*This discussion leads me to some general considerations on the notion of infinity. I point out the risk of confusion that such a notion generates if we mistake limitations of our mind and our intelligence with properties of the natural world, or hints of the supernatural.*

I point out the danger that is inherent when we try to fill up the mystery of the world with groundless solutions. In my opinion, uncertainty is preferable to unfounded certitudes.

Anthony Aguirre https://www.edge.org/conversation/next-step-infinityI spent the other day in the local university library reading up on current thought on infinity. The university in question is among one of the top twenty in the world so has access to the best up to date information available. Plus I had the assistance of a very helpful cosmology PhD student for a short time. One point to remember is flat earth believers would have severe problems with all this information as it’s at odds with their own beliefs. Most of the best references, unfortunately, require access through a university account. See references at the end. I also had coffee with my pal the mathematician and a physics colleague of his. We had a bit of a blather about infinity, though they kept losing me. The fallout from both that and my reading led me to the conclusion that while mathematics may have a place and use for infinity, physicists have little time for it, many of them not believing in its existence, in the real world/universe. That’s not to say that some physicists have not wrestled with the problem of considering it, though all the references I came across were all in relation to space and NOT objects. I have included link to a few papers that have global access though most were behind an academic barrier, which is unfortunate.

What becomes obvious very quickly after looking at a small fraction of the research that is available is the total cosmic gulf between conventional science and those who like to call themselves flat earth scientists. How anyone could entertain the notion of a flat earth infinite or otherwise after spending a day reading up on current research both in cosmology and physics is surely one of the mysteries of the universe.

Before I reply to all those people who have posted, who did so, in my opinion, without fully thinking through the implications I’d like to apologise for such a lengthy post.

Firstly let’s remember flat Earthers like Davis and his kind believe in a small near moon and sun with much smaller and nearer planets all floating around in an ether of unknown composition held in place by forces unknown and subjected to UA, whatever that is and its cause, and that’s not even including the idea of a dome. For them, gravity, as defined by Newton and later Einstein, does not exist. They also have other beliefs regarding the stars that are totally out of kilter with mainstream thought. They pretend a huge swathe of scientific discoveries and science fact are all faked. Given all that, the universe that this Davis plane supposedly exists in would have to, by virtue of flat earth belief, have very different laws of nature from the one described by mainstream science. This is why using mathematics (even though it’s off a dubious nature) that includes mainstream laws, such as gravity, for a situation that exists outside these laws is completely illogical. For any credibility, Davis would have to devise a different physics and use those flat earth principles as the basis for any calculation. This is just one of the reasons why all of the people who rejected my original thoughts on this subject are mistaken from the outset and their collective logic is flawed.

Thinking about infinity itself- While the term infinity is widely used and possibly believed in, without any evidence, it has simply been taken for granted that infinity is a logically coherent concept. Such an assumption In my view, shared by others much smarter than I, is mistaken and is a view held by many physicists. Infinity, when taken out from the world of numbers, is, in fact, a logical absurdity like a square circle or a four-sided triangle. We can write about such things but like infinity, they don’t exist in the physical world. Just because the word infinity exists and the concept used in mathematics does not then grant it a place in the real world.

https://philpapers.org/archive/SEWTCAIts in mathematics and philosophy that the majority of the thought and work on infinity has been done. The scale of natural numbers looks as though it has “no end”, but does that mean it is infinite? The discovery of irrational numbers that appear to go on and on never-ending without any discernible pattern or limit but does this never-ending or limitless equate to the same thing as infinite?

If you happen to look at the two sets of natural numbers, the entire set and the set composed of the odd numbers. The entire set of natural numbers appears to be bigger than the entire set of odd natural numbers because the set of odd natural numbers is just a subset of the natural numbers. It is taken by mathematicians that the two sets are infinite, one infinite set being bigger than the other. This suggests that infinite sets, in the world of mathematics can come in different “sizes. Is this idea applicable to the real world? Apparently, this was a problem for Galileo but much later not for Cantor, who said it could be resolved by logic and was in fact coherent in the philosophical world, but what about the real world?

Philosopher William Lane Craig uses a good analogy to show these mathematical contradictions involved with infinite sets and how they could produce impossible real-world situations. Craig asks us to imagine that he has an infinite number of marbles in his possession and that he wants to give you a set containing an infinite number of marbles.

One way he could do that would be to give you the entire set of marbles. In that case, he would have zero marbles left for himself. However, another way he could do it would be to give you all the odd-numbered marbles. Then he would still have an infinite number left over for himself, and you would have an infinite set too. You’d have just as many as he would. According to mathematicians, each of you would have just as many as Craig originally had before the marbles were divided into odd and even. How could that possibly translate to the real world? Mr Curiosity proposed this very situation in his thought experiment! Finite brains have real problems imagining any kind of infinity. If the universe started with an infinite number of atoms would they all have to be part of the infinite Davis plane if such a thing existed? or was it made up from odd atoms, all the even ones being reserved for other uses?

