like Red, Brown, Orange, Yellow, Green, Blue, Pink, Violet, Grey and perhaps do something special with White/Black. (11 basic colours)

A Russian will most likely split blue into light blue and dark blue. (12 basic colours)

Himba people have 5 basic colours:

Serandu – used to describe reds, browns, oranges and some yellows

Dambu – includes a variety of greens, reds, beige and yellows

Zuzu – used to described most dark colours, black, dark red, dark purple, dark blue, etc.

Vapa – used for some yellows and white

Buru – used to describe a collection of greens and blues


When I was a kid, it was "obvious" to me that dark green and light green were two completely different colors, and it frustrated me to no end that people wouldn't agree with me, yet insist that pink and red were different colors.


It’s a majorly weird thing. Knowing of a colour makes it obvious, but not having the concept embedded into your neurons means it isn’t split and out and distinguished when you experience the world. There are some African tribes with a very different knowledge of blue and green to us that makes the contrast very clear

https://www.bbc.com/future/article/20180419-the-words-that-c...



There is much confusion about the Greek color theory, and I can imagine that for this reason there is also lots of confusion about which word is used for which color. The Greeks with their arts were merely interested in representing humans accurately and not interested in making landscapes. This might also explain why there is not much attention for the color blue in the writings that survived from that time period.


Maybe it's just bad writing.


"Perano" is a terrible name. Some far better alternatives:

- neutronium

- catastrophic violet

- Rayleigh-Blue-Jeans


Well, it's the blue equivalent of pink. Blink? No. Periwinkle? Periwinfinite?

I get super irritated by kids books that teach seven colors. We have an impoverished color vocabulary, as a result. Can't even describe the color of infinite temperature, sheesh.



That list is decidedly NOT cognitively ergonomic. Ends up being worse than useless by giving an appearance of authority.

E.g. look at a periwinkle flower and look at the periwinkle in the list. They call periwinkle "Aero" but what is that?!

https://images.app.goo.gl/8Qs5FARoBhEwYG2N8

I think color names should only be included if they match objects, have historical precedent or are composed of these plus basic descriptors. Or approved by the trans galactic color authority.


Haven't you cherry-picked a periwinkle photo that fits your opinion? This one has more red to it and fits the colour listed on Wikipedia better.

https://www.atozflowers.com/wp-content/uploads/2017/12/Vinca...

Aero originates from the Royal Air Force, don't presume the name doesn't match historical precedent when you don't know of one. Of course there are tons of competing names for various colours (and also many competing views on what set of colour coordinates belongs under a particular named colour) across cultures.

The list above cannot hope to be objective or complete.


This is my go-to page for coming up with names for computers and other hardware. Some examples, past and present: amber, auburn, carmine, cerise, indigo, magnolia, periwinkle, scarlet.


I have done the same with this list before!



How about “Qabiff”, since it’s #94B1FF. :)


Is it just white? All I see is a white box as the color, though the text says otherwise.


It's blue for me. Sort of a pastel or sky blue.


Yeah, tested on firefox and chrome. It's a pastel blue.


On safari, can confirm it just looks white. Even tried turning off Night Shift.

Not sure if this is a gold dress blue dress situation.


On Safari on macOS it shows a missing image icon and the image source returns a 404 error, so this is not a perceptual thing. In Firefox it does work strangely enough.


What blue dress? It was clearly a gold dress :)


Yes it's absolutely a white box, at least for me on mobile Safari


Same here, mobile Safari.


Huh. I am also using MobileSafari (on iOS 12 and 14) and it is rendering as a blue.


Blue in Firefox.


I see something blueish.


Baez is also a noted category theoretician - I need to get around to reading https://link.springer.com/chapter/10.1007%2F978-3-642-12821-..., where he claims to find the conceptual framework unifying analogies behind physics, topology, logic, and computation. Discussion: https://news.ycombinator.com/item?id=15423027


“Perano” really sounds like it could be the name of some Italian village... oh wait: https://en.m.wikipedia.org/wiki/Perano


> gamma rays of arbitrarily high frequency

What a delightfully, understatedly terrifying phrase.


