Illustrating Olbers' paradox

No mention of any photons or energy coming from the stars. 1000 brightness, "turns out"? How much energy per second is that? How did you come up with that number?

What are you trying to say?

 

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C'mon, you're smarter than that. You just calculated a few posts ago the energy from photons required to saturate the entire image or one pixel. The calculation is linear, so the next step follows from that one. You have the brightness values per pixel and the total number of pixels: Put them together and divide!

You didn't finish your calculation. You calculate the number of photons that hit the detector per star, per shell, but didn't then multiply by the number of stars per shell and add together the shells. Your calculation reads as if the entire sensor is only picking the light up from one star at a time! You know that isn't true!

 

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REQUIRED is not RECEIVED. How much total energy is RECEIVED FROM THE STARS by the sensor surface per one second time interval? Not any brightness or other pixel properties, it must have units in photons per second or joules per second.

I don't think you know what are you talking about. Show me.

 

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It is the energy from the stars that the next step brings-in. Follow the calculation and it takes you where you say you want to go.
[...and you are aware that Watts = Joules per second, right?]

No. It is your turn to do the work required of you - I will not do it for you anymore: I'll just point you the way. You are aware that all you calculated is the photons received from one star in each shell, right? You are aware that the shells all contain different numbers of stars, right? You are aware that the camera just collects photons and doesn't care what shell/star they come from, right? You aren't as dense as you are acting, right? You let the cat out of the bag when you did those calculations yesterday: you revealed - finally, after 3 weeks - that you aren't incapable of doing any math. Now you need to continue doing the math.

 

Please answer the question directly. How much total energy is received by the sensor surface per one second time interval?

The number of photons received from each shell is sum of photons received from each star in that shell. Both numbers are defined and known, what is confusing you?

 

No. You have watts per square meter and square meters. You have proven that you aren't an idiot, so if you want watts, do the calculation yourself.

Right: and you didn't calculate it. You need to take what you calculated for each shell and multiply by the number of stars in each shell, then add the shells together. You aren't finished!

 

The number, what is it? Why is that so hard for you to say, why does it make you angry? You never defined the amount of energy received per star or per shell. You never said how much total energy is received by the sensor surface per one second time interval. All you have to do is simply write that number down. But you can not, because you do not know.

I did, it's all good. Do you see any problem?

 

I'm not angry, I'm being your teacher. Teachers make students learn by doing.

Correct: I did it per square meter, which IMO is better.

Apparently the problem is that you are trolling, because you clearly did not.

 

a.) "My stars", whatever they are, are not the stars in the sky

b.) "Saturation value" is not a property of the stars in the sky


How many photons are received by the sensor, per second, from one star in the first shell?

a.) "As it turns out" is not an explanation, it is excuse for arbitrary number "1000"

b.) Total brightness of 1000 doesn't make even a single pixel slightly bright


How many photons are received by the sensor, per second, from all the stars in the first shell?

a.) Brightness is calculated from energy received, not the other way around

b.) Energy received from only the 1st shell is not TOTAL energy received


Do you realize you concluded just the stars in the first shell overexposed the whole image?

You are not pointing to any specific problem. You are not asking any specific question. You are just waving hands. What exactly do you want to know? What exactly do you believe is the problem? Do you even know?

 

Ok, that's enough. I'm not going to get sucked-in to a did not/did to loop with you. I'm not 7 and you should stop acting like you are. You aren't stupid - you know what your calculations did - and your "my butler did it" comment makes it clear that you are just trolling (Perhaps you learned the tactic from Dinosaur?: post an explanation then ignore all responses to it, while claiming you received no response.). So I won't be chasing that one any further.

At this point, I'm sensing that you've figured out what your error is - if it ever really was an error - and are now just trolling rather than admitting you learned something (That's just sad). So I won't keep repeating myself and responding to your troll bait. If you ask legitimate questions, I'll answer them (often by prodding you on how to figure it out yourself), but that's it - the rest I won't keep answering with the same corrections over and over because you clearly aren't listening.

So, there is only one thing in your post to answer, and while it is just expanding on the previous several times I've answered it, since it was asked slightly differently and I want to put the finer point on it, I'll answer it again:

So I've already answered that by explaining why my calculation is organized the way it is and pointing out that it is easily reversible, but just to expand a little:

Look up and read the wiki for "photometry". And while you're at it, read through to the wiki on "flux", which shows that my use of watts/sq m is preferable to your watts/sensor.

 

No, I figured many of your errors that I am pointing out very specifically and asking very specific questions about, which you are unable to answer or even respond to coherently and actually address the point.

It is you who is supposed to figure out if there is any error in my presentation, I of course know there is not. You are not only unable to defend your position, you are also unable to see any flaw in what I have said. Double fail, you lose the debate.

Brightness is calculated from the energy received, not the other way around. You first want to make your image white, and then "calculate" the sky was indeed bright enough to make it so. You're funny. Total brightness of 1000 doesn't make even a single pixel slightly bright, pixel brightness range is up to 16,000 as you defined yourself. You never consider any photons or energy RECEIVED, your phantasmal image exist before it was taken. You considered only the 1st shell, and then concluded you calculated TOTAL energy received.

