# Anyone keen to photograph some candles, for scientific experiment?



## tris_d (Nov 13, 2012)

As a part of scientific experiment I'd appreciate if someone could take two photos of a candle. First photo should have a candle at distance one meter away, and on the second photo the candle should be two meters away from the camera. The exposure time and aperture size should be the same for both photos. It is important photo should not be over-exposed, that is the image should not contain any pixel with brightness higher than 99 (where 100 is max brightness).

The purpose is to prove whether this illustration is wrong, or not:





Cosmology | Stephen's Website


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## Bitter Jeweler (Nov 13, 2012)

It's wrong.


What do I win?


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## Helen B (Nov 13, 2012)

You win another like. You need them.


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## fjrabon (Nov 13, 2012)

The problem you're going to have is that in order to expose a photo such that a picture of a DIRECT FLAME isn't blown out, the picture will be so underexposed that noise will totally destroy any hope of precision accuracy.

Scientists have proven your photo is wrong.  If you don't trust that, why would you trust us?


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## Helen B (Nov 13, 2012)

Have you never seen a picture of a room full of candles? They are all the same brightness. The reason is that the inverse square law is exactly offset by the change in the area of the image of the candle flame*, so the image brightness stays the same. If you really want a careful example, I might do it later tonight if no-one else has beaten me to it.

*Excepting for a digital camera when an anti-aliasing filter enlarges the image of the flame significantly, thus spreading it over too many sensels, or when the image is appraoching the sensel size and spacing.


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## Bitter Jeweler (Nov 13, 2012)

Helen B said:


> You win another like. You need them.





*I DO!
4000 BABY! 
YEAH!*​


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## tris_d (Nov 13, 2012)

fjrabon said:


> The problem you're going to have is that in order to expose a photo such that a picture of a DIRECT FLAME isn't blown out, the picture will be so underexposed that noise will totally destroy any hope of precision accuracy.
> 
> Scientists have proven your photo is wrong.  If you don't trust that, why would you trust us?



If that guy could take a photo of a light bulb with only slight over-exposure then surely it can be done with a candle even better. And I don't care about the noise, if both flames are going to have the same brightness, then the second photo should not get four times dimmer just because of the noise.

That's not my photo. That's how they calculate the distance to the stars. If the brightness does not vary with the square of the distance as Wikipedia says, then how in the world do you think they can measure any distance? All the physics text books say is that intensity falls off with the  square of the distance - photons get spread out radially and so the  amount of photons (intensity) decreases with the square of the distance.  That's all they say, there is no relation in those equations to  apparent size what so ever. There is no article on the internet that mentions anything about any apparent size in relation to inverse square law, it is not part of the equation. 

You don't get it, I have no agenda here, it's all the same to me. Please stop arguing when there is no any argument. I didn't even get to the point to make any claims. We got stuck when I was trying to establish the basics, it is all the same to me. By the way, do you think there is any chance we could get moderators to re-open that thread? I don't want to bring that discussion here.


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## tris_d (Nov 13, 2012)

Helen B said:


> Have you never seen a picture of a room full of candles? They are all the same brightness. The reason is that the inverse square law is exactly offset by the change in the area of the image of the candle flame*, so the image brightness stays the same. If you really want a careful example, I might do it later tonight if no-one else has beaten me to it.
> 
> *Excepting for a digital camera when an anti-aliasing filter enlarges the image of the flame significantly, thus spreading it over too many sensels, or when the image is appraoching the sensel size and spacing.



Please do. At this point, after wasting so much time blabbering about it, I'm ready to pay for it even.


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## fjrabon (Nov 13, 2012)

tris_d said:


> fjrabon said:
> 
> 
> > The problem you're going to have is that in order to expose a photo such that a picture of a DIRECT FLAME isn't blown out, the picture will be so underexposed that noise will totally destroy any hope of precision accuracy.
> ...



That's because you can't measure the apparent size of stars because they are REALLY FREAKING FAR AWAY.  After the get to the point of being so small that our eyes or any precision instrument can't resolve a difference in size, then apparent brightness takes over.  

Here you go:

http://thornscompose.files.wordpress.com/2010/04/prayer-candles.jpg


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## 480sparky (Nov 13, 2012)

tris_d said:


> If the brightness does not vary with the square of the distance as Wikipedia says, then how in the world do you think they can measure any distance? ........



Red shift, for one.  Parallax, for another.  Quasars.  Cepheid variables.  SuperNovae.  GRBs.


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## unpopular (Nov 13, 2012)

this has been discussed already:

http://www.thephotoforum.com/forum/...ns/289251-really-stupid-physics-question.html


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## cool09 (Nov 13, 2012)

I'm not interested in candles or light bulbs but I would like to take a picture of Edison. Edison, NJ that is.

Or maybe as a science experiment since the Holidays are near you can take photos of colored light bulbs.

I know a lot of people in Colorado are lighting up right now.


Seriously, I do know a Physics teacher in another forum that can answer any question you have. At audiokarma.org (tybrad), amazing guy.


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## tris_d (Nov 13, 2012)

fjrabon said:


> tris_d said:
> 
> 
> > That's because you can't measure the apparent size of stars because they are REALLY FREAKING FAR AWAY.
> ...


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## 480sparky (Nov 13, 2012)

tris_d said:


> ......... There is apparent size, it's called Angular diameter. There is also radius, but none of them are part of the equation in regards to brightness, distance and inverse square law.
> ...........



Perhaps you would care to provide a list of how many stars (besides our own Sol) have had their angular diameter actually imaged?  Last I heard, the total was 1.


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## tris_d (Nov 13, 2012)

unpopular said:


> this has been discussed already:
> 
> http://www.thephotoforum.com/forum/...ns/289251-really-stupid-physics-question.html



Thank you.


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## tris_d (Nov 13, 2012)

480sparky said:


> tris_d said:
> 
> 
> > ......... There is apparent size, it's called Angular diameter. There is also radius, but none of them are part of the equation in regards to brightness, distance and inverse square law.
> ...



There is a list in that article. 

R Doradus     0.052&#8243;  0.062&#8243;     
Betelgeuse     0.049&#8243;  0.060&#8243;     
Eris     0.034"  0.089&#8243;     
Alphard     0.00909&#8243;     
Alpha Centauri A     0.007&#8243;     
Canopus     0.006&#8243;     
Sirius     0.005936&#8243;     
Altair     0.003&#8243;     
Deneb     0.002&#8243;     
Proxima Centauri     0.001&#8243;


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## 480sparky (Nov 13, 2012)

tris_d said:


> 480sparky said:
> 
> 
> > tris_d said:
> ...




Try again. Perhaps you would care to provide a list of how many stars (besides our  own Sol) have had their *angular diameter actually imaged*?


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## tris_d (Nov 13, 2012)

480sparky said:


> tris_d said:
> 
> 
> > If the brightness does not vary with the square of the distance as Wikipedia says, then how in the world do you think they can measure any distance? ........
> ...



Red shift is related to relative velocity. Parallax is limited to nearby stars, and everything else is based on brightness.


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## tris_d (Nov 13, 2012)

480sparky said:


> Try again. Perhaps you would care to provide a list of how many stars (besides our  own Sol) have had their *angular diameter actually imaged*?



What in the world do you want from me, what is your agenda? You try again on some Astronomy forum. Sheesh!


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## unpopular (Nov 13, 2012)

tris_d said:


> Red shift is related to relative velocity.



Astronomy fail.


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## tris_d (Nov 13, 2012)

unpopular said:


> tris_d said:
> 
> 
> > Red shift is related to relative velocity.
> ...



Meaning?


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## unpopular (Nov 13, 2012)

Meaning, all objects are moving apart from one another at a similar increasing rate, taking into account the speed of light you can determine their distance by the doppler effect.

Seriously. You're not about to upturn the universe through pictures of candles.


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## Helen B (Nov 13, 2012)

If you want to use the brightness of the candle to measure distance (or relative distance) it isn't the image brightness that you should be comparing. You should be comparing the number of photons that pass through a given aperture. You could integrate the brighness value of each pixel that  makes up the image of the candle flame.


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## tris_d (Nov 13, 2012)

unpopular said:


> Meaning, all objects are moving apart from one another at a similar increasing rate, taking into account the speed of light you can determine their distance by the doppler effect.



It's used as a helper for some methods which then use brightness to determine the distance. I am not aware it can be used to directly measure the distance.



> Seriously. You're not about to upturn the universe through pictures of candles.



Ah, yes. This thread is about photos of candles, so if you don't care to help me get those photos please just let me be.


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## tris_d (Nov 13, 2012)

Helen B said:


> If you want to use the brightness of the candle to measure distance (or relative distance) it isn't the image brightness that you should be comparing. You should be comparing the number of photons that pass through a given aperture. You could integrate the brighness value of each pixel that  makes up the image of the candle flame.



Number of photons (per surface area per unit time) is what light intensity is, and that's what determines image brightness. More photons - more brightness, right?


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## 480sparky (Nov 13, 2012)

tris_d said:


> .......and everything else is based on brightness.



Fail.


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## 480sparky (Nov 13, 2012)

unpopular said:


> Meaning, all objects are moving apart from one another at a similar increasing rate,.......



Called Hubble's Law.


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## pixmedic (Nov 13, 2012)

SCIENCE!


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## tris_d (Nov 13, 2012)

480sparky said:


> tris_d said:
> 
> 
> > .......and everything else is based on brightness.
> ...



You failed to articulate yourself. What are you doing, trying to outsmart me or something? Don't you have anything better to do? -- The only thing that was not mention and does not relate to brightness is 'gravitational lenses', which is terribly uncertain method.


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## Helen B (Nov 13, 2012)

tris_d said:


> Helen B said:
> 
> 
> > If you want to use the brightness of the candle to measure distance (or relative distance) it isn't the image brightness that you should be comparing. You should be comparing the number of photons that pass through a given aperture. You could integrate the brighness value of each pixel that  makes up the image of the candle flame.
> ...



Wrong. This is what you seem not to understand. The brightness of the image also depends on the area of the image. Half the photons, half the area: same image brightness. If using an image of the candles you need to take the image area into account. As I said, you need to integrate the brightness of the elements that make up the image.


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## 480sparky (Nov 13, 2012)

tris_d said:


> You failed to articulate yourself. What are you doing, trying to outsmart me or something? Don't you have anything better to do? -- The only thing that was not mention and does not relate to brightness is 'gravitational lenses', which is terribly uncertain method.



OK, if brightness is the only method that works for 'everything else', why won't it work for _everything_?  Why bother with parallax for all the close stuff?

And there's more methods used to establish distances that what has been mentioned in this thread.


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## tris_d (Nov 13, 2012)

Helen B said:


> The brightness of the image also depends on the area of the image. Half the photons, half the area: same image brightness. If using an image of the candles you need to take the image area into account. As I said, you need to integrate the brightness of the elements that make up the image.



Right. It's just that no one was able to point any reference about how inverse square law relates to apparent size. Can you point some reference about it maybe? Wikipedia doesn't seem to be aware of it:

Inverse-square law - Wikipedia, the free encyclopedia








It's not part of the equation. So how do you know, where do you pull your conclusions from?


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## unpopular (Nov 13, 2012)

^^ in other words, brightness is photon density over space. You could have all the photons of a very bright star beaming down onto a our retna, enough energy to instantly vaporize a hole through our head, or likewise, you could have all that energy distributed over such a large area that with only a few photons would ever enter our eye's aperture, making it entirely invisible. Regardless, the star emitted the same number of photons over any given time period, all that has changed is the density: it's brightness.

Go read Helen's comments on the link I provided, it discusses how light is focussed proportional to it's apparent brightness.

It's important to note that the nature of light isn't what we're seeing, and that our perception of things is based on focused light. In some ways, a sheet of exposed film left out on the table is more "accurate" than one behind a lens. Of course, we can't really make much sense of this.


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## tris_d (Nov 13, 2012)

480sparky said:


> tris_d said:
> 
> 
> > You failed to articulate yourself. What are you doing, trying to outsmart me or something? Don't you have anything better to do? -- The only thing that was not mention and does not relate to brightness is 'gravitational lenses', which is terribly uncertain method.
> ...



I have no idea what are we arguing about. Majority of methods are based on reading brightness, one way or another. Parallax is limited to nearby stars. That's all I said. Why bother with parallax? It offers more certainty, as far it is works, since 'standard candle' methods depend on some reference stars, like supernovas, and that by itself brings uncertainty into equation. -- Can you now take a camera and snap a few photos of some candles for me? I'll pay you, say $40 bucks, how about it?


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## Helen B (Nov 13, 2012)

Why would image size be mentioned in a discussion of the inverse square law, unless the brightness of an image was under consideration. Where do I draw my conclusion that the image area exactly compensates for the inverse square law? It is fundamental, simple optics. I'm amazed that you question it. If you have two identical objects, one 10 distance units away and the other 20 distance units away, what do _you_ think the ratio of the image areas will be (assuming that they are being imaged by the same system, and before considering focus effects)?


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## tris_d (Nov 14, 2012)

Helen B said:


> Why would image size be mentioned in a discussion of the inverse square law, unless the brightness of an image was under consideration. Where do I draw my conclusion that the image area exactly compensates for the inverse square law? It is fundamental, simple optics. I'm amazed that you question it. If you have two identical objects, one 10 distance units away and the other 20 distance units away, what do _you_ think the ratio of the image areas will be (assuming that they are being imaged by the same system, and before considering focus effects)?



I thought this thread was closed. Can we then continue our discussion here? -- We got so close to come to agreement. People were misunderstanding me thinking I was talking about my theory, but I stopped talking about it few days ago and I just wanted to establish the basics.


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## fjrabon (Nov 14, 2012)

tris_d said:


> Helen B said:
> 
> 
> > Why would image size be mentioned in a discussion of the inverse square law, unless the brightness of an image was under consideration. Where do I draw my conclusion that the image area exactly compensates for the inverse square law? It is fundamental, simple optics. I'm amazed that you question it. If you have two identical objects, one 10 distance units away and the other 20 distance units away, what do _you_ think the ratio of the image areas will be (assuming that they are being imaged by the same system, and before considering focus effects)?
> ...



what needs to be discussed still?  I gave you the pictures you asked for.  We've given you multiple explanations for why this is the case.  What more do you want?


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## fjrabon (Nov 14, 2012)

I'm not worked up about it, just generally confused about what is left to discuss.  The inverse square law has been completely understood for over 1000 years now.  The principals in the thread understand it.  If you can't figure out what else you're confused about, I'm not sure what is left to discuss.  I'm genuinely trying to help you with this, I'm a teacher, so I understand that sometimes students require multiple explanations to get something, but I don't even know what you're looking for any longer.  I don't really have an interest in joining the conversation about this, other than I enjoy teaching and figuring out new ways to explain things to people who don't get them.  Outside of that, I don't know what discussion there is left to have.


