The idea that the whole Universe could be represented by the square root of the continuous irrational number pi π can seem a totally insane idea. But I believe that it can be explained in a Totally Logical Intuitive way without having to use abstract mathematics.
This can be done if we think of the Universe as a continuum continuously expanding as an inverse sphere. The reason why it is inverse is because we are within the Universe look out, being able to look back in ‘time’ in every direction at the beauty of the stars.
We have a process of continuous energy exchange that is formed be the spontaneous absorption and emission of light. This is represented in quantum mechanics by the Quantum Wave Particle Function expanding out as an inverse sphere.
In this theory this forms part of one universal process with the Inverse Square Law of Newton’s gravity. The wave particle duality of light is acting like the bits or zeros and ones of a computer forming a blank canvas that we can interact with turning the possible into the actual within our own reference frame!
Time is an emergent property formed by a process of Spherical Symmetry Forming and Breaking that we see and feel as the future continuously coming into existence light photon by light photon relative to the position and energy and momentum of the atoms!
The extra dimensions of String Theory and parallel universes of Hugh Everett Many worlds Interpretation are just future possibilities and opportunities in our one three dimensional Universe of continuous energy exchange or what I like to call continuous creation.
In the mathematics of Hugh Everett’s Many Worlds Interpretations the Parallel Universes are all at right-angles to each other. In this theory this is because the electric and magnetic fields are always at right-angles to each other forming part of a process of continuous change that we see and feel as the continuum of ‘time’ itself.
The mathematics of this theory is easy to fellow because it represents the geometry and ratios of a dynamic process in three dimensional space!
The Universe is expanding in space and time forming what Einstein called spacetime. In this theory this expansion can be seen not just as galaxies expanding away from each other but also as future possibilities and opportunities relative to each individual!
An observer can never get to the edge of the Universe because he is creating his own spacetime relative to his energy. It makes no difference what galaxy you observe from because time and space are interlinked the greater the time dilation the greater the length contraction of space
In this way an infinite Universe fits within a finite sphere as long as the sphere is expanding continually in space and time as an infinity of possibilities that can be represented mathematically as the the square root of the continuous irrational number pi π.
This is because human mathematics in the beginning was based on the geometry of shapes that never change like squares, triangles and circles. But the geometry of the Universe is not statics like this. Therefore we have the irrational numbers like pi dropping out of our mathematics as a never ending infinite series of numbers representing the infinite nature of our Universe.
This theory can explain the paradoxes of mathematical infinity! These infinities are formed because we have a process of continuous creation that we see and feel as ‘time’ that has the geometry of spacetime.
A mathematician will interact with this universal process just like any other object continuously forming his or her own spacetime geometry therefore it is only logical that he or she will be able to divide that geometry into an infinite number of smaller parts as time unfolds.
The Universe is an interactive, dynamic expanding continuum and therefore we have the infinities of human mathematics!
We are all active participants in the dynamics of our Universe.
Within such a theory because the laws of physics are based on one universal process the Universe always seems to be fine-tuned or in perfect balance it can never expand into nothingness or undergo a big crunch collapsing in on its self because gravity is a secondary force to the electromagnetic force.