Abyssinia-iffat

The map above depicts the medieval region of Abyssinia-Iffat, a political entity that flourished during the thirteenth and fourteenth centuries CE. I chose Abyssinia-Iffat as the name of this website because it symbolizes the meeting of different traditions, ideas, and cultures. It therefore seems a fitting emblem for a website that explores diverse areas of human knowledge.





Author: Robleh Wais

The fallacy that Barrow and Tipler fall into with respect to ETIs arises because they believe in the certainty of the scientific method. 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 nineteenth-century astronomy. The explanation below is based on an analysis presented by physicist Hermann Bondi in his 1959 book The Universe at Large. I generally follow his description and add my own mathematical contribution to what he presented based on Olbers. I include it to show how Olbers’ paradoxical argument can be corrected.

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

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

  1. All regions of space are like or similar to our own. That is to say, there are stars that radiate light into space. There is an average distance between stars and planets—if there are, in fact, other planets—and it would be similar to the average distance in our region.
  2. The laws of physics apply everywhere in the universe.
  3. The universe is static.

Hermann Bondi described Obers’ argument based on the assumptions above.

Olbers built a model of the surrounding galaxies and the stars within them from the reference point of Earth. He envisioned two spheres, or shells, as he called them. They are concentric spheres with Earth at their center. The first sphere is at a distance R. The surface area of this sphere is equal to 4πR2. The second shell has a thickness H and a volume of 4πR2H. Let N represent the number density of stars in the shell 4πR2H. Then the total number of stars would be 4πR2HN. Let L represent the light sent out by any star in the second shell. Therefore, the total light sent out by all stars in the second shell is 4πR2HNL.

As stated earlier, however, Olbers wanted to know the intensity of the light coming to Earth, not merely its total amount. He reasoned that the intensity I of any given star is defined by the equation:

I = L / 4πR2

Thus, to obtain the total intensity, we must divide out the distance factor 4πR2. We now have a definite calculation of the intensity of starlight reaching Earth. It is clear that I = HNL should flood our planet with light. Olbers tried to explain this paradox by considering nebular dust as an obstructing agent. He realized, however, that these stellar bodies would eventually be irradiated by all the incoming starlight and would only increase the flood of light reaching Earth. So why did all the starlight streaming in not vaporize Earth?

The answer is simple to us today. We know that the universe is expanding. Galaxies are receding from one another, and every ray of starlight is actually traveling through an expanding universe as it moves toward Earth from receding galaxies. Although a more rigorous treatment of light propagation would involve a differential-geometric model of our universe, a simple modification to Olbers’ treatment, incorporating the present knowledge that the universe is expanding, can be made. It would immediately correct the paradox, even using his model.

Let us assume that the outer shell is expandable. Thus, we modify the term 4πR2 to:

N4πR2

where N represents a factor of expansion of the outer shell 4πR2.

As stated previously,

I = L / 4πR2

describes the intensity of light from any average star.

Replacing the spherical term in this equation with the new term gives the following. Since all the other variables in this equation are known, the only real variable is N:

I = L / N4πR2

If we take the limit of this equation, we get:

limN→∞ I = L / N4πR2 = 0

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

A well-formed model can be wrong, as the analysis above shows. Lacking factual information, this flawed model would appear to be correct. Olbers’ Paradox is reminiscent of the logical fallacy that Drs. Barrow and Tipler make, in that it used the scientific method to arrive at the wrong conclusion.

Return to the Barrow-Tipler Extraterrestrial Life Argument:

Alien Life in the Galaxy