6 ms·

> the world is continuous Is it though? Does it matter one way or the other? Do we think reality is the math in some way, or is the math a really darn good mod

> the world is continuous Is it though? Does it matter one way or the other? Do we think reality is the math in some way, or is the math a really darn good model of the reality?

greysphere 3y ago
Imagine there was a grid for space. For simplicity consider a regular grid of size 1unit in one direction and 1unit in a perpendicular direction. If such a grid existed, using one unit of ?something? would move you 1 unit along the axes of the grid, but you'd need 2 units of ?something? to move root2 units 45deg to the grid. Any discrete grid of any shape or size or pattern would have something like this, some sort of preferred alignment, but as far as we can tell there no such preference. Physics in free space is rotationally invariant and thus not on a grid thus continuous.
- chr1 3y ago
  You don't have to imagine an ordered grid. If grid unit is small enough (say plank length 1,6 10^-35) and the grid is chaotic, for the distances of ~ 10^-16 that we can measure, everything will look the same in all directions. This happens the same way in which steel demonstrates isotropic behavior although its microscopic structure is anisotropic. So there is no easy way to prove or disprove continuity of space.
  - mjburgess 3y ago
    The "underlying issue" often at stake in the debate is whether reality is a computer, since it would need to be discrete if so, and often whether a computer can be made to simulate it. However, what's missed here is that discrete is a necessary but not sufficient condition. Once you give any sort of plausible account of how reality could be discrete, as you've done here, you end up with non-computable aspects (eg., typically randomness). So the metagame is lost regardless: reality isnt a computer (/ no complete physical theories of reality are computable). Though the meta-meta-game around "simulation" is probably internally incoherent in itself -- whether reality is a computer or not would really have nothing to do with whether any properties had by it (eg., mass) are simulated. Since either you take reality to have this property and hence "simulation" doesn't make sense, or you take it to be faked. If it's faked, being computable or not is irrelevant. There's an infinite number of conceivable ways that, globally, all properties could be faked (eg., by a demon that is dreaming).
    - calf 3y ago
      Why is randomness non-computable? In computer science, the theorem is that the set of all Deterministic Finite Automata is equivalent to the set of all Nondeterministic Finite Automata. It is a non-obvious theorem that is a one page proof taught in every junior level theory of computation course. This theorem is what lets deterministic and nondeterministic Turing machines to be used interchangeably in many subsequent proof sketches in these classes.
      - nyssos 3y ago
        > Nondeterministic Finite Automata. The "Nondeterministic" in NFA means its transition function goes from states to sets of states, instead of from states to states. Informally, it can explore multiple paths in parallel for the cost of one. They're not probabilistic.
        calf 3y ago
        The computational semantics of the NFA simply requires that the next state be one of the allowable next states in the transition function d: Q x ∑ --> PowerSet(Q). Thus, this semantics implicitly encodes the notion that the machine is nondeterministically choosing the next state in each execution. The decision problem of whether an NFA accepts a string w is what allows for the informal parallel interpretation, that it accepts iff you imagine the computation is forking off a new thread at each nondeterministic branch. But to say that this not nondeterministic or not probabilistic is like saying the Many-Worlds Interpretation means there is no real superposition, or something like that. It's like saying a throw of a dice does not really involve probability because of a symmetry argument that a dice has six equal sides. Mainly, I don't understand that, because I see probability as a way to implement nondeterminism: a system is probabilistic only because it is making nondeterministic choices according to some probability distribution. And checking Sipser 2nd ed. p.368: "A probabilistic Turing machine is a type of nondeterministic Turing machine in which each step is a coin-flip step". Anyhow, my main issue was that the original commenter casually claimed that probability makes things (physics) uncomputable. But Turing computability has nothing to do with probability, since as I recall the closest concept is the Non-deterministic Turing Machine (NDTM) and with that it is a basic proof to show that NFAs vs. DFAs, as well as NDTMs vs. DTMs, are computationally equivalent and there are theorems for that. Meaning either they are using an idiosyncratic definition of computability or are ignorant of an introductory course on theory of computing which explains formally what Turing/Church's theories were about when clarifying the concept of computability. Okay or maybe they have a deeper philosophical disagreement with computability and complexity theorists - maybe they reject Sipser's definition above - but these are standard undergraduate curricula in CS by now and it could be argued that perhaps it is the non-CS experts who haven't thought deeply enough about what computability really is and would benefit from actually learning from these subdisciplines. I don't know, as they did not reply.
