✔ Universal Math is awesome
✔ New ways of seeing Number
✔ Numbers and Geometry
Universal Math is constructed from different axioms than the traditional mathematics we are accustomed to. Axioms form the basis of all mathematical systems. If we adjust these axioms, we change the concept of mathematics and they way we describe the Universe. The difference is, our new mathematical system is geometric in nature. With geometry at the heart of numbers, we could see numerous phenomena in a new light, from prime numbers and their distribution, to infinity of the Continuum Hypothesis, the Riemann hypothesis and imaginary numbers. Mathematics being the language of science, such a transformation inevitably leads to a transformation of how we see the world. Let’s examine the current system and make a comparison to the new and explain some of the details that reveal a new perspective of the number line.
Quantative and Qualitative Numbers
Numbers can be seen to represent qualitative things, and qualitative relationships. We count things, and different types can exist multifariously in any one moment of time. A thing is defined in space by its external boundary, which separates it from the space in which it exists. In geometry, we can draw a shape, such as a triangle or square, to represent a thing. Such shapes are formed when the boundary is completed, thus separating space from what is inside and outside the form.
The second type of number is qualitative, and can be expressed as a relationship between two points. The most obvious example is the passage of time. Only a single moment of time ever exists, and as time passes, so life moves on, the present becomes transformed into the past, giving way for the next future event. We measure this kind of number with a beginning and end point, from which we can gauge the relative scale or speed of an event.
For example, if someone turns around three times, we count the number of 360° rotations. Each rotation exists in its own span of time, and so it takes a relative length of time to complete three cycles. This is relative to the speed, and the time it takes to perform one revolution. We can plot four corner points of a square and give each a distance of one. If it takes one second to travel the distance of one, then a complete lap will take four seconds. If we change the shape to a triangle, then each lap will take three second to complete.
These two types of number, qualitative and quantitative, can be represented geometrically. Quantitative numbers use lines to define the boundaries of space. Qualitative numbers of use dots to define points in time.
The Number Line
Traditionally, numbers are placed on a one-dimensional line. This number line has a zero point at its centre, from which sets of whole natural numbers expand as units across the line in both directions, + 1, + 2, +3 and -1, -2, -3 and so on. The distance of these units is relative to each other. And in this way, we are able to measure and quantify our universe with the development of positive and negative numbers and their proof of validity. But, the number line itself consists of much more information than the naturally occurring whole numbers. It is common knowledge that between the numbers 1 and 0 exists the reciprocal values of every single whole number in existence. A reciprocal value is 1 divided by the whole number to produce a fraction which appears in the numerical space between 1 and 0, i.e. the reciprocal of 2 is 1/2 or 0.5.
Zero - the boundary of Infinity
The number Zero itself holds particular properties.
There are six mathematical functions based on four fundamental operations: addition, subtraction, multiplication and division. However, in Universal Maths there are secondary functions to division and multiplication.
For example, if we take a unit of something, we can add an identical unit to that thing and it becomes two units. This is traditional mathematical thought. Yet in a reality, where everything begins as one thing that is divided into a fractal matrix, we realise that the initiation of mathematics has a completely different starting point. The mathematical function is division, the division of light into dark or the division of an infinite numerical space into positive numbers and negative numbers with at the centre residing zero point mathematically speaking, addition and subtraction then are able to traverse the zero point.
For example, the number one can have two units subtracted from it to give a result of minus one or minus one can have two units added to it, to give it a value of plus one. However, the same cannot be said of division. Division is the process of diminishing towards the zero point without ever crossing it.
Let us take the concept of the division into two. If we take the number one and divide it in half, we get 0.5. If we divide it in half again, we get 0.125 divided again 0. 625, and so on into infinity, creating an ever smaller slice of numbers space. However, no point will we ever be able to cross the zero line using division alone. This means there is boundary around the number zero that separates the positive whole numbers and the negative whole numbers.
Zero Balance and Equilibrium
Next, let us examine something else called the square root.
The square root number is also similar to the process of division. But it takes two equal quantities and finds the root of a number which is comprised of those two quantities. Therefore, for example, the square root of nine is three, three times three is nine. This balance of two numbers we call the ‘zero of equilibrium’.
The zero of equilibrium exists between one type of number and another type of number. In other words, zero difference between the number 3 and the number 3.
And in that sense, we say it is a root number of the number nine. This is different from the concept of 00 difference and zero value. Now that we have this balance in equilibrium, the equilibrium is zero. What can we can, what we can do is we can reiterate the square root process and find that the number the result will diminish in size. With each iteration. If we start with a number above the number one, notice that the number diminishes towards one. And just this time, just as the zero can never be traversed by a division, so the number one will never be traversed via a square root