7 ms·

> fools us into thinking there is some inherent order -- which there isn't. Bold claim :) Even while maintaining a willful agnosticism about Platonic realism,

> 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.
- narag 3y ago
  I've seen statistics proposed as the force that makes reality, that would be fundamentally random, coherent. But statistics laws are themselves very strong when numbers get big.
- dr_dshiv 3y ago
  > There are not even two things exactly the same, as far as I can tell Aren’t all basic particles defined by the fact that they are exactly the same? And countable things rely on some difference, such as different spatial locations — or else they wouldn’t be countable, they’d just be the same. While two neutron stars are distinguishable they are also classifiable as a real type of star in a manner that seems to go beyond human perceptual idiosyncrasy. But I'm a deep Platonist/Pythagorean — so my bias is that "all is number" and the world is made of math. Math is real :)
  - antonvs 3y ago
    If the world is made of math, do new physical objects pop into being whenever a mathematician writes down or thinks of a structure or a proof? Or does only some math get to become physical? In general, your view seems like a definitional issue to me. If you want to call what the world is made of “math”, then what you and I mean by math are two different things, and using the same word to describe them only leads to confusion.
    - dr_dshiv 3y ago
      Well, we try to discover math. That’s straight forward?
      - antonvs 3y ago
        Again, definitional issues are critical here. I can make up all sorts of math that isn't really "discovered", it's more "invented". Most of it won't correspond usefully to the physical universe. See e.g.: https://plato.stanford.edu/entries/formalism-mathematics/ https://plato.stanford.edu/entries/formalism-mathematics/ : > "mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess." I take the brevity and lack of commitment to a position in your reply as an indication that you're not really willing or able to defend your position. That's fine, it's a complex topic, as the many articles on the SEP linked above attest. But if you want to claim "the world is made of math", then the onus is on you to define what you mean by that. To me, it looks a little incoherent.
derefr 3y ago
In other words, the Cartesian principle extended to two parties? Cogito sicut tu cogitas, ergo sum sicut structus es: I think as you think (at least for a moment); therefore, I am, at some level, structured as you are (at least for a moment); and therefore, there is order in the universe, at least in the temporary alignment of our structures that enables us to think along these same lines? (Saying nothing, of course, of whether you "exist." I may be a brain in a vat, and your thoughts may be the emission of an evil demon running a simulation — but that still means that my thoughts and the evil demon's simulation share structure that implies an underlying shared set of computational axioms!)
- ttctciyf 3y ago
  Yes, thank you!
pilgrim0 3y ago
> mustn't this in turn depend on some pre-existing regularity (i.e. order) in the universe? Yes. And such order exists within the observer, the mediators. We are measuring instruments. Scales are bound to the ruler and not to what’s being ruled. So mathematics represents order only in as much as there are people to validate it. Should all rulers be broken and forgotten, then there’s no measure at all. This is the same for those orders not yet established, that is, the future of science. Nevertheless, I do believe there’s a principle which allows order, but it’s not order itself, but a foundation of order, which I believe to be Unit. Unit is not mere duality, because duality implies two, Unit would be more like Cause-Effect, wherein one is the same as the other (either Cause-Cause, or Effect-Effect, doesn’t really matter). This is also different than yin-yang, since each is discrete, and discreetness itself cannot exist prior to Unit. I like to think that all numbers are qualities of Unit, and the whole of mathematical theories are different theories of Unit, so they will be consistent every time Unit is maintained consistently, when something “follows” from what has already “followed”, following some definition of “following”, whatever it may be. It would explain the effectiveness of mathematics in the sense that the whole Universe is Unit out of self-similar Unit. The fact that all of information can be encoded in 0s and 1s is a great illustration of the power of Unit, and the fact that binary streams only makes “sense” upon interpretation is a great illustration of consciousness, which is an expression of Bias. Even if the Universe would change so all of the physical “laws” would mutate, Unit would still persist unchanged. New things would still “follow”. I haven’t come across anyone realizing that a theory of “everything” can exist but be useless, just like the concept of “everything” is useless as a particularity, and theories aim to be particularly applicable, so a theory which really applies to every thing applies to no thing. This would be the utmost conclusion of Gödel‘s incompleteness. How would a theory of absolutely everything be different than an infinitely long ruler without any subdivisions, or even with infinitely many zero-spaced subdivisions? One wouldn’t be able to measure any particular thing with such universal ruler.
- smokel 3y ago
  Does your "principle which allows order" presume the existence of space and time, and more specifically the ordering of time? I would say that in a universe without time, "cause and effect" have little meaning. I think I lost your train of thought when you say that numbers are qualities of Unit. Does your universe involve only "Unit", or are there other principles at play as well?
zoogeny 3y ago
> mustn't this in turn depend on some pre-existing regularity Consider the set of all things, including the ordered and disordered. Consider the operation of taking subsets of that set. Consider that conscious entities such as us only arise in ordered subsets (for some definition of ordered). Those conscious entities would see their proximal environment as ordered. They might assume that the only things in the set of all things are those things that are ordered in the same way as the proximal environment from which they arose. Our universe may be just a subset of a subset. That is, our universe might be one kind of universe that has some apparent quantum-field or relativity-geometry based regularity. There might be some number of universes that share that kind of ordering and perhaps not in all of them conscious entities arise. It is still an interesting question to ask: why would conscious entities arise within this particular kind of ordered universe? But it no longer remains the question of whether or not regularity is a fundamental property of all possible states of existence. And in fact it leaves open the question as to whether or not some kind of consciousness (perhaps very different from our own) could arise in what would appear to us as chaotic universes.
- smokel 3y ago
  I spent quite some time thinking along these lines, but then I realized that it is very unlikely to be the case in our universe. If our world would be an "accidental" subset of the universe, with ordering, then how can it be that this ordering is so consistent? Would it not be more likely that we'd live in a world that has only some order, or varying order depending on one's position in space and time? For example, I would expect a lot more miracles to happen, but every physics experiment turns out to be extremely consistent. This led me to believe that there is another process at play. My thought experiment now assumes that observation enforces a certain kind of consistency in the laws of physics. That is, the systems that we use to observe something, must by their very existence result in very consistent patterns in the chaos. What this precisely looks like and how it operates is left as an exercise to the reader.
  - zoogeny 3y ago
    > observation enforces a certain kind of consistency in the laws of physics. That sounds like a typical chicken-and-egg problem. > how can it be that this ordering is so consistent? One thing that I didn't explicitly state is that the universe only needs to seem ordered. You are making an assumption that isn't necessarily founded. 99.9% of the time we aren't checking on the ordered state of the universe. It is the exceedingly rare case that we measure with sufficient granularity to expect to see quantum effect, for example. > I would expect a lot more miracles to happen I totally understand this. You might expect a table upon which your keyboard rests to change color as we pass through a chaotic portion of some multi-verse. But that assumes order can't exist at the time-scales of universes. Imagine it like a picture. The set of all possible pictures at 640x480 is massive but finite. The vast majority of images in that space are like white noise. But you've probably seen millions of images at that resolution that are totally coherent. You don't expect the middle block of some specific image to randomly be a different color. Same with a movie. The set of all sequences of 640x480 images at 30 fps with 1 minute duration is finite. It is full of total chaos. But when you watch a movie you don't expect chaos to ensue at any moment. If you consider our entire universe like a single image from the set of all images or a movie from the set of all movies, it isn't surprising that it is entirely ordered from beginning to end. It just feels weird because the scale in both time and space is so large in the case of the universe. But given the scale of the entire set, such a large subset having internal consistency isn't totally unreasonable.