  - greysphere 3y ago
    A chaotic grid would be macroscopically observable because random + random != 2 random, it's equal to 'bell curve'. Everything would be smeared as a function of distance, which we don't see. This characteristic is observable for metals as well. Steel becomes less flexible as it's worked because it's grains become smaller and more chaotic - A microscopic property with a macroscopic effect.
    - chr1 3y ago
      In physics you never have measurements differentiating between distance 2 and say 2+10^-20, and that gives enough space to hide any 'bell curve' you want.
    - tzs 3y ago
      If we are talking about a grid with a very small spacing, say around the Planck length, I don't see how we would be able to macroscopically observe it. Everything we can see move on the grid is at least 20 orders of magnitude bigger than the grid spacing. Any macroscopic objects we can experiment with are more like 30+ orders of magnitude bigger than the grid spacing and consist of numerous atoms that will all be moving within the object due to thermal jiggling over distances orders of magnitude bigger than the grid spacing.
psychoslave 3y ago
Given that no one, or at least no human, can experiment what reality in its whole, and as far as we want to honestly recognize the effective scope of our knowledge, probably we will never know in absolute terms. What matter is a subjective topic. What we all have in common is logistics constraints. So if some people set as a goal something that requires to settle if reality is more easily handled when modeled in continuous or discrete manner for logistical reasons, then it this scope it matters. But whatever you settle on, human brain is thus built that it can always assume that the perfectly fitting model is only valid in its scope which is built on top of an other more subtle level of reality which is on it’s part better modelized with an antithetic approach. Now, on a very personal out of blue opinion, I fail to see how any causal series might happen without an underlying continuous flow of event. I mean, supposing causal discontinuity is to my mind as relevant as supposing that universe as it is right now, actually just appeared, without anything we can think about it being relevant, and in the next instant could be completely different or nonexistent since universe is not bound in any remote way to what we might expect on our delusional just created sense of causality.
- lupire 3y ago
  Continuity just hides the ball. You say you can't comprehend how something can move from 1 to 2 discretely. But the paradoxical notion of infinite continuous change has been known since antiquity. It's faith either way. Discrete doesn't mean state changes are wholly globally arbitrary. Imagine a graph with nodes and edges, a state machine as computer sciences call it. I think it's easy to agree that the universe could be parsed by a regex ;-) Heck, imagine an integer on the number line that can go up or down. Worlfram has written a ton about this. Despite all his issues, his math is solid. (Which is not to say his physics is true.)
  - mrguyorama 3y ago
    Zeno's """Paradox""" was nonsense even in it's own time. Easier now that we understand Newton's laws of motion but his contemporaries were able to sufficiently dispute his idea even without them.
jerf 3y ago
There are many times in physics where people have thought they've had to choose between either one thing or its opposite, where both choices had clear deficiencies. The ultimate solution ended up being a new hybrid that nobody thought of for a long time. I kind of suspect "is the universe continuous versus discrete" will come down to that. I don't know what a hybrid of such things looks like. With our current conceptions it seems impossible. But it always does, before the breakthrough comes and then in hindsight all the people of the future will get to look back at us going "How could they not see this obvious thing?", to which my only defense is that you, dear future reader, only think it's obvious because it was handed to you on a silver platter and you'd be as confused as we are if you were back here with us.
- programjames 3y ago
  My guess is every physical value can be written as a sum of rational sines (i.e. sin(tau * a/b)).
benterix 3y ago
> Is it though? Does it matter one way or the other? These are two very different questions. As for the former, I don't believe there is consensus at this point with good arguments for and against. As for the latter, if we can reliably prove that the reality is not analog but digital, it has consequences at various levels, and we might make better choices when using math to describe it/make approximations.

