Big Just Got Bigger: God and Mathematics: Finale: Super Large Real Numbers! By Dr John Jensen

     Time to leave to go back home to the United States. I very much enjoyed coming to Australia once again, and I particularly enjoyed writing some mathematics  papers for you which is my form of relaxation. After all, I am not married, and devote my time to science, prayer, and devotion to our Lord Jesus Christ. I want to follow up one point made in my paper on mathematical finitism, the position that the idea of infinity is philosophically problematical and should be jettisoned from mathematics. A number of readers were interested in my mention of finite but super-large numbers, and I will explore this further now. I appreciated receiving many warm emails from fans of mathematical analysis, some on remote sheep stations in the centre of Australia, who also pass lonely evenings, studying advanced calculus  and real analysis.

First, let us return to Finitism, with some of the main papers being as follows
  https://www.math.uni-hamburg.de/home/loewe/HiPhI/Slides/bendegem.pdf
  http://www.jstor.org/stable/pdf/2272346.pdf?refreqid=excelsior%3A6e4ad837e563fca884ba1b46e6069c68 
  https://projecteuclid.org/download/pdf_1/euclid.ndjfl/1093634481
  https://www.jstor.org/stable/pdf/2273760.pdf?refreqid=excelsior%3A5a69fb898236f1f5f11fb5b134fa9c78

     Those in classical mathematics are Platonists who believe in a domain of abstract mathematical entities that exist outside of the physical universe and which mathematicians somehow connect with (although this connection is quite mystical and cannot be causal, for the abstract entities are not in space-time, but are eternal). Finitists are generally anti-Platonists, seeing mathematics as a human process, that requires constructability of numbers and mathematical structures. There is no abstract heaven of entities floating above us, so to speak. Consider then the largest possible number that could be constructed, as a mathematical object, although not actually constructed. Now, according to quantum theory, the smallest possible space is the Planck length of 1.6 x 10^ -35, which is 10^ -20 the size of a proton, which is unimaginably small. We are to suppose that the Planck “cube,” a space that could in theory be stacked to fill a 3-D “cube of the universe is then constructed. This cube space then will represent the base number which I will discuss in more detail shortly. Of course, no such cube could physically exist, as from General Relativity, we know that it would undergo gravitational collapse into a super-black hole, maybe leading to a new “Big Bang,” but don’t you worry about that. Also, if the universe does have 26 spatial dimensions as string theorists suppose, then let’s fill them up too with our mega-monster-number!

     The 3-D number cube is hypothesized to extend to not only the entire observable universe, thought to be according to received cosmology, of around 93 billion light years, a light year being the distance light travels in a year. So, our number cube extends from the Planck length up to 93 billion light years. And, while we are in the swing of things, extend the 3-D cube to include the unobservable universe, which is speeding away from us faster than the speed of light, at least 10^10^30 times bigger than the observable universe. We would have difficulty even representing all of this explicitly on paper.

     However, let us consider the units that form the basis of the Planck lengths. Here I suggest plugging in the largest previously constructed finite number:
  http://googology.wikia.com/wiki/Largest_valid_googologism
  https://blogs.scientificamerican.com/roots-of-unity/grahame28099s-number-is-too-big-for-me-to-tell-you-how-big-it-is/ 
  https://plus.maths.org/content/too-big-write-not-too-big-graham

     If the mathematical establishment accept that Graham’s number, which is an exponent which is too large to be written down in the finite universe, we can start where they finish, building upon the inconceivable. These are numbers so immense, that they are difficult to write down on a piece of paper, in any description.  But, each of our “atoms” consists of such a number Ϣ raised to the Ϣ, raised to the Ϣ, all the way in a super-vast tower function filling the entire finite universe! Such a number, which we may call $, is conceivable in broad outline, but far beyond explicit mathematical representation; we can write a story about it, and give a cook book recipe, but writing the number down in standard mathematical notation is impossible. Thus,  we have no possible method to work out whether this number is, say prime or composite. Nor does it even make sense to say, as the classical mathematician would do, that we can call this number X and add 1. How? There is no space in the universe to do anything as the entire universe is take up with this ultimate number. Sorry, no space for writing left, even in principle.

     So, we have presented the largest finite number yet constructed, and you read about it first, here. God bless all Australian patriots, and God bless President Trump! Long live a mathematics free from the atheist ideology of infinity!

 

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Tuesday, 22 September 2020
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