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## tris_d (Nov 14, 2012)

I am not arguing my theory, just trying to establish the facts. We now agree on great many things, I just want to clear it up a bit more and summarize it. Then I would like to apply what we have established to some practical examples in order gain complete understanding. Let me gather the stuff from the other thread and I'll put forward a few questions.


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## unpopular (Nov 14, 2012)

looks like they reopened tris' holding cell.


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## tris_d (Nov 14, 2012)

fjrabon said:
			
		

> As you can see, the 'blob' gets bigger, as the light gets dimmer.
> 
> What this doesn't mean was that if I was to look at the lamp directly  that the actual lamp itself would appear dimmer.  It's that the total  light falling on my eye would be less, because it's coming from a  smaller part of my visual frame, due to how our eyes focus.  Once you  take focus out of the equation, further light sources are actually in  some sense bigger the further they are.



Sources of light that radiate photons radially, such as point or a spherical light source, without lens would imprint bigger blob on a photo as distance increases, and the brightness of the pixel in the center of that blob would become less bright proportionally to the square of the distance. Ok?




> > Consider what Isaac said:
> > - "_If you have a spherical light source (like one     of those    oriental paper lanterns), it still follows the inverse     square law no    matter how close you are to it. You can think of this     as a quirk    peculiar to spheres._"
> >
> > Does what he said not mean if we photograph such spherical light source  it will produce less bright blob on the image proportionally to the  square of the distance, as if it was a point light source?
> ...



As light source gets further away its projected blob without lens gets bigger, so even when there is a lens with longer distance more light would just fly around it and miss the lens, so should we therefore not expect that brightness would fall off with the distance even when there is a lens because lens would proportionally receive less light as the distance increases?


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## amolitor (Nov 14, 2012)

tris_d said:


> Sources of light that radiate photons radially, such as point or a spherical light source, without lens would imprint bigger blob on a photo as distance increases, and the brightness of the pixel in the center of that blob would become less bright proportionally to the square of the distance. Ok?



No. "imprint a blob" is a meaningless phrase in this context. What you have said is, as scientists say "not even wrong"



tris_d said:


> As light source gets further away its projected blob without lens gets bigger, so even when there is a lens lots of light would just fly around it and miss the lens, so should we therefore not expect that brightness would fall off with the distance even when there is a lens because lens would proportionally receive less light as the distance increases?



No, we should not expect the brightness to fall off. The job of the lens in this context can be viewed as gathering up that proportionally smaller amount of light, and using it to render an image on the sensor that is _proportionally smaller, and equally as bright_. We photographers call this "focusing".


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## unpopular (Nov 14, 2012)

tris_d said:


> As light source gets further away its projected blob without lens gets bigger, so even when there is a lens with longer distance more light would just fly around it and miss the lens, so should we therefore not expect that brightness would fall off with the distance even when there is a lens because lens would proportionally receive less light as the distance increases?



Need a little more paint, partnah?


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## fjrabon (Nov 14, 2012)

tris_d said:


> fjrabon said:
> 
> 
> 
> ...



You seem to be confusing light fields and points of light as resolved by a lens or an eye.  

Lenses take light from a source that is hitting your eye, all across retina, and focuses it into a coherent image.  When you look at a candle, the light from that candle isn't hitting a small part of your eye, its hitting your whole eye, your whole body, the whole room.  Your eye focuses it.  Whatever size the flame looks like is based upon your distance to it, as the further you move away, the smaller part of your visual frame it takes up.  However, because your eye (or camera) focused the diffuse light back into a coherent image, you no longer get the dimming effect.  Your eye sees the candle as brightly as it would see it a few feet away.

So, if you focus the light you get the smaller effect, but not the dimmer effect.  If you were not to focus the light (essentially what holding a sheet of paper over the light does) you would get the dimming effect, but a corresponding increase in the 'spread' of the light (which is the whole reason the inverse square law works to begin with).  

This is why we kept telling you that you could represent stars as dimming, or getting smaller, but not both.

The reason why stars appear to get dimmer the further they get is because they are too far away for our eyes to focus on them.  We can only focus at an arbitrarily far point into space, and after that, things just look equally small.  Because we can't really focus on the objects in space, as they get further away, they simply look dimmer.  If, however, you had a telescope accurate enough to focus on them, they would look just as bright as anything else, even if they were very tiny.

Now, measuring the amount of light falling on an area from a light is a totally different matter.  If you're in a dark room and you have a light meter, as you move a flash light closer to the light meter, it will register more light.  As you move it away, it will register less.  However, if you took pictures of the same flashlight, the actual flashlight would seem equally as bright no matter the distance.  However, in the further picture it would be taking up less space in the visual frame.  What that means is that if you were to calculate the value the sensor read for the flashlight and multiply it by the area it took up in the frame, the flashlight that was further away would follow the rules of the inverse square law, because the less light is being illustrated by the light taking up less space in the frame.

again, indicating that you can illustrate the inverse square law as lights being dimmer, or lights being smaller, but not both.  Which was your original problem.


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## tris_d (Nov 14, 2012)

christop, I acknowledge what you said in that other thread, ASCII stuff and all that. I addressed it with the question to fjrabon in my previous post.




			
				Helen B said:
			
		

> E = t &#960; B / (4 N^2)
> 
> Where
> E is the image illumination,
> ...



It's not that it contradicts, the question is whether it has anything to do with inverse square law, which is all about the distance.


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## amolitor (Nov 14, 2012)

tris_d said:


> Helen B said:
> 
> 
> 
> ...



Helen's point is that image illumination (E) has nothing to do with distance. You claim that image illumination (E) does vary with distance.

One of you is right, and the other one is wrong. Guess which one?


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## fjrabon (Nov 14, 2012)

tris_d said:


> christop, I acknowledge what you said in that other thread, ASCII stuff and all that. I addressed it with the question to fjrabon in my previous post.
> 
> 
> 
> ...



It's not that it has to do with the inverse square law, it's that a properly focused image in some sense does away with the inverse square law in a 'brightness per inch' sense and instead turns the inverse square law into what we call 'perspective'.  When you've properly focused on an image, it no longer gets dimmer as it gets farther, it gets smaller when it gets farther.  Unless you have a lens doing this, it gets dimmer, but more spread out.


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## amolitor (Nov 14, 2012)

Hey Tris, could we skip past this boring "establishing some facts" part and get right to the part where you present your no doubt hilarious theory?


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## tris_d (Nov 14, 2012)

fjrabon said:


> You seem to be confusing light fields and points of light as resolved by a lens or an eye.
> 
> Lenses take light from a source that is hitting your eye, all across retina, and focuses it into a coherent image.  When you look at a candle, the light from that candle isn't hitting a small part of your eye, its hitting your whole eye, your whole body, the whole room.  Your eye focuses it.  Whatever size the flame looks like is based upon your distance to it, as the further you move away, the smaller part of your visual frame it takes up.  However, because your eye (or camera) focused the diffuse light back into a coherent image, you no longer get the dimming effect.  Your eye sees the candle as brightly as it would see it a few feet away.
> 
> ...



So the amount of light that hits the lens drops off with the distance, but the brightness stays the same as it proportionally gets focused on a smaller area on the image. Correct? 




> Now, measuring the amount of light falling on an area from a light is a  totally different matter.  If you're in a dark room and you have a light  meter, as you move a flash light closer to the light meter, it will  register more light.  As you move it away, it will register less.   However, if you took pictures of the same flashlight, the actual  flashlight would seem equally as bright no matter the distance.   However, in the further picture it would be taking up less space in the  visual frame.  What that means is that if you were to calculate the  value the sensor read for the flashlight and multiply it by the area it  took up in the frame, the flashlight that was further away would follow  the rules of the inverse square law, because the less light is being  illustrated by the light taking up less space in the frame.
> 
> again, indicating that you can illustrate the inverse square law as  lights being dimmer, or lights being smaller, but not both.  Which was  your original problem.



All right. I think we finally sorted this out. The thing is no one mentioned any lens or focus until Unpopular  replayed to me in that "stupid physics" thread. I suppose it was just  plain obvious to you, but it never occurred to me, it is not something I  could find in my physics text books in relation to inverse square law,  so you should cut me some slack about previous misunderstandings. 





> The reason why stars appear to get dimmer the further they get is because they are too far away for our eyes to focus on them.  We can only focus at an arbitrarily far point into space, and after that, things just look equally small.  Because we can't really focus on the objects in space, as they get further away, they simply look dimmer.  If, however, you had a telescope accurate enough to focus on them, they would look just as bright as anything else, even if they were very tiny.



Ah, the stars. Now we can finally get back to Olbers' paradox. So, when the light source get so far away that its focused projection covers no more than one pixel on the image, then the inverse square law starts to apply and the brightness drops off with the square of any further distance from that point on, ok?


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## tris_d (Nov 14, 2012)

amolitor said:


> Hey Tris, could we skip past this boring "establishing some facts" part and get right to the part where you present your no doubt hilarious theory?



Ok, here is question for you: does magnification make distant stars appear brighter?


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## amolitor (Nov 14, 2012)

tris_d said:


> amolitor said:
> 
> 
> > Hey Tris, could we skip past this boring "establishing some facts" part and get right to the part where you present your no doubt hilarious theory?
> ...



Define "appear brighter".


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## unpopular (Nov 14, 2012)

provided that the optical system's f-ratio is similar across magnification, the amount of light reaching the sensor will be similar. so no, magnification does not increase the appearance of brightness.


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## tris_d (Nov 14, 2012)

amolitor said:


> Define "appear brighter".









Ok, for simplicity lets just talk about gray-scale images, so the brightness is defined from 0 to 100 (in Photoshop), where 0 is black, 100 is white, and in between are shades of gray. And when talking about magnification of some star and its consequent brightness, I think what I am asking is just about the pixel in the very center of the "blob". -- By the way, do human eyes have some magnification property built-in, and can it vary for example as we focus to closer and further away objects?


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## christop (Nov 14, 2012)

tris_d said:


> So the amount of light that hits the lens drops off with the distance, but the brightness stays the same as it proportionally gets focused on a smaller area on the image. Correct?


Yep!



> All right. I think we finally sorted this out. The thing is no one mentioned any lens or focus until Unpopular  replayed to me in that "stupid physics" thread. I suppose it was just  plain obvious to you, but it never occurred to me, it is not something I  could find in my physics text books in relation to inverse square law,  so you should cut me some slack about previous misunderstandings.


I think that's fair enough. This is a photography forum, and you started a discussion about the physics of light, so I think most of us assumed that you already had some understanding of optics.



> Ah, the stars. Now we can finally get back to Olbers' paradox. So, when the light source get so far away that its focused projection covers no more than one pixel on the image, then the inverse square law starts to apply and the brightness drops off with the square of any further distance from that point on, ok?


Yeah, if a star covers less than a whole pixel, its size cannot be measured, but the brightness of the pixel becomes basically an average of the brightness of the star itself and the surrounding blackness of space. The pixel's brightness can then be used to estimate the angular size of the star relative to the size of a pixel and therefore its distance can be estimated. (I'm not sure if imaging sensors are used this way in reality, but I think the concept is correct.)


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## amolitor (Nov 14, 2012)

Ok, I think that sounds good to me.

Greater magnification is a somewhat problematic phrase as well, but I think we can work with it. There are two factors in play here, focal length, and aperture. Aperture is normally measured as the ratio of the lens opening to the focal length. So, if when we increase the focal length, we normally decrease the aperture. The answer to your question is, it depends.

Greater magnification is associated with longer focal lengths. When imaging the sky, this simply means that we're placing less of the area of the sky onto the sensor.

If you double the focal length (increasing magnification) while keeping aperture the same (for example, for from a 300mm f/2.8 lens to a 600mm f/2.8 lens), several things occur:

- less of the sky is imaged on to the sensor, 1/4 as much, to be exact.
- the size of the lens opening has doubled, which means the area of that opening has quadrupled, which means the light-gathering power has quadrupled.

The effect is that the apparent brightness of the stars will indeed quadruple. This is why building a bigger telescope is actually a helpful thing to do. Stars not previously visible are now visible, if you can build a telescope with a bigger hole for light to pass through, with more light gathering capability.

If you double the focal length but do not change the light gathering power of the system (for instance, inserting elements into a telescope system to increase the magnification) you will effectively cut the aperture in half. The will also have some effects:

- less of the sky is imaged on the sensor, 1/4 as much. Same as last time.
- the size of the lens opening is the SAME, the light gathering power is the SAME. The infinitesimal points which are the images of stars will remain at the same brightness.


This is why, in order to see deeper into the night sky, you cannot simply add elements on to the viewing end of the telescope. You must build a bigger telescope, with more light gathering power -- with a larger physical aperture through which light can pass.


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## christop (Nov 14, 2012)

amolitor said:


> If you double the focal length (increasing magnification) while keeping aperture the same (for example, for from a 300mm f/2.8 lens to a 600mm f/2.8 lens), several things occur:
> 
> - less of the sky is imaged on to the sensor, 1/4 as much, to be exact.
> - the size of the lens opening has doubled, which means the area of that opening has quadrupled, which means the light-gathering power has quadrupled.
> ...



Hold on... the light-gathering power with a physically larger aperture (but with the same f-number) is exactly counteracted by the increased "spreading" (or magnification) of the light on the imaging plane (the sensor). That's why the image doesn't change in brightness as you zoom in and out while keeping a fixed aperture.


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## amolitor (Nov 14, 2012)

Stars don't spread, they're infinitesimal points, for our purposes.

If you're taking a picture of a light bulb or an onion or a cow, then the image spreads out and smears the extra light across more sensor, and you are perfectly correct. Stars being imaged on a digital sensor won't make it past boundaries of the pixel, so the recorded number will be bigger for that single cell of the sensor's array. This is why I asked about "apparent brightness" 

With film.. I suspect the same thing will occur. My sense is that, in general, the star's image still is pretty much a point so it's just going to bang harder on the same single silver halide crystal, and render it more and more broken down, and hence darker in the negative. There might be something else going on there, though. Maybe the Airy Disk (sp?) becomes "resolvable" in an interesting way such that it makes sense to think of it as "bigger" rather than "brighter" in the land of astro film. I'm not an astro guy, I can just handle a little maths from time to time.


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## christop (Nov 14, 2012)

amolitor said:


> Stars don't spread, they're infinitesimal points, for our purposes.
> 
> If you're taking a picture of a light bulb or an onion or a cow, then the image spreads out and smears the extra light across more sensor, and you are perfectly correct. Stars being imaged on a digital sensor won't make it past boundaries of the pixel, so the recorded number will be bigger for that single cell of the sensor's array. This is why I asked about "apparent brightness"


Oh, I see. In that case you'd be correct.


