10/10/96

1. What do we mean by words such as 'Universe', 'Cosmos', and "World'? Actually the meanings of such words has changed over time in a sort of consistent way. In the beginning, each word was meant to refer to all that exists, or everything that is. Over the course of time, various people would ponder the title question and speculate that what was considered the 'world' of the time may not be all that exists. As scientific study progressed, it was discovered that indeed there was more to the 'world' than previously thought. Each time, the currently used word began to be used ambiguously; it was used both for the old concept as well as the newly expanded concept.

2 . So 'World' sometimes refers to all of existence, and other times to heavenly bodies such as planets and stars. Similarly, 'Universe' sometimes refers to all of existence and other times to a single galaxy.

3. This essay will attempt to show that it is time once again to expand our notion of 'all that is', or 'all of existence'. Unfortunately, there is no word available to express this concept that is not limited by the currently held beliefs about exactly what this comprises. Rather than coin a word, I will just use the phrase 'all that is'.

4. In the past, the list of things that existed usually consisted of tangible objects. For example, the earth and the things on it. It also contained the things that could be seen from earth like the sun, moon, stars, and planets. The inclusion of these things probably held nearly unanimous agreement among people; probably very few people denied the existence of these things.

5. In addition to these things, there were other places like Heaven and Hell, and personages such as God, Satan, Angels, Leprechauns, and Gremlins, the existence of each of which was believed by some people but not others.

6. With the advent of the Enlightenment and the advances in science, there are now two separate general notions of what is meant by 'all that is': the scientific and the religious. In my opinion, both are flawed. The religious view(s) (of which there are many) includes a whole assortment of beings and places that are based typically on ancient stories or someone's dreams. The scientific view is flawed, I believe, because it has limited itself to exclude some real possibilities. The rest of this essay is an attempt to explain why the scientific notion of the 'universe' should be considered for expansion.

7. To start with let's be clear about just what science considers to be 'all that is'. The scientific view is that nothing exists outside Einstein's 4-dimensional space-time continuum. In other words, 'all that is' consists of 3-dimensional space and its contents of galaxies, planets, dark matter, and whatever else, and one dimension of time in which all these spatial objects can participate in events. A basic tenet of science is that we needn't look outside this 4-dimensional space-time continuum in order to explain any phenomenon that we observe.

8. Theoretical scientists, however, sometimes bend the rule a little when they try to come up with mathematical equations that describe some complex relationships among various phenomena. In particular, in attempting to come up with unified field theories, scientists find that they have better success if they include additional dimensions of space and time beyond the official four. They are quick to explain that this does not mean that such extra dimensions actually exist, but that by including them, it just makes the mathematics work out easier. They also try to explain them away by saying that the extra dimensions are curled up so tightly and so small that we are unable to detect them with our instruments.

9. This is an indication to me that the armor is starting to crack. It is time to face the issue squarely and acknowledge that there is a real possibility that hyper spatial and hyper temporal dimensions really do exist. Once the possibility is acknowledged and scientists are free to inquire about what it might mean, I believe that we could be in for a major explosion of scientific knowledge.

10. To begin my argument, let me offer what I consider to be an airtight proof that at least one extra space-time dimension exists. We know from Einstien's General Theory of Relativity and many subsequent experimental verifications that our 4-dimensional space-time continuum is bent. We also know from a theorem in mathematics that in order for a manifold to be bent, it must be a subspace of a space of at least one dimension higher than the original manifold. Q.E.D.

11. Our ability to detect the curvature of space-time is analogous to the ability to detect the curvature of the earth's surface without leaving the surface. We know from high school geometry that in a plane, the sum of the angles of a triangle is always 180 degrees. If we set out to measure some really big triangles on the Earth's surface, we would find that the angles add up to more than 180 degrees.

12. Suppose for example that you started at the north pole and drew a 90 degree angle. Then you extended both legs of that angle clear down to the equator. Finally, you connected those ends with a line along the equator to form your triangle. Each of the two lines formed a 90 degree angle with the equator and your first angle was 90 degrees, so the sum of the angles in your triangle is 270 degrees. What's wrong?

13. What's wrong is that your triangle is not in a plane so the surface on which you drew your triangle must be bent. In a similar way, the curvature of 4-dimensional space-time has also been positively detected.

14. Although the mathematical theorem holds for all dimensions, it is easiest to visualize what it says by looking at a two dimensional piece of paper lying on a flat table. Disregarding the thickness of the paper, that flat plane of the table top is all that is necessary in principle to contain the paper. If you bend the piece of paper, however, then some part of it must lift off the table top and enter the space above the table. The bent paper now requires three dimensions in which to exist instead of the two that were sufficient when it was flat. In a similar way, since our 4-dimensional space-time continuum is curved, or bent, we know that it must be imbedded in at least a 5-dimensional space-time continuum.

15. With this realization, it becomes very exciting to consider what existence might be like in 5 or higher dimensions. It is a little less exciting, even sobering, to consider how we might access or detect anything about this existence.

16. The excitement stems from the mathematical nature of spaces of increasing dimensionality. There are mathematical functions such as exponential or gamma functions, that are considered to increase rapidly, but they are nothing compared to the increase in the complexity of space as dimensionality is increased.

17. To show you what I am talking about, consider the four dimensions that we live in. Start with one spatial dimension. The most complex thing that could exist is a sequence of dots painted on a thread. If we moved up by adding one more spatial dimension, we could have the Mona Lisa or any photograph. If instead, we added a temporal dimension to our single spatial dimension, we could have a Beethoven symphony. If we move up to two space and one time dimension, we could have movies, like Gone with the Wind. Or if we had three space and no time dimensions, we could have some very intricate statues, even cars and animal bodies, but no motion or change or life. Moving up to our familiar three space and one time dimension, we get the intricate structures of living organisms and animated life.

18. Each of these steps presents a vastly richer and complex possibility for existence than the levels below it. It is reasonable to assume that taking additional dimensional steps would lead to similarly greater richness of the possibilities for existence.