Many of the fundamental questions on the origin and structure of the universe have stumped all those with the highest IQs in the business. Astrophysicists, cosmologists and mathematicians have got quite a lot of it sorted out but a number of fundamental issues they can't agree on including how many dimensions exist in the universe. There are the obvious 4 dimensions: 3 spatial and one of time, which are apparent to us all on a large scale, as we go about our life and regulate the movement of planets, stars and galaxies. To include the micro (quantum) scale, that involves the behaviour of sub-atomic particles, the experts tell us we may need a lot more dimensions, maybe even eleven, seven of which we do not perceive as they are so small. One possibility is that the shape of the universe is a 4 dimensional sphere, sometimes called a hypersphere. This is clearly very difficult for us to comprehend as we are 3 dimensional beings but the concept is not new and has been suggested by several scientists, notably Alexander Friedmann and Einstein.  Other peculiar shapes have also been postulated eg. saddles, cones, doughnuts and horns but the sphere is one of Nature's preferred structures and the most energy stable. If an explosion occurred in a void the products would radiate outwards in a spherical shell around its source (ie. the "big bang). However, the universe does behave in principle very like an inflating balloon but with an extra dimension present.  Scientists have known for some time that the universe is expanding in a way that suggests it did so starting from a central source, rather like the surface of a balloon.  All the points on the surface (eg. galaxies) are moving away from each other; precisely what would happen if you marked several points on the surface of an inflating balloon. And astronomers have observed that this rate of expansion is accelerating. There is also evidence that space is curved, ie if you started a journey in a straight line and had enough time you would eventually arrive back where you started, as you would with a journey around a globe or a balloon's surface. There is currently some disagreement amongst cosmologists on this issue, some claim space may be "flat" but some recent research has hinted at positive curvature which would suggest a sphere (6). The point of origin of the big bang is likely to be at the centre of this hypersphere and therefore "perpendicular" to our 3D physical universe; we cannot travel there but in the 4th dimension we could. A 4 dimensional (4D) sphere also very neatly gives our 4th dimension, or time, a linear quality in keeping with the other 3 linear, spatial dimensions in which we exist. Time of course is the radius of the 4D sphere. We do not perceive time spatially as we exist on the "surface" of this 4D sphere but we feel its effects and as the sphere expands the radius lengthens at a corresponding rate.  In simple geometric terms the radius and circumference of a sphere are directly proportional regardless of the number of dimensions.  In some ways time for us is an illusion as we live in an everlasting present at the sphere's surface, or an alternative analogy would be that present time exists as the crest of a perpetual wave. We use the term time to describe the process of change and it appears to have direction (7). A possible consequence might be that if the universe stopped expanding then time would also stop. In fact this universal expansion may determine that everything is perpetually moving in 4 dimensions and if it ceased the universe would become "frozen." Another consequence would be that there is no possibility of time travel as we can not travel to a place (in the past or future) that does not exist. There is only one surface on the 4D sphere and that is the present (see space time diagram below). In theory it should be possible to measure time in feet and inches if we were able to determine the circumference of the universe, as a simple calculation would relate this to a value for the sphere's radius (ie. time).  Of further interest it has now been shown experimentally that the passage of time can be slowed by gravity (or mass), confirming Einstein's theory of relativity.  If our brains are prepared to comprehend the concept of 3 dimensional surface then, space, time and mass can be neatly described by visualising their effects on the geometry of such a surface.

The size of the universe is unbelievably vast.  The ratio of the volume of a sphere to its surface area is enormous and this would also apply to a hypersphere.  So there would be no shortage of space in the place where we may all eventually find ourselves.   The expansion within a volume is rather like observing raisins moving further apart in a rising cake.  And cosmologists use this analogy when viewing galaxies in our expanding universe on a cosmic scale.  But our 3D universe is only the "skin" on a 4D sphere.  With the consequences of an extra spatial dimension we must consider this process on a different scale.  So experiencing the expansion of space within a large expanding balloon is very different from the perspective of being at its surface.  "Our time becomes "their" spatial dimension.

Some Points of Numerical Interest

In theory, the size of all God's creation can be calculated if we know the radius R of the universe. Cosmologists tell us that the age of the universe is approximately 14 billion years. If the elongation of this radius has been occurring at the speed of light then that gives a value of 14 billion (14 x 109) light years for R. The formula for the volume of a hypersphere with 4 dimensions = π2/2 x R4.

And one light year is approximately 9.5 x 1012 kilometres.

So substituting this value for R, the volume of the universe =

π2/2 x (14 x 109 x 9.5 x 1012)4Which comes to 5 x 1092 volumetric kilometres.

This equation results in a fantastically large number and is probably a bit meaningless in reality. But this result is likely to be an underestimate because cosmologists tell us that there are galaxies so far away that light from them will never reach us. This is because they are receding from us at rate that exceeds the speed of light and the rate is accelerating. Or more accurately the space between us and those distant galaxies is expanding faster than light. That distance represents part of the circumference or perimeter of our universe which is equal to 2πR. There is a linear relationship between a radius and the circumference of a sphere or circle so they must lengthen at the same rate; if the circumference is accelerating then so is the radius. If the radius of the universe is extending at a speed greater than light and that rate is increasing, this would suggest that time is gradually speeding up also. This significance of this possibility is not clear. On a slightly frivolous note; I think we all feel that time passes more quickly as we get older.

Our 3D physical universe will have a "surface" volume of 2π2R3. So substituting the value for R as above we get a value of 4.6 x1070 cubic kilometres. If we substitute for the value for R in 2πR then the circumference of our 4D universe is about 90 billion light years. This maybe about right as astronomers say that any object more than 46 billion light years away is receding at greater than light speed and will always be beyond our visible horizon.