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## tris_d (Nov 14, 2012)

christop said:


> tris_d said:
> 
> 
> > So the amount of light that hits the lens drops off with the distance, but the brightness stays the same as it proportionally gets focused on a smaller area on the image. Correct?
> ...



Well, your patience paid off. I appreciate it, all of it, thank you very much. Thank you everyone else. And it's nice when people agree, makes me feel warm inside. It's just that... it's BORING!! So prepare to hate me once again as I'm now ready to prove the whole world wrong, or so I shall try. Brace yourself, here I come!


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## runnah (Nov 14, 2012)

Can't you accomplish the same effect with cars on a highway at night?

http://image1.masterfile.com/em_w/00/53/02/700-00530279w.jpg

Or am I missing the point?


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## christop (Nov 14, 2012)

runnah said:


> Can't you accomplish the same effect with cars on a highway at night?
> 
> http://image1.masterfile.com/em_w/00/53/02/700-00530279w.jpg
> 
> Or am I missing the point?



But all those lights are overexposed!

I think we've just concluded the discussion about candles and the inverse square law.


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## 480sparky (Nov 14, 2012)

runnah said:


> Can't you accomplish the same effect with cars on a highway at night?
> 
> http://image1.masterfile.com/em_w/00/53/02/700-00530279w.jpg
> 
> Or am I missing the point?



[h=1]Referral Denied[/h] You don't have permission to access "http://image1.masterfile.com/em_w/00/53/02/700-00530279w.jpg" on this server. Reference #24.e836d83f.1352931550.265fb872


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## tris_d (Nov 14, 2012)

runnah said:


> Can't you accomplish the same effect with cars on a highway at night?
> 
> http://image1.masterfile.com/em_w/00/53/02/700-00530279w.jpg
> 
> Or am I missing the point?



I can not open that image, it says: "Referral Denied". Can you please upload it here?


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## tris_d (Nov 14, 2012)

amolitor said:


> Ok, I think that sounds good to me.
> 
> Greater magnification is a somewhat problematic phrase as well, but I think we can work with it. There are two factors in play here, focal length, and aperture. Aperture is normally measured as the ratio of the lens opening to the focal length. So, if when we increase the focal length, we normally decrease the aperture. The answer to your question is, it depends.
> 
> ...



I think I understand. Let me see, would that mean that Hubble telescope does not use any magnification when taking photos of deep space? And if it does, how would that make anything look "better"?


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## 480sparky (Nov 14, 2012)

tris_d said:


> I can not open that image, it says: "Referral Denied". Can you please upload it here?



Only if you have rights. Posting images w/o rights is a no-no 'round here.


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## christop (Nov 14, 2012)

Magnification is a somewhat meaningless term when discussing camera lenses. Magnification is a ratio. The primary lenses used in cameras are defined by their focal length. A focal length is measured in millimeters (sometimes centimeters, or meters in the case of the Hubble telescope).

Hubble has a 57.6 meter focal length and a 2.4 meter aperture. So it has an aperture of f/24. Its sensor size is 4.5 m[sup]2[/sup] (4500000 mm[sup]2[/sup]).

Hubble Space Telescope - Wikipedia, the free encyclopedia

In comparison, my Canon DSLR has a sensor of about 337 mm[sup]2[/sup]. I currently have a "normal" lens on it which is 28mm f/2.5.

The Hubble lens would be roughly equivalent to a 500mm lens on my Canon, which could be used for wildlife photography (except an f/24 aperture would make it terrible for almost anything but space observation).

By the way, I can view the picture of cars on a highway by copying and pasting the link in my browser.


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## runnah (Nov 14, 2012)

tris_d said:


> runnah said:
> 
> 
> > Can't you accomplish the same effect with cars on a highway at night?
> ...



a long highway shot with car headlights in the foreground and half a mile in the background.


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## tris_d (Nov 14, 2012)

christop said:


> Magnification is a somewhat meaningless term when discussing camera lenses. Magnification is a ratio. The primary lenses used in cameras are defined by their focal length. A focal length is measured in millimeters (sometimes centimeters, or meters in the case of the Hubble telescope).
> 
> Hubble has a 57.6 meter focal length and a 2.4 meter aperture. So it has an aperture of f/24. Its sensor size is 4.5 m[SUP]2[/SUP] (4500000 mm[SUP]2[/SUP]).
> 
> ...



Having focal length, does that automatically imply there is some magnification, built in the lens itself? And if yes, then what other parameters could be changed to nullify that magnification?  


(I managed to open the picture of cars as per your instructions)


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## tris_d (Nov 14, 2012)

Stars on the left image representing closer stars are bright, and stars on the right image representing further away stars are  less bright. And if we go on like that the stars from any further away shell can only get even dimmer. Now, it seems to me no matter how many of those less bright  stars are, they could not appear any more bright than what their  individual brightness is. Where is the paradox?


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## 480sparky (Nov 14, 2012)

tris_d said:


> ........ Where is the paradox?



Try understanding 'infinity'.


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## tris_d (Nov 14, 2012)

480sparky said:


> tris_d said:
> 
> 
> > ........ Where is the paradox?
> ...



Whaaa...you want my head to explode?! Fortunately however there is no any infinity here. If every line of sight ends at some star, well that's where that line of   sight ENDS, and if every line of sight ends at some point, then there  is  nothing infinite about it. Even if there are infinite number of lines of sight. Which brings me to the question, are there infinite number of lines of sight per some certain area in the sky? 


Hey, the original Olbers' paradox thread is open again! Maybe we should move there?


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## 480sparky (Nov 14, 2012)

tris_d said:


> ....... If every line of sight ends at some star, well that's where that line of   sight ENDS, ...........



New flash..... they all don't.


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## tris_d (Nov 14, 2012)

480sparky said:


> tris_d said:
> 
> 
> > ....... If every line of sight ends at some star, well that's where that line of   sight ENDS, ...........
> ...



I have no idea what point you are trying to make. I think it's the premise of Olbers' paradox that every line of sight ends at some star, so I don't see how what you said makes sense, or how it matters to what I originally said about those two pictures.


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## 480sparky (Nov 14, 2012)

tris_d said:


> 480sparky said:
> 
> 
> > tris_d said:
> ...



I'm referring to what I quoted.  It's not that hard to figure out.  

Olbers' Paradox doesn't state every line of sight ends in a star.  It stated that IF the universe was infinite, then that would be true.  Of course, his observation was made during a time when the universe was assumed to be static, and not expanding as is the current model.  Given an infinite universe, every line of sight will end in a star, but we may not be able to see it with the visible spectrum because if a star is far enough away, the Doppler Effect will render it invisible to our eyes.


That said, since whatever doesn't make sense to you, you immediately and summarily dismiss based on your own prejudices and preconceived notions, I'm done here.


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## Derrel (Nov 14, 2012)

If somebody can arrange for 8,10,12,or even up to 24 bikini-clad women to show up in one location, I will gladly buy a bunch of candles and will undertake this challenge, and will photograph the chit outta this here candle thing...but otherwise,without the bikinis...it's a non-starter...


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## tris_d (Nov 14, 2012)

Derrel said:


> If somebody can arrange for 8,10,12,or even up to 24 bikini-clad women to show up in one location, I will gladly buy a bunch of candles and will undertake this challenge, and will photograph the chit outta this here candle thing...but otherwise,without the bikinis...it's a non-starter...



Hehe. We sorted it out, the illustration is wrong. Good luck with bikini-clad women.


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## amolitor (Nov 14, 2012)

Olber's paradox is stupid, it turns out. Infinities are more complicated than that.

In an infinite universe with an infinite number of stars, with pretty much whatever other parameters you want, you can arrange to have whatever percentage of the night sky you like be completely blank out to infinity, regardless of whether the stars get brighter, dimmer, or what have you.

In fact, if your universe was a sphere, you could have infinitely many "stars" made up of finite white dots pasted to the inside of your sphere. If I was allowed to make the little white dots arbitrarily small - never zero, but arbitrarily close to zero, I can fit in an infinity of them on the finite surface of the sphere, and cover as little of that sphere's surface as you like.


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## tris_d (Nov 14, 2012)

480sparky said:


> I'm referring to what I quoted.  It's not that hard to figure out.



Sorry. I didn't realize at first you cut my quote to point out what you were referring to, but still your point was unclear.




> Olbers' Paradox doesn't state every line of sight ends in a star.  It stated that IF the universe was infinite, then that would be true.



Yes, which is why I think I have to use the same premise to prove the original conclusion was wrong, but I don't see infinity matters anyway.




> Of course, his observation was made during a time when the universe was assumed to be static, and not expanding as is the current model.  Given an infinite universe, every line of sight will end in a star, but we may not be able to see it with the visible spectrum because if a star is far enough away, the Doppler Effect will render it invisible to our eyes.



It's all the same to me, that does not invalidate inverse square law would be what explains the "darkness". Finite and expanding universe would just make it even darker.




> That said, since whatever doesn't make sense to you, you immediately and summarily dismiss based on your own prejudices and preconceived notions, I'm done here.



What did I dismiss? I don't think I dismissed anything you said, I'm giving you my response here. And unlike most of the people on the internet I have no problem to admit when I am wrong, because it means that I learned something new. You prove me wrong and I will thank you for it, like I did in the previous discussion.


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## unpopular (Nov 14, 2012)

post a photo or gtfo.


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## tris_d (Nov 14, 2012)

unpopular said:


> post a photo or gtfo.



Are you talking to me? What photo? What "gtfo" means?


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## fjrabon (Nov 14, 2012)

tris_d said:


> it seems to me no matter how many of those less bright  stars are, they could not appear any more bright than what their  individual brightness is. Where is the paradox?



Not to dredge this back up, but this is where you are wrong.  When stars get arbitrarily close, our eyes begin resolving them as a single star, and then the two stars dimness is additive, and they seem brighter.  There are all sorts of 'dual' stars, that are much brighter than they should be, because they are 2 stars combined.  ie if there are two stars, that are very close to one another in our angular vision, and let's say one brightness is 10 units, and the other star is 6 brightness, they will appear to our eyes as one star of brightness 16.  This concept is the backbone behind olber's paradox, as originally conceived.  

The big killer of olber's paradox is the fact that the universe had a beginning and is expanding.  Two key assumptions to the paradox are that the universe has always been around and that it is static.


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## unpopular (Nov 14, 2012)

tris_d said:


> What photo?



my point exactly.


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## tris_d (Nov 14, 2012)

fjrabon said:


> When stars get arbitrarily close, our eyes begin resolving them as a single star, and then the two stars dimness is additive, and they seem brighter.  There are all sorts of 'dual' stars, that are much brighter than they should be, because they are 2 stars combined.  ie if there are two stars, that are very close to one another in our angular vision, and let's say one brightness is 10 units, and the other star is 6 brightness, they will appear to our eyes as one star of brightness 16.  This concept is the backbone behind olber's paradox, as originally conceived.



That's about where we left it off when we went on about candles argument. I'm pretty sure nothing like that was related to Olbers' paradox, and I've read many papers and internet articles about the paradox. In any case, where did you get that? Is that in knowledge written in Astronomy text books, is it some photography related effect, where do I confirm what you just said? Can you give me some link or tell me what do I google for?




> The big killer of olber's paradox is the fact that the universe had a beginning and is expanding.  Two key assumptions to the paradox are that the universe has always been around and that it is static.



That does not invalidate inverse square law would be what explains the  "darkness". Finite and expanding universe would just make it even  darker.


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## fjrabon (Nov 14, 2012)

tris_d said:


> fjrabon said:
> 
> 
> > When stars get arbitrarily close, our eyes begin resolving them as a single star, and then the two stars dimness is additive, and they seem brighter.  There are all sorts of 'dual' stars, that are much brighter than they should be, because they are 2 stars combined.  ie if there are two stars, that are very close to one another in our angular vision, and let's say one brightness is 10 units, and the other star is 6 brightness, they will appear to our eyes as one star of brightness 16.  This concept is the backbone behind olber's paradox, as originally conceived.
> ...



It's the well known idea of if you want to double your light, you add another light.  You get twice as much light.  When the two points are close enough they look like one, and since there is twice as much light, coming from the same seeming point, the apparent brightness is doubled.  

Any photographer who has ever used multiple speedlights to double their light power understands this concept extremely well.


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## tris_d (Nov 14, 2012)

fjrabon said:


> It's the well known idea of if you want to double your light, you add another light.  You get twice as much light.  When the two points are close enough they look like one, and since there is twice as much light, coming from the same seeming point, the apparent brightness is doubled.
> 
> Any photographer who has ever used multiple speedlights to double their light power understands this concept extremely well.



Photographers don't use point light sources. And in why would it even matter whether the stars are close or not? Look, I'm open to what you are saying, but that's far from enough to convince me. I need references and some more practical proof to confirm it would work as you're suggesting it would. And I'll help you to prove me wrong, just tell me what to google for.


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## fjrabon (Nov 14, 2012)

tris_d said:


> fjrabon said:
> 
> 
> > It's the well known idea of if you want to double your light, you add another light.  You get twice as much light.  When the two points are close enough they look like one, and since there is twice as much light, coming from the same seeming point, the apparent brightness is doubled.
> ...



Because the whole reason why stars appear to get dimmer is that our eyes can't resolve their size.  When two stars are close enough in our visual plane to be unresolvable as two distinct points, then the same thing happens.  Just like our eyes couldn't resolve the size of distant sources and thus just makes them appear dimmer instead of smaller, two arbitrarily close points, when our eyes can't resolve them as separate points, the apparent brightness is additive between the two stars individual brightness.  

If you can't get this, I am just done.  This is a well understood concept, and I am telling you that it is true, in various astronomy texts 

here is just one link that talks about double (or more) stars, and why they look brighter.  it's estimated that up to 50% of the visible stars in our universe are actually multiple stars combining their brightness to increase their visibility.

Fun with double and variable stars - Astronomy Magazine


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## Helen B (Nov 14, 2012)

I have the impression that you haven't yet really understood the relationship between distance and apparent brightness. 

Instead of using our current understanding of the universe to explain Olbers' Paradox, you are using your misunderstanding of simple principles to try to explain it.


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## tris_d (Nov 14, 2012)

fjrabon said:


> Because the whole reason why stars appear to get dimmer is that our eyes can't resolve their size.  When two stars are close enough in our visual plane to be unresolvable as two distinct points, then the same thing happens.  Just like our eyes couldn't resolve the size of distant sources and thus just makes them appear dimmer instead of smaller, two arbitrarily close points, when our eyes can't resolve them as separate points, the apparent brightness is additive between the two stars individual brightness.
> 
> If you can't get this, I am just done.  This is a well understood concept, and I am telling you that it is true, in various astronomy texts
> 
> ...



