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I have liked intuitionism from the very moment I first heard about it. I often entertain the idea that all the patterns we observe are merely things that match

• barrenko 3y ago
  It's not chaos, it's infinitely ordered order most would rather die than accept.
  • kibwen 3y ago
    The system began at chaos and is seeking order, though the existence of inherently unpredictable quantum effects means that there's plenty of chaos to go around.
• danbruc 3y ago
  I often entertain the idea that all the patterns we observe are merely things that match our capability of understanding. This could explain the "unreasonable effectiveness of mathematics in the natural sciences". I have a similar but somewhat different take on this. The universe comes first, it behaves - for what ever reasons - in the way it does. Than we humans show up and invent logic, a set of rules that is useful to reason about our universe. It either rains or it doesn't makes sense in our universe. But the universe could potentially have been different, for example something like the many-worlds interpretation but where the inhabitants of that universe can experience all the branches. Their logic might say it rains and it doesn't. Other ideas like objects, properties, space, time, causation or countability might also be influenced by the way our universe works and how we perceive it and they might be far from universal or useful across different possible universes. On top of that we than construct mathematics and explore what all the things are that we can build from those ideas and our laws of logic. It should probably not be especially surprising that we can on the one hand construct things that are not realized in our universe and on the other hand find structures that are useful for describing and understanding our universe.
  • Nasrudith 3y ago
    I suspect something opposite, that math comes before the universe because the universe needs math but math doesn't need the universe. Math only calls for internal consistency which radically does not depend upon the universe. It describe perfectly self-consistent realities that do not exist. Math could model say for instance a world of continuous matter as opposed to our mostly empty matter for instance. We have calculated numbers larger than the universe itself could render after all.
    • smokel 3y ago
      I beg to differ. Math typically requires abstract thought, symbols, and humans to produce and enjoy it. Especially the latter is quite a dependency. We could reduce the requirements down to an implementation of a Turing machine, or something similar. (For the argument I simply ignore whether the machine is conscious -- that seems irrelevant in this context.) That still requires some kind of discrete switch, which may seem fairly minimal to a human observer, but in reality consists of tens of thousands of atoms to operate. Atoms used to be simple, but turn out to be quite complex as well. Representing, say, a circle in a fairly minimal system such as this would probably require the cooperation of millions of atoms.
• ttctciyf 3y ago
  > fools us into thinking there is some inherent order -- which there isn't. Bold claim :) Even while maintaining a willful agnosticism about Platonic realism, it seems clear that the business of doing mathematics - intuitionistic or otherwise - depends on the ability to state and follow unambiguous rules, or else how to establish a proof within some axiomatic system or other? But if mathematicians have this ability, even as an asymptotic ideal, and are able to make judgments as to when rules are not being followed correctly, mustn't this in turn depend on some pre-existing regularity (i.e. order) in the universe? Ineluctable physical law seems a natural candidate for this order.
  • smokel 3y ago
    Thank you for your reply. I'll try some more! :) I noticed that in nature (i.e. in the physical universe) there appears to be no logic. There are not even two things exactly the same, as far as I can tell. So that lead me to believe that "counting" (or abstraction) is not even a property of the universe, but possibly only a human (or animal, or Turing machine) construct. To me, logic only starts to occur when a very complex amalgam of matter comes together [1] to realize a discrete switch. Using these discrete switches, organisms build memory and abstraction mechanisms, start counting, and do mathematics. So my thesis is that things that are considered to be "basic" by most, such as logic or mathematics, are in fact quite specific systems built on top of chaos. From there, it remains to be proven that all physical laws that we observe are no more than projections of the chaos onto such a system. Perhaps a metaphor that helps to take on my perspective, is to look at a screen filled with random noise, and then observe some patterns in there. Now replace the screen with an infinite dimensional set of chaos, and then observe a pattern that is our universe. With the added twist that we are part of this chaos, and observing the pattern, possibly in the form of physical laws. Of course, there are many problems with this theory. What does the chaos reside in? How can there be discernible parts in the chaos? Is time an emergent property inside the chaos? How can it be that the patterns that we observe are so consistent? However, to me this theory seems more fruitful than merely accepting that we cannot say anything about things that science cannot observe, or that some deity created all this. [1] With "comes together" I do not refer to a dynamic process, but to the accidental occurrence of stuff in such a shape or form. Obviously, my ridiculous theory asserts a chaos chock full of dimensions, where time and space are but supporting actors.