> the world is continuous Is it though? Does it matter one way or the other? Do we think reality is the math in some way, or is the math a really darn good model of the reality?

greysphere 3y ago

Imagine there was a grid for space. For simplicity consider a regular grid of size 1unit in one direction and 1unit in a perpendicular direction. If such a grid existed, using one unit of ?something? would move you 1 unit along the axes of the grid, but you'd need 2 units of ?something? to move root2 units 45deg to the grid. Any discrete grid of any shape or size or pattern would have something like this, some sort of preferred alignment, but as far as we can tell there no such preference. Physics in free space is rotationally invariant and thus not on a grid thus continuous.

chr1 3y ago
You don't have to imagine an ordered grid. If grid unit is small enough (say plank length 1,6 10^-35) and the grid is chaotic, for the distances of ~ 10^-16 that we can measure, everything will look the same in all directions. This happens the same way in which steel demonstrates isotropic behavior although its microscopic structure is anisotropic. So there is no easy way to prove or disprove continuity of space.
- mjburgess 3y ago
  The "underlying issue" often at stake in the debate is whether reality is a computer, since it would need to be discrete if so, and often whether a computer can be made to simulate it. However, what's missed here is that discrete is a necessary but not sufficient condition. Once you give any sort of plausible account of how reality could be discrete, as you've done here, you end up with non-computable aspects (eg., typically randomness). So the metagame is lost regardless: reality isnt a computer (/ no complete physical theories of reality are computable). Though the meta-meta-game around "simulation" is probably internally incoherent in itself -- whether reality is a computer or not would really have nothing to do with whether any properties had by it (eg., mass) are simulated. Since either you take reality to have this property and hence "simulation" doesn't make sense, or you take it to be faked. If it's faked, being computable or not is irrelevant. There's an infinite number of conceivable ways that, globally, all properties could be faked (eg., by a demon that is dreaming).
  - calf 3y ago
    Why is randomness non-computable? In computer science, the theorem is that the set of all Deterministic Finite Automata is equivalent to the set of all Nondeterministic Finite Automata. It is a non-obvious theorem that is a one page proof taught in every junior level theory of computation course. This theorem is what lets deterministic and nondeterministic Turing machines to be used interchangeably in many subsequent proof sketches in these classes.
    - nyssos 3y ago
      > Nondeterministic Finite Automata. The "Nondeterministic" in NFA means its transition function goes from states to sets of states, instead of from states to states. Informally, it can explore multiple paths in parallel for the cost of one. They're not probabilistic.
      - calf 3y ago
        The computational semantics of the NFA simply requires that the next state be one of the allowable next states in the transition function d: Q x ∑ --> PowerSet(Q). Thus, this semantics implicitly encodes the notion that the machine is nondeterministically choosing the next state in each execution. The decision problem of whether an NFA accepts a string w is what allows for the informal parallel interpretation, that it accepts iff you imagine the computation is forking off a new thread at each nondeterministic branch. But to say that this not nondeterministic or not probabilistic is like saying the Many-Worlds Interpretation means there is no real superposition, or something like that. It's like saying a throw of a dice does not really involve probability because of a symmetry argument that a dice has six equal sides. Mainly, I don't understand that, because I see probability as a way to implement nondeterminism: a system is probabilistic only because it is making nondeterministic choices according to some probability distribution. And checking Sipser 2nd ed. p.368: "A probabilistic Turing machine is a type of nondeterministic Turing machine in which each step is a coin-flip step". Anyhow, my main issue was that the original commenter casually claimed that probability makes things (physics) uncomputable. But Turing computability has nothing to do with probability, since as I recall the closest concept is the Non-deterministic Turing Machine (NDTM) and with that it is a basic proof to show that NFAs vs. DFAs, as well as NDTMs vs. DTMs, are computationally equivalent and there are theorems for that. Meaning either they are using an idiosyncratic definition of computability or are ignorant of an introductory course on theory of computing which explains formally what Turing/Church's theories were about when clarifying the concept of computability. Okay or maybe they have a deeper philosophical disagreement with computability and complexity theorists - maybe they reject Sipser's definition above - but these are standard undergraduate curricula in CS by now and it could be argued that perhaps it is the non-CS experts who haven't thought deeply enough about what computability really is and would benefit from actually learning from these subdisciplines. I don't know, as they did not reply.
- greysphere 3y ago
  A chaotic grid would be macroscopically observable because random + random != 2 random, it's equal to 'bell curve'. Everything would be smeared as a function of distance, which we don't see. This characteristic is observable for metals as well. Steel becomes less flexible as it's worked because it's grains become smaller and more chaotic - A microscopic property with a macroscopic effect.
  - chr1 3y ago
    In physics you never have measurements differentiating between distance 2 and say 2+10^-20, and that gives enough space to hide any 'bell curve' you want.
  - tzs 3y ago
    If we are talking about a grid with a very small spacing, say around the Planck length, I don't see how we would be able to macroscopically observe it. Everything we can see move on the grid is at least 20 orders of magnitude bigger than the grid spacing. Any macroscopic objects we can experiment with are more like 30+ orders of magnitude bigger than the grid spacing and consist of numerous atoms that will all be moving within the object due to thermal jiggling over distances orders of magnitude bigger than the grid spacing.

