An example of the failure of Plasma Cosmology

[Hans Blaster]

Olbers’ paradox was based on astronomy of the early 19th century and didn’t take into account stars having a finite age and the Milky Way was not the universe.
Ironically the infinite age of a static universe takes care of Olbers’ paradox but by substituting one problem for another; instead of the sky being bright at night, the universe is in a cold dark state devoid of stars.

If PC was to explain how stars are recycled over an infinite time span despite the increase in entropy then Olbers’ paradox does becomes relevant with the night sky being bright due to the light of galaxies and not individual stars.
Peratt’s comments about the stars (=galaxies) not being uniformly distributed is contradicted by galaxy surveys which show at scales beyond 100 Mpc the universe does become homogeneous and isotropic.

In an expanding cosmology Olbers' paradox is not relevant due to an event horizon.
Galaxies on the Hubble sphere Dₕ have recessional velocities dDₕ/dt = c and any galaxy within the Hubble radius is observable.
A galaxy with a recession velocity v > c emitting photons back towards the observer, has a relative recession velocity of v – c in the observer’s frame.
(Note the SR Lorentz transformations don’t apply since v is not in the interval 0 ≤ v < c).
The surface of Dₕ becomes an event horizon with a radius where dDₕ/dt = c.
The Hubble sphere is receding (since expansion is accelerating) and photons will not reach the observer if dDₕ/dt = c < v - c, or in other words the galaxy is outside the Hubble sphere.

So...

I was checking the latest activity over on the EU minions board and found an active thread about Olber's paradox. The most shocking thing was a reference to a "paper" (just a document, not published anywhere) by one of the newer "scientists" at EU central, electrical engineer Don Scott:
https://www.electric-cosmos.org/Olber.pdf

After getting the basic scenario and math of the classical Olber's paradox correct on the first page, Scott then proceeds to argue that the sum (in an infinite Universe, no less) should be terminated at a few hundred light years because (get this) *the eye can't see individual stars*. (Oh boy, this is bad!) As if we needed to see every individual star for it to light up the retina or a CCD. (He also makes some sort of argument about photographic plates or CCDs being able to see fainter because the exposure time can be extended in ways the eye cannot. I'm not sure what his point is here.) Perhaps the dumbest part of this "can't be seen by the eye" argument is that he actually mentions far more distant object visible to the naked eye like M31 (Andromeda galaxy) noting that is made of many stars. THAT'S THE POINT DON! Many stars can add up to make a discernible signal in the eye, or a CCD, and there is no "cut-off" to the integration in Olber's paradox so long as the horizon is infinitely far away and there is no "edge" to the distribution of stars/galaxies. Oy vey!

 

[sjastro]

To add to Hans Blaster’s comments;

Scott could not have picked a worse possible example in using the Andromeda galaxy M31.
Its visual magnitude of 4 as he admits is based on a point source for a single star.
Even the ancients knew M31 was not a point source but was catalogued as a “cloudy star”.
Since M31 has angular dimensions that are barely discernible to the naked eye, the surface brightness is the realistic description not the visual magnitude.
M31 has a surface brightness approximately 16 magnitude/arcsec².

I prefer to use the LMC (Large Magellanic Cloud) which is a satellite galaxy of the Milky Way as an example to refute Scott’s nonsense.
It is easily visible to the naked eye to southern hemisphere observers under rural skies and is 158,000 light years distance.
According to Scott it should be invisible as each individual star in the LMC cannot be observed beyond 600+ light years!!
The galaxy is visible as the naked eye cannot resolve the LMC into individual stars; we observe the integrated brightness of “overlapping photons” spread out over the angular dimension of the galaxy which is simply the surface brightness

 

[RealityCheck01]

And what about Milky Way groups of stars visible with the naked eye?
Double Cluster

The Double Cluster (also known as Caldwell 14) consists of the open clusters NGC 869 and NGC 884 (often designated h Persei and χ Persei, respectively), which are close together in the constellation Perseus. Both visible with the naked eye, NGC 869 and NGC 884 lie at a distance of 7,500 light years.[1]

 

[sjastro]

And what about Milky Way groups of stars visible with the naked eye?
Double Cluster

We have a few other naked eye candidates in the southern hemisphere which fail Scott's logic such as the Small Magellanic Cloud at 201,000 light years or the globular cluster Omega Centauri at 15,800 light years.

