Illustrating Olbers' paradox

The amount of light received depends on your arbitrary decision about some "precision"? Precision of what exactly? And it also depends on "how far we want to take this to resolve"? What does that mean, what in the world is that?

You're mumbling. You are out of your comfort zone where you actually need to think for yourself instead of repeating what you've been told. You have nothing to say, you have no clue what are you talking about, and what little you say is just vague and ambiguous gibberish. Disappointing.

What was the total amount of energy received, what equation did you use? How did you get 2000 shells, what equation did you use? How did you get brightness value, what equation did you use?


It is not my hypothetical detector, in your calculations it is yours. My hypothetical detector is the same as in the real world, unlike yours. To calculate brightness with my detector properties like exposure time and film speed must be defined, just like in the real world. Your detector is a phantasy, came from some dream world where the time stands still and everything is happening in a single instant. Wake up!

 

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Since what you quoted is clearly the opening sentence of a paragraph that answers the question, your failure to quote much less show you have understood the rest of the paragraph implies to me that you haven't even read it. So try again: read what I wrote and if you still don't understand, respond, specifically, to the explanations given in that paragraph and I'll explain in more detail.

I present math and you present insults. I doubt anyone else who sees this is really all that confused about who stands where here.

Oy, really? I gave you the numbers 0.16 and 1000 and said that when you use them you get 160 and you can't figure out what equation I used to do that? REALLY???! This has got to be one of the more spectacular displays of of math ignorance I've ever seen. But ok, I'll play along:

b = a*y

y = number of shells
b = "pixel color-brightness" of the sum of "y" shells
a = .....already defined. Go back and look at the last page if you forgot already.

Again: you provided the simulated images here, not me. If you want to do something with the exposure time and film speed, feel free: since it is your simulation, you get to define them and you can use them however you want. But they play no role in my analysis.

Also, need I remind you that you have already made claims about brightness - at least quantitative - so you are contradicting yourself to say you can't calculate anything to do with brightness without that information. You've already done brightness analysis without it -- you just haven't done it with math, even though you could (as I've shown).

In any case, I've now shown you everything required to build the next few thousand shells, so there's no more analysis required to explain the images. So I'll post them for you shortly.

 

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[Note: Please read and think about the whole post before replying to any of it to make sure you don't ask questions that are answered later, as you often do...]

Ok, at this point I think you've agreed to all the pieces of the logic individually, so now we can assemble them into the whole picture.

I've created the third and fourth shells by modifying the second shell you provided. For the third shell, I made 3 copies of the second shell, rotated 90 degrees from each other, flattened (combined) them, then reduced their luminance by 1/4:

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For the fourth shell, I made 3 copies of the 3rd shell and shifted them a few pixels from each other, flattened (combined) them, then reduced their brightness by 1/4:

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Some stats, FYI:
-Each star in the first shell has a peak "pixel color-brightness" value of 160.
-Each star in the second shell has a peak "pixel color-brightness" value of 40.
-Each star in the third shell has a peak "pixel color-brightness" value of 10.
-Each star in the fourth shell has a peak "pixel color-brightness" value of 3.

In your flat pictures, the pixels in the "white" square have "pixel color-brightness" values of 191 and the pixels in the "grey" square have "pixel color-brightness" values of 47.

At this point, the stars in the individual shells are already too dim to see, but as you have agreed, they all still contain/capture the same amount of light. Now we start combining the shells (the thing you've inexplicably/inexcusably chosen not to do).

Here's the first four shells stuck together:

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Now, while you have agreed that each shell adds the same amount of light to the picture, clearly after three shells, adding the fourth makes no difference in our perception of the result. So that's it, then; the rest add nothing and the paradox is broken, right?

Wrong.

Since the stars are randomly distributed, at some point, the shells contain more stars than pixels and will appear to our eyes and camera as uniformly "bright". That point is with about the 7th shell. I say "about" because what we would first "see" on the 5th and 6th shells is grainy grey, like the static on a poor TV reception, but darker. But each shell would contain more stars than the last and thus be closer to a smooth distribution. Further, since the individual shells are too dim to see anyway, the difference from completely smooth is only apparent on those first three anyway. Thus:

After four shells, all shells can be modeled as uniformly "bright", with no noticeable error.