I get that, but that does not change anything. Binary stars are brighter than one star would be, but still they appear less bright the further away they are. See those gray dots on the image below, many of them are binary stars and single stars millions of times brighter than Sun, yet when they are far away they appear dim.







Apparent magnitude - Wikipedia, the free encyclopedia_
- Note that brightness varies with distance; *an extremely bright object  may appear quite dim, if it is far away*. Brightness varies inversely with the square of the distance._


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## fjrabon (Nov 14, 2012)

tris_d said:


> fjrabon said:
> 
> 
> > Because the whole reason why stars appear to get dimmer is that our eyes can't resolve their size.  When two stars are close enough in our visual plane to be unresolvable as two distinct points, then the same thing happens.  Just like our eyes couldn't resolve the size of distant sources and thus just makes them appear dimmer instead of smaller, two arbitrarily close points, when our eyes can't resolve them as separate points, the apparent brightness is additive between the two stars individual brightness.
> ...



Yes, we all understand the inverse square law.  My point is that the whole theory behind olber's paradox is that as you get infinite space, you get infinite stars, infinitely densely packed in the visual field.  And since light is additive, it would appear bright, even if each individual component star was quite dim.  In fact most stars we see, couldn't be seen by our eyes, if they weren't binary stars.  Because stars can add together in their brightness, it enables many more stars to be easily seen, that would otherwise take very powerful microscopes.  Now, if we had infinite space that was static, and no atmospheric dust, and infinite duration of the universe, and no dark matter, then we very much would have Olber's perfectly bright sky.  Because even though stars would be very dim as they got far away, there would be infinity of them, perfectly coating the visual field, making it appear as a gigantic curved plane.  THink instead of a binary star, an infinitary star.  ie a binary star made out of infinity stars.  That's what Olber's paradox is about.  Now, of course we have an expanding universe, that had a beginning, and has dust in space, and has dark matter in space, and stars burn out and are born, so none of the background assumptions that created Olber's paradox are actually true.

However, the one single thing that you think that explains away Olber's paradox, the inverse square law and how it relates to how we see light, is actually the very thing that actually makes Olber's paradox viable.  Your issue with it is literally the only reason it MIGHT have worked, if all the other assumptions hadn't been wrong.


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## tris_d (Nov 15, 2012)

fjrabon said:


> My point is that the whole theory behind olber's paradox is that as you get infinite space, you get infinite stars, infinitely densely packed in the visual field.



If every line of sight ends at some star, that's where that line of    sight ENDS, and if every line of sight ends at some point, then there   is  nothing infinite about it. Yes, it will be densely packed, as it is, some stars bright, some stars less bright, and some very distant stars as bright as black.




> And since light is additive, it would appear bright, even if each individual component star was quite dim.



How do you suppose many gray dots would add up to become many white dots?









> In fact most stars we see, couldn't be seen by our eyes, if they weren't binary stars.  Because stars can add together in their brightness, it enables many more stars to be easily seen, that would otherwise take very powerful microscopes.  Now, if we had infinite space that was static, and no atmospheric dust, and infinite duration of the universe, and no dark matter, then we very much would have Olber's perfectly bright sky.  Because even though stars would be very dim as they got far away, there would be infinity of them, perfectly coating the visual field, making it appear as a gigantic curved plane.



If some stars are bright and other less bright, how do you arrive to conclusion there would be uniform brightness across the sky?




> THink instead of a binary star, an infinitary star.  ie a binary star made out of infinity stars.  That's what Olber's paradox is about.  Now, of course we have an expanding universe, that had a beginning, and has dust in space, and has dark matter in space, and stars burn out and are born, so none of the background assumptions that created Olber's paradox are actually true.



You can not compare them all with binary stars as if they are all that close next to each other. When they are really close they appear as one star, but otherwise two stars that appear next to one another, one of them is more likely to be millions of light years closer to us than the other. Finite and expanding universe does not invalidate inverse square law could be what explains the   "darkness" of the night sky, it would just make it even   darker.




> However, the one single thing that you think that explains away Olber's paradox, the inverse square law and how it relates to how we see light, is actually the very thing that actually makes Olber's paradox viable.  Your issue with it is literally the only reason it MIGHT have worked, if all the other assumptions hadn't been wrong.



The inverse square law makes Olbers' paradox viable? Why, how? Might have worked? Can you rephrase what do you mean to say?


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## fjrabon (Nov 15, 2012)

tris_d said:


> fjrabon said:
> 
> 
> > My point is that the whole theory behind olber's paradox is that as you get infinite space, you get infinite stars, infinitely densely packed in the visual field.
> ...



You made so many wrong statements above that are just demonstrably wrong by reading even an elementary astronomy text that I can't even begin.  It took us like what, 3 days to explain one of the most confoundingly simple and easy to understand physics laws in the known universe to you, now, from reading the above, it seems like we're going to have to explain several more issues, and that you don't fully understand the original issue either.  Now you can't get that if you pack a bunch of stars very densely in the visual plane they seem very bright, despite it being an EXTREMELY well known ASTRONOMICAL FACT.


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## Helen B (Nov 15, 2012)

The relationship between the inverse square law and image area (angular area) is at the heart of Olbers' (sic) Paradox. If you don't understand this you don't understand the Paradox. You can't use the inverse square law to refute the Paradox, because it is implicit in it. This is not earth-shattering news.

You are misunderstanding why distant stars appear dim (assuming a static universe of infinite age): it is not because they are far away, it is because the imaging system cannot resolve them at their true angular size. They get smeared out to the minimum angular size the system can resolve, so their imaged area becomes "incorrect". 

All in all, we are still stuck at square one with you.


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## Helen B (Nov 15, 2012)

One last attempt.

Try this as a thought experiment.

Imagine the universe is static and is infinitely old. You blast off from earth in a vehicle we have yet to imagine, maybe a 250 cc BSA Starfire that doesn't leak oil, at an incredible speed away from the Sun. As you get further from the Sun it gets smaller in your rear-view mirror, but stays just as bright because the inverse square law is offset by the decreasing angular area of the Sun. 

You have the iPhone 6 with you to take some pictures of your trip: it has a perfect lens with no aberrations and it does not suffer from diffraction. Just imagine that at distance x from the Sun the image of the Sun occupies four sensels and during the exposure sixteen photons pass through the lens' aperture. That is an illumination of four photons per sensel. Now, at distance 2x the image occupies only one sensel, and only four photons get through the aperture. That is still the same illumination of four photons per sensel.

You reach 4x and now only one photon from the Sun gets through the aperture and the perfect image occupies a quarter of the one sensel's area. That is still the same illumination (one photon per quarter sensel or four photons per sensel) but it looks dimmer to the imaging system because the system does not know that the image only occupies a quarter sensel.

Olbers' Paradox says that the Sun is not the only star illuminating that sensel now. There is an infinite number of them, all filling the sensel at an illumination of four photons per sensel,even though their individual images do not fill the sensel or provide all four photons. Their added images fill the sensel and provide all four photons, and all the other sensels are similarly filled. They sky looks bright. Thus the inverse square law is part of Olbers' Paradox.

This is greatly simplified, and it ignores lots of things that are happening, and sorry for using photons, but I hope it is appropriate for the simple theory behind Olbers' Paradox.


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## amolitor (Nov 15, 2012)

Yup.

Tris has given up on "candles look dimmer farther away" but has latched on to "but stars do" to carry the fight forward.

Stars, as Helen points out, ALSO DO NOT DIM as they recede. They also remain at the same brightness, but get smaller. The realities of imaging systems make the star's smaller-ness render as a less bright spot. That's an artifact of the fact that we're imaging it, not reality. 

Anyways, as I have pointed out many times, Olber's paradox is stupid on many fronts. It made sense back in the day, but it represents a huge misunderstanding of so many different things that it's meaningless noise.


----------



## fjrabon (Nov 15, 2012)

yes, ultimately the way you conceive olber's paradox, it wouldn't have been a paradox to begin with.  you dont understand the problem that you're trying to solve to begin with.


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## amolitor (Nov 15, 2012)

I guess you could make a modified version of Olber's paradox, which states that if the universe were infinite with infinitely many stars, then any picture we took of the sky should be completely white.

Then you could point out that it's not.

Then you could wave your hands over the inverse square law, and note that stars, as imaged on the sensor, get dimmer and dimmer as they are farther and farther away, and say "See? That's why the night sky is black!".

Then some right b*st*rd like me comes along and says "Yes, but in an infinite universe with infinitely many stars, you're not imaging a single star in each pixel of your sensor. You are imaging INFINITELY MANY stars. AT EVERY SINGLE PIXEL!"


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## unpopular (Nov 15, 2012)

amolitor said:


> Tris has given up on "candles look dimmer farther away" but has latched on to "but stars do" to carry the fight forward.



Keep on pantin' dem targets, tris! You's be a good marksman afturall!


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## tris_d (Nov 15, 2012)

fjrabon said:


> You made so many wrong statements above that are just demonstrably wrong by reading even an elementary astronomy text that I can't even begin.  It took us like what, 3 days to explain one of the most confoundingly simple and easy to understand physics laws in the known universe to you, now, from reading the above, it seems like we're going to have to explain several more issues, and that you don't fully understand the original issue either.



You made many wrong statements and I explained to you why each one of them is wrong. Being unable to address my response or point any reference that can confirm any of what you said makes it obvious you have no idea what are you talking about and are pulling stuff out of your hat.




> Now you can't get that if you pack a bunch of stars very densely in the  visual plane they seem very bright, despite it being an EXTREMELY well  known ASTRONOMICAL FACT.



Stars do not lay on a plane. You keep forgetting distribution of stars is 3-dimensional. If what you're said is astronomical fact and extremely well known, then why can you not point any link that confirms your statement?


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## tris_d (Nov 15, 2012)

Helen B said:


> The relationship between the inverse square law and image area (angular area) is at the heart of Olbers' (sic) Paradox. If you don't understand this you don't understand the Paradox. You can't use the inverse square law to refute the Paradox, because it is implicit in it. This is not earth-shattering news.



It is implicit based on false premise and wrong calculation. You don't understand that proving some paradox is wrong means proving its premise is wrong. 




> You are misunderstanding why distant stars appear dim (assuming a static universe of infinite age):



Apparent magnitude - Wikipedia, the free encyclopedia
* - Note that brightness varies with distance; an extremely bright object may appear quite dim, if it is far away. Brightness varies inversely with the square of the distance.*

How many time do I have to quote this for you to understand why distant stars appear dim? 

Is Wikipedia wrong, what say you?


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## tris_d (Nov 15, 2012)

fjrabon said:


> yes, ultimately the way you conceive olber's paradox, it wouldn't have been a paradox to begin with.  you dont understand the problem that you're trying to solve to begin with.



You don't understand that proving some paradox is wrong means proving its premise is wrong.


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## unpopular (Nov 15, 2012)

must be a long snow day.


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## amolitor (Nov 15, 2012)

tris_d said:


> fjrabon said:
> 
> 
> > yes, ultimately the way you conceive olber's paradox, it wouldn't have been a paradox to begin with.  you dont understand the problem that you're trying to solve to begin with.
> ...



No.

To prove a statement false you can do any of the following, at least:

- demonstrate that one or more of the premises is false
- demonstrate that the reasoning applied to the premises, to produce the statement, is incorrect
- provide a counter-example


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## tris_d (Nov 15, 2012)

Helen B said:


> Olbers' Paradox says that the Sun is not the only star illuminating that sensel now. There is an infinite number of them, all filling the sensel at an illumination of four photons per sensel,even though their individual images do not fill the sensel or provide all four photons.



There can not be infinite number of stars. Closer stars occlude further away stars, do you understand? I already explained this several times, it's amazing how can you keep ignoring it: - *If every line of sight ends at some star, well that's where that line of    sight ENDS, and if every line of sight ends at some point, then there   is  nothing infinite about it.
*



> Their added images fill the sensel and provide all four photons, and all  the other sensels are similarly filled. They sky looks bright. Thus the  inverse square law is part of Olbers' Paradox.



Wikipedia says further away stars appear dim due to inverse square law. How can something that appears dim also appear bright? How can many gray dots add up to become many white dots, can you explain?


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## amolitor (Nov 15, 2012)

tris_d said:


> Helen B said:
> 
> 
> > Olbers' Paradox says that the Sun is not the only star illuminating that sensel now. There is an infinite number of them, all filling the sensel at an illumination of four photons per sensel,even though their individual images do not fill the sensel or provide all four photons.
> ...



This is completely wrong. You can most certainly include an infinite number of stars in a field of view, without any occlusion. Make the first star very large: 1 degree of arc, the next star half that big: 1/2 a degree of arc, the next one half of that: 1/4 of a degree of arc, and so on. With this sequence, I can actually place an infinite number of stars in a row, and take up only 2 degrees of arc. I have placed infinitely many stars, non-occluding, into the sky in a very very very very small section of the sky.

Note that I can accomplish this with an infinite number of carefully placed stars all the same size. The each star is simply twice as far away as the previous star, and they are lined up relative to the observer so that they are almost, but not quite, in a straight line.


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## tris_d (Nov 15, 2012)

amolitor said:


> tris_d said:
> 
> 
> > fjrabon said:
> ...



Yes, I am demonstrating that both the premise and reasoning (calculation) applied to that premise is wrong. 

- Olbers' paradox fails to consider image surface area
 - Olbers' paradox fails to consider image resolution 
- Olbers' paradox fails to consider time of exposure
- Olbers' paradox fails to realize closer stars occlude further away stars


And I am also providing a counter-example, here it is:






Many gray dots do not add up to become many white dots.


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## amolitor (Nov 15, 2012)

Olber's paradox also fails to include a suitable discussion of hamburgers.

Basically, you're pretty badly equipped to mount much of an attack on Olber's paradox. You don't reason particularly well, which is not an insult, most people don't reason particularly well. You also don't understand infinities at all, which is really going to be a problem since understanding the problems with Olber's idea is as much about infinities as anything else (again, not an insult, most people don't understand infinity worth a damn either). Lastly, you're fixated on a particular "solution" to the problem which isn't particularly relevant.

Olber's paradox is simply, manifestly, wrong. The night sky is black. Done.

Understanding the reasons why it's wrong in this universe, and in other hypothetical ones, is a little tricky. You really have to understand infinities better than you do.

Why don't you go attack Zeno's paradox first? It's actually more closely related than is obvious.