psychoslave 3y ago

Given that no one, or at least no human, can experiment what reality in its whole, and as far as we want to honestly recognize the effective scope of our knowledge, probably we will never know in absolute terms. What matter is a subjective topic. What we all have in common is logistics constraints. So if some people set as a goal something that requires to settle if reality is more easily handled when modeled in continuous or discrete manner for logistical reasons, then it this scope it matters. But whatever you settle on, human brain is thus built that it can always assume that the perfectly fitting model is only valid in its scope which is built on top of an other more subtle level of reality which is on it’s part better modelized with an antithetic approach. Now, on a very personal out of blue opinion, I fail to see how any causal series might happen without an underlying continuous flow of event. I mean, supposing causal discontinuity is to my mind as relevant as supposing that universe as it is right now, actually just appeared, without anything we can think about it being relevant, and in the next instant could be completely different or nonexistent since universe is not bound in any remote way to what we might expect on our delusional just created sense of causality.

lupire 3y ago
Continuity just hides the ball. You say you can't comprehend how something can move from 1 to 2 discretely. But the paradoxical notion of infinite continuous change has been known since antiquity. It's faith either way. Discrete doesn't mean state changes are wholly globally arbitrary. Imagine a graph with nodes and edges, a state machine as computer sciences call it. I think it's easy to agree that the universe could be parsed by a regex ;-) Heck, imagine an integer on the number line that can go up or down. Worlfram has written a ton about this. Despite all his issues, his math is solid. (Which is not to say his physics is true.)
- mrguyorama 3y ago
  Zeno's """Paradox""" was nonsense even in it's own time. Easier now that we understand Newton's laws of motion but his contemporaries were able to sufficiently dispute his idea even without them.

jerf 3y ago

There are many times in physics where people have thought they've had to choose between either one thing or its opposite, where both choices had clear deficiencies. The ultimate solution ended up being a new hybrid that nobody thought of for a long time. I kind of suspect "is the universe continuous versus discrete" will come down to that. I don't know what a hybrid of such things looks like. With our current conceptions it seems impossible. But it always does, before the breakthrough comes and then in hindsight all the people of the future will get to look back at us going "How could they not see this obvious thing?", to which my only defense is that you, dear future reader, only think it's obvious because it was handed to you on a silver platter and you'd be as confused as we are if you were back here with us.

programjames 3y ago
My guess is every physical value can be written as a sum of rational sines (i.e. sin(tau * a/b)).

benterix 3y ago

> Is it though? Does it matter one way or the other? These are two very different questions. As for the former, I don't believe there is consensus at this point with good arguments for and against. As for the latter, if we can reliably prove that the reality is not analog but digital, it has consequences at various levels, and we might make better choices when using math to describe it/make approximations.