So, here's what each successive shell looks like, from 5 - infinity (if we can go that far):

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Looks black, doesn't it? Well as it turns out, in our 0-255 level representation, it is, exactly black. Why? Because as I said before, 0.16 is the "average pixel color-brightness" value of each shell and 0.16 rounds to zero when you only have whole numbers available. But while we can't see it on this single shell (just like in real life, we can't see individual stars that are below a certain threshold), if you pile enough onto each pixel, they become visible.

So here's what the first four shells, plus 100 more look like:

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Still pretty much a black background? ("average pixel color-brightness" value of the next 100 shells: 16)

How about the next 1000? ("average pixel color-brightness" value of the next 1000 shells: 160)

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Surely, you must see it now, right? So where does it end? Even with your nearly nonexistent math skills, I'm sure you can calculate how many shells we would need to add together to exceed the "average pixel color-brightness" value of your "white" square? Or how many shells it would take to saturate the image completely? So where does it end? What does Olbers' universe look like with this simulation?

The math/simulations I've presented would imply that an infinite number of shells would be infinitely bright. But Olbers' paradox predicts that after a while, stars will start blocking each other, limiting the maximum brightness to be that of the surface of the sun. I haven't taken that into account: I've shown this linear, but what you'd actually get only starts off linear, then after a while asymptotically flattens and approaches the surface brightness of the sun, as btr's analysis models. But here's the beautiful thing about this thread/simulation: Your pulled-out-of-thin-air belief is so wrong, it doesn't matter! What you've presented for modeling is a simulation of the night sky, along with the claim that we'd never even exceed the "apparent" (by your made-up measure) brightness of the stars in the first shell! But that brightness is orders of magnitude dimmer than the sun's surface brightness and therefore orders of magnitude below the point where star overlap starts to matter!

So there you have it: even by your made-up, qualitative picking of "brightness", a 1,000 shell Olbers' universe is "brighter" than you thought it could be, by a wide margin.

Questions/comments? Understand yet?

 

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Average brightness per shell: (10*255)/(250*250) = 0.041
Average brightness after 2,000 shells: 2000*0.041 = 82

number of shells = what?

 

Where did the "10" come from?

The actual number of shells is infinite. But the number of shells required to saturate your hypothetical detector is much lower and should be easy for you to calculate from the information/equations I provided. Give it a try. Show us you have, at least, 7th grade math skill.

 

Would it be possible for you to numerically express total amount of energy received? What equation would you use?

If you want to know the truth you need to use the same tools and methods you would use in the real world.

 

First shell has 10 stars, each 255 bits bright.

You know the number of shells required to overexpose the image. But to answer the question you need to know the number of shells actually captured by the camera. Do you know?

 

Yes, the math is pretty simple and builds on the analysis I've done so far. So are you saying you are ready for the next step? Are you acknowledging that your original thesis - your original understanding of Olbers' paradox - was wrong and you accept my analysis?

 

So then where did you get the 255? That isn't what your picture shows. Are you starting to define a new scenario?

The number of actual shells is infinite. Based on the laws of probability, the camera captures light from all of them. But I don't think you recognize that that is a wrong question.

 

I do not accept. You can not calculate total energy received because you do not have any time interval defined.

Do you really think your sensor would work in the real world?

I suppose you are referring to blur. It doesn't matter.

Does your camera have exposure time setting like real world cameras? What number was exposure time set on when you took the photo?

 

What you are demanding that I prove is not part of your original claim. Separate questions get separate answers. Have you forgotten your original claim?

Again: your sensor. But yes, I see nothing wrong with your sensor, based on the limited information you have provided on it.

I have no idea what "blur" means in this conyext: I meant exactly what I asked. Please answer my questions.

All cameras have exposure settings, but you took the picture, not me, so you will have to tell me....but again, this is separate from your original claim.

 

I'm asking you to calculate total energy received so you can understand that you can not do it, in hope you will come to your senses. You are fooling no one but yourself by avoiding questions. If you want to see the truth, you really have to open your eyes first.

1/1000 of a second exposure time, f/256 aperture size, and ISO-100 film speed. From now on that's my official sensor. What's yours?

I guess "motion-blur" is puzzling word for you then. However you got more brightness from the 1st shell is fine with me. I said it doesn't matter.

I didn't take it, I only started taking it. The exposure time has not run out yet in my picture, there was 0.1 seconds left when you took over. There you have it, what will average pixel brightness be now?