> And according to the experts who sip latte all day and make up names for colors, this color is called ‘Perano’

Unexpectedly salty coming from a pure mathematician! But maybe it's just professional jealousy of a field that comes up with new terms regularly? ;)


He's a mathematical physicist.


If 0 Kelvin means object particles at complete stop and >0K meaning particles moving at a certain speed, shouldn't infinite temperature be impossible, since no particle can move faster than the speed of light?


The temperature of a low-pressure non-relativistic gas is indeed related to the average speed of the atoms in a simple way. However, temperature, in the general case, is more closely related to the average energy of a particle (so the energy and temperature can both grow without bound as the speed approaches closer and closer to the speed of light). However, even that "definition" of temperature is rather imprecise.


Weird and cool!

Is the low-pressure low-speed definition of temperature a special case of the relativistic definition, or a completely different concept?

What is the precise definition of temperature?

How do these definitions relate to our everyday understanding of temperature, i.e. feeling hot/cold?

Or which textbook should I read to find out?

Sorry for asking so much...


Great questions!

There are many mathematically equivalent versions of the "complete" definition. My favorite is the zeroth law of thermodynamics: If body A and B have the same temperature (meaning there is no heat flow between them when they touch) and body B and C have the same temperature, then body A and C also have the same temperature. Basically, you define the words "thermal equilibrium" to mean "there is no heat flow when they touch" and you also define temperature to be the quantity that is equal in that case. This together with the "conservation of energy" and "growth of entropy" (basically the axioms of thermodynamics) is sufficient to derive most properties of temperature you know.

If you have already defined entropy in some other way, you can say "the temperature of an object tells you how much the entropy of the object rises for a unit rise in the internal heat energy of the object":

ΔEntropy = ΔEnergy / Temperature

If you have not yet defined entropy, but have defined temperature (which I personally see as easier to understand), then the above equation can be your definition of entropy.

Notice that "definition" just needs to be mathematically sound (i.e., self consistent). But for a physicist to want to use such definitions, they *also* need to be practical. Any of the (equivalent) definitions above are a fair choice, as they happen to be the self-consistent principles which do lead to behavior like the one we experimentally observe.

I do imagine that a rigorous mathematician might have a reason to prefer one of the aforementioned definitions more than the other. I do not have such concerns.

Lastly, concerning the gases: If you happen to know that gases are made out of moving atoms then you can do a bit more. Mind you, you can build most of thermodynamics without that knowledge. But if you know that fact, then you can derive that temperature is related to some measure of average energy per atom. If the atoms are relativistic, then energy per atom will need to be written in the relativistic form (which does not grow to infinity as velocity approaches the speed of light). At lower speeds, the formula for the energy becomes numerically indistinguishable from the one from classical mechanics.

See https://en.wikipedia.org/wiki/Zeroth_law_of_thermodynamics#F...

Then I would suggest reading:

- https://en.wikipedia.org/wiki/Zeroth_law_of_thermodynamics in its entirety

- https://en.wikipedia.org/wiki/Temperature

- https://en.wikipedia.org/wiki/Thermodynamic_temperature


There are more problems than just that. The point is that the color converges to a single value, so even as you approach infinity it stops changing.


Temperature is proportional to kinetic energy only in specific conditions. In its more general definition, temperature is how energy changes with entropy. You can have temperatures tending towards infinity, and even negative temperatures.


0 K doesn't mean complete stop. That's not allowed by quantum mechanics.


Isn't 0 K not allowed by quantum mechanics anyway?


It is a temperature that can be described. You just can't do an experiment that reaches it.

But on its description, there are probably plenty of movement (depends on what your particles are).


Wouldn't infinite temperature object emit infinite amount of energy at all wavelengths, making the spectrum (and color) ill-defined?


Not at all wavelengths. An object of finite size and infinite temperature can produce all the wavelengths, but the probability of it generating, say visible light is really low approaching 0. So you can think about the relative number of visible photons you could observe and that gives you a color.

