WHAT IS MATHEMATICS?
Why do so many intelligent adults think that anything beyond simple arithmetic is ‘Greek to them’, and too hard to learn? Why are otherwise smart people intimidated by a simple equation like A2+B2= C2? The answer is simple: It’s because of the way math is taught in our schools. There is little or no explanation of what math really is in simple, basic terms. This is because educators want to make mathematics practical.
Before the calculator and the computer, we sometimes needed to do things like make change, or find the area or volume of something, so we were taught a set of rules for dealing with numbers that would allow you to add, subtract, multiply and divide so you could do simple calculations and balance your checkbook. Now you don’t even have to know how to do that; your smart phone will do it for you. No one needs to know how to do ‘long’ division anymore, let alone how to deal with equations, unless you want to be a scientist or a technician. Then you’ll have to learn some math skills, but even then, it is not considered necessary to know what underlies the operations and processes of applied mathematics. Mathematics has been broken up into a number of disciplines that seem to be almost unrelated, except for the fact that they all use numbers. In this way, mathematics has become no more than tools to be used for solving problems that can be quantized, i.e., reduced to numbers. But reality exists in meaningful mathematical structures and patterns. Mathematics can be much more than a tool for problem solving. Mathematics can be used to understand and explain the essential nature of reality. Mathematics is the basic structure of reality expressed in numbers.
THE MISUNDERSTANDING OF MATH
The way math is taught in our schools is like telling a story by starting somewhere in the middle and expecting the listener to already know the back story. The fact that it even works sometimes, attests to the fact that the real basics of math are analogous to the way your brain actually works. Mathematics should be easy to learn because mathematical logic is the most natural thing there is for the brain. Every conscious being instinctively knows the logic underlying mathematics from the beginning of life. But we soon forget the basic structure of reality, because it is the part of our consciousness that is taken for granted. In the multiplicity of experiences on this planet, we are drawn out of the conscious realization of basic truths at an early age, and very soon we can’t see the forest for the trees.
Learning the terminology of the calculus of Newton and Leibniz, the advanced math of science, is like learning a foreign language: you are confronted with sophisticated terms like complex algebraic polynomials, measurement variables, discrete and continuous functions, limits, infinite series, and infinitesimals. You have to learn that a continuous function can approach a specific finite value as an independent variable of the function approaches zero. Then you can begin to calculate things like the orbit of a satellite, or the trajectory of a rocket. But this is a giant leap into some of the more exotic trees of the forest of mathematics that neglects the basics. Even the small jump into calculating your utilities bills, neglects the logical basics of mathematics.
WHY THE CALCULUS OF NEWTON DOES NOT WORK
AT THE QUANTUM LEVEL
The fact that the calculus of Newton and Leibniz is inappropriate for use at the quantum level was explained in the post “WHOLE NUMBER SEQUENCES AND QUANTUM REALITY”. But this is so important that it is worth repeating here:
The mathematics used by scientists today has, as its most important system of logic, the calculus of infinitesimal change, which was developed by Leibniz and Newton, about 350 years ago. But the calculus of Newton and Leibniz simply does not work at the quantum level. Why? Because it depends on the assumption that reality can be divided into ever smaller bits, and this is not actually the case. We have known for more than 70 years that we exist in a quantized world. There is a smallest bit, beyond which no division is possible. The calculus works as well as it does only because that smallest bit is so much smaller than anything we can directly measure, that for the purposes of building things from skyscrapers to microscopic electronic circuits, the error is not significant. But for describing quantum phenomena, the calculus is totally inappropriate and leads too much of the so-called ‘weirdness’ of quantum experiments.
The calculus of Newton and Leibniz, like science in general today, does not involve consciousness. The new calculus of TDVP does, and I believe that the average person is more than capable of learning enough of the new mathematical and geometrical logic to understand how consciousness can be included as a real part of the mathematical description of reality. I believe that I can teach anyone of average intelligence the basics of the calculus of distinctions.
