God and the Mathematics of Infinity


Drawing on the science and mathematics of infinity, physicist and mathematician H. Chris Ransford analyzes the traditional concept of godhood and reaches surprising conclusions.

Cutting a long story short, the use of mathematical tools to analyse Godhood and some of the issues related to Godhood leads to a few mathematically compelling and incontrovertible insights, some of which may appear squarely counter-intuitive. god-and-the-mathematics-of-infinity
These include:

– Godhood and any prescriptive religion cannot possibly have anything to do with each other. The unpredictable phenomenon of emergence ensures that it is impossible in principle to second-guess, let alone to speak on behalf, of the Infinite. It is just impossible to do so, and, to use an ancient perceptive phrase, the ways of the Infinite are indeed, mathematically, wholly impenetrable. Any affirmation of knowledge of what the Infinite wants, of what “pleases” the Infinite, is just plain delusional, perhaps not much else than a psychological ‘projection’. In the context of emergence, even the very meanings of such words as ‘want’ or ‘please’ at that scale of application become unknowable.

Reinforcing, this view is independently proven anew by another route – i.e., by the simple mathematics of trying to map infinity, or the Infinite, onto a finite environment (such as ours): e.g., map a three dimensional map of planet Earth onto a 2-D flat surface, and you end up with the huge distortions of the Mercator (or of any other) projection. Now try to go down by two dimensions instead of one, from the earlier 3‑D to 2-D, to now from 3-D to 1-D – try and map the Earth upon a 1-D environment instead (i.e., a line segment), and now all of the information is lost, as opposed to being only hopelessly distorted in the earlier case. Picture what information warpage and loss would accrue from trying to map higher or infinite dimensionality onto 4-D spacetime.

– Another insight from mathematical analysis is that an infinite Godhood is a mathematical unobservable – that is, there is no way mathematically to either prove or disprove Its existence. Either It exists, or it does not, and that’s all you can ever say – which rejoins the insight of many. Georg Cantor reached the same conclusion from a quite different angle and set of considerations. One mathematical reason for this (independently corroborated by other considerations such as Cantor’s), is that if you start from any finite base or environment, you can always generate absolutely huge numbers and environments from that finite base (through the application of combinatorics], but you can however never break into infinity. There is a stark, for ever unbridgeable gap between finiteness and infinity. No one knows for sure whether the universe [or any wider metaverse) is finite, but if it is it cannot accommodate any infinite Godhood. If it is infinite, analysis shows that it can only ever be of a lower-ranking infinity (technically, a lower-ranking aleph number metric) and hence it cannot accommodate an apex Infinity either: if a Godhood exists, then it is largely out of the material universe or metaverse. Other considerations also show that It has to exist out of time, although it is difficult for us to picture this. Which leads to another insight, or rather, supports another insight reached through another route, which is …..

– The universe does not need a Godhood at all to exist: it can exist by the simple agency of the known laws of physics. But ….. the reverse may not be true: a Godhood may need a universe to exist. The gist of the argument, put into everyday rather than mathematical language, is that unless new actual reality is produced all the time from within an infinite pool of potential reality, then any Godhood would become trapped into stasis – a gilded cage of ‘been there, done that’ – unless new actualization occurs. The Godhood is everywhere and everywhen within an infinite metaverse: whatever it is, It’s been there, It’s done that, unless things change and transform and create new layers of actuality. If that did not happen, the Godhood would become akin to some kind of curator of a museum universe caught in infinite stasis. In such a universe, nothing new would ever happen in the multi-dimensional fullness of apparent time – a timeless, infinite, and well-known static universe. Teilhard de Chardin’s Omega point has been reached, and apex infinity Godhood has become encaged within a well known infinity. Unless …..  reality itself is kept open-ended, so that new layers of reality keep being generated, and the Omega point is in fact an asymptote instead of a point. To enable that generation, an engine of creation of new materiality must exist. This generation must be able to happen – in other words, there must exist a mechanism, an engine whereby creation can occur. If the whole Universe accommodating a Godhood were suffused throughout with, say, only infinite godhood (and other infinite attributes), then nothing could ever happen: no work nor movement can be generated from an environment everywhere bathed in the same infinite quality – the same infinite this or that: there is a necessity for something less than infinite goodness, or than infinite this or that attribute, for Godhood to be in a position to not become restricted to a role of curator. To weave new reality from the fabric of that universe, some differentials, some crimps in the fabric are needed (which, incidentally, is exactly the second Law of Thermodynamics.) Have we just created a measure of evil? Yes, if we appropriately define ‘a measure of evil’ as anything less than infinite goodness. Being caught in pure timelessness and in unchangeable memories of multidimensional spacetime (the future, the past and space itself, of any dimensionalities) would amount to a relinquishing of full Godhood. This is why the ‘Word’ may, occasionally, become ‘Flesh’, as the phrase goes, so that stasis be kept at bay. Stephen Hawking’s argument that probably no God exists because It definitely is not needed to create the Universe, has been squarely turned on its head, becoming that it is a perfect Godhood who would stand in need of a less than perfect Universe, rather than the other way around.

There is much more – for instance, mathematical analysis incontrovertibly establishes the total inability of even an ideal human language to convey godlike thoughts.

As is the case in all human endeavors, all areas of research in the sciences, all industries whether good or hollow and/or nefarious, religions must and do exist within an economic system. Careers are made, dedicated buildings and schools and systems are built and run, theses defended, salaries paid, and so on. This sometimes leads to entrenched attitudes, to old paradigms being defended well past their due date. Isn’t it high time, in the 21st century, to wonder whether prescriptive religions should finally be laid to rest, and ought not better be replaced with purely contemplative ones, likely truer to the Spirit of any possible Godhood.

To Read more, see God and the Mathematics of Infinity by H. Chris Ransford.

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