Natural order, including mathematical order, is produced when ontically autonomous concepts get together and produce a resonating whole. This mechanism results in a universe characterized by interconnectedness between phenomena.
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Phenomenon explained : "Natural order connects diverse phenomena". Some natural law applies to a wide variety of things, resulting in common behaviour. For example, we observe that the energy of a closed system is conserved, whatever occurs within that system and whatever the diversity that system happens to contain. |
The nature of natural order
The problems with mainstream science stem from a fundamental misunderstanding as to the nature of natural order. The misunderstanding can be stated simply: it is assumed that if diverse phenomena combine to produce coherent behaviour, the phenomena must be related to each other. There must be some core commonality that can be analysed and exposed, which produces the coherent behaviour. For example, time and space combine to produce the behaviour we know under the name of General Relativity, therefore, it is reasoned, they must be aspects of the same thing.
Euler's jewel
Everybody with some mathematical education should know that this assumption is flawed. For it is contradicted by a mathematical result which is commonly known as Euler’s jewel, the formula eiπ + 1 = 0. In words: “e” to the power “i” times pi, plus one is equal to zero. In the eighteenth century this formula was considered to be the shortest proof of the existence of God. It is reported that the atheist French philosopher Diderot, on a visit to the Russian court in St. Petersburg, was silenced with the words: e to the i pi plus one is zero, therefore God exists. And although there are currently not that many mathematicians who find this argument convincing, Euler’s jewel undeniably has an elegance and beauty which borders on the divine. It should surprise no one that in 1988 the readers of the Mathematical Intelligencer voted it to be the most beautiful mathematical equation of all time.
What makes Euler’s jewel so special? For a large part, that has to do with its ingredients. The numbers e, i, pi, 1 and 0 are the most fundamental numbers in mathematics. But for the rest they appear to have very little to do with each other. They each have their own purpose, history and character (you could almost speak of personality). For starters, let us take the number “1”: the number of unity, of staying itself, the beginning of all counting. What does it have to do with zero: the origin, the universal equalizer, something and nothing at the same time? Or with pi, the ratio of the diameter of a circle to its circumference, a number that the ancient Greeks considered to be mysterious because it cannot be expressed as the ratio of two numbers. Or with the number “e”, which is used to describe the rate of growth of things that grow faster as they grow bigger, which makes it the number of life. Or with “i”, the square root of minus one, first dubbed the imaginary number by mathematicians because negative numbers were not supposed to have square roots, but, as it later turned out, indispensable for quantum mechanics.
It is not just the ingredients, but also the recipe that makes Euler’s jewel so special. It contains the three fundamental operations of arithmetic: addition, multiplication and exponentiation. The other operations - subtraction, division and the taking of roots – are merely variations of these fundamental operations. Although the formula is beautiful, it is not its beauty that concerns us here. It is the fact that the formula combines the ingredients according to the recipe to achieve a unification, whereas an analytical approach would incline us to the conclusion that they have little to do with each other. Evidently, we cannot exclude the existence of profound connections between entities that we have analysed and placed in separate compartments. Unity can arise out of diversity, unity that has nothing to do with common denominators or with one element supplying what another lacks, but of a different order altogether.
Interconnectedness
In QO, the ability of such unity to exist is a fundamental property of the fabric of the cosmos. Any combination of waves can combine, and if the combination resonates, it persists, producing a unity of a different order than its ingredients. Resonance dictates the phenomena. Conversely, that which does not resonate cannot exist. The concept of resonance makes it possible to discuss whether the universe needs to be as it is. Could, for example, “e” to the power “i” times pi, plus one have turned out to be equal to, say, 42? I am inclined to the opinion that it could not, and that the nature of the resonance mechanism is such that it had to be zero.
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Credibility: This explanation depends on the assertion that quantum mechanics applies equally well to abstract concepts as to things physical, which is a simple hypothesis, with an Occam Score of 0010. Mainstream science does not have an explanation for how diverse phenomena happen to be connected, so any such explanation must involve a gap, with an Occam Score of at least 0100, which is more than two notches worse than 0010. Therefore the QO explanation must be regarded as foundationally credible. |