 

[sjastro]

The self professed polymath genius at EU central still doesn’t get it about Olbers’ paradox and continues to rely on personal insults to make a point.
Olbers’ paradox was known to Kepler and Halley before Olber and along with others such as Kelvin and Poe never found the “obvious” flaws the self professed polymath genius and Scott claim whose versions incidentally contradict each other!!
What Kepler et al knew along with any preschooler which apparently the self professed polymath genius and Scott do not is the angular separation of objects such goalposts, trees and stationary people decreases with increasing distance from the observer.
In the geometrically flat infinite static universe the same principle applies to stars and galaxies.

So while the self professed polymath genius and Scott should consult a preschooler to resolve this dilemma, for the rest here is the mathematical and scientific description.
It can be shown the distance r can have a finite value before all stars (or galaxies) have a zero angular separation in a static universe by summing the shells up to this value.
Before discussing this here are some preliminaries.
The absolute luminosity L of a star is defined as the amount of energy radiated by a star per unit time and the surface brightness B is the luminosity per unit surface.
The apparent luminosity l of a star at a distance r of absolute luminosity L is l = L/4πr² which is the inverse square law.
Suppose the number of stars with luminosity L is N and their average number density in a sphere of radius r is n = N/V where V is the volume.
If the surface area of an average star is A then its brightness B = L/A.

The number of stars in the shell of radius r and thickness dr is 4πr²ndr.
The total radiation observed in an infinitely large static universe is found by integrating the spherical shells from 0 to ∞.

In fact you don’t need an infinite number of shells and stars to show the night sky becomes bright.
Despite being point sources, stars subtend a solid angle Ω = A/r² steradians.
At a certain radius R each individual star will have zero angular separation from any other star and the solid angle Ω = 4π steradians covers the entire sky.
Under this condition;

Solving for R gives R = 1/An.
The integrated brightness from these stars alone are therefore;

In Olbers’ time B = L/A was considered to be the brightness of the Sun which the night sky would attain.

 

[Hans Blaster]

The self professed polymath genius at EU central still doesn’t get it about Olbers’ paradox and continues to rely on personal insults to make a point.

I noticed this as well, and was planing to write a little about surface brightness for the good of any of our readers over here on CF. (And anyone that might see our thread through the links from EU central, after all that's how *I* found CF several years ago.) Sigh.

 

[sjastro]

I noticed this as well, and was planing to write a little about surface brightness for the good of any of our readers over here on CF. (And anyone that might see our thread through the links from EU central, after all that's how *I* found CF several years ago.) Sigh.

Consider it a badge of honour you are now a big enough threat at EU central to be subject to personal abuse.
You now belong to a select group of CF members which include RealityCheck01, Selfsim and myself.
By all means write up an article on surface brightness, not only for the educational value here but for the more moderate members at EU central viewing this thread.

 

[Hans Blaster]

The galaxy is visible as the naked eye cannot resolve the LMC into individual stars; we observe the integrated brightness of “overlapping photons” spread out over the angular dimension of the galaxy which is simply the surface brightness

OK, let's talk about surface brightness. The Large Magellanic Cloud, LMC, is a satellite galaxy of the Milky Way located 50 kpc away and visible from the southern hemisphere. It covers an area about 10x10 degrees or 100 square degrees. (A square degree is a unit of solid angle like the steradians used in sjastro's post above. The full sky is about 41,000 sq.deg.)

A thought experiment...

We've built a telescope on the Atacama desert and masked out everything that isn't the LMC. Our detector is counting 10,000 photons per second from the LMC.

The surface brightness is just the number of photons (or the total energy of the light) arriving per unit of solid angle.* In our idealized case, the surface brightness (10,000 photons/sec)/(100 sq.deg.) = 100 photons/sec/sq.deg. Not too hard.

If we could move our idealized LMC to twice it the distance (i.e., to 100 kpc) the total photon count in our telescope would fall as given by the inverse square law (1/r^2) by a factor of 4 to one quarter of the original detected count: 2,500 photons/sec. Now because it is twice as far away it covers less of the sky. It is only now 5x5 degrees and has an area of 25 sq.deg. The surface brightness is now: (2,500 photons/sec)/(25 sq.deg.) = 100 photons/sec/sq.deg. (Wait is that the same value????)