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## tris_d (Nov 15, 2012)

amolitor said:


> This is completely wrong. You can most certainly include an infinite number of stars in a field of view, without any occlusion. Make the first star very large: 1 degree of arc, the next star half that big: 1/2 a degree of arc, the next one half of that: 1/4 of a degree of arc, and so on. With this sequence, I can actually place an infinite number of stars in a row, and take up only 2 degrees of arc. I have placed infinitely many stars, non-occluding, into the sky in a very very very very small section of the sky.
> 
> Note that I can accomplish this with an infinite number of carefully placed stars all the same size. The each star is simply twice as far away as the previous star, and they are lined up relative to the observer so that they are almost, but not quite, in a straight line.



That's where image resolution comes into equation. And what's the  brightness of sun-like star with angular size of  1/x, where x goes towards infinity?


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## amolitor (Nov 15, 2012)

I should note that if I am constructing a universe, I can MOST CERTAINLY place an infinite number of stars into an infinite universe so as to render the night sky as seen from some hypothetical viewing point has these properties:

- an infinite number of stars are in view, non-occluded
- the sky is uniformly bright, at any brightness you choose

It happens that the universe we live in is not so constructed.


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## tris_d (Nov 15, 2012)

amolitor said:


> Olber's paradox also fails to include a suitable discussion of hamburgers.
> 
> Basically, you're pretty badly equipped to mount much of an attack on Olber's paradox. You don't reason particularly well, which is not an insult, most people don't reason particularly well. You also don't understand infinities at all, which is really going to be a problem since understanding the problems with Olber's idea is as much about infinities as anything else (again, not an insult, most people don't understand infinity worth a damn either). Lastly, you're fixated on a particular "solution" to the problem which isn't particularly relevant.
> 
> ...



You are pretty badly equipped to invalidate any of what I said. You don't reason well. You don't understand the problem and you are unable to address what said, except to say that I'm wrong. Your objections are without substance and devoid of any reasoning and logic, thus irrelevant. 

You really have to understand infinities better than you do.




> Why don't you go attack Zeno's paradox first? It's actually more closely related than is obvious.



Zeno's paradox is resolved by Planck scale limits. Either discrete space or discrete time resolves Zeno's paradox, that is if space or time is digital instead of analogue.


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## christop (Nov 15, 2012)

tris_d said:


> That's where image resolution comes into equation. And what's the  brightness of sun-like star with angular size of  1/x, where x goes towards infinity?



Image resolution does not come into play. And the actual brightness of such a star is the same as any other star at any other finite distance.


I know this has been partially covered before, but I think it needs to be brought up again.

For any given imaging system with a particular set of imaging parameters (sensor density, focal length, aperture, etc), the smallest image that can be resolved by that system will have a fixed angular size (measured in milliarcseconds). The angular size of a star varies by its size and distance from the observer. When a star becomes smaller than the smallest image that can be resolved by an imaging system, we can no longer measure the distance of the star by its size. Instead, we can measure the brightness _of the sensel_ to determine the distance to the star. The brightness of the star itself does not dim. Only the measured sensel's brightness dims because the star occupies a smaller portion of the sensel.

Here's another ASCII art. 


....star
.....|
.... V
_____o_____
\........./
.\......./
..\...../
...\.../
....\./
.....V

The "o" is the actual star. The line below the star is the image of the star that can be resolved by an imaging system. The "V" shape represents the resolving limit of the imaging system. The actual angular size of the cone will be much, much narrower than shown here (perhaps a few milliarcseconds, rather than the 20 degrees or so shown here). The star is far smaller than the system can resolve. Therefore *only the star's image appears dimmer than the star actually is*.

On the other hand, if "every line of sight ends at some star", then each sensel would be completely "covered" by stars, and each sensel would be as bright as a star. So space would be white. Your conclusion that the inverse square law comes into play to disprove or resolve the paradox here is incorrect.


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## amolitor (Nov 15, 2012)

tris_d said:


> amolitor said:
> 
> 
> > > Why don't you go attack Zeno's paradox first? It's actually more closely related than is obvious.
> ...


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## christop (Nov 15, 2012)

amolitor said:


> tris_d said:
> 
> 
> > Zeno's paradox is resolved by Planck scale limits. Either discrete space or discrete time resolves Zeno's paradox, that is if space or time is digital instead of analogue.
> ...



It's basic Calculus.


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## amolitor (Nov 15, 2012)

I've been watching internet kooks for.. huh, 20+ years now. I have never quite gotten a handle on where the fun is in just being told that you are wrong, over and over and over.


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## tris_d (Nov 15, 2012)

amolitor said:


> It will come as no surprise to the astute reader that this is completely wrong. In a continuous space/continuous time universe, Zeno's paradox is still flawed, and, no surprise, it has to do with infinite summations and how they actually work.



Don't blame me for your inability to understand.

Zeno's paradoxes - Wikipedia, the free encyclopedia
_- Another proposed solution is to question one of the assumptions  Zeno  used in his paradoxes (particularly the Dichotomy), which is that   between any two different points in space (or time), there is always   another point. Without this assumption there are only a finite number of   distances between two points, hence there is no infinite sequence of   movements, and the paradox is resolved. The ideas of Planck length and Planck time in modern physics place a limit on the measurement of time and space, if not on time and space themselves._


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## amolitor (Nov 15, 2012)

tris_d said:


> amolitor said:
> 
> 
> > It will come as no surprise to the astute reader that this is completely wrong. In a continuous space/continuous time universe, Zeno's paradox is still flawed, and, no surprise, it has to do with infinite summations and how they actually work.
> ...



Missed the part where I said "In a continuous space/continuous time universe, Zeno's paradox is still flawed" didn't you?


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## tris_d (Nov 15, 2012)

christop said:


> Image resolution does not come into play. And the actual brightness of such a star is the same as any other star at any other finite distance.



Apparent magnitude - Wikipedia, the free encyclopedia
_- The apparent magnitude (m) of a celestial body is a measure of its *brightness as seen by an observer *on Earth_




> Therefore *only the star's image appears dimmer than the star actually is*.



Of course, and that's what we see. No one is saying the star itself actually starts to radiate less light.



> On the other hand, if "every line of sight ends at some star", then each sensel would be completely "covered" by stars, and each sensel would be as bright as a star. So space would be white. Your conclusion that the inverse square law comes into play to disprove or resolve the paradox here is incorrect.



Yes, it gets covered by stars, but not of the same apparent brightness. Some stars are bright, some less bright, and some very distant stars as bright as black. 







How do you suppose those less bright stars add up to become bright stars?


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## tris_d (Nov 15, 2012)

amolitor said:


> Missed the part where I said "In a continuous space/continuous time universe, Zeno's paradox is still flawed" didn't you?



I don't know, sorry if I did. I'm angry because everyone has condescending attitude, even though I might very well be older and more educated in relevant subjects than most of you. So now I'm starting to act like an arrogant bum-hole too.


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## fjrabon (Nov 15, 2012)

Here's the issue, you were unwilling to believe that candles did not get dimmer as they moved farther away, until we literally had to take pictures and prove you wrong. 

Now you refuse to believe that this principal also works for stars, and you won't believe it unless we can somehow create a universe that is static where Olber's paradox holds. Despite we've shown you it does happen to a limited extent when two gray dots add to one white dot (that's what binary stars do, well understood and verifiable fact). You refuse to believe that this would generalize to an infinite case. 

Unfortunately, we don't have access to a static, infinite universe, therefore you will never believe us, because we can't take a picture of what happens in a finite static universe. If you didn't believe us when we tried to explain what happens with an everyday item like a candle, I don't expect you to understand or believe us about a harder to understand item like a star billions of light years away. 

And yes, I understand Zeno's paradox. I took real analysis, which in some ways is a class about dealing with Zeno's paradox in a formal mathematical sense. Ie formally proving calculus. 

Previously, I had some sense we could address your misunderstandings with pictures of lights. Here we are up against a theoretical bulkhead, that you can't just take pictures of, thus I am out. You have to understand physics, astronomy, math and optics. You've shown no inclination to do so and stick firmly to some half baked idea that has been refuted for thousands of years. 

Good luck with your quest tris, your failure doomed quixotic quest will lead you nowhere and hopefully you find a bizarre sort of peace there.


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## jhodges10 (Nov 15, 2012)

Clicked in to see why this kept popping up as active. Seems to be a bit over my head, think I'll go back to watching The Big Bang Theory to get my fill of physics.


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## Helen B (Nov 15, 2012)

tris_d said:


> Helen B said:
> 
> 
> > The relationship between the inverse square law and image area (angular area) is at the heart of Olbers' (sic) Paradox. If you don't understand this you don't understand the Paradox. You can't use the inverse square law to refute the Paradox, because it is implicit in it. This is not earth-shattering news.
> ...



There is no contradiction between what I am saying and what Wikipedia says. Please read what I have written more carefully.



tris_d said:


> Helen B said:
> 
> 
> > Olbers' Paradox says that the Sun is not the only star illuminating that  sensel now. There is an infinite number of them, all filling the sensel  at an illumination of four photons per sensel,even though their  individual images do not fill the sensel or provide all four photons.
> ...



There can be an infinite number of stars, but it doesn't matter if some are blocked. There only have to be enough to fill the sensel. This is what Olbers' Paradox is all about. We have explained why they appear to be grey dots, though they aren't really grey dots. Please give us some sign that you have begun to understand the physics of this, because so far you have shown no real understanding.

Could you state your version of Olbers' Paradox?


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## christop (Nov 15, 2012)

tris_d said:


> I'm angry because everyone has condescending attitude, even though I might very well be older and more educated in relevant subjects than most of you. So now I'm starting to act like an arrogant bum-hole too.



You might be older than most of use, and you might even be more "educated", but you have demonstrated over and over that you in fact do not have a good understanding of the relevant subjects as those with whom you are arguing. There's nothing wrong with being ignorant. It is wrong to refuse to admit to your own ignorance while being arrogant about it.


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## christop (Nov 15, 2012)

Let's work with a single sensel here.

Imagine that a star covers 1% of the area of that sensel due to its distance. The brightness of that sensel will be 1% of the brightness of a single star.

Now imagine that you have 10 stars inside the area of the sensel, none of them occluding another star. The brightness of the sensel is now 10% of the brightness of a star.

Next imagine that you have 100 stars inside the same area such that no star occludes another. Now the entire sensel area is covered by stars, and "all lines of sight ends at some star". The brightness of the sensel is now 100% of the brightness of a star.

Of course, in reality you cannot have 100 stars arranged like this, but you could have some stars at 10 times the distance, each contributing 0.01% of the brightness of a star, or some stars at half the distance, each contributing 4% of the brightness of a star to the sensel. Remember, we also have infinite stars, so there could be no visible gap between stars.

However the stars are arranged, if every line of sight "ends at some star", you would have a sensel value equivalent to the brightness of one star.


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## amolitor (Nov 15, 2012)

tris_d said:


> amolitor said:
> 
> 
> > Missed the part where I said "In a continuous space/continuous time universe, Zeno's paradox is still flawed" didn't you?
> ...



Apology accepted, of course!

Assuming that you are older and better educated than others on the internet is always a risky proposition. I am about 99% sure that I am better educated in relevant subject matter than you are, for instance, but there's still that 1%. Also, I'm pretty old.

I'm surprised that you're not challenging my remarks on universes in which the sky IS white, or universes in which there are infinitely many stars simultaneously visible.


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## tris_d (Nov 15, 2012)

fjrabon said:


> Now you can't get that if you pack a bunch of stars very densely in the   visual plane they seem very bright, despite it being an EXTREMELY well   known ASTRONOMICAL FACT.



Again, can you point to any link which can confirm that EXTREMELY well   known ASTRONOMICAL FACT you are talking about?


Stars do no lay on the same plane. You keep forgetting distribution of stars is 3-dimensional.


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## tris_d (Nov 15, 2012)

Helen B said:


> There is no contradiction between what I am saying and what Wikipedia says. Please read what I have written more carefully.



You either agree that inverse square law makes distant stars appear less bright, or not. I take it you agree. And I agree too.




> There can be an infinite number of stars, but it doesn't matter if some are blocked. There only have to be enough to fill the sensel. This is what Olbers' Paradox is all about. We have explained why they appear to be grey dots, though they aren't really grey dots.



Of course they are not actually gray dots, they appear to be from where we look at it. It is up to you now to explain why do you think they would add up to appear as uniformly bright sky.





> Please give us some sign that you have begun to understand the physics of this, because so far you have shown no real understanding.
> 
> Could you state your version of Olbers' Paradox?



There is no my version of Olbers' Paradox, I am saying the premise of the paradox is wrong and thus conclusion is wrong.

Because so far you have shown no real understanding, please give us some sign that you have begun to understand the logic fallacy of your conclusion the night sky would appear uniformly bright by explaining why do you imagine dim stars would add up to appear as bright stars.


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## christop (Nov 15, 2012)

Here's another thought experiment I just thought of.

Say you were taking a picture of one of those traffic lights that is made up of a bunch of LED's. If you have a high-resolution camera, you would be able to resolve each individual LED that makes up the light. If you have a low-resolution camera (like a digital camera from the 90's or one of those cheap key-chain cameras), you cannot resolve each individual LED. In fact, multiple LED's will crowd into a single pixel in your low-res camera. The overall brightness of the traffic light in each camera would be the same (when using the same exposure settings), would it not? Or would you argue that the low-res camera would produce a dimmer image of the traffic light simply because the LED's cannot be individually resolved, no matter how many LED's you put in the space of a single pixel?

Each individual LED would appear to be dim in the low-res camera image (because they are smaller than a pixel), but since there are many LED's in the same apparent area, the brightnesses of all the LED's add up.


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## tris_d (Nov 15, 2012)

christop said:


> Let's work with a single sensel here.
> 
> Imagine that a star covers 1% of the area of that sensel due to its distance. The brightness of that sensel will be 1% of the brightness of a single star.
> 
> ...



That's exactly what is wrong with the original calculation. It ignores image resolution and sums all the intensity into only one pixel. If your eyes had 1x1 resolution you would indeed see nothing but "bright night sky".


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## christop (Nov 15, 2012)

tris_d said:


> That's exactly what is wrong with the original calculation. It ignores image resolution and sums all the intensity into only one pixel. If your eyes had 1x1 resolution you would indeed see nothing but "bright night sky".



So now you're saying that image resolution affects brightness? Fascinating!


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## pgriz (Nov 15, 2012)

Tris_d, what is your motivation for pursuing this discussion, both on this forum and on the other ones?  And why are you so doggedly persistent when it appears your question has been answered?