And so again, you never answered what was the TOTAL energy RECEIVED by the sensor during one second exposure time. Instead you concluded just the stars in the first shell overexposed the whole image. Do you even realize? How many photons are received by the sensor, per second, from one star in the first shell?

 

Code:

Shell 1: stars= 1 [SQ:1]  --  ph/star= 100000.000000
Shell 2: stars= 4 [SQ:2]  --  ph/star= 25000.000000
Shell 3: stars= 16 [SQ:4]  --  ph/star= 6250.000000
Shell 4: stars= 64 [SQ:8]  --  ph/star= 1562.500000
Shell 5: stars= 256 [SQ:16]  --  ph/star= 390.625000
Shell 6: stars= 1,024 [SQ:32]  --  ph/star= 97.656250
Shell 7: stars= 4,096 [SQ:64]  --  ph/star= 24.414063
Shell 8: stars= 16,384 [SQ:128]  --  ph/star= 6.103516
--------------------------------------------------------------- ph/star
Shell 9: stars= 65,536 [SQ:256]  --  ph/star= 1.525879
--------------------------------------------------------------- 0.0
Shell 10: stars= 262,144 [SQ:512]  --  ph/star= 0.381470
Shell 11: stars= 1,048,576 [SQ:1024]  --  ph/star= 0.095367
Shell 12: stars= 4,194,304 [SQ:2048]  --  ph/star= 0.023842
Shell 13: stars= 16,777,216 [SQ:4096]  --  ph/star= 0.005960
Shell 14: stars= 67,108,864 [SQ:8192]  --  ph/star= 0.001490

To make it easier to follow the numbers I changed image resolution to 512x512 and started with narrow field of view with only one visible star from the first shell. Instead of plotting random dots to illustrate stars in a shell I draw their "area" as if they were arranged one next to another. "SQ" number in brackets above is the size of the rectangle side in pixels. Stars in the 1st and 2nd shell are bit larger than their total area or "rectangle size" due to overexposure.

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Stars in the 6th shell are almost invisible even if when they are all together, so I had to draw white border to represent their total area and that of every other later shell. Stars in the 9th shell are completely invisible, their 1-2 photons per second is not enough to knock an electron and register any increase in brightness. 6 photons per second is the minimum to increase the brightness by 1/16,000 of the total pixel brightness range, per Russty's definition.

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Code:

Shell 10: stars= 262,144 [SQ:512]  --  ph/star= 0.381470
Shell 11: stars= 1,048,576 [SQ:1024]  --  ph/star= 0.095367
Shell 12: stars= 4,194,304 [SQ:2048]  --  ph/star= 0.023842
Shell 13: stars= 16,777,216 [SQ:4096]  --  ph/star= 0.005960
Shell 14: stars= 67,108,864 [SQ:8192]  --  ph/star= 0.001490

There are two different visual effects in interplay now, and the time variable becomes ever so increasingly important. The stars in the 10th shell actually take up the whole image, there is one star of the 10th shell per every pixel of the image, but we don't receive ANY photons per second from 62% of them, and from those 38% of the stars that we do receive some photons from, it will only be just a single photon on average, with constantly shifting direction where it comes from each second. The stars in the 10th shell are again literally invisible for any exposure time less than one second.

There are two stars of the 11th shell per every pixel of the image, but we only receive any photons from only 10% of them, and even if there are now two stars per every pixel, when randomly distributed every second it will again be only just a single photon per star per second on average, every time from some different direction. And so on, and so on, this is true for any other later shell until foreground stars finally occlude all the background stars and the calculation is done. These stars simply can not be seen due to the low rate of their incoming photons without proportionally increased exposure time, especially since every second these occasional single photons come from different directions. Accumulate, that's the answer, but to accumulate you need to increase the exposure time. Simple as that. Didn't we already know this from observing Hubble Deep Field?

 

I'm trying to follow this thread and my general comments are that Russ_Watters seems to be making a sincere attempt at resolving the confusion here, while the following two comments are just silly:

These both presume to falsify Olber's Paradox using a very specific piece of technology which is limited to X number of pixels with exposure time and sensitivity. Olber's Paradox is a mathematical fact and would need to be refuted mathematically. All of this crap about "255 bits saturation" is completely irrelevant. In such a Universe where Olber's Paradox could be seen we could, you know, simply walk outside and use our EYEBALLS to verify the fact.

 

Of course. Do you really believe there can exist "brightness" without or outside some specific sensor, without something that will evaluate those photons incident on its surface area? It can not, brightness is a subjective property, just like a thought can not exist without the brain. Brightness is in the eye of the beholder.

Then please define "brightness" mathematically, what units does it have?

 

So, that post is all old nonsense - essentially everything in it is wrongness that has already been addressed - and in keeping with my previous post, it is unworthy of a response. If anything, it seems your grasp of my calculations is declining instead of increasing. That's probably on purpose. Fortunately, you followed it with a post that contains actual content to respond to:

So this is all fine, with the caveat that in this simulation, you've started with 1 star in the image instead of 10, so your density is lower than in your previous simulation.

