Wednesday, February 22, 2017
QUESTIONING COMPLEX NUMBERS – CAN ANYONE EXPLAIN?
We came across one video explaining complex numbers, or as it calls lateral numbers, based on the concept of coordinates, dimension, number system, negative numbers, etc., without defining these terms precisely. Coordinates are based on an arbitrarily fixed origin. Thus, when we shift the number represented by it “laterally”, we are modifying the position of the origin also. This is because, coordinates are drawn on a graph, which is one two dimensional surface. Objects in the real world are three dimensional. Thus, the graph is one dimension less than physical objects. When we shift the coordinates on the graph laterally incorporating another dimension, what we are doing is moving into the fourth physical dimension. Thus, three dimensional position is no longer relevant. Thus, which origin we are referring to if we laterally spread in some direction other than the z-axis? If we are spreading into z-axis, what call it lateral expansion?
Dimension is the interface between the internal structural space (what which extends to all of its internal structure) and external relational space (that which relates it to other objects of the universe). Since we observe objects through electromagnetic radiation, where the electric field, the magnetic field and the direction of motion are mutually perpendicular, we have three mutually perpendicular dimensions. In solids, these dimensions retain the structure invariant under mutual transformation of the dimensions – if length is changed to breadth or height, the structure remains unchanged. Thus, the dimension is the spread of the object in mutually perpendicular directions. Since this is not applicable in case of liquids (which get their dimension based on the solid container because it spreads out to the external relational space), or gases (for the same reason), they are described by their “quantity”, which is the same as mass. Since time does not fulfill this definition, time is not a “dimension” like that of limited objects, but since objects exist in space and perceived in time, both space and time coexist. Can there be any extra-spatial dimension? If so, why it has not been discovered in more than a century’s time? Can we believe in theories like string theory and its variants as representing reality, when the very foundation of these – ten or eleven extra dimensions have proved to be nonexistent?
Number is a property of all limited substances by which we differentiate between similars (limited, because otherwise we cannot differentiate between objects, as we will not know what is beyond our perceivable limit). If there are no similars, it is one. If there are similars, then it is many, which gives rise to number sequence – 2,3,4,….n, based on sequential perception of one’s. Infinity is like one, but with a difference. In the case of one, the object is limited and its dimensions are clearly perceived. In the case of infinity, these dimensions are not fully perceptible. For this reason, infinities coexist, but cannot interact, because interaction involves motion from one position and alignment to another. An infinite object is present everywhere – hence cannot have motion. For this reason, infinities are not used in mathematics. Space, time, coordinates and consciousness are the only infinities in the universe. Fractions are based on the above principle, but the the unit of “one” is changed to equal the denominator. Mathematics is the science of accumulation and reduction of numbers linearly (addition and subtraction) or non-linearly (multiplication and division) in a logically consistent manner (between similar or partially similar objects). Square and square-root are non-linear accumulation or reduction of similars.
We do mathematics with physical objects that have numbers. All actions are carried out at here-now. Thus, mathematics is carried out at here-now. Otherwise we only perceive the meaning or concept of symbols representing objects – not do the act of mathematics with them. Zero is something that does not exist at here-now, but exists elsewhere. If I say, the number of apples here is zero, I imply, apples exist elsewhere, but not at here-now. Negative numbers represent exchanged ownership. If I had 5 apples, which I gave to another for some consideration, then I owe something else in exchange for apples. This is represented mathematically as I owe -5 apples. Thus, negative numbers are real numbers and their accumulation and reduction are carried out just as real numbers with exchanged ownership. The statement 2-3 = -1 has meaning only when we associate it with physical objects. All it means is that I had two objects (say apples) and I had given someone three apples – by implication meaning, I had taken the extra one from someone with some consideration. Since I do not have any apples with me at here-now, but only some exchange consideration, I cannot do mathematics with apples except some other consideration (by getting these from others or by taking from others and giving to another with some more consideration). But no non-linear reduction of apples (square-root) is possible with negative numbers as I do not have it at here-now.
The concept of complex numbers was introduced by Euler, when he tried to solve the equation x^2 + 1 = 0. But is there any physical system where this equation is fulfilled? The answer is no. If we rewrite the equation as x^2 = -1, still then it will not lead to mathematics or physics because squaring is done with not only the numbers, but also signs. Two negative signs square up to positive as per the mathematical rules. Then how can x^2 be equal to -1? Further if i denotes square root of -1, what about the equations x^2 + 2 = 0, x^2 + 3 = 0, x^2 + 5 = 0, x^2 + 7 = 0, etc.? Why do not we invent suitable terms to explain square roots of -2,-3,-5,-7, etc? In that case, the required symbols will be infinite and doing mathematics will be impossible. For this reason, complex numbers cannot be used in computer programming. Some people say complex numbers include real numbers and more. In that case, dream should be used instead of observation, because dream includes what we observe and more. May be for that reason modern scientists are including dream with observation to formulate theories based on extra-dimensions, strings, foams, chamelions, axions, gravitons, sparticles, bare mass, bare charge, dark matter, dark energy, expansion of the universe (even though it is not observed in less than galactic scales and we observe ), inflation, etc. But their dream costs humanity huge costs, which could otherwise have been enough to eradicate poverty from the world. Should dreams get primacy over real sufferings of the world?