I deleted an earlier post about belief in God as I don’t think it gave a true representation of my feelings on the subject.
Why is there a discussion on “belief in God” at all on an astronomy web-site? Because it is a question I am often asked when giving talks on deep-sky imaging to clubs and societies.
I still stand by my statement that I do not “believe” in God because I do not believe in anything - I either know something, or I don’t (or at least I think I know something, even if I am actually incorrect). My belief, or non-belief in a God has absolutely nothing to do with God’s possible existence. God can of course exist whether I believe in the existence of God, or not.
So maybe the more discerning question is not whether I believe in God or not but whether God exists or not – and that question is a lot tougher to answer.
It would be inappropriate for me to use the word “believe” in this piece, so to avoid that contradiction I will use the word “think” I think that the question of God’s existence is intimately bound up with the existence (or not) of infinity. From the earliest times the idea that the Ein Sof, the absolute infinite, and God were inextricably linked (if not indeed the same thing) has been discussed by philosophers and mathematicians alike. I do not see any evidence that a true infinity of anything exists in the Universe (although we must remember that absence of evidence is not evidence of absence). Very, very big numbers are involved of course, but even the biggest numbers we contemplate, say the total number of photons in the Universe) fall far short of infinity. The only place I know where infinity exists is in the mathematical world, but I do not equate mathematics with God as I have already stated in an earlier article. Mathematics is just an example of where true infinity not only exists, but thrives. Let us not also forget that mathematics describes the physical world extremely well, so although a true infinity as such may not exist in the real physical world, a thought system (mathematics) which can accommodate infinity, can also very accurately describe a system in which actual infinities do not occur. Perhaps this is not surprising. A highly complex system can always contain a less complex system as a subset. For example, Newton’s Laws can be found as a low-velocity case in considering Einstein’s Special Relativity.
Can we get any further? Perhaps just a little. If this Universe is ultimately finite without any infinite quantities contained within it (I don’t consider the asymptotic infinity considered to be at the “centre” of a black-hole to be an example of an infinite quantity – but I could be wrong!) then if we equate God with true infinity it appears that God must be extra, or ultra-Universal. I don’t really have a problem with that. An infinite God that transcends the whole Universe is what it’s all about after all, isn’t it?
So although God is not Mathematics, Mathematics allows us to work with infinity, so Mathematics might give us a clue as to what God might be. The Absolute Infinite was contemplated by Georg Cantor as an infinity that transcended the transfinite numbers. It should be noted that Cantor also equated the Absolute Infinite with God! Cantor believed that the Absolute Infinite possessed mathematical properties including the reflection principle which states that every property of the Absolute Infinite is also held by some smaller object. It is sad to relate that Georg Cantor, along with several other famous mathematicians/physicists who dared to venture into the realm of the infinite encountered severe mental problems which ultimately led to death.
How is it possible for a finite human Mind to contemplate and work with infinite quantities, in other words, how is it possible to know God? I suppose the trite answer is that the human mind cannot in fact do this, and it leads to madness and death, which in itself is extremely interesting observation, because as we all know “Whom the Gods would destroy, they first make mad”. But now consider the reason our finite minds can work with the Infinite is due to the reflection principle, so that every property of the Absolute Infinite is also held by some smaller object – ourselves for example!
I therefore postulate that it is possible for us “smaller objects” to know “the Mind of God” (if God exists) – but that particular quest is fraught with extreme danger.
But does this answer the original question of God’s actual existence? No it does not. But in giving an example of a true infinity, an Ein Sof, we are at least provided with the possibility of the existence of a God, and that has to be a good place to start.