Reference:
The modern definition of mathematics is that it is the science of patterns. Their properties are almost completely abstract than that of having the semblance of concreteness. There are many varieties of patterns found in nature. These can be numerical patterns, geometrical patterns, kinematical patterns, behavioral patterns, recreational patterns, electoral patterns, statistical patterns, and many others. The common purpose of mathematics for the studies of all these different patterns is to make the invisibly abstract concepts become visibly concrete objects. The number 1 has no meaning by itself until it is associated to a concrete object as 1 apple, 1 human being, 1 planet earth, 1 universe, 1 true God. But can the statement “1 space” be meaningfully posted? It makes sense to say that 1 apple and 1 apple is 2 apples because it is possible to see the separateness between them. But what is 1 space and 1 space? If distinction can be made then it is called quantized space. Quantized space is absolutely invisible! But if its oneness cannot be separated into, to which at the least, one two-ness then it is not quantizable. It remains as 1 continuum. If the continuum can be separated into two-nesses then quantization is possible. The ideal two-nesses are the antitheses found in nature: yin/yang, male/female, good/evil, matter/antimatter, apple/not-apple, particle/field, particle/wave, space/time, absolute rest/absolute motion, life/death.
- Keith Devlin, “The Language of Mathematics,” Freeman, New York, 1998
- Morris Kline, “Mathematical Thought From Ancient to Modern Times,” 3 Volumes, Oxford University, New York, 1972
- R. Courant, H. Robbins, “What is Mathematics,” Oxford, New York, 1941
The existence of one antithesis guarantees the existence of the other. But these existences do not necessarily need to be in equal proportions.
In a theory of quantized space, absolute acceleration can become the antithesis of distance in such a way that their inner product is square of light speed.
[math] \mathbf{a} \cdot \mathbf{r} = c^2 [/math]


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