Problems inherent in the initial creation of the Davis Plane

As I’ve previously mentioned Davis invokes gravity in his ‘calculation’ an entity he claims does not exist. In regard to how gravity shapes the Cosmos there exists a fairly robust account of how matter tends to clump together to form primitive structures that eventually lead to planet-sized objects, there is non-known mechanism to explain how an infinite structure could come into being or resist the force of gravity at some stage in its ‘creation’. This is where things become rather crazy. Could an object make the transition from finite to infinite, whatever that means! I don’t think so. In the mind of Davis does he imagine the plane was created or just come into existence? I don't know and I suppose he has no idea either.

It is known that in the real world of the very small gravity appears not to hold good. Does the same thing also occur when gravity deals with very large star-sized objects, never mind the infinite, leading to the creation of the idea of dark matter and dark energy to solve the conundrum of why rapidly orbiting stars don’t fly off into the Cosmos?

It appears as far as we know that there is no case of infinity in nature be it the very, small the very dense or the very large.

Because assuming the natural number scale to be infinite results in logical contradictions, we must conclude that the natural number scale, even when extended toward no clearly defined end (or “indefinitely”), is really finite in the sense that the scale terminates where we leave it incomplete. Consequently, any set of objects accurately designated with values from the finite scale of numbers must also be finite— no matter how vast or extended how far beyond our ability to compute. Otherwise, we again end up with the internal contradictions of the infinite. So, the number of stars and planets in the Universe, for example, must be finite even if they are in number vast beyond any scale of computation that could in actual practice be defined (i.e., indefinite). No matter how large the number of stars and planets is in the Universe, that number must be finite since all sets, to be without logical contradiction, must be finite.

The other problem for an infinite object to exist Moreland has correctly concluded that if the past were infinite, then the Universe would have had to have undergone an actual infinite series of steps to get to the present, which is impossible. And since one cannot cross an actual infinite, then the past must have been finite. For the infinite Davis plane to exist it follows that there must have been an infinite amount of time to allow for its creation….in other words, its total bollocks.

Lagrange Lecture: Methodology of Numerical Computations with Infinities and Infinitesimals.Yaroslav Sergeyev - 2010 - Rendiconti Del Seminario Matematico dell'Università E Del Politecnico di Torino68 (2):95–113.

Philosophy and Cosmology 2012 (The Journal of International Society of Philosophy and Cosmology (ISPC) ).Oleg Bazaluk (ed.) - 2012 - ISPC

Part IV. Perspectives on Infinity From Physics and Cosmology : 7. Some Considerations on Infinity in Physics / Carlo Rovelli ; 8. Cosmological Intimations of Infinity / Anthony Aguirre ; 9. Infinity and the Nostalgia of the Stars/ Marco Bersanelli ; 10. Infinities in Cosmology. [REVIEW]Michael Heller - 2011 - In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press.

Actual Versus Potential Infinity (BPhil Manuscript.).Anne Newstead - 1997 - Dissertation, University of Oxford

The Case Against Infinity.Kip Sewell - manuscript

The Universe Around Them: Cosmology and Cosmic Renewal in Indianized South-East Asia.H. G. Quaritch Wales - 1977 - A. Probsthain.

Theism and Physical Cosmology.Hans Halvorson - 2010 - In Charles Taliaferro, Victoria Harrison & Stewart Goetz (eds.), Routledge Companion to Theism.

Infinity: New Research Frontiers.Michał Heller & W. H. Woodin (eds.) - 2011 - Cambridge University Press.

Cosmic Agnosticism.Timothy E. Eastman - 2007 - Process Studies 36 (2):181-197.

The Harmony of the Spheres: Speculations on Western Man's Ever-Changing Views of the Cosmos, From Hesiod (700 B.C.) to Newton (1650 A.D.). [REVIEW]Robert Navon - 1991 - Selene Books.

Philosophy and Cosmology 2008 (The Journal of International Society of Philosophy and Cosmology (ISPC) ).Oleg Bazaluk (ed.) - 2008 - ISPC.

Philosophy and Cosmology 2011 (The Journal of International Society of Philosophy and Cosmology (ISPC) ).Oleg Bazaluk (ed.) - 2011 - ISPC.

On Describing the Total Universe as the Non-Self-Similar Fractal (NSSF) Set.Tim Crowther - manuscript

Cosmology and Political Culture in Early China.Aihe Wang - 2000 - Cambridge University Press