My gripe with this is that if our understanding of quantum mechanics and general relativity is correct there is a limit of temperature. When a photon has a wavelength equal or smaller than the Planck length said photon contains enough energy to create a black hole. So, the upper limit of temperature should be the point at which the generation of black holes dominates the spectrum.


You can still take the ratio of infinities and get a finite result.


Looks like the frame color of a C64 screen.


It’s a secret plot by Atari to fry off the C64 users and rule the world. Fortunately, one is just a POKE53280,0:POKE53281,0:POKE646,1 away from evading this.


Imagine in the far-distant future (past) where advanced machines have taken up the hobby of emulating the history of the earth on C64.


So it is then at least how I entered my current world. Close enough to the Big Bang, I suppose.


Considering that temperature is related to how agitated are the particles of a material and that there is a limit of how fast something can move (speed of light); doesn't it imposes an upper limit on the temperature?

I mean, replacing v_rms by c in equation 3 in https://chem.libretexts.org/Bookshelves/Physical_and_Theoret... gives us an upper limit for the temperature of a gas, right?


That is a somewhat simplified definition of temperature. While there's a parallel discussion on the same topic at [0], the term you're looking for is Planck temperature [1]. There is no "upper cap" on temperature per se, but we also don't have any models for describing what would happen beyond that point. See [2] for more discussion.

[0] https://news.ycombinator.com/item?id=29963147

[1] https://en.wikipedia.org/wiki/Planck_units#Planck_temperatur...

[2] https://physics.stackexchange.com/q/420670/43412


The general concept is correct but there are a few issues with the article:

- Specific RGB values always depend on a selected white balance temperature. If the WB temp is the same as the object's temp it would be white, not blue. If the WB temp were higher than the object's temp it would appear red.

EDIT: the article does say sRGB which implies a 6500K wb.

- "infinitely hot" is not physically possible. The Neutron star example is fine, that temp would be around 10^12 K

At that temperature virtually all of the emission would be in gamma rays, but emission in the visible spectrum would not be zero. Blue wavelengths would be stronger than green, which would be stronger than red so the color would appear Blue for any "normal" white balance temp (like 5500 K).


It explicitly says sRGB which has commonly agreed white spot of 6500K. And thus it's reasonable assumption that photo of neutron star displayed on common monitor would have such color.

Infinity is a well understood mathematical construct. I don't know what is the issue with evaluating limit value of some function, in this case color, "at infinity"? Nowhere it says it's physically possible.


Boy am I glad to see this color!

I was writing a black hole simulator, and needed to figure out the color shift of the stars as one approaches the black hole. The calculation gave me this blue at the one end of the spectrum which was very underwhelming tbh. For some reason I always though this color would be either 0xffffff, or some deep blue. Glad that my calculation is finally confirmed to be right!


It looks a similar colour to Cerenkov radiation. How similar? Is that a coincidence?


Converting wavelength to sRGB is remarkably difficult. The conversion used here doesn't look quite right (see for example the sodium D lines), but I have never been able to figure out how to do much better.


Colors of pure wavelengths are outside of the sRGB gamut and cannot be converted to sRGB, only approximated. Color of infinite temperature, on the other hand, is inside the sRGB gamut so no complication here.


I'm not talking about the out-of-gamut problem. I'm saying that the standard algorithms simply do an awful job, such that you can easily beat them by eye.

This is in the context of trying to produce the closest sRGB colors to a set of LEDs, for use in documentation. No published method could actually do it. I did have to assume the LED was a single-wavelength source, gaussian with specified FWHM, or Lorentzian, rather than measuring the spectrum (I was too lazy to mess with the spectrophotometer), but I don't think that would have made the difference for an LED.


One major issue is that most displays aren’t properly calibrated to sRGB. Once I got two monitors profiled and calibrated properly, suddenly most of these algorithms matched much more closely than I had expected.


For once, a good article. Short, clear, to the point. Thank you, author.