So all of that is fine as well, but as with post #176, you stopped before creating the final image. The final image is all of the shells added together. So you need to take that 2 photons per second per 10 pixels from the 11th shell and add it to the 2 photon per second for the 12th, 13th, 14th, etc. Again: the detector is not looking at the shells individually, it is collecting photons from all of them at once.

 

You didn't do the homework I assigned. While "brightness" is not a technical term, one common way of measuring light from stars, that would apply well to Olbers' paradox is radiative flux, in units of watts/sq m.

http://en.wikipedia.org/wiki/Flux

The technique for actually measuring it, which I outlined the calculations and procedure for in the case of Olbers' paradox is called photometry:

http://en.wikipedia.org/wiki/Photometry_(astronomy)
This is exactly the technique I applied to my calculations.

 

Stop trolling. I repeat, these are your errors:

1.) Brightness is calculated from the energy received, not the other way around.

2.) Total brightness of 1000 doesn't make even a single pixel slightly bright, yet you concluded it made the whole image white.

3.) You never considered any photons or energy RECEIVED, your phantasmal image exists before it was taken.

4.) You considered only the stars in the 1st shell, and then wrongly concluded you calculated the TOTAL energy received.

Density of the stars in the sky is the same, it's just narrower field of view, it doesn't change the brightness of the sky.

And? What are you trying to say? What's the problem? -- It takes 10 seconds on average for the next photon to arrive from the same star in the 11th shell, it takes 42 seconds for the stars in the 12th shell, and so on. At best we get some extra twinkle of the foreground stars due to occasional photons from the background stars and we get grainy "blackness" between the visible stars, a "noise", and that's all.

 

None of those are even correct interpretations of what I did, much less flaws, and all have already been explained. Again: no new ground, so no additional response required. Reread the last two pages and do it more carefully this time.

Or don't: looks like from your math that you're making the same "mistakes" and more. IE, for #3 you didn't calculate energy either -- despite harping on me not doing it for days -- and you made no connection between your photon count, which you pulled out of the air, and the pixel brightness value.

Narrowing the field of view requires that you change either the camera or the optics. If you use a physically larger telescope of the same focal ratio, it doesn't change the brightness, but if you add a barlow to increase the focal length of an existing telescope, the brightness is reduced. It isn't a critical issue which one you choose, I just wanted to point it out for completeness since you are being so loose with your scenario while trying (unsuccessfully) to nitpick mine: No, your scenario and math are not more rigorous and complete than mine.

However, regardless of all your griping about my measurement of energy/photons received, you instead pulled a number straight out of the air, with no basis in anything. Is it accurate? I don't know and neither do you.

Worse or just more ironic, depending on your point of view, despite your pretense that you don't understand how I got the 1,000 total brightness value, you nevertheless used it correctly (if not quite precisely) when you did your calculation/simulation. You are only pretending not to understand, when it is convenient for you.

And even more worse, despite starting with a photon count, you made no connection between it and your simulated images. For all your irrelevant criticism of me doing the calculation backwards, you went one step worse and skipped the calculation altogether...thus, of course, proving all of your complaining about my initial refusal to calculate photons and watts irrelevant. You proved, mathematically, that you are trolling: You know all that math I did was unnecessary, you just wanted something to complain about, even though you knew it was irrelevant.

"At best" = you are guessing. All of the pictures you created are pictures of individual shells, based on math only done for individual shells. You haven't added the shells together yet to see what the brightness adds up to for the actual image taken by the camera. Do the math:

Each shell sends 100,000 photons to the detector. So how many photons do 1,000 shells send to the detector? 5,000 shells? 20,000 shells?

This is simple math. Until you do it, you aren't finished with your simulation.

 

That will do just fine. So how much of radiative flux there is in Olbers' paradox universe? Can you get that number from the equations used for the original solution of the paradox?

You say the darndest things. That only works in the real world, after you take an actual photo. In a hypothetical world you do not know how the image looks like if you first don't know how bright is the sky. [rolls eyes] You can not actually take a photo in a hypothetical universe, you know? If you want it, you first need to make it. And you can only make it if you first know how much energy is coming from the sky per unit time per unit area. Stars first, image second, always remember.

 

Of course you can; That's what I did, for your version of the paradox. All you have to do to get the original version is to repeat my calculations, but with Olbers' starting assumptions.

The process works the same, forward or backwards, in the real world or the hypothetical. You can start with the sky and telescope and calculate what the image looks like or you can start with the image and calculate what the sky looked like. You are asking for the former, but you provided the latter. That choice is fine, but it isn't the one you want, which is your fault because you made the choice when you provided the starting information (the picture).

That is precisely what you did when you provided said photo. Again, you are arguing against your own scenario here. In either case, none of this is really relevant - it doesn't have anything to do with the calculations either you or I did, both of which are fine, except that yours are not finished.

Worse, you are still doing it. Mere hours ago you posted an image that you made from scratch, with no calculation of how it should look! Now you're criticising me for something you also did (but not as thoroughly as I did it).