4 ms·

"Is it a lucky coincidence that mathematical and physical reality can be formulated in terms of our current cognitive abilities, or is it just that, tautologica

by csdvrx 4y ago

"Is it a lucky coincidence that mathematical and physical reality can be formulated in terms of our current cognitive abilities, or is it just that, tautologically, we cannot conceive of any aspects of mathematical and physical reality that cannot be formulated in terms of our cognitive capabilities?" This nails it. Also, I have a simpler take: we acknowledge the limits of our perceptions (ex: can't see behind your head) and we have studied them in detail (ex: blind spot in the eye, where the optic nerve goes) but we haven't done nearly as much for our cognition. Why?

blackbear_ 4y ago
What kind of hypothesis and experiment would you set up to explore that?
goatlover 4y ago
The philosopher Colin McGinn has suggested that certain philosophical questions which have gone unanswered despite much attention are evidence for human cognitive limitations. He calls this cognitive closure. The nature of consciousness being one such example.
- philipov 4y ago
  Absence of evidence is not evidence of absence, though. We have had other questions that have sat unanswered for centuries that had a breakthrough and were figured out when the time was right. The answer might just be eluding us because there are other questions we need to solve first. https://en.wikipedia.org/wiki/Evidence_of_absence https://en.wikipedia.org/wiki/Evidence_of_absence
  - bumby 4y ago
    How would you relate that to the OP's example of the nature of consciousness? The hard problem of consciousness seems particularly suited to avoid the mechanisms that "we" "know" anything (e.g., objective evidence and the scientific method).
  - mistermann 4y ago
    > Absence of evidence is not evidence of absence, though. It is evidence for it, but not proof. There's an essay somewhere out there go into more detail on the matter. Relevant to the article: is meme-based cognition net beneficial or harmful? What if examined across different dimensions? Also: is it still net beneficial that humanity invests most of its resources in studying physical reality, or might studying metaphysical reality generate a larger return on investment? Might there be a way to ~trick humanity into being able to discuss such ideas in a serious manner?
  - the_af 4y ago
    From your link: > Despite what the expression may seem to imply, a lack of evidence can be informative. For example, when testing a new drug, if no harmful effects are observed then this suggests that the drug is safe. Evidence of absence is at least a non-arbitrary but partial suggestion of absence.
- optimalsolver 4y ago
  How would you distinguish cognitive limitations from having insufficient data?
  - goatlover 4y ago
    When the issue is primarily conceptual and is unlikely to be settled by more data. That's the argument made for the hard problem of consciousness. It's not about evidence, since the nature of evidence is objective and abstract, while consciousness is subjective and concrete. Similarly with metaphysical matters, evidence isn't going to tell us whether the nature of reality or causation is X, because the evidence is empirically-based. Which won't tell you whether Kant, Hume, Berkeley or Tegmark is right. Maybe reality is all mathematical, mental, contingent, or unknowable, but how would evidence decide the matter?
knorker 4y ago
With one caveat: We can understand things without understanding them. You can understand the steps without understanding the why. My favorite example: https://www.smbc-comics.com/index.php?db=comics&id=1914 https://www.smbc-comics.com/index.php?db=comics&id=1914 So a question can be "can we create a model we don't really understand?". For which the answer is partially yes, since nobody can visualize 4D, but we can math it. But yes, maybe there are indivisible mental building blocks we can't even understand. Flatland comes to mind.
- gjm11 4y ago
  I'm not sure that's really an example of "understanding the steps without understanding the why". I'd say it's an example where there's no more to "understanding the why" than "understanding the steps", and the only actual problem is the expectation that something you can describe fairly simply ought to have a proof that doesn't require any calculation.
  - knorker 4y ago
    The comic? That's not how I read it. To me it's exactly that you have all the pieces, all the steps, but still find it completely unreasonable that it works. > the only actual problem is the expectation that something you can describe fairly simply ought to have a proof that doesn't require any calculation. No, to me it's not like that. It's easy to explain that the "angle" of a graph of ln x is 1/x, but after you've explained calculus to someone, and they understand it, they will NOT say "but why?". I'm also not sure why anyone would expect a proof of a math trick to not involve math or calculation.
    - gjm11 4y ago
      Hmm. I thought what the comic was aiming at was not "Even though I have seen a proof, I still cannot really believe that it works" but "Even though I have seen a proof, I don't feel that I fully understand why it works" and I think the latter is because (so far as I can currently tell) there isn't any simple way to see at a glance that it works. You just have to do the calculation. (I am not sure whether I am actually disagreeing with you here. It depends on what you mean by "completely unreasonable". I would not, personally, at all say that it feels completely unreasonable that the algorithm works.) Compare, e.g., a different multiplication algorithm: "Russian peasant multiplication", the thing with the doubling and halving. (Look it up if not familiar.) This is another technique where at first glance you might be completely baffled. But with this one, you can, once you understand what's going on, pretty much see at a glance how and why it works. (It's just binary. The halving and checking for remainder delivers the bits of one number, least significant first. The doubling gives you the other number times powers of 2, starting from 1. You add the 2^k.n values corresponding to bits 2^k present in the binary representation of m.) You could write that explanation out in a form that looks like calculation, but I don't think you should. Once you see the idea behind it, the only need for the calculation is to verify that there isn't an off-by-one error or something. In contrast, for the Polish hand thing, there isn't (so far as I know) an explanation that doesn't involve calculation, and (for me) the calculation is a bit too big to fit comfortably in my working memory. So there's the sense of "I can see that this is right but I can't see it at a glance, even though the thing it's proving is rather simple", and that's the nearest thing I have to a "but whyyyyyyy?" reaction. For me (as for you) d/dx log x = 1/x doesn't provoke the same reaction, and I think there are two reasons. 1. The thing being proved is a bit less elementary so there's not so much temptation to expect something "obvious". 2. The explanation isn't very calculation-heavy; to whatever extent you understand it, what you've got is a series of basically-simple steps leading to the conclusion. (For instance, if you're happy to start from d/dx exp x = exp x, then you really can see at a glance that d/dx log x = 1/x, because since log and exp are one another's inverses their graphs are one another's reflections in the line y=x. No calculation at all required.)
mistermann 4y ago
> Also, I have a simpler take: we acknowledge the limits of our perceptions (ex: can't see behind your head) and we have studied them in detail (ex: blind spot in the eye, where the optic nerve goes) To some degree. > but we haven't done nearly as much for our cognition. Why? Observe the variety of things that happen when individual instances of cognition are criticized, and consider whether some of them may introduce limitations into The System. For potential greater efficiency, constrain your study only to ~smart people rather than focusing on idiots, which seems to irresistibly draw our attention.
NoToP 4y ago
There's a complete opposite possibility that the rules of the universe are computational, and that our math seems suited to represent it all because any system complex enough to require a turing machine to parse is capable of representing anything and everything within our turing-machine-equivlant universe. In this case, there is no cognitive blind spot, we really are seeing it all.