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.

narag 3y ago
I've seen statistics proposed as the force that makes reality, that would be fundamentally random, coherent. But statistics laws are themselves very strong when numbers get big.
dr_dshiv 3y ago
> There are not even two things exactly the same, as far as I can tell Aren’t all basic particles defined by the fact that they are exactly the same? And countable things rely on some difference, such as different spatial locations — or else they wouldn’t be countable, they’d just be the same. While two neutron stars are distinguishable they are also classifiable as a real type of star in a manner that seems to go beyond human perceptual idiosyncrasy. But I'm a deep Platonist/Pythagorean — so my bias is that "all is number" and the world is made of math. Math is real :)
- antonvs 3y ago
  If the world is made of math, do new physical objects pop into being whenever a mathematician writes down or thinks of a structure or a proof? Or does only some math get to become physical? In general, your view seems like a definitional issue to me. If you want to call what the world is made of “math”, then what you and I mean by math are two different things, and using the same word to describe them only leads to confusion.
  - dr_dshiv 3y ago
    Well, we try to discover math. That’s straight forward?
    - antonvs 3y ago
      Again, definitional issues are critical here. I can make up all sorts of math that isn't really "discovered", it's more "invented". Most of it won't correspond usefully to the physical universe. See e.g.: https://plato.stanford.edu/entries/formalism-mathematics/ https://plato.stanford.edu/entries/formalism-mathematics/ : > "mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess." I take the brevity and lack of commitment to a position in your reply as an indication that you're not really willing or able to defend your position. That's fine, it's a complex topic, as the many articles on the SEP linked above attest. But if you want to claim "the world is made of math", then the onus is on you to define what you mean by that. To me, it looks a little incoherent.

derefr 3y ago

In other words, the Cartesian principle extended to two parties? Cogito sicut tu cogitas, ergo sum sicut structus es: I think as you think (at least for a moment); therefore, I am, at some level, structured as you are (at least for a moment); and therefore, there is order in the universe, at least in the temporary alignment of our structures that enables us to think along these same lines? (Saying nothing, of course, of whether you "exist." I may be a brain in a vat, and your thoughts may be the emission of an evil demon running a simulation — but that still means that my thoughts and the evil demon's simulation share structure that implies an underlying shared set of computational axioms!)

ttctciyf 3y ago
Yes, thank you!

