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Questions about the hard limits of human intelligence

97 points by ColinWright 4y ago

mikewarot 4y ago
This is a duplicate of https://news.ycombinator.com/item?id=32799953 https://news.ycombinator.com/item?id=32799953
- ColinWright 4y ago
  I first submitted it at least a day ago, I think probably at least three days ago. Clearly it's been put into the "Second Chance" pool, because I did not resubmit this. Mods: You might want to merge the discussions. @dang
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?
    - 4y ago
- 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.
phkahler 4y ago
>> Soon I start to wonder about concepts that I don’t know exist: concepts whose existence I can never even suspect, let alone contemplate. What can I ever know about that which lies beyond the limits of what I can even imagine? I find it more interesting or even frightening to contemplate those differences among humans today. For those with an IQ in the 90's, what thoughts and concepts am I able to understand that they can't? And likewise, what am I personally not able to to grok that some of the smartest people can? Even within engineering and software I find that some practitioners have a hard time with some things I find easy, and I have a hard time with concepts others find easy. It may just be differing backgrounds, but what if these are differences in raw cognitive capability? Levels of abstraction seem real if not well defined.
- chrsig 4y ago
  > It may just be differing backgrounds, but what if these are differences in raw cognitive capability? Honestly, I think ignorance may be bliss. I loathe to think about what arrogance, bigotry, and manifestations of depression would pop up had we concrete ways to measure capability.
  - anonporridge 4y ago
    Ignorance isn't a real option. If the truth is knowable, someone will find it eventually. The best you can do is opt yourself into ignorance. You can't opt everyone around you into the same ignorance. And by opting yourself into ignorance, you potentially create a competitive advantage for those who don't have the same hangups for facing ugly truths as you do.
  - phkahler 4y ago
    >> Honestly, I think ignorance may be bliss. I loathe to think about what arrogance, bigotry, and manifestations of depression would pop up had we concrete ways to measure capability. That's why I find the idea somewhat frightening. But that is also what makes it a far more interesting (relevant) question.
- barrysteve 4y ago
  What difference would it make? We treat poor and rich as equals... or should. Amputees are not treated any less than athletes. These questions impose artifical beliefs as plausible theorems
sdenton4 4y ago
>> "What is truly stunning about the fact that modern science and mathematics are formulated through a sequence of marks is its exclusivity: nothing other than these finite sequences of symbols is ever found in modern mathematical reasoning." Well that's simply not true. We draw pictures all the time. But putting that aside... Written mathematics is a serialized form of mathematical understanding, meant to be decoded by other mathematicians. The understanding itself is often very non-textual, and the process of serialization and deserialization can be extremely difficult. And the reasoning process itself often proceeds in non-textual ways, prior to the process of serialization.
- NoToP 4y ago
  You kind of just described the language faculty as well.
  - tgv 4y ago
    Everyday language is an entirely different thing. I don't think we can "serialize" maths at a speed of 3 symbols per second. I also think your OP is quite wrong. What (s)he calls serialization, is attempting to formulate and test an idea in a "proof language", where a successful and correct string determines the validity. A normal sentence has an entirely different use. Math is (much) more like programming than speaking.
    - kevinventullo 4y ago
      That said, much of modern mathematics is still fairly informal, with “the proof is left to the reader” implicitly showing up in nearly every written sentence for the sake of brevity.
ngvrnd 4y ago
“Wovon man nicht sprechen kann, darüber muß man schweigen.” L. Wittgenstein
- eyeundersand 4y ago
  "Whereof one can not speak, thereof one must be silent." (per google translate)
glitchc 4y ago
This refrain has been repeated through time immemorial, stretching as far back as the ancient Mediterranean, Chinese and Vedic cultures. They have consistently been wrong. Ergo, the conclusion I draw is that if there is a limit to human intelligence, we are not even close to it.
- x86x87 4y ago
  I believe that humans and human intelligence is pretty limited. We are overcoming our limitations by using abstractions and tools. People today are not significant smarter than people 5000 years ago. We just have better tools which allow us to create better tech which in turn allows us to create better tools. And we keep going.
- lm28469 4y ago
  Knowledge or intelligence ?
barrysteve 4y ago
Why would you ask this question and not bump into God? That concept of a living inside a computer simulation, asking if we can know the unknowable, even bumping into Marduk... is answerable by the divine. Though the parable about the ten ox was kind of cool. Hackernews loves to revisit the zen and the art of motorcycle maintenance in many different forms, yet the answer is always the same. The 'No thing' in the ten ox parable, in zen and the art, in this articles pondering about what is unknowable, is god...
- brink 4y ago
  Wholeheartedly agree. Our intrinsic existence with its beginning and its end is a contradiction, so I define God as "the unknowable thing that we came from", the "container of time and space". If it's reasonable to assume that there's consciousness down here, it's also relatively safe to assume that there's some form of more complete consciousness in the higher thing that we came from.
- pessimizer 4y ago
  Saying something is only answerable by the divine is just like saying that you refuse to answer something. The unknowable is not answerable by the unknowable.
