Why do toddlers have a logarithmic understanding of numbers?

[Petahanks]

I’ve read that the light we can see coming from the sun originates from the suns photosphere which can be modeled as a black body emitter with a temperature of 5760 K. If I use Wien’s displacement law with this temperature to find out where the peak wavelength is:

Peak = (2.8977*10^-3)/5760 = 503 nm

I get 503 nanometers, which is indisputably a green color and not yellow. So why do we perceive the sun as yellowish and not green at all? And it’s the same thing if you light a match: you can see the blue parts and the more yellow/red parts, which I guess means that somewhere in between we should be seeing green? But we/I dont. And furthermore I was under the impression that the human eye is most sensitive to green color so if something is peaking in the green range how come we can’t see it??

 

[Orodruin]

What you have computed is the peak of the spectrum. The spectrum is not discrete but contains a continuum of wavelengths which affects how you see it. When you see an object heating up going from red to yellow to blue, the spectrum is heavily biased towards longer wavelengths for the red (objects colder than the Sun) and shorter wavelengths for the blue (objects warmer than the Sun). Since the Sun peaks in the middle of your visible range, the spectrum does not change as much and therefore does not particularly favour any wavelength. Therefore, the Sun is essentially white. However, when a significant amount of scattering occurs in the atmosphere (the longer the light has to travel, the more scattering) the scattering happens mainly for shorter wavelengths (this is why the sky is blue!). This tends to shift the Sun's apparent colour to yellowish or red when it is close to the horizon.

That the Sun's spectral peak is in the green wavelength range and that our peak sensitivity is for green is also not a coincidence, but a natural cause of evolution - Nature would be stupid to equip us with an instrument that could detect wavelengths that are not around and we would not last long with such sight.

 

[Petahanks]

Since the Sun peaks in the middle of your visible range, the spectrum does not change as much and therefore does not particularly favour any wavelength. Therefore, the Sun is essentially white.

Sorry but I don’t understand what you mean by “does not favour any wavelength”. I understand that the spectrum covers all colors but it has the highest intensity in the green range, so why do we perceive none of it?

And I don’t think you can explain away the lack of greenness by scattering in the sky, even when the sun is at its highest I still perceive it as pretty much bright yellow. And if the sky was what’s distorting its color then it should look very different if you take a picture at it from space, which from what I’ve seen isn’t the case. And the only time the sun would be white is if it had an equal intensity across all wavelengths in the visible range and our eyes were equally sensitive to all of those wavelengths – so in other words never?

 

[Doug Huffman]

We do perceive some of it, in the Green Flash, for instance.

 

[BobG]

Orodruin's first paragraph is correct, but Phil Plait's explanation is still probably better.

http://blogs.discovermagazine.com/badastronomy/2008/07/29/why-are-there-no-green-stars/

It has more to do with your eyes than the Sun (or other stars), themselves.

 

[Orodruin]

Sorry but I don’t understand what you mean by “does not favour any wavelength”. I understand that the spectrum covers all colors but it has the highest intensity in the green range, so why do we perceive none of it?

The maximum is a maximum and so the derivative of the intensity per wavelength is zero. This means that the intensity varies very little with wavelength compared to what it does away from this wavelength for objects that are much warmer or much colder. That the largest intensity is green does not tell you much if you do not consider how much larger it is at the same time.

And I don’t think you can explain away the lack of greenness by scattering in the sky, even when the sun is at its highest I still perceive it as pretty much bright yellow.

You should not be looking at the Sun directly.

And if the sky was what’s distorting its color then it should look very different if you take a picture at it from space, which from what I’ve seen isn’t the case.

It is.

Also note that the colour your mind tells you the Sun is is also cultural to some extent. In Japan, school kids paint red suns.

Phil Plait's explanation is still probably better.

http://blogs.discovermagazine.com/badastronomy/2008/07/29/why-are-there-no-green-stars/

So the only way to see a star as being green is for it to be only emitting green light. But as you can see from the graph above, that’s pretty much impossible. Any star emitting mostly green will be putting out lots of red and blue as well, making the star look white.

This is the main point I made above, even if the Sun emits most intensity in green, it will still emit a lot of red and blue wavelengths as well.

 

[Petahanks]

Orodruin's first paragraph is correct, but Phil Plait's explanation is still probably better.

http://blogs.discovermagazine.com/badastronomy/2008/07/29/why-are-there-no-green-stars/

It has more to do with your eyes than the Sun (or other stars), themselves.

Wow, that article was like literally made to answer my exact question! :)

But honestly, after read it, I still don’t fully understand why it doesn’t appear greenish.

If I understood the article correctly the sun is in fact mostly green but the eyes/brains of humans are too weak to perceive it. And this is how the article explained human vision:

“Cones are triggered by varying amounts. An orange, for example, gets the red cones going about twice as much as the green ones, but leaves the blue ones alone. When the brain receives the signal from the three cones, it says "This must be an object that is orange." ”

And I guess this is supposed to convince the reader that we can’t see green stars. But when I read it I don’t think it makes any sense at all, because the light from the sun should be the same as in the orange example: less blue – more green – less yellow/red should result in a color with a greenish tint!?