 

So that's a yes; Yes, you forgot what we were talking about/what you originally claimed. Let me refresh your memory:

You are a pretty poor writer and phrased that both as a question and statement at the same time, so I'll reword it into a proper thesis statement:

If we continue to draw other shells, the stars in every subsequent shell are only going to get dimmer and dimmer, so this procedure will not produce a uniformly bright (white) image.

That's your thesis. Recognize it? Now:
1. You've acknowledged that every shell contains the same amount of light.
2. You've properly (if vaguely) described the procedure to draw the images of the shells (I've just provided rigor and done the actual work.).
3. You've acknowledged that the shells get added together, so the sum of the first two shells captures twice as much light as one shell alone (etc.).

So your error is only in actually doing the assembly of the pictures to produce the uniformly bright white image that you say won't happen. I've now done it, you've seen it, you haven't pointed out any flaws in any of the analysis (only suggested additional analysis of new and unrelated issues). So at this point, we really should be on the same page that your orignal claim was false. You've acknowledged all of the pieces and methods, but are now simply refusing to acknowledge the result, despite not seeing any flaws in the analysis.

I can do it, but as you can see, I already produced the resulting images without it. So clearly, it wasn't required. Again: basically where we're at is that you're claiming something like that I've never been to Washington DC and refuse to drop the claim despite me showing you a picture of me next to the Washington Monumument. At this point, you are simply looking reality in the face and refusing to accept it. And you're focusing on the road traffic on the route to DC as if it has any bearing on the result you've already seen.

I haven't avoided a single question. Indeed, several times I said you weren't ready for the answer yet because you hadn't gone through all the steps to reach it, but in each case I eventually led you there. And I will again. But you must go through the steps. What you are doing is avoiding answers by asking new questions without first accepting the answers that you got.

Note also: Olbers' paradox has been around for a while and is what it is. This thread is about your claim that his logic should lead to a different result. The entire burden of proof here is on you, so you aren't entitled to ask questions: you are responsible for providing the full analysis to prove your claim. Instead, *I've* done all the analysis that you should have done. You can ignore my result as you've ignored his, ignore your responsibility, ignore whatever you want, but that path doesn't lead to you proving your claim or learning anything.

[sigh] At this point, you are producing purposely nonsensical and contradictory constraints in order to sabbotage your own model. I'm not sure I've ever seen anything quite like it. It is like self-delusion, but it is conscious: you are consciously sabbotaging your own path to learning with this trolling. To keep with the Washington DC analogy, it's like you've slashed the tires on your own car to prove I can't go to Washington DC even though I've already been there and didn't even take your car anyway!

[sigh] I know what motion blur is, but I didn't bring it up, you did, so the relevance is something for you to explain, not me. Have you lost track of that already? The questions I asked were:
-Where did you get the 255?
-Are you starting to define a new scenario?

These should not be difficult questions for you to answer and you seem to be losing track of your thought processes. I'm really starting to have doubts about your comprehension capabilities here. Trolling or not, understanding Olbers' paradox may simply be beyond your ability.

The first two sentences there are gibberish, but it doesn't matter because the answer to the third sentence is that because exposure time isn't part of the analysis, nothing has changed in the result: 0.16 per pixel per shell.

 

Calculating an 'average' perhaps made you believe your image is uniformly bright, but really it is not. You also need to discount all the photons that hit pixels already at 255 bits brightness.

You never explained how did you come up with 2000 shells, huh? Wrong number, pal, you should have stopped at 14.

First shell has 10 stars, each 255 bits bright. That's how I originally made the image and told you should too make your stars one pixels size.

 

humbleteleskop, first of all I must apologise for not replying sooner. Sorry about that.

Carrying on from where we left off:

Suffice it to say that your answers to my questions, which you can review by following the links in the quote tags, were incorrect (I asked for the number of photons in each case, to within 5%, and asked you to show your working).

I was curious. My questions were designed to gauge how much of an understanding you have of the physics being discussed. Someone with a basic knowledge of 3D Euclidean geometry, geometric optics and the very basics of quantum mechanics (i.e. enough to know what E = hf means) would have been able to answer those questions with relative ease. Someone without such an understanding probably doesn't yet know enough physics to follow the argument behind Olber's paradox.