Now let's move our idealized LMC to 10 times the original distance (500 kpc). The total photon count goes down by (1/10)^2, a factor of 100 to 100 photons/sec at our telescope. This version of the LMC looks smaller on the sky, one-tenth the size on each side and now only 1x1 degree (1 sq.deg.). What about surface brightness of this version: (100 photons/sec)/(1 sq.deg.) = 100 photons/sec/sq.deg.

Three versions of the same galaxy. Three different sizes and total observed luminosities, but for all three the surface brightness is the same. This is because surface brightness is invariant with distance.

But isn't made of stars, how does that work? Do star's have surface brightness? (Yes.)

Let's imagine our simplified LMC as consisting of 10,000,000 identical stars. (It's a small galaxy.) If the whole LMC shines 10,000 photons/sec and all of these stars are the same, then each one will have a measured luminosity at our telescope of 0.001 photons/sec. This just means that from each star a photon will be detected at the telescope every 1000 seconds. (on average). The 10,000 photons that arrive will come from 10,000 (random) stars within the LMC. Even though it would be hard to detect any *individual* star with this setup (given only one photon every 1000 seconds on average, the exposure to detect a star would be reeaaaaallllyy long) we can still detect the diffuse light from the over collection of stars.

What is the surface brightness of these stars? Well, if we move one of our stars close enough to have an area of 1 sq.deg it would be about 1 AU away (the distance to the Sun from the Earth; the Sun has a diameter of 1/2 degree so it is a little smaller than 1 sq.deg. on the sky.) The LMC is about 10,000,000,000 AU away so these stars would be (10,000,000,000)^2 time more luminous than the 0.001 photons/sec over a square degree. The surface brightness of the individual stars is then 100,000,000,000,000,000 photons/sec/sq.deg. (1e17 photons/sec/sq.deg.). This too, is of course invariant. The solid angle of the star at the LMC distance is the very tiny 1e-20 sq.deg. (i.e., with a diameter of about 1e-10 degree, about 300,000 times smaller than the resolving capability of the telescope with the sharpest view.) Collectively only a very tiny fraction of the area of the galaxy. If we could resolve the stars we would see this galaxy as mostly dark with tiny specs of stars.

How this impacts Olbers' paradox

Though unresolved in our telescopes (and only a few stars in our own neighborhood have been resolved) the surface brightness of the distant stars are the same as for our own Sun, they only seem dim because they cover only a very tiny area. If there we could see out into an infinite universe with a uniform density of stars (or density of galaxies made of stars), then each shell of stars (or galaxies) will have the same, but small, area of the sky covered with stars at that same surface brightness. An infinite series of shells will eventually result in the tiny area in each shell adding up to the whole sky at the same surface brightness as a star.


*It is also given per unit of area at the Earth, but for simplicity we'll just use our telescope as the "unit of area".

 

[Hans Blaster]

Consider it a badge of honour you are now a big enough threat at EU central to be subject to personal abuse.
You now belong to a select group of CF members which include RealityCheck01, Selfsim and myself.

I'm disappointed they took so long. Maybe I wasn't hitting them hard enough.

 

[RealityCheck01]

The self professed polymath genius at EU central still doesn’t get it about Olbers’ paradox and continues to rely on personal insults to make a point.
Olbers’ paradox was known to Kepler and Halley before Olber and along with others such as Kelvin and Poe never found the “obvious” flaws the self professed polymath genius and Scott claim whose versions incidentally contradict each other!!

That brings up a couple of more points about Scott's "solution" to Olbers’ paradox.
The classical paradox is not only about naked eyes. Kepler, etc. had telescopes. The paradox applies to all astronomical observations. Look at the night sky or point a telescope at night sky and it should be uniformly bright. Scott has a strawman argument about naked eyes.
The modern paradox includes modern telescopes such as the Hubble Space Telescope that can see galaxies billions of light-years away. That destroys Scott's "solution".

 

[Hans Blaster]

Perhaps I should add one more thing about surface brightness and unresolved objects...

Eventually, if you place an object too far away it will have too small an angular extent to separate it from other objects and they will blend together. The tiny pixels of your computer screen are unnoticeable because your eye can't resolve them at normal viewing distances. Neighboring pixels blend together to form a smooth image feature. The same is true with the photographic plates of the past and CCDs of the present used to image astronomical objects through telescopes.