If our eyes apparently happens to work exactly like the RGB color space, then going into photoshop and blending for example the color R=200 G=255 B=200 should give a similar color to how we perceive the sun.. But if I do that it results in a greenish tint!

 

[Petahanks]

The maximum is a maximum and so the derivative of the intensity per wavelength is zero. This means that the intensity varies very little with wavelength compared to what it does away from this wavelength for objects that are much warmer or much colder. That the largest intensity is green does not tell you much if you do not consider how much larger it is at the same time..

I don’t understand: is our vision somehow based on the derivative of the light rather than the absolute intensity?

 

[marcus]

Hanks, I just want to point out something interesting about color vision (which could help understand what you are asking about).

Our eye has R G and B receptors. If you have two spotlights one R and one B and you shine them together on the same screen, the mix does not look like the wavelength in the middle.

The brain does not AVERAGE WAVELENGTHS in what would seem like a simple logical way to us (now that we know the wavelengths of the visible spectrum)

Even though the wavelength 500 nm green is the average between wavelengths R on one side and B on the other, if you mix R and B light the brain does not say "green"

And if you mix R G and B light with G in the middle being the peak, the brain does not say "green"
it says there is a mixture of G with the result sensation of R+B which is a kind of purple that is the COMPLEMENT of green
and it calls that mix "white".

So the brain is wired with a certain logic to produce sensations, which is not a naive intuitive logic, like averaging the wavelengths.
The 6000 Kelvin thermal spectrum does indeed have a peak at G, but it also has lots and lots of R and B, and when you mix that R and B you do not get green, you get a sensation which, for the brain, is complementary to G, so that mixing G with that R+B gives the sensation of "white".

White is not a color. It is nowhere in the rainbow. It is a sensation which the brain is wired to produce when it gets a mix which is similar to the mix you get in sunlight, the thermal 6000 Kelvin mix, a kind of balanced blend.

When you ask "why isn't the sun green?" you are asking a question about BIOLOGICAL EVOLUTION. why did our brain logic evolve the wiring it did which produces a color neutral ("white") sensation when we get a certain balanced blend of stimulation of the R, G, and B receptors. What was the survival and reproductive advantage of this particular brain-wiring, to our monkey ancestors?

 

[Petahanks]

Hanks, I just want to point out something interesting about color vision (which could help understand what you are asking about).

Our eye has R G and B receptors. If you have two spotlights one R and one B and you shine them together on the same screen, the mix does not look like the wavelength in the middle.

The brain does not AVERAGE WAVELENGTHS in what would seem like a simple logical way to us (now that we know the wavelengths of the visible spectrum)

Even though the wavelength 500 nm green is the average between wavelengths R on one side and B on the other, if you mix R and B light the brain does not say "green"

And if you mix R G and B light with G in the middle being the peak, the brain does not say "green"
it says there is a mixture of G with the result sensation of R+B which is a kind of purple that is the COMPLEMENT of green
and it calls that mix "white".

So the brain is wired with a certain logic to produce sensations, which is not a naive intuitive logic, like averaging the wavelengths.
The 6000 Kelvin thermal spectrum does indeed have a peak at G, but it also has lots and lots of R and B, and when you mix that R and B you do not get green, you get a sensation which, for the brain, is complementary to G, so that mixing G with that R+B gives the sensation of "white".

White is not a color. It is nowhere in the rainbow. It is a sensation which the brain is wired to produce when it gets a mix which is similar to the mix you get in sunlight, the thermal 6000 Kelvin mix, a kind of balanced blend.

When you ask "why isn't the sun green?" you are asking a question about BIOLOGICAL EVOLUTION. why did our brain logic evolve the wiring it did which produces a color neutral ("white") sensation when we get a certain balanced blend of stimulation of the R, G, and B receptors. What was the survival and reproductive advantage of this particular brain-wiring, to our monkey ancestors?

What an amazing answer, thank you that was just what I wanted to hear!

You wouldn’t happen to know the source of this information so I can reference it in a report I’m writing? Or is this just your own personal deep knowledge accumulated under a long time?

 

[Chronos]

Marcus is not even 100 [yet], so his knowledge is not age based, cosmologically speaking.

 

[BobG]

"So the brain is wired with a certain logic to produce sensations, which is not a naive intuitive logic, like averaging the wavelengths."

I'm not going to pretend to be an expert on how the brain processes colors, but there is a similar thing with how young toddlers process numbers.

Toddlers have an inherent concept of numbers and even recognize the difference between one object, two objects, three objects, four objects. But, beyond that, their concept of numbers is more logarithmic than linear. If a group has twice as many objects as the other, they know which group has more, etc. There's no way they can assess which group is larger if they're anywhere close to the same size.