by csdvrx 4y ago

blackbear_ 4y ago

What kind of hypothesis and experiment would you set up to explore that?

goatlover 4y ago

The philosopher Colin McGinn has suggested that certain philosophical questions which have gone unanswered despite much attention are evidence for human cognitive limitations. He calls this cognitive closure. The nature of consciousness being one such example.

philipov 4y ago
Absence of evidence is not evidence of absence, though. We have had other questions that have sat unanswered for centuries that had a breakthrough and were figured out when the time was right. The answer might just be eluding us because there are other questions we need to solve first. https://en.wikipedia.org/wiki/Evidence_of_absence https://en.wikipedia.org/wiki/Evidence_of_absence
- bumby 4y ago
  How would you relate that to the OP's example of the nature of consciousness? The hard problem of consciousness seems particularly suited to avoid the mechanisms that "we" "know" anything (e.g., objective evidence and the scientific method).
- mistermann 4y ago
  > Absence of evidence is not evidence of absence, though. It is evidence for it, but not proof. There's an essay somewhere out there go into more detail on the matter. Relevant to the article: is meme-based cognition net beneficial or harmful? What if examined across different dimensions? Also: is it still net beneficial that humanity invests most of its resources in studying physical reality, or might studying metaphysical reality generate a larger return on investment? Might there be a way to ~trick humanity into being able to discuss such ideas in a serious manner?
- the_af 4y ago
  From your link: > Despite what the expression may seem to imply, a lack of evidence can be informative. For example, when testing a new drug, if no harmful effects are observed then this suggests that the drug is safe. Evidence of absence is at least a non-arbitrary but partial suggestion of absence.
optimalsolver 4y ago
How would you distinguish cognitive limitations from having insufficient data?
- goatlover 4y ago
  When the issue is primarily conceptual and is unlikely to be settled by more data. That's the argument made for the hard problem of consciousness. It's not about evidence, since the nature of evidence is objective and abstract, while consciousness is subjective and concrete. Similarly with metaphysical matters, evidence isn't going to tell us whether the nature of reality or causation is X, because the evidence is empirically-based. Which won't tell you whether Kant, Hume, Berkeley or Tegmark is right. Maybe reality is all mathematical, mental, contingent, or unknowable, but how would evidence decide the matter?

