The above argument, using time, eternity, finite matter, statistical probability...etc., might sound as if a scientific proof has been rendered, making an open and tightly shut case of the theory. However, this is not the case. Let us examine the above argument carefully. Even if we accept that time is infinite and matter and space are finite in the universe, it does not immediately follow, therefore, "Eternal Recurrence" is a fact. That, indeed, is a farfetched conclusion. First of all, let us take the "proof" at its face value and accept it fully. Even if true, it is only a mathematical "probability," not a mathematical "certainty." As we mentioned at the end of the mathematical description, there is no way to predict the future. Furthermore, the premises that space and matter are finite while time is infinite, has yet to be proved. Science has, so far, failed to confirm or deny the finitude of the universe. Astrophysics has yet to map the entire universe, and even the very possibility of that idea is becoming arguable and doubtful. We still have no way of knowing as to whether space or matter in the universe has any limit. The further away we look, we find galaxies and more galaxies, all speeding away from us at faster and faster rate of velocities, accelerating away from us.

We try to measure velocities with the speed of light and distances with light years, and still, the universe has become so vast, velocities so great, that even as we write the numbers, we are hard pressed to imagine or comprehend their meaning. Furthermore, the universe continues to expand at greater and greater pace, suggesting that space is not limited or finite. The concept of finite matter and space in physics is becoming much like the Medieval concept, the "Dome of the sky," the ceiling above the earth, beyond which God was believed to reside, sitting on his "golden throne of glory." We now know that there is no such ceiling above us called "sky." It is just empty space, the atmosphere. So, the very foundation of the above "pseudoscientific" argument is flawed. There simply, is no evidence to support the statement that space and matter in the universe are finite. These assumptions are simply not true. Matter and space may very well be, and most likely are, infinite. The doctrine of Eternal Recurrence has no legs to stand on in science. Matter, space and time are proving ever more elusive, and appear to be merely different forms of one and the same fundamental substance of the universe -- energy. Perhaps, that may be the new name for God?

Even within finite matter, the possibility for infinity does, indeed, exist. The ancient Greek legend of Achilles, racing 10 times faster than a turtle but forever unable to catch up comes to mind. If I have a glass of water and always take a sip of only one tenth of the water, and leave nine tenth in the glass, the water in the glass will never run out. And I can sip from one glass of water forever and ever, as long as I sip only one tenth of if. Here is an example of infinity within that which is finite -- a glass of water. We can have an infinite recurrence -- sipping -- even within the finite substance. This proves the foundation, as well as the conclusion of the doctrine of Eternal Recurrence, to be totally baseless. In order for a "natural" event to take place there are a host of other events, by coincidence or design, that need to come together and happen at exactly the same time. Many chemical reactions in the lab often fail to take place precisely because, either the quantity of one, or other of the ingredients, the temperature, pressure, type of mix, the grind, or blend, some or all of the above, were not at exactly the correct point during the experiment. Such failures occur in spite of the full and active participation and cooperation of the chemist, who keeps repeating and trying his hardest to get the reaction to take place. Now, imagine if these chemicals were left to themselves to roam randomly throughout the universe and an eternity of time to elapse, and we would expect for the chemical reaction to come about by sheer coincidence or luck.

Even though, with the above arguments, we have already debunked both the foundation and the conclusion of "Eternal Recurrence," to further illustrate its absurdity, let us consider this. We can start with a flask, totally evacuated and begin to introduce a few molecules into the vacuum. Left to them selves, the molecules would randomly float all over the space inside the flask. To make this illustration more realistic, let the size of the flask be as large as the sky and as wide as the horizon. When one looks at the horizon as far as the eye can see, it is about a fifty miles radius and a hundred miles in diameter. The height of the sky too, up to the upper mesosphere is about a hundred miles. So let us imagine a balloon shaped flask, which has been evacuated. Let us also increase the size of these molecules to the size of an average potato to make it easier to visualize. Into this flask let us introduce a spinning gyro, which is free to roam randomly, anywhere and everywhere. If we color two potatoes, one red and one blue, and glue them each on opposite periphery of the gyro and let it spin, it would spin in the flask forever and ever, but the two potatoes will never come together. Just because space is finite and matter too, does not immediately follow that things can arrange and rearrange themselves in any number of permutations.

It is possible that any and even all arrangements can be prevented because of forces that prevent the limited matter from ever coming together. This is the real meaning of Enrico Fermi's law of gaps in the spectrum of energy/matter. Energy, and thereby, matter can exist only in specific places (energy bands.) The concept of randomness is immediately cut to pieces. The things that happen can only happen in specific energy bands, and not everywhere else. A mathematical can, and might permutation might exist, but it may be just that. It can exist only as a concept in our imagination, but there could be physical impossibilities that prevent its becoming a reality. Therefore, we have many "mathematical permutations" that will never take place even if we wait forever and ever, even as the two potatoes glued at opposite ends of the spinning gyro that can never meet, no matter for how long the gyro spins in the flask.