I love John Baez's blog too! But actually I think his long winded, mathematically challenging posts are more interesting. Like this series

https://johncarlosbaez.wordpress.com/2012/01/19/classical-me...

https://johncarlosbaez.wordpress.com/2012/01/23/classical-me...

https://johncarlosbaez.wordpress.com/2021/09/23/classical-me...

https://johncarlosbaez.wordpress.com/2021/09/26/classical-me...

An excerpt from the first article:

> The big picture

> Now let’s step back and think about what’s going on.

> Lately I’ve been trying to unify a bunch of ‘extremal principles’, including:

> 1) the principle of least action

> 2) the principle of least energy

> 3) the principle of maximum entropy

> 4) the principle of maximum simplicity, or Occam’s razor

> In my post on quantropy I explained how the first three principles fit into a single framework if we treat Planck’s constant as an imaginary temperature. The guiding principle of this framework is

> maximize entropy

> subject to the constraints imposed by what you believe

> And that’s nice, because E. T. Jaynes has made a powerful case for this principle.

> However, when the temperature is imaginary, entropy is so different that it may deserves a new name: say, ‘quantropy’. In particular, it’s complex-valued, so instead of maximizing it we have to look for stationary points: places where its first derivative is zero. But this isn’t so bad. Indeed, a lot of minimum and maximum principles are really ‘stationary principles’ if you examine them carefully.

> What about the fourth principle: Occam’s razor? We can formalize this using algorithmic probability theory. Occam’s razor then becomes yet another special case of

> maximize entropy

> subject the constraints imposed by what you believe

> once we realize that algorithmic entropy is a special case of ordinary entropy.


I haven’t seen the math for the conversion of the article but typically the conversion from CCT to xy/uv are given for a particular domain. One of the conversion with the largest domain, i.e. Ohno m, covers domain [1000K, 100000K]: https://github.com/colour-science/colour/blob/develop/colour...

Infinity is very much in extrapolation territory.


Not really, since the shape of the blackbody emissions curve converges (when restricted to the visible wavelength range and normalized). 10^5 K should be very close to infinity.


“Not really” to which part?


That it's not an extrapolation. The physics part converges and stops varying.


The article actually points out to the fact that colour is not dependent on the Planck’s Law: “So, for an extremely hot blackbody, the spectrum of light we can actually see with our eyes is governed by the Rayleigh–Jeans law. This law says the color doesn’t depend on the temperature: only the brightness does!”

But then the Rayleigh-Jeans Law has been shown to be incorrect, see Ultraviolet Catastrophe.


Well yes but no: it's still the correct infrared limit (or high-temperature limit) of Planck's law, in fact Wikipedia has the derivation from one to the other:

https://en.wikipedia.org/wiki/Rayleigh%E2%80%93Jeans_law#Com...


The colour computed in the article is anything but infrared, it is at the other end of the planckian locus.


When physicists say something is true in the infrared limit, they mean that it is true for low enough wavelengths. In this case the exact definition of "low enough" depends on the temperature. If the temperature is high enough, then that set of "low enough" wavelengths will include the entire visible part of the spectrum. So as T goes to infinity, the light that we can actually see will get brighter and brighter, but the relative power emitted at different wavelengths will stay the same, so the colour will stay the same. But that's just in the visible region. There will be higher and higher frequency x rays and gamma rays emitted, eventually to the point of being lethal to a human observer.


That's why they said infrared or high-temperature.

Combined it's: Anywhere the temperature is high relative to the frequencies being analyzed.


Microsoft should change their BSOD screen background color to this.


Is the color depth 24bit on blue/white part?


Can someone explain this to me with undergraduate level math?


The color you perceive is a weighted average of the intensities of different wavelengths of light that hit your eye. Ultra-violet and infra-red have a weight of zero (invisible). Most colors not at the edge of visible spectrum have weights that are roughly the same order of magnitude.

Hot bodies emit various wavelengths, but the distribution of intensities is roughly a bell curve. If you sum up all these intensities, but weight them by the aforementioned weights in the previous paragraph, you would calculate what color would be perceived when looking at that object.

Barely glowing hot objects emit a ton of infra-red (with perceptual weight zero) and a bit in the visual spectrum, on the red end of it (with a non-zero weight). So we perceive a red glow.

