Infinities & Numbers as Representations of Real Things and The Apparition of Soup Bowls

I am not a mathematician; I enjoy philosophical thought however so I have a few comments of a philosophical nature about numbers here.

I had read J.D. Barrow’s ‘The Infinite Book’ and recently added another fine book of Barrow’s to my summer reading list- ‘The Book of Nothing’. This book is quite an interesting elaboration of zero and nothing as an idea in math and philosophy as well as physics and cosmology.

Barrow described the social evolution of number systems in various civilizations such as Mayan, Babylonian and Indian. It is easy to see the correlation of abstract representations of real things that are counted to symbols that represent the things. Real substances are represented in the abstract by symbols, and the meanings or validity of the symbolic representation coincides with the accurate representation of the substances quantitatively.

I believe that relationship is the basis for much or all of mathematical validity.

Our base ten number system decimal system’s 1-9 are symbols that originated largely in India as Brahmin culture numbers as early as 300 B.C. The Indian numbering system and ideas about zero eventually made its way to Arab civilization and Europe. The point is that the symbols might be anything.

Georg Cantor’s work on infinite series is discussed in The Infinite Book. Abstract mathematical infinities seem to arise as abstract representational phenomena.

If one has a barrel of soup and subtracts no real quantity from it, that might be done and infinite number of times; one divided by zero equals infinity.

If one has a circle with ordinal measuring unit spacing on it such as whole even numbers one can insert and infinitely smaller ordinal series of numbers within it infinitely.

It is possible to insert an infinite number of differently ordered infinite series within any given infinite series or finite series or segment with differently ordered series.

Cantor’s transfinite series may be a way of representing the theoretical capacity of infinity to contain an infinite number of dissimilar, variegated ordered mathematical series representing infinity. That is something like saying that in an infinite barrel of soup there is an infinite number of ways of increasing the size of the bowls of soup served from it in unlimited quantities. Representing those bowls and serving size and numbers in structured and infinite series would be a phenomenal activity never completed if one wanted to describe every possible size combination of bowl, spoon and serving size and number issued.

If there is a finite barrel of soup the kind of infinity that can be made to describe potential servings of soup is limited however. I am not sure if the real barrel of soup could be represented by the Surreal Numbers of John Conway. I am not sure that any numbering system for infinite series could not itself be permutated infinitely. 1 could become 1A, 2 could become 2A and so on. Logicians differentiate symbols occasionally with a ‘representation (prime); 1’ and 1’’ could be the start of infinite series of representing real substances like soup.

So if one wants to subdivide the serving size of an infinite barrel of soup infinitely obviously one could with forever smaller portions. Making a Mandelbrot fractalization landscape formula representing infinitely decreasing quantum bowls of soup-perhaps shrinking down to a smaller quantum representational level as each soup bowl field is consumed might be one way of making a finite algorithm representing infinite reduction.
The use of a Mandelbrot fractal sequence as a way to model the expansion or contraction of a given form of order of structure consistently at various magnitudes obviously can suggest to some philosophical thought a potential for representing quantum mechanical structures immersed in various environments that would cause the usual model assembly to change its formations quantitatively and perhaps model it’s new characteristics as particle/waves and forces of the Universe.

The point is that one may make infinite series only in one direction-the direction of reduction, when one must confine infinities to a real barrel of soup or other finite substance.

Whole numbers, even and odd numbers, countable infinities and non-countable infinities made from real numbers; these seem to be no more than detached from real substance potential series of representation.
W.V.O. Quine’s book Elements of Logic described how to build a system of logic. Number systems seem to be sets for representing relations to real substances. Newton’s law of gravity falling off at the square root of the distance between objects seems representative of the most simple fundamental association of mathematical representation to real substance; planets etc.

Mathematics in this Universe seems to have a requirement that it conform to the being and nothingness relationships of substances of matter. It is perhaps possible to imagine a universe where the pluralism of objects of this universe and its logical, original monistic unified field were represented with a different way of being…

Perhaps the spin values of quantum particles or of quantum effects providing not obvious or consistent arithmetic assumptions in appearance and combination might be given. The way the universe at the observable level ordinarily is though, if one substance is divided in portions then numbers that represent its quantitative features must conform to meaning indicating the new number of portions.

Any arbitrary numerical series of representation could have any sort of size r dimension infinitely and would work to represent portions of the soup so long as its existential parameters coincided with the actual quantitative characteristics of the barrel of soup for instance. The series of numbers might be letters or other symbols with structured quantitative value-even with extra dimensions as subscripts within every bowl.

That’s all I had to write about infinite series and numbers here; they seem to be potential infinities rather than necessarily corresponding to real substance; potential descriptions of meanings.

J.D. Barrow’s ‘The Book of Nothing’ mentions that ‘bindu’ was an ancient Sanskrit word for nothingness as a point. I guess that sort of point is something equivalent to the notion of a tiny micro-loop or string as a fundamental quantum foundation for mass.

Of course the Brahmin of The Indus Civilization had the idea of a monistic creator issuing the Universe in various kalpas of 50 billion years or so perhaps from an infinitely small zero state in nothing before inflating another cycle of existence. In the Book of Jeremiah God says that everyone knows Him and just develops intentional forgetfulness (perhaps because of the fallen nature of mankind)-so this kind of speculation is actually good enough. Numbering and quantifying nearly infinitely small loops or strings that exist potentially or actually as some sort of a unified, monistic state of being in an apparent pluralism for forms isn’t a simple matter mathematically. It is good that scientists are working on the association of transfinite infinities in representational mathematical systems with the real world of the Universe at physics research facilities as time moves on.