• simonh 3y ago
  The physical world is a persistent system that exhibits highly consistent behaviour. Because the behaviour is consistent we can describe it in a highly consistent formal language, mathematics. What Plato called forms are just descriptions. We have a description of what a circle is, and anything that matches that description is a circle.
  • peteradio 3y ago
    Highly consistent!? Not really. Some things are, but like OP just said, those are the ones we glom onto. But don't mistake some things for every things, there's a whole big wide world out there. We can hardly describe a ripple in a stream let alone why I've had the 5th argument in five weeks about the order I have to fix the kitchen with me wife, yet my intuition told me it was a comin.
    • simonh 3y ago
      So you consistently perceive streams, the world, have a body, a life, a wife, a kitchen with a flaw that has persisted over time, an order in to fix it. Also the world is consistent enough that you could predict that argument in advance. That sounds like an awful lot of consistency :)
      • peteradio 3y ago
        Yes, I've already conceded that some things are consistent. Will you concede that we tend to glom onto them or will I interpret your reply where you once again glommed onto them as a concession? ;)
        • archgoon 3y ago
          It's not glomming on when these things are basically the core aspects of reality. You haven't really come to grips with what a world that was mostly inconsistent would look like.
          • 3y ago
• GoblinSlayer 3y ago
  If universe was total chaos, then we would observe it, because absence of chaos isn't required by anthropic principle, but instead we observe universe to have at most pseudorandom processes, therefore universe isn't total chaos.
  • smokel 3y ago
    My point is that we as humans can observe only a (highly structured) part of the chaos. I am merely assuming a chaotic universe, because that seems more reasonable than an empty universe or an ordered universe. (Yes I know that one cannot use "reasonable" as an argument for a context in which human arguments do not apply. The entire thing is a thought experiment, nothing more.)
• timeagain 3y ago
  To paraphrase Wittgenstein, is it more likely that we “discovered” chess or that we invented it? He suggests all of mathematics should be thought of in this way, as more and more complex ways of stating tautologies.
• downsplat 3y ago
  I get the appeal, it's a minimalism thing. The thinking mind makes up patterns and checks them against each other, there is no ultimate reality, blah blah blah. Besides, a mathematical ground truth would be a kind of transcendence, in that it's prior to human thought, which makes it uncomfortably close to ideas of God. Still, I've come around basically to mathematical platonism. The structure is out there, we just happen to be smart enough to tease some of it out. I have two arguments for this. The first is the very existence of long-standing problems, and their eventual resolution either way. For centuries we were able to wonder whether Fermat's last "theorem" (which was really a conjecture at the time) was actually true, and eventually Wiles came around with an extremely complicated proof and it was settled. And we do believe that math/logic is consistent enough that someone else couldn't just have followed a different train of thought and come up with a proof of the opposite. How does a strict intuitionist account for this kind of situation? The second, and possibly deeper argument, has to do with structural equivalences. I've been out of the field for decades, but I know that a standard trick in academic math is to develop structural equivalences between disparate fields. You want to prove something in an area of math, but it's hard, so you prove that the whole structure of that subfield has a one-to-one correspondence with the structure of another subfield, and then prove the corresponding theorem in the other subfield, which happens to be easier (see: analytic number theory). Again, this sounds like exploring an existing territory, not like arbitrarily building thought-bridges here and there. The bridges are where they are, and if you try to build one where reality didn't put it, your proof will get nowhere. An even stronger form of this is that, in advanced mathematics, all kinds of notions of universality appear all the time. One of the most famous is probably computability theory. Just using a few basic symbols (say, integers, first order logic and some additive operations), you get theories of varying power. But as soon as you hit a certain level of richness, bang, all of a sudden, you've hit computability. Your theory is rich enough to embed a Turing machine, and therefore is exactly as rich and expressive as any other computable - even if one is based on numbers and multiplication, and the other on graphs or some such other weird thing. Universality shows up in lots of places. I'm too far out of the field to remember them, but it starts with the very integer numbers - there are plenty of ways to formalize their initial construction, but the eventual result is exactly the same. At this point my general thinking is that the bulk of the structure is pre-given. I have no special conjecture to make about how that comes to be - it's all a logical structure, prior to matter or thought, so unlike physics, it's not like there could be another universe out there with different basic mathematics.
• joe-collins 3y ago
  Isn't this just the anthropic principle from a different angle?