Let’s look now at our possibilities. If the universe is created from a single point, what we have is only this point. We will denote it the “Origin” and will be written with capital O. having the Origin, we can never talk about anything outside this Origin. All our physical experience is coming from inside. So, what really we have here? The answer is: “One” which is a number denoting “inside the Origin”. The Origin has some “attributes” that will evolve later but meanwhile all of them are valued as “Zeros”. No physics yet, however the point is the most basic geometry. Asking questions like: from where this point comes from or what “cause” it to evolve to the universe we are familiar with can’t be answered here. We know that there was this Origin and “something” happened to it that give the universe its nature. The right question is: what happened to the Origin? Rather than how it happened or who or what cause it to happen. If we agree that the point is a true geometry, it should have dimensions. Since all the point inner attributes are “zero”, we can say that it has zero dimensions. If we are sure that this Origin point had been break the only possibility to break it is by increasing its dimensions. Note that one dimensional geometry resemble a line, however in our case with the Origin we cannot talk about a “normal” line that is composed from several points. Think about a point exposed to huge tension. Still it’s a point, but has one dimension. Before this the Origin can be safely thought of as a static point. Now this one dimension point should try to return to the original static state. Am I introducing any power here? Yes, and we cannot ask about it. We don’t have physics yet? Maybe we have. It’s not our intension or direction to measure this power. We don’t have any measurement units. We have nothing static to use as a base. All we know is that: application of this power to the Origin is the main cause that finally yields to the universe. We use the word “power” here only as estimate, since we can never be sure what it was. We will conclude that the Origin is trying to go back to the static point state.
If there is no way to go back to the static state “which is true given that we are here now in a huge universe”, what are the other possibilities for this tiny geometry to “be” in less tense state? We have four possibilities: to expand as whole; to split or divide into connected geometries, to spin or “move” or to expand into more dimensions. Maybe it will be useful now to introduce an example: think about a little girl blowing “soap” to generate bubbles from her toy. The case with Origin is so different however we want some hints to evaluate our possibilities. In the soap bubbles case: first it’s one 3D “three dimensional” bubble, then it expands as whole, then split to smaller bubbles that tend to be closer and all the time the bubbles move around themselves, each other and a virtual center. Let’s now assume the same actions order for the Origin.
The Origin will first be expanded as whole in one dimension. This will not have any sense if it’s the only thing that happened. From where did numbers, geometry and physics evolve? We will assume now the Origin introduced a second dimension “expanded in 2D”. Note that we can assume spinning or movement too. We can’t talk about speed or any other feature of this movement here. All we know is that it’s a try to go back to static state and it was not enough. What a point expanded in tow dimensions should look like? A quick answer will be a “circle”. Should this tiny circle be like normal circles? Can we use π to make our calculations? How precise should be the value of π that will be used? Dead end! Let’s be brave and search for a way to get the exact π value (if any). Another issue here: when we say 2D what coordinate system we use here? The answer is simply: we don’t know. Since we are talking about the original geometry; we are constructing the coordinate system itself. The geometry is creating a coordinate system and expands over it. The only important attribute is dimensions “independence”.
Giving exact value for π is actually a very old problem. So many criteria were used to estimate the value of π. Some of them are pure mathematical, some are pure geometrical and few use mathematical expressions with hidden “or embedded” geometrical features. What is the most promising criterion to give the ultimate value? I will propose the very old criterion using the most modern technologies and methods. That is draw and measure. We need to draw bigger circles and measure using smaller units both the circumference C and the radios r. then substitute the measured values in the circumference equation.
Let r be the circle radius, R=2r and C be the circle Circumference
The biggest circle should touch the universe boundaries, and the smallest measuring unit is the basic unit of Matter which we are trying to describe here. Impossible! In fact no; we can still look at the universe exactly at the point when the first “Matteron” was created or evolved. We will have a good shot to calculate π exactly. But what about our Origin circle? Since we are not sure it looks like any other circle or not and at the same time the circle is our best estimation, let’s try to calculate π. To do so, let’s look at any circle diminishing to a point. What is supposed to happen just near the point state will look like our case with the Origin. Since we are seeking the value of π lets write down the following limit expression:
For the first instance we can say that when R approach zero the limit should approach ∞. How big is ∞ anyhow? The answer is another mystery. A closer look, we can see that when R gets smaller, C also gets smaller. We have an idea about the value of π; we use the limit to get more précised value. So ∞ or a big number is not the right answer. Another good point here is why we use R instead of C to evaluate the limit? We already know that R < C hold true for all circles. So R will reach zero before C. lets now draw our circle inside a square. Since the Origin geometry is created and dominated by the circle, the square will start to collapse into an identical circle at some stage. We can evaluate the value of π just before the square stops to be a “normal” square. We can see here the square area which holds to be greater that the circle area will approach the value of the circle area beyond that stage.
Let A(Square) be the square area, A be the circle area.
Since A can be substituted by R2, it can be easily seen that π is approaching 2. What happened beyond that stage give rise to a fraction part greater than 1 that should be multiplied by 2 to evaluate π.
Lets now introduce another dimension to our spinning tiny Origin. We will have 3D expanded point. Following the same approach using a cube and a sphere we can write:
Let V be the Sphere volume
π value is approaching 3. Now looking back at Limit (1) we can see that π approach 1. Note that always the limit gives rise to the fraction part which is greater than 1. Note also that the value of π integer part is exactly the number of dimensions used.
Returning back to our Origin geometry, adding more dimensions is theoretically working to reduce the tense. However we know that in our Only One available universe π value is a little greater than 3. Since we eliminate any chance for fractions because we are working on the level that “numbers” are born and a fractional dimension at this level will break the dimensions independency; this measured fraction in π as we know it should have come from somewhere else.
The Origin at this stage is a tiny 3D geometry that is spinning and still not close to stability. The last action that happened is slicing or “dividing”. The origin sliced to huge number of “near” similar pieces that are all connected together. Whether you call it Big Bang or you find any other theory to calculate exactly how all those pieces come, I think it is less important. Did we ask any question about how the Origin expanded from 1 into more dimensions? This is the same thing. We don’t have any meaning for “Time” just before the slicing; “Time” is created by slicing. So what is “Time”? What is “distance” in the first place? There is a famous statement referred to Einstein. He said that “Time is what we can measure by a clock and Distance is what we can measure with a Ruler”. Even if we neglect the hard questions and take Einstein definitions, we need to define the “clock” and the “ruler” which is hard too. First: measurement needs static bases. Even if you think about Relativity to eliminate the need for ultimate static base, you will still need “mass” and “energy” to be well defined first. Second: since the universe is a huge interconnected network of spinning matterons, any measurement tool will be connected to the measurement subject. Those questions will be discussed later.
To conclude this section: we have defined the Matteron in a reasonable way. We proved that π is not a constant number. Rather it’s a measurement ratio that can tell us so much about the meaning of time and how big and old our universe is.