I'm sorry that I misjudged the level of your prior knowledge; I guess my posts to you may as well have been in Sanskrit or Sindarin. On the other hand, acquiring the necessary education is not at all difficult, so this is something you can easily remedy if you so wish. I wish you good luck, whatever you choose to do.

 

You misunderstood...which is kind of odd, because while you quoted the word 'average' inline with your resopnse, the word doesn't appear in the actual quote you got from me...

The first few shells are, quite obviously, not uniformly bright. You can actually see the individual stars and black spots. But as you can see in the simulations I generated, as you get to the higher and higher level shells, they get close and closer to being uniformly bright. And since our detector is only 250x250 pixels and the number of stars is orders of magnitude itself, the picture (if not quite the reality) is, exactly, uniformly bright for the later shells and combinations of shells.

I did explain this in detail in post #143, so please go back and [re]read it so you can understand why this is true.

They aren't bits, but in any case, none of the pixels are at 255 luminance value in any of the simulated images. So your objection is moot (you are objecting to something that doesn't exist).

Perhaps it was round-about, but it really should have been obvious: I picked easy-to-calculate orders of magnitude and intervals for, essentially, a guess-and-check exercise. I'm not claiming that Olbers' paradox includes only 2000 shells -- indeed, I exlpicitly stated that it includes an infinite number of shells. But Humbleteleskop's Paradox only contains two shells, so all I needed to do was show enough shells to clearly demonstrate how Olbers' Paradox differs from Humbleteleskop's.

Are you going to explain why you believe that? Again: this thread is all about your claims and you have a responsibility to explain and prove them. I should not have to ask every time you pull out a new nonsense claim.

Huh? What are you talking about? Can you repost the image you are describing? I haven't seen it: the image you've posted a dozen times in two threads contains stars that are circular blobs of a dozen pixels, non-uniform in brightness, and with maximum values that are not 255. What are you trying to pull?

 

With your line of sight, that is your field of view, your perspective is unsurprisingly narrow. Don't blame me for your own inability to understand.

 

Loss of detail due to overexposure is unsurprising. You do not know if that would happen, you do not know how uniform it is. Without knowing pixel sensitivity and exposure time you can not know ANYTHING about what will happen to image brightness.

The exposure time ran out. Do you understand the number of visible shells would depend on exposure time and film speed?

I said it doesn't matter. I am not disputing your average pixel brightness per shell. I am telling you it is completely meaningless without defined exposure time and pixel sensitivity.

 

Your ignorance is a serious problem -- and I don't mean the fact that you are ignorant, I mean the fact that you are fighting to hide it (not that you really could, with your failure to demonstrate even the most basic of math skills) and fighting to remain ignorant.

As I explained recently in another thread, ignorance itself is neither a weakness or a virtue, but the default starting point for all of us. What we do with our ignorance is part of what defines our character. Openly admitting - even embracing - your ignorance is a virtue. Fighting to hide it and maintain it is a severe fault. It is sad to see.

 

The simulated images you provided to me are not saturated and the simulated images I generated from them are not saturated. And if they become saturated, that only proves you wrong since your entire claim is the image brightness never goes up. So I have no idea what you are trying to pull here - you seem to be arguing against yourself. .

Again, I've demonstrated what happens and I didn't need it. If my analysis is flawed, show me where and/or show me your analysis. At this point, you are simply looking reality in the face and saying no.

What exposure time? Clearly, you are just guessing: you didn't calculate that 14 shells (you didn't even specify an exposure time!), you simply pulled it out of thin air.

The camera is not imaging and constructing the different shells separately, it is only registering all the light that hits it at once, regardless of which shell the light comes from. It only knows the total light it receives, not which shell it came from. So no, the number of visible shells is not 14. I'd ask you how you calculated it, but we both know you just pulled it out of thin air.

Jeez. You started the line of discussion you are now dodging. I suppose you posted:
"Average brightness per shell: (10*255)/(250*250) = 0.041"

...in response to my statement of incredulity that you couldn't figure out how I did my a simple math problem when all the numbers were sitting next to each other and you just had to figure out how they fit into an equation, but I didn't ask for and didn't need it. I suppose you took a shot in the dark and missed and now are trying to cover-up your error with trolling/dodging. Whatever - I can let it go because it never mattered to begin with. It's pathetic, but not new.