Saturday, February 27, 2016


I have argued in these posts that mathematics is far more than a tool invented by human beings for solving problems that can be translated into numbers; that in fact, the logical structure of mathematics is a reflection of the logical structure of the universe. If I am right, mathematical theorems, like the Pythagorean Theorem, Fermat’s Last Theorem, and Gӧdel’s Incompleteness Theorems embody deep facts about reality and the universe. In this post, I will demonstrate this with an example: the history of our knowledge about the universe.

Gӧdel’s Incompleteness Theorems prove that no logical system is ever complete. The universe, which I believe is the ultimate logical system, is the ultimate example. The observable physical universe appears to be expanding away from us at a rate that is always greater than our ability to observe it. During my lifetime, astronomers’ estimates of the size of the universe have been revised upward a number of times. I remember headlines like: “Astronomers say the universe is twice as large as we thought it was!” And: “The size of the universe is three times as great as previously estimated.” And, on it went. In 1928, an astronomer from Iowa, Edwin Hubble, discovered that the red shift in light from distant stars increased with the distance to the star, indicating that the universe might be expanding.

Hubble reasoned that an expanding universe, if it started expanding from a point at some time in the past, the size of the universe would depend upon the length of time back to the ‘big bang’ beginning. Using the best estimate of distance at the time, which was based on how the brightness of a certain well-known type of star varies with distance, he estimated the size of the universe. His estimate of the age of the universe, however, was less that the carbon-dated age of the oldest rocks on the Earth! Obviously, something was wrong.

Only 8 years after his epic discovery of the red shift, Hubble had doubts that the universe was actually expanding. He was quoted in a Time Magazine article, dated December 14, 1936 saying:
To assume that the shifts really indicate receding velocity forces one to adopt a very curious model of the universe …The model is closed and very small – a large fraction of it can be observed with existing telescopes – and is packed with matter to the very threshold of perception … In short, the necessary adjustments and compensations suggest that the [expanding universe] model may be a forced interpretation of the data.

But, in spite of Hubble’s misgivings about the expanding universe theory, the big bang theory is generally accepted as fact by mainstream astronomy and current data from the Hubble Space Telescope indicate that the universe is 10 times greater than Hubble estimated in 1936. In just 80 years, our best estimate of the size of the universe has increased ten-fold.

The current Hubble Telescope data also indicate that the rate of expansion of the universe is increasing, and the red-shift in the light from sources at the edge of the visible universe indicates that they are flying away with velocities approaching the speed of light. This begs the question: If the universe is expanding at light speed, is it not effectively infinite?

In the last post, we saw that the discovery of non-physical gimmel as a real part of the stable structure of space-time consciousness reality, leads to the following conclusion: Recognition of the role of consciousness as the organizing factor of physical reality, if we take any point in the nine-dimensional domain containing the physical universe as the space-time point of origin of the universe as we know it, we find that Hydrogen, Deuterium and Helium atoms had to already exist then and there, and this means that, as indicated by the calculus of distinctions, the expanding universe is a perceptual reality, measurable in 3S-1T, but it is ultimately an illusion. 

This illusion we call the physical universe is completely consistent with the hypothesis that the universe exists as a logical system subject to Gӧdel’s Incompleteness Theorems.


  1. Well, Ed, illusion or otherwise, in my mystically-initiated opinion, it should be well worth the life-after-life ride; as the Ultimate Force will always have a Joker in hand, so speak, to serve the never-ending occasion. IJN!

    1. I agree Brian! Without the life-after-life ride, how would Reality ever experience the ecstasy of Infinity in finite form?