THE CALCULUS OF DISTINCTIONS
Oh, oh! There’s that word calculus again. You may object to my declaration that I can teach anyone the basics of a calculus, on the grounds that only a handful of geniuses like Leibniz and Newton understood the calculus when it was introduced. In fact, I will tell you that only a few people understand the calculus today. Even most scientists and engineers do not understand the calculus. They have learned the terminology, and they have accepted the fact that the calculus works to solve difficult problems, and they know how to use it, but most of them have no idea what it really is, or why it works the way it does. They simply plug numbers into equations and turn the crank to get an answer, and they use tables of certain useful functions and solutions to differential equations, taking advantage of work done by others years ago.
Of course, that’s practical. There’s no need to re-invent the wheel to build a car. It’s analogous to the way we can know how to turn on the TV, or use our computers and smart phones without having a clue about how they work. Just like you don’t have to understand what electricity is to use it, you only need to know how to flip a switch, scientists, engineers and technicians only need to know how to apply the calculus; they don’t have to understand how or why it works.
But here’s the good news: the calculus of distinctions is easier to understand than the calculus used today. It is more basic than the calculus of Newton and Leibniz; it works the way your mind works. And learning the basics of the calculus of distinctions is like starting at the beginning of the story, not in the middle. One way to say this is: The calculus of distinctions is logically prior to all mathematical expression.
The awareness of reality begins with the first distinction drawn by a conscious entity: the distinction of self from other. And the distinction of self from other begins with the awareness of a feeling of being inside, as opposed to outside, experienced as I am ‘in here’, everything else is ‘out there’. This distinction is a necessary precursor to drawing distinctions within self, and in other. It is the basis of all awareness of separation and combination, similarity and difference, equivalence and counting, and thus all mathematics. The distinctions of past, present and future lead to awareness of cause and effect, and finally, all science and knowledge. Thus, the calculus of distinctions is the logic of calculation, and distinctions are the objects of that calculation.
In the current teaching of mathematics, the necessarily prior conscious act of the drawing of the distinctions of self from other, and the acts of the drawing of distinctions in self and other, are not acknowledged, even though they are the basis of all quantization, observation and measurement. They are ignored because they are so basic. If they are recognized at all, they are considered to be given without question, so that the student can get on with the practical business of learning how to do calculations consisting of applying the basic operation of calculation, which is addition, its secondary extension, called multiplication, and their reversals, subtraction and division, to objects that are assumed to be completely separate from the consciousness of the one doing the calculation. As we now know from the revelations of relativity and quantum mechanics, this separation is an illusion.
THE ETERNAL TRIANGLE:
MATTER, ENERGY AND CONSCIOUSNESS
So what is consciousness? Consciousness is impossible to define using the current materialistic paradigm of science because it is the only thing that is experienced directly. Physical reality is only experienced indirectly through the senses and extensions of them. Consciousness is inseparably entangled with our experience of physical reality, but trying to explain it purely in terms of external physical reality is like trying to explain the experience of ‘in here’ using only the objective terms of ‘out there’.
WHAT CONSCIOUSNESS DOES
Having established the primary importance of consciousness, let’s look at what consciousness does and how it does it. The functions of consciousness are triadic: The primary function of consciousness is drawing the distinction of self from other. The secondary function of consciousness is the drawing of distinctions in other. And the tertiary function of consciousness is the organization of distinctions into logical patterns. Reality as we experience it is triadic, consisting of consciousness, distinctions and logical patterns of distinctions. All distinctions exhibit the triadic structure of content, boundary of containment, and extent. To describe the quantized nature of physical reality, we must measure distinctions using a basic quantum unit. The variations of size, shape and content of distinctions are describable in whole numbers of the basic units. There are three kinds of variables of measurement: variables of content, extent and intent. Each of these are triadic, i.e. they are distinguished in three ways: Content is distinguished as mass, energy and consciousness. Extent is distinguished as space, time and consciousness. Intent is distinguished as information, meaning and purpose.
In this series of posts we will see how the most basic quantum unit, which we call the Triadic Rotational Unit of Equivalence, is derived from particle collider data, and how the calculus of distinctions applied to physical reality using the TRUE quantum unit as the unitary distinction proves that the substance of reality is composed of three forms measurable as mass, energy and a third form that we are calling gimmel. The existence of this eternally entangled triad also proves that a primary form of consciousness existed before the first particle of the physical universe could have come out of any big bang origin event.