Extremely ludicrously hot objects emit a ton of ultra-violet, X-ray and gamma rays (all with zero weight for visual perception), but also a bit on the blue end of the visible spectrum (with a non-zero weight for perception). So they look blue. Well, they would have looked blue, if the invisible bombardment of gamma rays did not immediately evaporate you.


A hot object emits light over a wide range of frequencies.

At the low end of those frequencies, the intensity at each fequency is roughly proportional to the object's temperature multiplied by the frequency squared.

Once an object is hot enough, all of visible light is in the low end of the frequency range. Which means the ratios between all visible frequencies are based on frequency squared and nothing else.

That gives us a specific spectrum, where blue is about twice as intense as red. That spectrum has a specific color, the same color as #94B1FF.

(Note that other RGB values also represent the same color at different brightnesses. That's fine, because we're not worried about brightness in this math. Brightness scales linearly with the temperature of the object.)



So, for an extremely hot blackbody, the spectrum of light we can actually see with our eyes is governed by the Rayleigh–Jeans law.

This doesn't make sense to me. If we're talking about what color our eyes would see, all our cones would be 100% saturated. Correct me if I'm wrong, but we would still perceive that as white regardless of where the spectrum peak is.


Looks like the color is simply normalized so that one of the values is at maximum (255) and the others follow the shape of the spectrum. It's all very theoretical. If you're talking about what's physically possible, then you could just stop at "infinite temperature" instead of going into eye cones. Maybe if a body's temperature approaches infinity, you could get this color by standing at a sufficient distance, or wearing adequate sunglasses with uniform attenuation, or doing the correct safety squint like we do at the workshop.


See that's the problem. The author is using the "color our eyes would actually see" thing but only in arbitrary ways that generate pageviews. It's inconsistent and dishonest.


I've always felt that temperature is one of the quantities what was wrongly defined. As a consequence, It's working against you in most of the thermodynamics formulas. A better concept would have been (1/T).


Well, defining it so it's proportional to pressure etc. wasn't the worst idea.


It looks like the blue equivalent of pink. But what is that, Periwinkle?


I'd go with Periwinkle. My periwinkles, though, are a rather sad, washed-out, faintly bluish white.


Your soil pH may be off.


Hmmm. Too acid, or too alkaline?

I had no idea that periwinkles were touchy about such matters. I thought they were considered an invasive weed that can grow on waste ground.


decent. I'm curious what it would be for a human tetrachromat (likely female) seeing in r4 space. Sadly, I can never know.


Nice to know when it hits


how about the color of negative temperatures?


Assuming Planck's law still holds it should start absorbing radiation instead.

That said Planck's law derives from Gibb's distribution and applying that rule to it suggests it immediately radiates all energy, until it stops having a negative temperature so I'm not sure if negative temperature is compatible with thermal radiation.


If an absolute lack of all energy is 0, a negative temperature is kinda hard to reason about.


Negative temperatures are a thing, but you need to reframe temperature from inherent heat to energy flow between systems.

https://en.wikipedia.org/wiki/Negative_temperature


Visited (from safari and chrome) on iPhone, it looks like entirely white [1]. It appears as the correct bluish colour on desktop. Might be just me. No idea why.

[1] https://i.imgur.com/Bp1AW3u.png


It also doesn't work from Safari on desktop, showing the little blue square with the question mark in it icon.

Right-clicking and opening the image in its own tab works.

Inspecting both, the server is setting Content-Type to "image/webp" on the page (and sending 58 bytes), but setting it to "image/png" when displayed in its own tab (and sending 139 bytes).

On the request Safari says it can accept "image/webp,image/png,image/svg+xml,image/*;q=0.8,video/*;q=0.8,*/*;q=0.5" so the server choosing to send a webp is fine. For some reason apparently Safari cannot display this particular webp.

The graph below that on the page, the one of intensity vs. frequency, is also a webp and Safari has no trouble with it.


Seems it's not just me; here's the correct colour:

https://imgur.com/a/OdHLrl9


Same here!




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