An isolated object (one that is not confused with another) will eventually, if moved far away, have too small a solid angle for the invariant surface brightness to deliver enough light to the detector to remain above the detection threshold of the detector, whether the rods and cones in the eye or the pixels of a CCD. Once an object appears to small to resolve (and this is the case for *every* star in the sky for the eye, except the Sun and virtually every star in the sky even for a CCD attached to a telescope) the surface brightness is impossible to determine from that image alone.

 

[sjastro]

OK, let's talk about surface brightness. The Large Magellanic Cloud, LMC, is a satellite galaxy of the Milky Way located 50 kpc away and visible from the southern hemisphere. It covers an area about 10x10 degrees or 100 square degrees. (A square degree is a unit of solid angle like the steradians used in sjastro's post above. The full sky is about 41,000 sq.deg.)

A thought experiment...

We've built a telescope on the Atacama desert and masked out everything that isn't the LMC. Our detector is counting 10,000 photons per second from the LMC.

The surface brightness is just the number of photons (or the total energy of the light) arriving per unit of solid angle.* In our idealized case, the surface brightness (10,000 photons/sec)/(100 sq.deg.) = 100 photons/sec/sq.deg. Not too hard.

If we could move our idealized LMC to twice it the distance (i.e., to 100 kpc) the total photon count in our telescope would fall as given by the inverse square law (1/r^2) by a factor of 4 to one quarter of the original detected count: 2,500 photons/sec. Now because it is twice as far away it covers less of the sky. It is only now 5x5 degrees and has an area of 25 sq.deg. The surface brightness is now: (2,500 photons/sec)/(25 sq.deg.) = 100 photons/sec/sq.deg. (Wait is that the same value????)

Now let's move our idealized LMC to 10 times the original distance (500 kpc). The total photon count goes down by (1/10)^2, a factor of 100 to 100 photons/sec at our telescope. This version of the LMC looks smaller on the sky, one-tenth the size on each side and now only 1x1 degree (1 sq.deg.). What about surface brightness of this version: (100 photons/sec)/(1 sq.deg.) = 100 photons/sec/sq.deg.

Three versions of the same galaxy. Three different sizes and total observed luminosities, but for all three the surface brightness is the same. This is because surface brightness is invariant with distance.

But isn't made of stars, how does that work? Do star's have surface brightness? (Yes.)

Let's imagine our simplified LMC as consisting of 10,000,000 identical stars. (It's a small galaxy.) If the whole LMC shines 10,000 photons/sec and all of these stars are the same, then each one will have a measured luminosity at our telescope of 0.001 photons/sec. This just means that from each star a photon will be detected at the telescope every 1000 seconds. (on average). The 10,000 photons that arrive will come from 10,000 (random) stars within the LMC. Even though it would be hard to detect any *individual* star with this setup (given only one photon every 1000 seconds on average, the exposure to detect a star would be reeaaaaallllyy long) we can still detect the diffuse light from the over collection of stars.

What is the surface brightness of these stars? Well, if we move one of our stars close enough to have an area of 1 sq.deg it would be about 1 AU away (the distance to the Sun from the Earth; the Sun has a diameter of 1/2 degree so it is a little smaller than 1 sq.deg. on the sky.) The LMC is about 10,000,000,000 AU away so these stars would be (10,000,000,000)^2 time more luminous than the 0.001 photons/sec over a square degree. The surface brightness of the individual stars is then 100,000,000,000,000,000 photons/sec/sq.deg. (1e17 photons/sec/sq.deg.). This too, is of course invariant. The solid angle of the star at the LMC distance is the very tiny 1e-20 sq.deg. (i.e., with a diameter of about 1e-10 degree, about 300,000 times smaller than the resolving capability of the telescope with the sharpest view.) Collectively only a very tiny fraction of the area of the galaxy. If we could resolve the stars we would see this galaxy as mostly dark with tiny specs of stars.

How this impacts Olbers' paradox

Though unresolved in our telescopes (and only a few stars in our own neighborhood have been resolved) the surface brightness of the distant stars are the same as for our own Sun, they only seem dim because they cover only a very tiny area. If there we could see out into an infinite universe with a uniform density of stars (or density of galaxies made of stars), then each shell of stars (or galaxies) will have the same, but small, area of the sky covered with stars at that same surface brightness. An infinite series of shells will eventually result in the tiny area in each shell adding up to the whole sky at the same surface brightness as a star.


*It is also given per unit of area at the Earth, but for simplicity we'll just use our telescope as the "unit of area".