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## amolitor (Nov 15, 2012)

tris_d said:


> That's exactly what is wrong with the original calculation. It ignores image resolution and sums all the intensity into only one pixel. If your eyes had 1x1 resolution you would indeed see nothing but "bright night sky".



Huh? It would see the average brightness of the night sky, which is pretty darn close to black.

Are now claiming that Olber's paradox is resolved by "proper" consideration of sensor resolution?


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## tris_d (Nov 15, 2012)

amolitor said:


> I'm surprised that you're not challenging my remarks on universes in which the sky IS white, or universes in which there are infinitely many stars simultaneously visible.



There is a difference between night sky being UNIFORMLY bright and just bright. Owls see the night sky is quite bright, but not uniformly bright. Olbers' paradox concludes the night sky would be uniformly bright, given its original premise and the way it's treated, and that's what I am trying to prove is wrong.







Is the night sky on this photo bright or not? Take that image with longer exposure, or adjust the contrast, or use more sensitive film or... well, you know better, but the point is the brightness is in the eye of the beholder. So I'm not talking about whether the night sky is bright or not, that's relative, I'm saying original treatment of Olbers' paradox wrongly concluded the night sky would be UNIFORMLY bright. But if some stars are less bright than others, due to inverse square law as Wikipedia says, then  I say it is inverse square law that makes the night sky appear just the  way we see it, that is NOT UNIFORMLY or EQUALLY bright at every point you look at it.


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## tris_d (Nov 15, 2012)

christop said:


> tris_d said:
> 
> 
> > That's exactly what is wrong with the original calculation. It ignores image resolution and sums all the intensity into only one pixel. If your eyes had 1x1 resolution you would indeed see nothing but "bright night sky".
> ...



That's what you said too. In your example you added stars in the field of view and accordingly the brightness of the single pixel increased. But if you had sufficient resolution each star would project onto its own spatial location and the intensity would not get summed up but each dot would have its own brightness. Yes?

Many gray dots dispersed over some surface area is not the same thing as many gray dots summed at one pixel, is it?


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## christop (Nov 15, 2012)

tris_d said:


> christop said:
> 
> 
> > tris_d said:
> ...



Ok... read (or re-read) my thought experiment about taking pictures of an LED traffic light which pretty much summed up the issue of different resolutions.


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## tris_d (Nov 15, 2012)

amolitor said:


> tris_d said:
> 
> 
> > That's exactly what is wrong with the original calculation. It ignores image resolution and sums all the intensity into only one pixel. If your eyes had 1x1 resolution you would indeed see nothing but "bright night sky".
> ...



I said that at the very beginning. Now you tell me, if you photograph 10 street lights at night with image resolution of 1000x1000 and then once more with image resolution 1x1, would 1x1 image be brighter than 1000x1000 image? Can image with 1x1 resolution have any other brightness than UNIFORM? That's why original treatment of Olbers's paradox gets the result indicating uniform brightness, because by ignoring image resolution they sum up all the intensity into only one pixel and of course they will get uniform brightness. Ok?


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## tris_d (Nov 15, 2012)

christop said:


> Ok... read (or re-read) my thought experiment about taking pictures of an LED traffic light which pretty much summed up the issue of different resolutions.



You re-read what I said. Can image with resolution of only one pixel give you any other brightness than uniform?


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## amolitor (Nov 15, 2012)

Tris, I can describe a universe with an infinite number of stars in it, all visible from a designated viewing point, all non-occluding, where from that viewing point the sky is uniformly bright.

It is not THIS universe, and it is is infinite in extent. But I can describe it.


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## tris_d (Nov 15, 2012)

pgriz said:


> Tris_d, what is your motivation for pursuing this discussion, both on this forum and on the other ones?  And why are you so doggedly persistent when it appears your question has been answered?



I want to publish a paper, thus I want challenge my conclusions to make sure I did not make any mistakes in my reasoning. I'm posting this on more than one forum simply because more people know more and so I can speed up this verification process. Please join the discussion.


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## pixmedic (Nov 15, 2012)

I like pie


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## christop (Nov 15, 2012)

tris_d said:


> christop said:
> 
> 
> > Ok... read (or re-read) my thought experiment about taking pictures of an LED traffic light which pretty much summed up the issue of different resolutions.
> ...



Nope. I'm not arguing against that.

The brightness of a single-pixel image is the same as the average brightness of an image with higher resolution.

Edit: oh, and "uniform" is not a brightness.


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## unpopular (Nov 15, 2012)

it's like a black hole in here...


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## amolitor (Nov 15, 2012)

Where were you planning to send this paper for publication?

I've published the odd thing here and there.


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## christop (Nov 15, 2012)

tris_d: I re-read what you said and replied to it. Now I want you to re-read my post about the traffic light and to comment on what you agree or disagree with.


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## Helen B (Nov 15, 2012)

tris_d said:


> pgriz said:
> 
> 
> > Tris_d, what is your motivation for pursuing this discussion, both on this forum and on the other ones?  And why are you so doggedly persistent when it appears your question has been answered?
> ...



Please just publish the paper. Have it peer reviewed first, of course. There are huge mistakes in your reasoning, but you don't want to, or can't see them. You can't even discuss them scientifically.

There's no conflict between asserting that the radiant energy from a star (or a candle) passing through a unit area at an observer decreases according to the inverse square law and the assertion that the brightness of a 'perfect' image does not decrease with distance. If you don't understand that you don't understand the reasoning behind Olbers' Paradox.

I asked you for your version of Olbers' Paradox because I wanted to read it in your words, with your reasoning. If you are going to write a technical paper that description will have to be in it.


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## unpopular (Nov 15, 2012)

tris - have you even actually ever read a peer reviewed study? I mean, the study itself and not just the abstract or USA Today version?

Do you even know what a paper is supposed to look like? Or for that matter, how to even cite works?

Being that as far as I can tell your primary source here is wikipedia, I sort of have my doubts.


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## tris_d (Nov 15, 2012)

christop said:


> tris_d: I re-read what you said and replied to it. Now I want you to re-read my post about the traffic light and to comment on what you agree or disagree with.



I didn't get to that post at the time I replied, I was referring to your previous post.



> The overall brightness of the traffic light in each camera would be the  same (when using the same exposure settings), would it not? Or would you  argue that the low-res camera would produce a dimmer image of the  traffic light simply because the LED's cannot be individually resolved,  no matter how many LED's you put in the space of a single pixel?



I'm saying lower resolution would produce higher overall brightness when looking at the picture as a whole. I'm not sure about that, you tell me and I will trust you. But the point that is really important in regards to resolution and Olbers' paradox is that if you ignore resolution in mathematical equations, as they did, you practically work with 1x1 resolution, and thus you can not get any other result but the one that indicates uniform brightness. One pixel can only have one overall brightness, that's my point.


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## tris_d (Nov 15, 2012)

amolitor said:


> Where were you planning to send this paper for publication?
> 
> I've published the odd thing here and there.



Anywhere I can. I know most of the journals will not even consider it when they realize it does not go along with what they've been putting in text books for more than several hundred years. Lets write the paper together, and then we will share Nobel prize when we finally manage to convince them, if ever. If you look at the history of science you will notice scientists like to hold onto their opinions dogmatically as if it is religion.


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## unpopular (Nov 15, 2012)

I suppose if you're going to be publishing in UFO Weekly, it doesn't matter what you say. You could claim Nikolai Tesla told you.


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## christop (Nov 15, 2012)

tris_d said:


> I'm saying lower resolution would produce higher overall brightness when looking at the picture as a whole.


That would exactly contradict what you've been saying about the effects of resolution on brightness. You effectively have been saying that lower resolution would _decrease_ brightness.



> I'm not sure about that, you tell me and I will trust you.


The overall brightness does not change. It's the same as taking a large image file and scaling it down to create a thumbnail for the Web. A proper scaling algorithm will not change the brightness of the image. It simply decreases the resolution.


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## runnah (Nov 15, 2012)

unpopular said:


> I suppose if you're going to be publishing in UFO Weekly, it doesn't matter what you say. You could claim Nikolai Tesla told you.



Did you see "The Prestige?". I thought Bowie did a great job as Tesla.


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## tris_d (Nov 15, 2012)

christop said:


> The overall brightness does not change. It's the same as taking a large image file and scaling it down to create a thumbnail for the Web. A proper scaling algorithm will not change the brightness of the image. It simply decreases the resolution.



Photo of 10 street lights at night with image resolution of  1000x1000 has the same overall brightness as it would image with 10x10 or 1x1 resolution have? I expected pixels would receive much more light individually when there is less of them. -- In any case, that's not important. Brightness is relative to exposure time, which is also ignored by the original treatment of Olbers' paradox. And the most important thing in the whole story is about UNIFORM brightness. That is when they ignore resolution the result can not indicate any other brightness but uniform.


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## tris_d (Nov 15, 2012)

Helen B said:


> Please just publish the paper. Have it peer reviewed first, of course. There are huge mistakes in your reasoning, but you don't want to, or can't see them. You can't even discuss them scientifically.
> 
> There's no conflict between asserting that the radiant energy from a star (or a candle) passing through a unit area at an observer decreases according to the inverse square law and the assertion that the brightness of a 'perfect' image does not decrease with distance. If you don't understand that you don't understand the reasoning behind Olbers' Paradox.
> 
> I asked you for your version of Olbers' Paradox because I wanted to read it in your words, with your reasoning. If you are going to write a technical paper that description will have to be in it.



You just keep repeating how I'm wrong and that I do not understand, but you fail to actually address what I say. 


a.) Original treatment of Olbers' paradox regarding inverse square law concludes the night sky would be UNIFORMLY bright.
True, false?

b.) If stars appear less bright due to inverse square law, then it's inverse square law what makes the night sky NOT UNIFORMLY bright.
True, false?


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## spacefuzz (Nov 15, 2012)

wait what, this is still being "discussed"?


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## Helen B (Nov 15, 2012)

tris_d said:


> Helen B said:
> 
> 
> > Please just publish the paper. Have it peer reviewed first, of course. There are huge mistakes in your reasoning, but you don't want to, or can't see them. You can't even discuss them scientifically.
> ...



I have been addressing what you have said, as have others, but it hasn't been getting through. Very frustrating, and a real waste of time trying to help you. What is the point in trying?

a) True
b) False - The inverse square law is not the reason for the lack of uniform brightness. Olbers' Paradox has been explained adequately without having to misunderstand the inverse square law.


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## tris_d (Nov 15, 2012)

Helen B said:


> a) True
> b) False - The inverse square law is not the reason for the lack of uniform brightness.



Previously you agreed inverse square law is what defines DIFFERENCES in apparent brightness of the stars, due to distances and according to inverse square law, as Wikipedia says. And now you just said inverse square law is NOT responsible for any DIFFERENCES in apparent brightness across the night sky. Check and mate, my friend.


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## unpopular (Nov 15, 2012)

Around here there is one rule that mast not be broken: don't doubt Helen. Ever.

---

seriously dude. you're not the one with a degree from RIT. She is.


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## jake337 (Nov 15, 2012)




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## tris_d (Nov 15, 2012)

unpopular said:


> Around here there is one rule that mast not be broken: don't doubt Helen. Ever.
> 
> ---
> 
> seriously dude. you're not the one with a degree from RIT. She is.



My rule is to doubt everything, myself included. C'mon, the conclusion comes off directly from this statement:

Apparent magnitude - Wikipedia, the free encyclopedia
_- Note that brightness varies with distance; an extremely bright object may appear quite dim, if it is far away. Brightness varies inversely with the square of the distance._

You don't need to know anything but English to realize that if inverse square laws is what defines the brightness of the stars that it is also what makes the night sky not be equally bright.


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## Helen B (Nov 15, 2012)

tris_d said:


> Helen B said:
> 
> 
> > a) True
> ...



You haven't read what I have written (or you have read it and misunderstood it). The inverse square law can be, and is, used to find distances. I have said that. I have also explained why the inverse square law does not affect image illumination. These two statements are not contradictory. The inverse square law affects the radiant power passing through unit area at the observer (one meaning of the unscientific word 'brightness'). The distance to the object also determines image size. Image size together with the arriving power determine image illumination (another meaning of the word 'brightness'). No contradiction there. I've further explained what happens when the image size falls below the minimum receptor size.


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## tris_d (Nov 15, 2012)

Helen B said:


> You haven't read what I have written (or you have read it and misunderstood it). The inverse square law can be, and is, used to find distances. I have said that. I have also explained why the inverse square law does not affect image illumination. These two statements are not contradictory. The inverse square law affects the radiant power passing through unit area at the observer (one meaning of the unscientific word 'brightness'). The distance to the object also determines image size. Image size together with the arriving power determine image illumination (another meaning of the word 'brightness'). No contradiction there. I've further explained what happens when the image size falls below the minimum receptor size.



At least you are not insulting me now, I appreciate that.

I don't see how any of that explains why would distant stars, given the same exposure time, appear as bright as closer brighter stars. It is logical that if inverse square law defines differences in brightness it would also be what defines non-uniform brightness. But then they used wrong math and destroyed their own logic, hence the "paradox". But they were not aware of such thing as "resolution" at the time, not in mathematical sense anyway, and they ignored it which gave them result that sums all the intensity into only one pixel. Do the correct math by including image resolution into the equation and the result will indicate non-uniform brightness.


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## Derrel (Nov 15, 2012)

unpopular said:


> Around here there is one rule that mast not be broken: don't doubt Helen. Ever.
> 
> ---
> 
> seriously dude. you're not the one with a degree from RIT. She is.



Word.


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## amolitor (Nov 15, 2012)

Oh pish, I have a degree too, and just look at me.

Tris, you have zero chance of getting anything published and I think you know that. But good luck with it.


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## Derrel (Nov 15, 2012)

amolitor said:


> Oh pish, I have a degree too, and just look at me.
> 
> Tris, you have zero chance of getting anything published and I think you know that. But good luck with it.



Yeah, Andrew, we know....but you see that hair Helen has in her avatar pic???? She RIPPED THAT HAIR RIGHT OUT of the scalp of some dude who crossed her in an argument and called her a dummy...


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## Helen B (Nov 15, 2012)

tris_d said:


> Helen B said:
> 
> 
> > You haven't read what I have written (or you have read it and misunderstood it). The inverse square law can be, and is, used to find distances. I have said that. I have also explained why the inverse square law does not affect image illumination. These two statements are not contradictory. The inverse square law affects the radiant power passing through unit area at the observer (one meaning of the unscientific word 'brightness'). The distance to the object also determines image size. Image size together with the arriving power determine image illumination (another meaning of the word 'brightness'). No contradiction there. I've further explained what happens when the image size falls below the minimum receptor size.
> ...



