The fallacy that Barrow and Tipler fall into with respect to
ETIs is because they believe in the certainty of the scientific method. And it is a reliable and sound way to discover
truths about reality provided it is applied within the correct set of
assumptions. For an example of how
this method can go wrong, we turn to 19^{th} century astronomy. The
explanation below is based on an analysis presented by physicist Hermann Bondi
in his 1959 book *The Universe at Large.*
I follow his description in general and add my own mathematical addition
to what he presented based on Olbers. I
add it, to show how Olber’s paradoxical argument can be corrected.

19^{th} century German astronomer, Heinrich Wilhelm Oblers first proposed an argument concerning
starlight coming to Earth from distant galaxies in 1826. It later became known
as Obler’s Paradox. Oblers made a few
assumptions about our galaxy and the stars in it, and then proposed what to him
seemed to be a paradoxical result. He
wondered why the night sky wasn’t full of starlight. It was well-known in this century that there were millions of distant stars. Moreover, he wondered with many millions of
stars and numerous distant galaxies, why the flood of starlight reaching us didn’t
vaporize the Earth. First, lets look at
his assumptions and then show how he calculated the intensity of incoming
starlight to the Earth.

Oblers made the following assumptions. I have taken the most basic assumptions in the interest of brevity:

- All regions of space are like or similar to our own. That is to say, there are stars that radiate light to space. there is an average distance between stars and planets (if there were in fact other planets) and it would be similar to our region.

- The law of physics apply everywhere in the universe.

- The universe is static.

Hermann Bondi described Oblers argument based on the above assumptions.

Oblers built a model of the
surrounding galaxies, and stars within them from the reference point of
Earth. He envisions 2 spheres or shells
as he called them. They are concentric
circles with Earth at their center. The
first circle is at a distance **R**. The volume of this sphere is equal to **4пR ^{2}**. The second shell has a thickness

The answer is simple to us today. We know that the universe is expanding. The galaxies are receding from one another and every ray of starlight is actually getting farther and farther away from as it travels to Earth from all the receding galaxies. Actually, while a more rigorous treatment of light propagation would involve a differential geometric model of our universe, a simple modification to Obler’s treatment incorporating the present knowledge that the universe is expanding can be made. It would immediately correct the paradox, even using his model.

Lets assume that the outer shell volume is expandable. Thus,
we modify the term **4пR ^{2} **to

Where **N** represents a factor of expansion of the outer shell **4пR ^{2} **

** **

As stated previously**, I=L/4пR ^{2}**
describes the intensity of light of any average star

** **

Replacing the spherical volume in this equation with the new term we get the following. Since all the other variables in this equation are known the only real variable is N.

**I=L/ N4пR ^{2}. **If we take the Limit of this equation we get

**Lim** **I=L/N4пR ^{2}= 0 **

_{Lim
N->∞}

That is, as the outer shell expands toward infinity, the intensity of starlight reaching Earth tends to zero. And this is exactly what the Big Bang theory predicts.

A well-formed model can be wrong, as the above analysis shows. Lacking factual information, this flawed model would appear to be correct. Obler’s paradox is reminiscent of the logical fallacy that Drs. Barrow and Tipler are making, in that it used the Scientific Method to arrive at the wrong conclusion.

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