Thanks for the write up.
The feedback from EU central is Ostiches one and all......

 

[sjastro]

The self professed polymath genius/spokeperson is in fine form referring to my post#85 as “boneheaded maths”.
Instead of explicitly refuting the equations he sends his readers off on a wild goose chase to a thread in this forum and expects the readers to wade through the thread to reach the same conclusion.
What it clearly shows the individual doesn’t comprehend the maths at all and is hoping the audience at EU central is either mathematically illiterate or just plain stupid to fall for his deception.

What is so absurdly ridiculous is how this individual thinks the radius of the first shell in Olbers’ paradox has to be set at 1AU; why because the Sun is 1AU from Earth!!!
He doesn’t seem to comprehend Olbers’ paradox is about the night sky and an object in the shell is also a nighttime object.
The preschooler mentioned in post#85 should inform him the sun is not a nighttime object.
Furthermore his take on Olbers’ paradox completely contradicts Scott’s ideas in the process which is rather comical as he initially set out to defend Scott.

Olbers’ paradox can either be treated as a sphere of radius r surrounded by infinitesimally thin shells like layers around an onion as in post#85 in which case integral calculus is used to sum the shells, or as discrete concentric thicker shells around a sphere at regular distance intervals.
In both cases the radius r of the closest shell is an arbitrary value and set at cosmological scales to not only reflect the Universe is considerably larger than 1AU but is also homogenous at this scale.

 

[Hans Blaster]

What is so absurdly ridiculous is how this individual thinks the radius of the first shell in Olbers’ paradox has to be set at 1AU; why because the Sun is 1AU from Earth!!!

I mean, the whole concept behind Olbers' paradox is built around the notion that the *density* of stars is uniform. The density of randomly placed discrete objects is not well defined for volumes with only 1 object in it. Any such calculation has be "smooth" in its distribution of those discrete objects. For stars in the local portion of the Galaxy, that kind of smoothness in the density of stars will require minimum volumes at least 5-10 pc in diameter with the stellar density in "stars/cubic pc". Starting the integration a few parsecs away and using the measured density (or frankly *any* finite density as the integral is *infinite*) will result in full coverage of the sky with stars. Sigh.

If this is an act (the 1 AU initial volume) it's a persistent one, but I suspect it real. Sad. We've tried to inform, but you can't make 'em learn.

 

[Hans Blaster]

Olbers’ paradox can either be treated as a sphere of radius r surrounded by infinitesimally thin shells like layers around an onion as in post#85 in which case integral calculus is used to sum the shells, or as discrete concentric thicker shells around a sphere at regular distance intervals.
In both cases the radius r of the closest shell is an arbitrary value and set at cosmological scales to not only reflect the Universe is considerably larger than 1AU but is also homogenous at this scale.

Argh! I just realized my last post said the same thing. I should have read your full post.

 

[sjastro]

If this is an act (the 1 AU initial volume) it's a persistent one, but I suspect it real. Sad. We've tried to inform, but you can't make 'em learn.

He continues to double down on this nonsense.
I hope he apologies to Scott for throwing him under the bus after trying to defend him.
Maybe the the crowd at EU central will learn not to trust this character.

 

[sjastro]

Olbers’ paradox is not refuted by the nonsensical claim surface brightness follows the inverse square law.
This is shown by observation.

Since a star or galaxy subtends a solid angle πR²/r² where πR² is the surface area at a distance r from the observer, the SB (surface brightness) can be expressed as;

SB = (L/rₗ²)(πR²/r²)

where L is the absolute luminosity, rₗ is the luminosity distance and is a good approximation to the measured distance r (rₗ ≈ r) in Euclidean space where r is not too large.
In an expanding cosmology rₗ² = (1+z)²r₀² and R² = r₀²/(1+z)² where (1+z) is the expansion factor, r₀ is the distance in the rest frame.
Combining these into the above equation, the SB is of the form;

SB ~ (1+z)⁻⁴

In a static universe the SB is constant and independent of z which plasma cosmologists such as Lerner have asserted, but since the resident genius at EU central thinks SB follows the inverse square law he has thrown Lerner under the bus like Scott.

In the case of an inverse square law, the SB is of the form.

SB ~ (1+z)⁻²

This can be put to the test by measuring the surface brightness of elliptical galaxies in galaxy clusters up to z ~ 0.6.
The advantage in using elliptical galaxies is the surface brightness is more even when compared to spiral and irregular galaxies.

