Dear Ajay Pokhrel,

i now read your essay. You raise many questions regarding maths. I agree that mathematics seems not only as representing meaning, i think it was invented in a meaningful process – not by humans, but, well by God.

Just look at the multitude of different patterns which are hidden in Pascal’s triangle. I cannot count them all, but i remember that even the most...

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Dear Ajay Pokhrel,

i now read your essay. You raise many questions regarding maths. I agree that mathematics seems not only as representing meaning, i think it was invented in a meaningful process – not by humans, but, well by God.

Just look at the multitude of different patterns which are hidden in Pascal’s triangle. I cannot count them all, but i remember that even the most elegant series that converges to Pi was found within it. And yes, the fibonacci numbers have also been discovered within it. For me, this triangle is the most astonishing mathematical object (as a layman of course), because it is so simple and contains so much complexity. Even the harmonic series is contained in it (http://www.cut-the-knot.org/arithmetic/algebra/BinomialReci
procalsInPascal.shtml)

Well, a proponent of a mathematical universe would say, yes, that’s it – God is much to complicated as a realistic identification with the most fundamental level of reality, maths should be the correct candidate. But i think this conclusion is made to fast. Because for example the Nilakantha series (http://www.cut-the-knot.org/arithmetic/algebra/PiInPascal.s
html) resembles the areas of pythagorean triangles in its denominators, such that the natural numbers are given in an increasing order and is contained in Pascal’s triangle. The latter can even be viewed as a Sierpinski triangle, when on cuts out the even numbers. Moreover, the diagonals of a complete Pascal’s triangle reproduce the figurate numbers of simplices, starting with a diagonal of only the digit ‘1’, then the diagonal of the natural numbers, the diagonal of the triangular numbers, tetrahedral numbers and pentatope numbers.

Therefore, such a simple pyramid of such simple numbers, ordered in such a simple way, cries out for an explanation. Maths itself does not explain it. Its just a plain fact, like the different digits of Pi and their normal distribution. Nonetheless, all these structures, even those who appear to us as random (for example the different digits of Pi, for there is no obvious reason that this number must necessarily start with the digit 3, there is no obvious threesome property of a circle and its diameter, so why couldn’t it not start with the digit 4 or 5? Surely, if so, the whole maths should be altered to make it consistent with it) can be easily compressed by Pascal’s triangle.

My conclusion is that maths as well as our ordinary human logics was invented by God, means by an intelligent creator who can in some respect be considered as the personalization of infinity and eternity. Assuming maths to be the fundamental level of existence instead does not make much sense to me, because it does not explain how such an amazingly meaningfull and consistent structure should float around in a sea of nothingness for all eternity and at some point in ‘time’ should generate a physical world. Even if it does the latter since eternal timespans, it would not make more sense to me. Assuming God has the advantage that only his existence has to be presupposed and some metaphysical properties, and not infinitely many connections and relations as for the case of maths. Alternatively one could assume that logic and maths are properties of God (although not the only ones, because some creative force and power is needed to breath fire into the equations).

Best wishes,

Stefan Weckbach

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