knorker 4y ago

With one caveat: We can understand things without understanding them. You can understand the steps without understanding the why. My favorite example: https://www.smbc-comics.com/index.php?db=comics&id=1914 https://www.smbc-comics.com/index.php?db=comics&id=1914 So a question can be "can we create a model we don't really understand?". For which the answer is partially yes, since nobody can visualize 4D, but we can math it. But yes, maybe there are indivisible mental building blocks we can't even understand. Flatland comes to mind.

gjm11 4y ago
I'm not sure that's really an example of "understanding the steps without understanding the why". I'd say it's an example where there's no more to "understanding the why" than "understanding the steps", and the only actual problem is the expectation that something you can describe fairly simply ought to have a proof that doesn't require any calculation.
- knorker 4y ago
  The comic? That's not how I read it. To me it's exactly that you have all the pieces, all the steps, but still find it completely unreasonable that it works. > the only actual problem is the expectation that something you can describe fairly simply ought to have a proof that doesn't require any calculation. No, to me it's not like that. It's easy to explain that the "angle" of a graph of ln x is 1/x, but after you've explained calculus to someone, and they understand it, they will NOT say "but why?". I'm also not sure why anyone would expect a proof of a math trick to not involve math or calculation.
  - gjm11 4y ago
    Hmm. I thought what the comic was aiming at was not "Even though I have seen a proof, I still cannot really believe that it works" but "Even though I have seen a proof, I don't feel that I fully understand why it works" and I think the latter is because (so far as I can currently tell) there isn't any simple way to see at a glance that it works. You just have to do the calculation. (I am not sure whether I am actually disagreeing with you here. It depends on what you mean by "completely unreasonable". I would not, personally, at all say that it feels completely unreasonable that the algorithm works.) Compare, e.g., a different multiplication algorithm: "Russian peasant multiplication", the thing with the doubling and halving. (Look it up if not familiar.) This is another technique where at first glance you might be completely baffled. But with this one, you can, once you understand what's going on, pretty much see at a glance how and why it works. (It's just binary. The halving and checking for remainder delivers the bits of one number, least significant first. The doubling gives you the other number times powers of 2, starting from 1. You add the 2^k.n values corresponding to bits 2^k present in the binary representation of m.) You could write that explanation out in a form that looks like calculation, but I don't think you should. Once you see the idea behind it, the only need for the calculation is to verify that there isn't an off-by-one error or something. In contrast, for the Polish hand thing, there isn't (so far as I know) an explanation that doesn't involve calculation, and (for me) the calculation is a bit too big to fit comfortably in my working memory. So there's the sense of "I can see that this is right but I can't see it at a glance, even though the thing it's proving is rather simple", and that's the nearest thing I have to a "but whyyyyyyy?" reaction. For me (as for you) d/dx log x = 1/x doesn't provoke the same reaction, and I think there are two reasons. 1. The thing being proved is a bit less elementary so there's not so much temptation to expect something "obvious". 2. The explanation isn't very calculation-heavy; to whatever extent you understand it, what you've got is a series of basically-simple steps leading to the conclusion. (For instance, if you're happy to start from d/dx exp x = exp x, then you really can see at a glance that d/dx log x = 1/x, because since log and exp are one another's inverses their graphs are one another's reflections in the line y=x. No calculation at all required.)

mistermann 4y ago

> Also, I have a simpler take: we acknowledge the limits of our perceptions (ex: can't see behind your head) and we have studied them in detail (ex: blind spot in the eye, where the optic nerve goes) To some degree. > but we haven't done nearly as much for our cognition. Why? Observe the variety of things that happen when individual instances of cognition are criticized, and consider whether some of them may introduce limitations into The System. For potential greater efficiency, constrain your study only to ~smart people rather than focusing on idiots, which seems to irresistibly draw our attention.

NoToP 4y ago

There's a complete opposite possibility that the rules of the universe are computational, and that our math seems suited to represent it all because any system complex enough to require a turing machine to parse is capable of representing anything and everything within our turing-machine-equivlant universe. In this case, there is no cognitive blind spot, we really are seeing it all.