pilgrim0 3y ago

> mustn't this in turn depend on some pre-existing regularity (i.e. order) in the universe? Yes. And such order exists within the observer, the mediators. We are measuring instruments. Scales are bound to the ruler and not to what’s being ruled. So mathematics represents order only in as much as there are people to validate it. Should all rulers be broken and forgotten, then there’s no measure at all. This is the same for those orders not yet established, that is, the future of science. Nevertheless, I do believe there’s a principle which allows order, but it’s not order itself, but a foundation of order, which I believe to be Unit. Unit is not mere duality, because duality implies two, Unit would be more like Cause-Effect, wherein one is the same as the other (either Cause-Cause, or Effect-Effect, doesn’t really matter). This is also different than yin-yang, since each is discrete, and discreetness itself cannot exist prior to Unit. I like to think that all numbers are qualities of Unit, and the whole of mathematical theories are different theories of Unit, so they will be consistent every time Unit is maintained consistently, when something “follows” from what has already “followed”, following some definition of “following”, whatever it may be. It would explain the effectiveness of mathematics in the sense that the whole Universe is Unit out of self-similar Unit. The fact that all of information can be encoded in 0s and 1s is a great illustration of the power of Unit, and the fact that binary streams only makes “sense” upon interpretation is a great illustration of consciousness, which is an expression of Bias. Even if the Universe would change so all of the physical “laws” would mutate, Unit would still persist unchanged. New things would still “follow”. I haven’t come across anyone realizing that a theory of “everything” can exist but be useless, just like the concept of “everything” is useless as a particularity, and theories aim to be particularly applicable, so a theory which really applies to every thing applies to no thing. This would be the utmost conclusion of Gödel‘s incompleteness. How would a theory of absolutely everything be different than an infinitely long ruler without any subdivisions, or even with infinitely many zero-spaced subdivisions? One wouldn’t be able to measure any particular thing with such universal ruler.

smokel 3y ago
Does your "principle which allows order" presume the existence of space and time, and more specifically the ordering of time? I would say that in a universe without time, "cause and effect" have little meaning. I think I lost your train of thought when you say that numbers are qualities of Unit. Does your universe involve only "Unit", or are there other principles at play as well?

zoogeny 3y ago

> mustn't this in turn depend on some pre-existing regularity Consider the set of all things, including the ordered and disordered. Consider the operation of taking subsets of that set. Consider that conscious entities such as us only arise in ordered subsets (for some definition of ordered). Those conscious entities would see their proximal environment as ordered. They might assume that the only things in the set of all things are those things that are ordered in the same way as the proximal environment from which they arose. Our universe may be just a subset of a subset. That is, our universe might be one kind of universe that has some apparent quantum-field or relativity-geometry based regularity. There might be some number of universes that share that kind of ordering and perhaps not in all of them conscious entities arise. It is still an interesting question to ask: why would conscious entities arise within this particular kind of ordered universe? But it no longer remains the question of whether or not regularity is a fundamental property of all possible states of existence. And in fact it leaves open the question as to whether or not some kind of consciousness (perhaps very different from our own) could arise in what would appear to us as chaotic universes.

smokel 3y ago
I spent quite some time thinking along these lines, but then I realized that it is very unlikely to be the case in our universe. If our world would be an "accidental" subset of the universe, with ordering, then how can it be that this ordering is so consistent? Would it not be more likely that we'd live in a world that has only some order, or varying order depending on one's position in space and time? For example, I would expect a lot more miracles to happen, but every physics experiment turns out to be extremely consistent. This led me to believe that there is another process at play. My thought experiment now assumes that observation enforces a certain kind of consistency in the laws of physics. That is, the systems that we use to observe something, must by their very existence result in very consistent patterns in the chaos. What this precisely looks like and how it operates is left as an exercise to the reader.
- zoogeny 3y ago
  > observation enforces a certain kind of consistency in the laws of physics. That sounds like a typical chicken-and-egg problem. > how can it be that this ordering is so consistent? One thing that I didn't explicitly state is that the universe only needs to seem ordered. You are making an assumption that isn't necessarily founded. 99.9% of the time we aren't checking on the ordered state of the universe. It is the exceedingly rare case that we measure with sufficient granularity to expect to see quantum effect, for example. > I would expect a lot more miracles to happen I totally understand this. You might expect a table upon which your keyboard rests to change color as we pass through a chaotic portion of some multi-verse. But that assumes order can't exist at the time-scales of universes. Imagine it like a picture. The set of all possible pictures at 640x480 is massive but finite. The vast majority of images in that space are like white noise. But you've probably seen millions of images at that resolution that are totally coherent. You don't expect the middle block of some specific image to randomly be a different color. Same with a movie. The set of all sequences of 640x480 images at 30 fps with 1 minute duration is finite. It is full of total chaos. But when you watch a movie you don't expect chaos to ensue at any moment. If you consider our entire universe like a single image from the set of all images or a movie from the set of all movies, it isn't surprising that it is entirely ordered from beginning to end. It just feels weird because the scale in both time and space is so large in the case of the universe. But given the scale of the entire set, such a large subset having internal consistency isn't totally unreasonable.