It would be helpful to be clearer about what you mean by brightness in the above paragraph. You seem to be using the same word to refer to two different properties. It would be much easier to read and to try to follow your reasoning. What is the 'wrong math'? You do realize that the logic behind the Paradox is resolution-independent, don't you?


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## tris_d (Nov 15, 2012)

Helen B said:


> It would be helpful to be clearer about what you mean by brightness in the above paragraph.



Apparent magnitude - Wikipedia, the free encyclopedia
_- The apparent magnitude (m) of a celestial body is a measure of its *brightness as seen by an observer on Earth*_


Basically, intensity is a property of light itself and brightness is a property of an image.




> What is the 'wrong math'? You do realize that the logic behind the Paradox is resolution-independent, don't you?



Do you realize that without resolution you don't have pixels which brightness you need to compare in order to deduce whether their brightness is the same or not across the sensor surface area receiving the light? How do you expect to deduce whether the brightness is uniform or not if you sum all the intensity into only one variable? Of course it will be uniform when your result can only hold one value. You need an array, a matrix, that can hold multiple values related to spatial distribution of received light.


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## unpopular (Nov 15, 2012)

amolitor said:


> Oh pish, I have a degree too, and just look at me.
> 
> Tris, you have zero chance of getting anything published and I think you know that. But good luck with it.



you're doing just fine. :roll:


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## unpopular (Nov 15, 2012)

tris_d said:


> Do you realize that without resolution you don't have pixels which brightness you need to compare in order to deduce whether their brightness is the same or not across the sensor surface area receiving the light? How do you expect to deduce whether the brightness is uniform or not if you sum all the intensity into only one variable? Of course it will be uniform when your result can only hold one value. You need an array, a matrix, that can hold multiple values related to spatial distribution of received light.



o_0


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## thetrue (Nov 15, 2012)

HOLD EVERYTHING!!!!!!!!!! I figured out what the misunderstanding is. OP has been citing ONLY wiki, that ultra reliable source for any information on any subject.....:rolls eyes:


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## unpopular (Nov 16, 2012)

see, i'd agree. except that as far as I can tell everything he's cited from wiki is 100% accurate.

i'm pretty sure this is a matter of user error.


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## thetrue (Nov 16, 2012)

Idk, I haven't clicked on a single link in the thread. I thought it was supposed to be someone taking a picture of a candle, not a big debate about physics and astrology that near literally has nothing to do with pushing the shutter release and enjoying the result...


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## christop (Nov 16, 2012)

Alright, here's a stupid little picture I made. The left column of squares is from a 4x4 array of sensels from a high-resolution sensor. The right column of squares is a 1x1 array of sensels from a low-resolution sensor.







As you can see, the top left square has a single star occupying the area of 4 sensels. We're lucky that our star is square so that it neatly aligns to our sensel grid.  Each sensel receives 100% illumination from this star. The top right square is what the low-resolution sensor sees. The star occupies only 25% of the low-resolution sensel's area. The sensel registers a value of 25% illumination, which is the average illumination value of the 4x4 area of the high-resolution sensor (4 illuminated sensels / 16 sensels = 25% illumination).

The second row is like the first but has three more distant stars added to the image. These stars are twice as far as the first star in the center, so they each occupy an area of 1 sensel. Now 7 of the high-resolution sensels "see" light coming from a star.

The more distant stars each contribute only one fourth as much light (radiant power) as the first star, due to the inverse square law, but the image of each star also has only one fourth as much area as the first star, so they all produce the same illumination in the image (100% sensel values in this example). You have recently accepted this as a fact. You would be contradicting yourself if you now claimed that the distant stars would be "dim gray pixels" or something to that effect.

The low-resolution sensel on the right "sees" an illumination of 43.75% this time (7 illuminated sensels / 16 sensels = 43.75% illumination).

The third row is the same story as the second row: a few more stars are added to the mix (12 illuminated sensels / 16 sensels = 75% illumination).

Now we get to the bottom row. More stars are added (or maybe a single star at half the distance of the first star steps in front and occludes all the other stars). All 16 sensels in this sample are collecting light from some star, whether a near star or a distant star. The single sensel on the right is now completely "covered" with stars, so it too registers a value of 100% illumination (16 illuminated sensels / 16 sensels = 100% illumination).

One thing to take from this is that the illumination of "nearby" stars (stars that cannot be resolved individually) such as binary stars is indeed additive. If you had really thought about my LED traffic light experiment, you would come to the same conclusion. Each LED would have a small contribution to the illumination of each sensel in the low-resolution camera in that experiment, but many LED's would occupy a sensel. The illuminations would add up.

So _regardless_ of image resolution, the model of the Universe proposed in Olber's paradox would be uniformly bright (neglecting phenomena such as local variations in brightness of each individual star--sunspots and the like).


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## tris_d (Nov 16, 2012)

christop said:


> As you can see, the top left square has a single star occupying the area of 4 sensels. We're lucky that our star is square so that it neatly aligns to our sensel grid.  Each sensel receives 100% illumination from this star. The top right square is what the low-resolution sensor sees. The star occupies only 25% of the low-resolution sensel's area. The sensel registers a value of 25% illumination, which is the average illumination value of the 4x4 area of the high-resolution sensor (4 illuminated sensels / 16 sensels = 25% illumination).



The right side is not correct. It's an AVERAGE of all 16 pixels, but if you truly had 1x1 image that single pixel would collect all the light and have summed brightness of all the pixels on the left. The same would be true for all the other rows. Single pixel image would always be as bright as the sum of all the pixels from the left, all the light would end up at that single pixel.





> The second row is like the first but has three more distant stars added to the image. These stars are twice as far as the first star in the center, so they each occupy an area of 1 sensel. Now 7 of the high-resolution sensels "see" light coming from a star.



You should have all the stars be the same size (point sources), where further ones would be less bright.




> The more distant stars each contribute only one fourth as much light (radiant power) as the first star, due to the inverse square law, but the image of each star also has only one fourth as much area as the first star, so they all produce the same illumination in the image (100% sensel values in this example). You have recently accepted this as a fact. You would be contradicting yourself if you now claimed that the distant stars would be "dim gray pixels" or something to that effect.



Yes, I learned my lesson and I appreciate it. But there is only few dozen stars that have "resolvable" angular size, so for general case scenarios you should make all the stars be point light sources.  





> One thing to take from this is that the illumination of "nearby" stars (stars that cannot be resolved individually) such as binary stars is indeed additive. If you had really thought about my LED traffic light experiment, you would come to the same conclusion. Each LED would have a small contribution to the illumination of each sensel in the low-resolution camera in that experiment, but many LED's would occupy a sensel. The illuminations would add up.



I have no idea what point you are addressing. Illumination would add up just by having a single pixel instead of many pixels. 




> So _regardless_ of image resolution, the model of the Universe proposed in Olber's paradox would be uniformly bright (neglecting phenomena such as local variations in brightness of each individual star--sunspots and the like).



You got uniform brightness when you averaged the image from the left into only one pixel. That's not regardless of resolution, that is what automatically comes with ONE PIXEL resolution. And you are neglecting little fluctuations in brightness of individual stars, as if that would make some difference, but you are completely ignoring further away stars would be dimmer than closer stars. These are not candles any more, stars are point light sources and they get dimmer with the distance


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## Helen B (Nov 16, 2012)

tris_d said:


> Helen B said:
> 
> 
> > > What is the 'wrong math'? You do realize that the logic behind the Paradox is resolution-independent, don't you?
> ...


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## tris_d (Nov 16, 2012)

Helen B said:


> That is not what 'resolution-independent' means.



That is not addressing my question. Here it is again:

How do you expect to deduce whether the brightness is uniform or not if you sum all the intensity into only one number?


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## amolitor (Nov 16, 2012)

Tris, do you not see that if I can describe a universe in which

- all the conditions of Olber's Paradox hold true
- the inverse square law applies
- and the night sky is pure white

your thesis disintegrates?

Proof by contradiction - Wikipedia, the free encyclopedia


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## Helen B (Nov 16, 2012)

tris_d said:


> Helen B said:
> 
> 
> > That is not what 'resolution-independent' means.
> ...



I have addressed your question by explaining that resolution independence does not mean summing all the intensities into one number. Now you really are trolling.


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## tris_d (Nov 16, 2012)

Helen B said:


> I have addressed your question by explaining that resolution independence does not mean summing all the intensities into one number.



There is no such thing as 'resolution-independent'. I am not talking about your imaginary dictionary, I am referring to mathematics and equations used in original treatment of Olbers' paradox. And there they do sum up all the intensity into one number called 'total intensity'. Here is how it goes:

http://www.asterism.org/tutorials/tut09-1.htm






_Since the area of a sphere of radius r is

A = 4p r2 (1)

the volume of such a shell is

V = 4p r2t (2)

If the density of each of the luminous objects within the shell is "n",  then the total number of these objects in the shell must be

N = 4p r2nt (3)

Now let us ask just what amount of energy such a shell will send to the  Earth. Since the shell's thickness is small, it is reasonable to assume  that the entire shell is at a distance "r" from the earth. The energy,  E, emitted by any source at distance r, produces an intensity, "I", over  a given area, A, on the Earth of (inverse square law)

I = E/4p r2 (4)

The total intensity received on the Earth from all the sources in the  shell r units away must then be the intensity produced by each source  times the total number of sources or

T = IN (5)

Substituting the value of N previously calculated into the above, we find that

T = tnE (6)

We notice at once that the total energy received from any chosen shell  does not depend upon its distance from us (no r in the above equation).  The total energy received from all the shells is the sum of the  contributions of each shell. If there are M shells this total is

S = tnEM (7)

But there is an infinite number of shells and so the total intensity on  the earth must be infinite. Therefore, the nighttime sky should be  blindingly bright!



--//--

_How do you expect to deduce whether the brightness is uniform or not if your result is a single number?


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## tris_d (Nov 16, 2012)

amolitor said:


> Tris, do you not see that if I can describe a universe in which
> 
> - all the conditions of Olber's Paradox hold true
> - the inverse square law applies
> ...



Go on and try.


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## pgriz (Nov 16, 2012)

Tris_d, your profile doesn't show a location, but it does appear that you may be a resident of the the lovely town of La Mancha.


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## amolitor (Nov 16, 2012)

tris_d said:


> amolitor said:
> 
> 
> > Tris, do you not see that if I can describe a universe in which
> ...



You didn't answer my question. I'm not going to go to the effort of writing up such a description if you don't first see why it would be interesting.


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## tris_d (Nov 16, 2012)

amolitor said:


> You didn't answer my question. I'm not going to go to the effort of writing up such a description if you don't first see why it would be interesting.



I thought it was obvious my invitation implies that I agree to what you said. -- I expect you will just repeat the original treatment of Olbers' paradox which would be slightly amusing, or alternatively you could come up with something different, in which case you would not only be proving me wrong, but also the original treatment of the paradox just like I do, and that would highly amusing.


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## fjrabon (Nov 16, 2012)

thetrue said:


> Idk, I haven't clicked on a single link in the thread. I thought it was supposed to be someone taking a picture of a candle, not a big debate about physics and astrology that near literally has nothing to do with pushing the shutter release and enjoying the result...



We did that a long time ago.  It was in a different thread that got locked though.  His original theory that candles get dimmer as they get farther away was disproven with a photograph I took of a lamp.  However, he more or less just ignored that and now seems to have a theory that while it doesn't happen for candles, it does happen for stars.


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## Helen B (Nov 16, 2012)

tris_d said:


> Helen B said:
> 
> 
> > I have addressed your question by explaining that resolution  independence does not mean summing all the intensities into one number.
> ...



That's  a bit of an odd thing to say. Resolution independent means that the  result doesn't depend on the resolution chosen. Both words are in real  dictionaries, and they have a meaning, so I don't need to use an  imaginary dictionary.



> I am referring to mathematics and  equations used in original treatment of Olbers' paradox. And there they  do sum up all the intensity into one number called 'total intensity'.  Here is how it goes:
> 
> Olbers' Paradox
> 
> ...



Well,  it's a trivial exercise to show that the above reasoning can be applied  to any resolution, which in this case would mean any solid angle  element (&#948;&#937. (This is normal scientific reasoning.) The above result is  independent of the solid angle you choose. The method can be used to  show that no matter what solid angle you select, the same result will  happen. It's blindingly obvious. It would be literally blinding in this  case, because as we have already discussed, the above ignores  obstruction (see (9) in post #192 above, or the next paragraph in the  article you part copied-and-pasted). The same method, adjusted to take  obstruction into account, can also be used to show that the brightness  of any solid angle element of the sky has the brightness of a nearby  star - ie that all possible selections of &#948;&#937; however large or small  (resolution independent) have the luminous emittance of a star surface  and the sky is thus uniformly bright.

Is there any point in me wasting any more time on this?


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## jake337 (Nov 16, 2012)




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## amolitor (Nov 16, 2012)

Ok, then.

Let us assume that the inverse-square law applies throughout.

I will actually describe a universe with an extremely regular distribution of an infinite number of stars, for which the night sky is uniformly bright. This can be converted to one with a random distribution of stars as follows:

- adjust the distance of each star from the viewer by a random degree, while simultaneously adjusting the size and brightness of the star so that its appearance to the viewer is unchanged. I.E. if you move it farther away, make it bigger, and if you move it closer, make it smaller. If you started with identical stars, this randomizes the size and intensity of the stars, as a little bonus.
- Now observe that since the sky is uniformly bright, I can take, for example, any two 1 degree by 1 degree squares in the sky, and swap them, without changing the appearance of the sky. This is effectively rotating stars around. The stars within the square are at varying distances, but we're rotating them around the viewer, maintaining the original distances. Randomly select pairs of squares of random dimension, and swap them. This "shuffles" the rotational position of stars. Do this as much as you like, until a suitable degree of randomness has been achieved.

So, it will suffice to show a regular distribution of an infinite number of identical stars, which produces a uniform sky brightness.

----

For the regular distribution of stars let us make an observation. I can fill any region of the sky to uniform brightness with a finite number of identical stars as follows:

- select a distance from the viewer, any distance will do
- fill the region with your stars, spacing them very close together in a regular grid, this will leave gaps, of course
- fill the gaps with a second layer of stars behind the first grid of stars. You may use the same size and intensity of star. We know that placing them further away makes them, like a candle, smaller, but not less bright.
- you might need a third or fourth layer, honestly, but it's a small number of layers to fill 100% of the gaps, if you packed the stars together pretty tightly to start with. You're just covering a piece of paper with overlapping circles, in effect.

-----

Now, select half of the night sky. Fill it as indicated above. You have used a finite number of stars.

