Instead, we might use the old analogy of a rubber sheet. Imagine two objects on the sheet, each on either side of a valley. The tendency is for the objects to roll toward each other down their respective sides of the valley until they meet at the bottom. However, as they attempt to do this, the rubber sheet expands laterally, widening the valley even as the balls roll down it. If the widening of the sheet is rapid enough, it will cause the distance between the balls to increase, despite their efforts to roll downhill toward each other.

]]>Your site is interesting and I would read more of it if I only had more spare time! All the best in your endeavours as I think what you do is quite meaningful.

]]>(1) The post appears to state that the sum of an infinite number of terms is infinity. This is of course not the case. Consider the following sum of an infinite number of terms: S = 1 + 1/2 + 1/4 + 1/8 + … where each term is half the value of its predecessor. If we divide each term by 2, we discover that S/2 = 1/2 + 1/4 + 1/8 + … If we subtract this new sum from the original sum like term by like term, we actually remove the infinite scope: (S – S/2) = 1 + (1/2 – 1/2) + (1/4 – 1/4) + … simplifies to S/2 = 1, from which S, the sum of the original sequence of terms, is determined to be 2, which is obviously finite. These terms could be the brightness of stars. We might imagine that the decreasing terms represent the stars’ perceived brightness to us, which dims with distance.

(2) Olmers’ Paradox requires that the age of the universe is infinite.

If the age of the universe is instead finite (as we know to be the case), then it must violate another requirement, namely:

(3) Olmers’ Paradox requires that we can see for ever – that the visible universe be infinite in linear diameter.

This is not the case because (a) the age of the universe is finite (b) the speed of light is finite. Thus there is a finite distance that light can possibly have travelled since the beginning of time.

(4) Olmers’ Paradox requires an infinite number of stars to be regularly distributed in an infinite universe.

We do not know if there are an infinite number of stars. We do not know if there is an infinite number of stars that are (or were in the past) within our potential perception. But we think the number of stars that we can ever know about is likely to be finite, and number around one septillion (10^24). So we probably fail OP (4) at the first part, and luckily don’t have to consider whether star distribution remains “normal” in places we can never know.

WHAT THIS MEANS:

I did not “resolve” Olmers’ Paradox by explaining some unexpected aspect of it, I instead “refuted” it. Olmers’ Paradox has some prerequisites. For the paradox to exist at all, the prerequisites must hold. But several of them are false. Therefore Olmers’ Paradox does not even exist. But don’t shed a tear for Olmers. His name should never have been associated with it. Kepler or Digges would have been much more appropriate. And don’t shed a tear for the Paradox itself. Even Edgar Allan Poe was able to dispel the notion that it ever was a paradox (in his poem Enigma).

bewginner intermediate and advanced. ]]>

When viewing bright planets like Venus close to the horizon through a telescope I’ve been able to see wisps of far off clouds begin to pass over the planet. If these clouds are far away and not illuminated by city lights you wouldn’t see them with the naked eye. And if you’re staring at a bright object as a cloud passes by it may seem as if the rapidly fading object is zooming away at high speed! Then, as the cloud thins out or passes by, the object may seem to zoom back and forth, or right at you.

Don’t get me wrong. Science shows us a universe beyond our comprehension and billions of years of biological evolution unique to island Earth would make all life on Earth of supreme comparative scientific value to advanced space faring species. So if that bright light gets too bright, look out! They may want a sample.

]]>