​

When SB is plotted against log(1+z);

As can be seen, the data is consistent with SB ~ (1+z)⁻⁴ for an expanding universe; not SB = constant for a static universe, and definitely not the idiotic idea of an inverse square law SB ~ (1+z)⁻² in a static universe.

 

[sjastro]

Over at EU central the self professed polymath genius continues to perpetrate the lie about correcting my maths mistakes and anyone who thinks surface brightness doesn’t follow the inverse square law is basically an imbecile.
It’s not even my maths the origins of which predate Olbers.

Using the polymath’s own standards, Olbers was also an imbecile for considering surface brightness being independent of the inverse square law.
In fact Olbers’ paradox was known at least two and a half centuries before his time, starting with the chump Thomas Digges; the maths can be traced back to the idiot astronomer Jean Philippe Loys de Cheseaux who corrected the mistakes of the moron Edmund Halley who was the first to provide a mathematical description.
The knuckle head Johannes Kepler expanded on the paradox and also was the first to propose the inverse square law of light.
It shows what a numbskull Kepler must have been for describing the paradox and the inverse square law of light in the same breath.
Others who expounded the paradox over the ages were the dullard scientist Otto Von Guericke, the cretin author Bernard De Fontenelle, the birdbrain astronomer Christian Huygens, the airhead writer Edgar Allan Poe, the bonehead physicist Lord Kelvin and the dimwitted steady state cosmologist Hermann Bondi.

Fast forward to modern times; my previous post showed a couple of graphs contradicting the inverse square law based on the works of those collective halfwits Pahre et al.
Even Lerner and Scott fail the polymath's intelligence test.
Not to be outdone the ignoramus Eric Lerner counters Pahre with his own interpretation which incidentally was thoroughly debunked in this extensive thread.
According to Lerner;

The Tolman test for surface brightness dimming was originally proposed as a test for the expansion of the Universe. The test, which is independent of the details of the assumed cosmology,is based on comparisons of the surface brightness (SB) of identical objects at different cosmological distances. Claims have been made that the Tolman test provides compelling evidence against a static model for the Universe. In this paper we reconsider this subject by adopting a static Euclidean Universe with a linear Hubble relation at all z (which is not the standard Einstein- de Sitter model),resulting in a relation between flux and luminosity that is virtually indistinguishable from the one used for LCDM models. Based on the analysis of the UV surface brightness of luminous disk galaxies from HUDF and GALEX datasets, reaching from the local Universe to z ~ 5 we show that the surface brightness remains constant as expected in a SEU.

Even the braindead Don Scott makes it perfectly clear surface brightness does not follow the inverse square law but is truncated due to “limitations” of the human eye.

(Step 4) These two effects cancel each other. So, every spherical shell of radius r should add the same small additional amount of light....
.... The point is this – it should now be obvious – the infinite sum described in steps (4-5), above, is incorrect. The sum stops (is truncated) at a radial distance of some 600+ light years for the typical star (and somewhere beyond that for even the brightest ones).

To add insult to injury the polymath has failed to pull the wool over the eyes at EU central as one nincompoop dissenter has pointed out surface brightness does not conform to the inverse square law.

Given the polymath thinks anyone who disagrees with him on this subject is fundamentally stupid adds to the saying “It takes one to know one” or from a different perspective as described by John Cleese there are some who are so stupid they are too stupid to realize how stupid they are.

 

[Hans Blaster]

The sad thing is that on those intellectually dark places on the Web where there is a stubborn refusal to comprehend the paradox, is that it's just a geometry problem. [Particularly for the classical form.] For ANY infinite cloud of discrete objects of finite size there will not be any directions that do not intersect an object at some distance. For Olbers' paradox, these finite objects are stars, so when we look in any direction we are always looking at the surface of some star.

Even finite clouds of such objects can reach that state of filling the sky. That our sky isn't full of stars says something about the finite range of the horizon and the density of stars. [Hint: the density is *not* 1 star/AU^3.]

It occurs to me that this failure to comprehend Olbers' paradox is related the failure to comprehend gaseous blackbodies.

 

[sjastro]

The sad thing is that on those intellectually dark places on the Web where there is a stubborn refusal to comprehend the paradox..........

If you read the hysterical response to your post at EU central you might to want change your assessment from "stubborn refusal to comprehend the paradox" to "incapable of comprehending the paradox."