On “Infinity” and “numbers”

  • On “Infinity” and “numbers”

    Posted by Steffen on March 2, 2024 at 12:17 am

    I see a lot of people in here throwing the term “infinity” around as if that’s a number. Infinite space, infinite detail / fractal universe theories; infinity as the result of a calculation; Pi is talked about as if it was a number, despite being the result of an infinite sum.

    Before we get into the word studies, a premise: definitions of words must match the definitions of related words, otherwise, we have evidence for a corruption of language. For example: adultery was re-defined by the church as intercourse without the blessing of a priest (church or government approved marriage). But the related words (to adulterate, adulterated, etc.) all have coherent meanings that differ from this definition. Adultery means the act of mixing, confusing, polluting, and in the context of the bible means the confusing or obfuscating of bloodline relations (via re-marriage, polygamy, “open relationships”, prostitution and what not — these all result in unclear relations between children and their multiple “possible parents”, as well as an obfuscation of degrees of relation). Remember, back in those days, the firstborn son became the head of the household, and inheritance was based on who the father was.

    So, let us start from the very beginning of mathematics. The word “Number” is etymologically derived from the count of things, i.e., it is derived from the action of counting. If you look up the wiktionary for it, it is pretty clear. Especially if you filter out meanings that were added much later in history by modern mathematicians. A number, by its etymology, is the result of the process of counting/numbering things. Strictly speaking, only natural numbers can be considered numbers, by the meaning and origin of the word. Other things should have other names, because it makes a big difference.

    Now let’s look at “infinity” or “infinite”: in-finite — non-ending. Also un-bounded, etc. Feel free to look that up on wiktionary, too. Again, ignore later re-definitions of the word by mathematicians, they have corrupted language with their re-definitions.

    When you now combine both terms: infinite number, you arrive at the compound term: in-finite number — non-ending count. Tell me how a count that by definition never ends, results in anything whatsoever? This is nonsense. And Cantor with his aleph numbers and cardinality of infinite sets should be put into a hall of shame for his sophistry. If the counting of two things never ends (i.e., never yields any result), how can you then act as that result exists and call it a number? And then claim to examine properties of those? The treatment of infinities as numbers in mathematics have completely annihilated the meaning of infinity, creating an oxymoronic or meaningless framework. If terms are up for grabs and the name doesn’t need to have any special meaning related to what it is labelling, you are free to continue with your infinities, but I am incapable of accepting infinite things as existing, as did most ancient mathematicians.

    Infinity has always been accepted as a possibility, a potential, and was used as an attribute to describe that you can use arbitrarily large values for some variable. But it was never intended to be become a value. I never understood what mathematicians mean by infinity, because the language they use to describe it is contradictory by its etymology. So if you guys talk about infinite universes, I can easily accept that space has no boundaries, because space is the potential for the position of things. But if you say that there is infinite detail, that defies imagination and understanding. For this reason, ancient Greeks already had the concept of an atom, an indivisible fundamental building block of everything.

    You are using a word that has been corrupted by mathematics and no clear meaning (or even contradictory meaning, since the modern understanding of infinity is derived from infinite numbers à la Cantor), and you base your understanding of the universe on top of that. How can you understand something in terms of concepts that are invalid? Unless you can come up with a proper and clean definition to use for what you currently call infinity, your theories are fundamentally invalid.

    Steffen replied 1 month, 1 week ago 2 Members · 3 Replies
  • 3 Replies
  • Jerry

    March 2, 2024 at 12:51 am

    I must say I admire your logical approach and knowledgable insights. I’d say I agree almost completely with your view of infinity. For many years I’ve highly disagreed with much that is popular in theoretical physics, such as parallel universes and the multiverse. One point that I feel is worthy of consideration though, is the possibility that the universe is infinite in time and space. I don’t know of anything that could prevent them going on forever. You might have referred to numbers which apply only to physical phenomena, for instance, instead of the abstract features of time and space.

    • This reply was modified 1 month, 1 week ago by  Jerry.
    • Steffen

      March 2, 2024 at 1:46 am

      That is why I said: “I can easily accept that space has no boundaries, because space is the potential for the position of things.” The same goes for time. There is no reason to believe for time to be bounded (at least into the future — I find it hard to imagine time as not having a definite starting point, especially as a Christian it makes little sense to me, but it’s also immaterial whether there was or was not a definite start of time). So I fully agree that time and space should be infinite, or unending. Space is not an physical object in itself. So there is no reason why it should have a boundary.

      My problem with infinite space as often proposed here is that it is often assumed to contain infinite fractal structures that have infinite size and infinite levels detail as you “zoom in”. That “the void” has no boundaries is perfectly reasonable to me as I do not think the void is a thing to begin with, and just like I initially came to disagree with Einstein because I refuse to believe that a void can be bent or distorted, I also think that everything by necessity has to exist within an infinite void, unless it is somehow looping around on itself or something, which is also absurd.

      “I don’t know of anything that could prevent them going on forever. You might have referred to numbers which apply only to physical phenomena, for instance, instead of the abstract features of time and space.”

      If you had a clock and started counting time, forever, you would never actually arrive at an infinite number. You would always be able to add another revolution of the clock to the count. So in that sense, infinity is again, just expressing the ability of time or space to contain arbitrarily large (but finite) values.

      • Steffen

        March 2, 2024 at 2:06 am

        To be more precise, my main point of contention against infinite levels of detail downwards in scale is that if you can always physically divide something into two halves, and you did that forever, you would arrive at potentially infinitely many mini-grains of sand from a single initial grain of sand. I must say I find the threshold explanation of photon emission pretty good, in that it unloads multiple units of light at once, and only does so once it overflows, instead of a single photon which is in multiple locations at once. But I would still insist that you can’t arbitrarily split a single luminous discharge from a single atom into arbitrarily many light particles. There should still be a finite number of them, and each of those “photons” should be indivisible. Because otherwise, even finite amounts of matter are made out of infinitely fine-grained “dust”, in infinite quantities. From a programming viewpoint, it simply makes no sense to require infinite amounts of data to represent the contents of a finite chunk of space (the position and velocity of each infinitesimal particle within that space).

        Either I misunderstood David de Hilster when he spoke about it, and he just means there are probably multiple additional levels of finer scale to the universe that we do not yet know of, or he really means infinite subdivision of every particle exists, and everything is a compound particle of sorts. But you cannot have an infinite chain downwards of everything being compounded of something even smaller, like an infinite matroska doll, or at least it defies my imagination.