Whatever sky remains unfilled, select half of that, and fill it in with a finite number of the same size and intensity of stars as the previous step, but placed twice as far away as the previous collection of stars. They are farther away, but will, like a candle, appear the same brightness . This will take about 2x as many stars as the previous step, despite the region being half the size.

Continue, filling in half of what remains at each step. This will require an infinite number of steps. Each region filled will require more stars, but each step requires only a finite number of stars, and produces a region of the same brightness as the previous region.

When you are done, you will have uniform sky brightness and an infinite number of stars, in an extremely regular pattern

Shuffle these stars as suggested at the beginning of this post, to produce a random distribution of that infinitude of stars, without disturbing the uniform sky brightness.

Now you are done.

Whatever reasoning you have to demonstrate that the inverse square law produces a dark night sky, it will fail in this universe. Since it fails in this case, it must be logically incorrect.


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## rexbobcat (Nov 16, 2012)

How did something so simply ten into a physics lesson?

Regardless of mathematical equations (eww). A light source will always remain at the same brightness from its origin unless there is something in the air to impede its light. :/

Why is this so complicated?


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## fjrabon (Nov 16, 2012)

the ultimate issue here seems to be that Tris views the inverse square law as a sort of magic law that just holds. Sort of like the way that pi is 3.14159265...... What I think he doesn't get, which we've been trying to explain to him, is why the inverse square law holds. If he really understood why the inverse square law holds, he'd see that this whole thing he's been talking about is less than a puff of smoke. It's a misconception based on a half understanding of the inverse square law. 

He's sort of latched on to the idea that things get dimmer as they get farther away, but sort of ignored the 'because their light spreads out over greater space' aspect. And then he's flat out ignoring that when light from two different sources combine, their 'brightness' is additive. He also seems to have a hard time understanding the distinction from the amount of illumination provided by a point source to a reference point (what the inverse square law is talking about) and the object's apparent brightness when focused upon (WHICH THE INVERSE SQUARE LAW DOESN'T ADDRESS)

I think the simplest way I can address this fundamental issue is this Tris:

The inverse square law has nothing to do with how bright an object looks to your eye. It was never meant to, that's not what it's used for in physics. The inverse square law is used to show the amount of TOTAL light provided by a point source to a given amount of area in a reference plane. ie it only measures the total amount of light an object provides, not how bright a focused dot 'looks'.

We've all tried to explain this to him like 1239847 times in the course of these 3 or 4 threads, so I don't expect that misconception to change any time soon.​


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## jwbryson1 (Nov 16, 2012)

.


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## christop (Nov 16, 2012)

tris_d said:


> The right side is not correct. It's an AVERAGE of all 16 pixels, but if you truly had 1x1 image that single pixel would collect all the light and have summed brightness of all the pixels on the left. The same would be true for all the other rows. Single pixel image would always be as bright as the sum of all the pixels from the left, all the light would end up at that single pixel.



It is exactly the illumination a low-resolution sensor would produce. Sensors are calibrated to produce an illumination based on not only how much light is collected by its sensels but also on the _area_ of the sensels. Larger sensels (lower resolution) obviously receive more light than smaller sensels if all else is equal. So the light-to-illumination conversion mechanism (amplifier circuitry or what have you) must take the sensel's area into account when computing the sensel's illumination. In my example the light received by the larger sensel must be amplified by 1/16 relative to the small sensel.

What's most concerning is that you are now claiming that lower resolution makes the image "brighter". You previously claimed the opposite. So which is it? Does lower resolution make the image brighter or dimmer? (Hint: it's neither). I can see why you're confused.



> You should have all the stars be the same size (point sources), where further ones would be less bright.





> Yes, I learned my lesson and I appreciate it. But there is only few dozen stars that have "resolvable" angular size, so for general case scenarios you should make all the stars be point light sources.


Why? Stars are not point sources. Stars have finite size. The small sensels in my example are part of an "ideal" high-resolution imaging sensor which is capable of resolving each individual star. The low-resolution sensor (on the right) cannot resolve each star individually so we can estimate the size of a star from the illumination of a sensel (the top right sensel's illumination is 25% so we can estimate the angular size and therefore the distance of the star).



> I have no idea what point you are addressing. Illumination would add up just by having a single pixel instead of many pixels.


Exactly. Illumination adds up.



> You got uniform brightness when you averaged the image from the left into only one pixel. That's not regardless of resolution, that is what automatically comes with ONE PIXEL resolution. And you are neglecting little fluctuations in brightness of individual stars, as if that would make some difference, but you are completely ignoring further away stars would be dimmer than closer stars. These are not candles any more, stars are point light sources and they get dimmer with the distance


You apparently didn't notice that all stars were individually resolved in the left image (the high-resolution sensor) and that the illumination of all 16 sensels in the bottom-left image is still uniform. I could have added an even higher-resolution sensor image which would also have been uniform illumination. Perhaps I should have added sensel grid lines to make it more obvious that each sensel is still an individual, independent sensel.


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## pgriz (Nov 16, 2012)

@ Helen B:  Regarding 





> Is there any point in me wasting any more time on this?



Probably not, but I do very much appreciate your clear (at least to some of us) explanations.  Once we're past this particular conrundum, we can probably start addressing the question of how many angels can dance on a head of a pin.  But that may devolve into a discussion of the footprint size of each class of angel, and the variation in pin head sizes.


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## tris_d (Nov 16, 2012)

Helen B said:


> tris_d said:
> 
> 
> > That's  a bit of an odd thing to say. Resolution independent means that  the  result doesn't depend on the resolution chosen. Both words are in  real  dictionaries, and they have a meaning, so I don't need to use an   imaginary dictionary.
> ...


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## amolitor (Nov 16, 2012)

Tris, I have no trouble following Helen's posts.

I cannot follow your posts at all, they appear to simply be strings on non-sequiturs with some keywords sprinkled in. I say "appear" here quite deliberately -- I pass, in this post, no judgement on whether your remarks are correct or not. My point here is to note that if you plan to write a paper about this, you need to work on your expository skills. A publishable paper exists to communicate ideas to other people, and your writing on this forum simply doesn't accomplish that. As a people, I can state firmly that you have succeeded in communicating no ideas at all to me. My sense is that you have not communicated successfully with anyone else in this forum, either.

You should consider what to do about that, before sitting down to write your paper.


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## tris_d (Nov 16, 2012)

amolitor said:


> Ok, then.
> 
> Let us assume that the inverse-square law applies throughout.
> 
> ...



That's wrong. If we adjust the night to look like a pink unicorn then when you look above at the night sky you see a pink unicorn.




> If you started with identical stars, this randomizes the size and intensity of the stars, as a little bonus.
> - Now observe that since the sky is uniformly bright, I can take, for example, any two 1 degree by 1 degree squares in the sky, and swap them, without changing the appearance of the sky. This is effectively rotating stars around. The stars within the square are at varying distances, but we're rotating them around the viewer, maintaining the original distances. Randomly select pairs of squares of random dimension, and swap them. This "shuffles" the rotational position of stars. Do this as much as you like, until a suitable degree of randomness has been achieved.
> 
> So, it will suffice to show a regular distribution of an infinite number of identical stars, which produces a uniform sky brightness.



No. Since the night sky looks like a pink unicorn, I can take, for example, any two 1 degree by 1 degree squares in the  sky, and swap them, without changing the appearance of the sky.




> Whatever reasoning you have to demonstrate that the inverse square law produces a dark night sky, it will fail in this universe. Since it fails in this case, it must be logically incorrect.



Don't you have anything better to do?


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## amolitor (Nov 16, 2012)

Are you actually under the impression that repeating back fragments of my remarks, and sprinkling them with snarky bits, constitutes a rebuttal?

This is, at least, the second time you've replied to me in this fashion. As a published scientist, I can assure you that it's not a good road to getting a paper into print.


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## The_Traveler (Nov 16, 2012)

I am quite pleased I didn't get caught up in this thread. but have clumped trid_d along with others in this group referred to below.


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## unpopular (Nov 16, 2012)

I say we just abandon ship and ignore all future liter which tris casts.

I still say he's a genuine physicist just trying to **** with us.

---

amolitor - just curious, what field of science did you study?


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## amolitor (Nov 16, 2012)

I was a mathematician once upon a time. These days I write software.


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## tris_d (Nov 16, 2012)

amolitor said:


> Tris, I have no trouble following Helen's posts.
> 
> I cannot follow your posts at all, they appear to simply be strings on non-sequiturs with some keywords sprinkled in. I say "appear" here quite deliberately -- I pass, in this post, no judgement on whether your remarks are correct or not. My point here is to note that if you plan to write a paper about this, you need to work on your expository skills. A publishable paper exists to communicate ideas to other people, and your writing on this forum simply doesn't accomplish that. As a people, I can state firmly that you have succeeded in communicating no ideas at all to me. My sense is that you have not communicated successfully with anyone else in this forum, either.
> 
> You should consider what to do about that, before sitting down to write your paper.



What part do you not understand?

1.) We are talking about an image of the night sky, formed by human  eyes or a camera, and why does it look the way it looks. 

2.) Solid angle has nothing to do with resolution or distribution.  Distribution involves a sequence, that is more than one number.

3.) If the result of some equation is a single number, then it can not have any distribution, it's  "uniform" just by being a single.







4.) If we calculate total intensity for either of those two images above we would get a  result that is a single scalar number.

5.) If we look at the value of "total intensity" for either of those two images the result will indicate they are bright  and uniform.

6.) If we take resolution into  account we can realize "total intensity" does not accurately describe brightness nor its distribution.


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## christop (Nov 16, 2012)

unpopular said:


> I still say he's a genuine physicist just trying to **** with us.



I think he really is a computer programmer as he says he is. When I was a less experienced programmer, I was also arrogant (to a much, much lesser degree) about how much I knew, and I came up with what I thought were "new" ideas which turned out to be fundamentally flawed and would never work in practice. By the time I got to my teenage years I had learned how much I _didn't_ know. Luckily for me I didn't have access to the WWW (it was probably before the Web was invented) to flaunt my own ridiculous and laughable ideas.


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## unpopular (Nov 16, 2012)

whats worse is that there will be a record if this madness for all eternity.


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## Helen B (Nov 16, 2012)

Well, it looks like no matter what I write tris isn't going to read it, tris is just going to reply to what tris thinks I have written. Here's an excellent example of tris' imagination:



tris_d said:


> Helen B said:
> 
> 
> > That's  a bit of an odd thing to say. Resolution independent means that  the  result doesn't depend on the resolution chosen. Both words are in  real  dictionaries, and they have a meaning, so I don't need to use an   imaginary dictionary.
> ...



Note how '_the result doesn't depend on the resolution chosen_' has been switched for '_Your result being a single scalar number is not "resolution independent", it is COMPLETELY WITHOUT any resolution_ '. See how tris thinks that a result that is valid for any chosen resolution suddenly becomes one with no resolution at all? Resolution becomes no resolution in tris' mind. Puzzling, isn't it?





> Solid angle has nothing to do with resolution



Tris has no idea what the relationship between solid angle and resolution is and yet tris claims that tris knows about this subject. 



> Don't you realize if you take "resolution independent" approach and calculate total intensity of either of those two images above you get a single number that would make you believe those images are both bright and uniform, which is obviously not the case if you take resolution into account. Do you understand now why such mathematics is wrong and unsuitable to deduce anything about any distribution or actual brightness?



It's fairly obvious that different resolutions would result in different values for the degree of uniformity, so this comparison would not meet the requirement for 'resolution independence'. For some weird reason, tris doesn't get that, simple as it is.


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## amolitor (Nov 16, 2012)

tris_d said:


> What part do you not understand?
> 
> 1.) We are talking about an image of the night sky, formed by human  eyes or a camera, and why does it look the way it looks.



Ok.



tris_d said:


> 2.) Solid angle has nothing to do with resolution or distribution.  Distribution involves a sequence, that is more than one number.



Solid angle is pretty much the same thing as resolution. Given a lens, focusing an image of the night sky on a sensor, what gets imaged onto a pixel (or any square region of the sensor) IS a solid angle. So, #2 is wrong on this point.

We usually say "population" or "sample" when dealing with distributions, but sure, I'll grant you "sequence"



tris_d said:


> 3.) If the result of some equation is a single number, then it can not have any distribution, it's  "uniform" just by being a single.



Ok.



tris_d said:


> 4.) If we calculate total intensity for either of those two images above we would get a  result that is a single scalar number.



Ok.



tris_d said:


> 5.) If we look at the value of "total intensity" for either of those two images the result will indicate they are bright  and uniform.



I understand what you're saying here, sure. Note in passing that "uniform" is a word use to describe a distribution, so you're being sloppy with your terminology. Regardless, #5 seems to be simply a repetition of #4.

At this point you've argued, successfully, that "total intensity does not have a distribution, because it's a scalar". It's not clear what point #1 has to do with anything at this point, since "total intensity" has only a tenuous connection with what the night sky looks like.



tris_d said:


> 6.) If we take resolution into  account we can realize "total intensity" does not accurately describe brightness nor its distribution.



What? This is where the wheels fall off. Where did resolution come from? What does resolution have to do with anything in your remarks #1 through #5? You don't even mention resolution, except to make what appears to be an incorrect side remark in #2, above. Resolution appears to be completely unrelated to "total intensity", which is surely nothing more than the integral of light intensity over the entire sky (or whatever subset of it you're interested in).

If I were refereeing this, I would probably make remarks very much like what I wrote above, and recommend that the paper be rejected for now, with the author urged to re-organize the ideas in the paper and try to make clearer what the point, if any, is.


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## tris_d (Nov 16, 2012)

amolitor said:


> I was a mathematician once upon a time. These days I write software.



Then perhaps you would like to hear about some of the stuff I made.

Tic-Tac-Toe game using artificial neural network with only a single layer perceptron, mapping 255,168 combinations into only 81 bytes!!! It does not use CPU, but it works on graphic video card hardware (GPU) by utilizing textures and parallel processing. Here is a full listing of the source code: 

Driver-Man's operating system
OpenGL & OpenGL ES demos - gameBoX Linux

Driver-Man's MAME emulator for Android phones *with online scoreborad*, featuring *new input  method* for mobile devices and new gameplay elements for classic arcade  games: 






Unfortunately friendly neighborhood Driver-Man, that's me, has a lots of enemies so this is not available for download on the Google Market at the moment, but if someone wants to try it out let me know. I'll upload new version on the market after New Year. 


There is Amazing Driver-Man comic book on the market, if you wanna see just how crazy I am:


There are few more comic books that I have not yet published. Here are some snippets...


You don't see this kind of stuff every day, eh? Hehee, I'm craaazy! 

It's my gift, my curse. Who am I? I'm your friendly neighborhood Driver-Man!


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