- gjm11 4y ago
  If "God" is the answer to every question (or at least every sufficiently ultimate-sounding question) then I suggest it is not really a useful answer to any question. Frankly, what you say comes across to me as "How dare all these people talk about deep mysterious things without giving my preferred Answer To All Deep Mysterious Things?". Well, maybe your answer is wrong. Or maybe somehow more than one can be right. Or maybe there are in fact multiple Deep Mysterious Things that don't all have the same answer. Or maybe, as you clearly think is obvious, those other people are all wrong because the only right answer to any Deep Mysterious Thing is "God". But you might consider the following: if your current beliefs imply that anyone who asks questions like these should "bump into God", then the fact that someone asks questions like these and doesn't indicates that something in your current beliefs is wrong. Still more, the fact that (as you complain of in your last paragraph) people frequently ask such questions without "bumping into God".
deleted 4y ago
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mikewarot 4y ago
If we use Flowers for Algernon[1] as a model for reasoning about levels of intelligence, what's really different about Charlie as he progresses through the story is not the nature of his intelligence, but simply the depth of his mental stack. Once you have access to external means of storing context and knowledge, and a deep enough stack to keep the pointers to those contexts handy, you can slowly, but surely, grind through anything. It's possible (but silly) to set up an 8 bit based IMSAI computer with access to terabytes of disk space, have it emulate a 64bit CPU with loads of RAM, and grind through DALL-E... the state space of a 64bit CPU with all of its registers is well within the 64k address range of the S-100 bus. I strongly believe there is nothing I can't learn, eventually. Physical skills and grace are another matter, but learning is something I think is unlimited for most people, if they're curious about the subject. [1] https://www.sdfo.org/gj/stories/flowersforalgernon.pdf https://www.sdfo.org/gj/stories/flowersforalgernon.pdf
- ColinWright 4y ago
  There's an interesting bit in Chocky[0] where Matthew, Chocky's "host", (hereinafter "M/C") asks his father, on behalf of Chocky: "Why do cows stop?" M/C has noticed that the cows have seen the farmer open the gate to let them through hundreds of times, and they seem to want to go through, but seem unable to work out how to open the gate for themselves. M/C argues that intelligence shouldn't be limited, and you should just be able to build and build and build forever. But the cows don't seem able to do that. In Pure Maths we know that we can have strictly increasing sequences that are unbounded above, but we can also have strictly increasing sequences that are bounded. How do we know intelligence (by analogy) is the former, and not the latter? More, some sequences grow incredibly slowly, and maybe we are limited in practice even if not limited in theory. [0] https://en.wikipedia.org/wiki/Chocky https://en.wikipedia.org/wiki/Chocky
  - aatd86 4y ago
    Very nice way to put it. Quite clever. The other thing is that there is a dependence on physical perception. Even if one has exceptional raw processing power, if one has no data to apply it to, intelligence can't express itself. To a degree, we are only intelligent because we exist i.e. we perceive. Processing power is useless without inputs.
renewiltord 4y ago
Thoughts that come to mind as I read: - why has increased energy availability stopped increasing cognitive ability in the massive leaps it used to? - I definitely know there are things that I struggle to grok that a few people rapidly do, and there are things that I rapidly grok that others fail to - and often this appears monotonically so general intelligence appears real - is modern intelligence just the result of sufficiently diverse training? i.e. do we have similar brains to our ancient ancestors just with far superior stimulation? - I suspect that all sorts of models will arise from the same base machine (our brains) scaled up (more neurons with more density and more energy). It's likely that physical constraints - energy use, mother birth canal - are bigger determiners since we have decoupled high intelligence from gener survival now - I find the simulation discussion tiresome. It seems masturbatory because it is so indulgent but does not advance thought. No one ever provides future hypotheses that are useful from a sim perspective or future thought experiments that go anywhere or testable experiments. I think the sim theory is a philosophical dead end and we'll conclude that one day. - If new cognition is needed, is it possible from the brain scale-up I mentioned before? Or is it like an aleph0 to aleph1 transition? I suspect there is a Turing completeness to cognition - in that there are some base laws which makes access to all math possible. - however, if scale-up is possible and if math is all accessible, we could imagine set-sets who are specialized optimized intelligence. Does the general absence of these imply that we haven't yet decoupled general intelligence from individual outcome? - I don't think direct experimentation on the limits of our intelligence will yield any outcome. I do think that we will eventually invent either biological or electronic super intelligences and this will likely result in conclusions that reveal something here. - I do notice that on psychedelics I become more susceptible to the idea that there is some greater truth out there that I'm just barely missing but considering that I never produce anything from that - perhaps this Missing Greater Truth feeling is actually a lesser form of consciousness - I.e. it's what you get when you leave intelligence and full consciousness behind. It's what bootstraps things. Anyway, I subscribe to that side because I find a slightly losing-myself feeling when I attempt to fully chase the "ideas I can't hold" concept.
- sinenomine 4y ago
  I like the questions, esp. this one: > If new cognition is needed, is it possible from the brain scale-up I mentioned before? Or is it like an aleph0 to aleph1 transition? I suspect there is a Turing completeness to cognition - in that there are some base laws which makes access to all math possible. There is indirect evidence from multiple studies of ML models and animal intelligence pointing in the direction of "scaling up is good for intelligence, if your system isn't limited by global connectivity too much". If you want to know more, see https://www.gwern.net/Scaling-hypothesis https://www.gwern.net/Scaling-hypothesis and Haier's The Neuroscience of Intelligence.
peterweyand 4y ago
To anyone interested I wrote a small paper on this and I'm looking around for commentary. It's mostly a philosophy paper, but it considers AI as well. I then go on to discuss moral and ethical questions. Here's a link to the latest draft. I don't know that it will ever be good enough to be an academic paper, but maybe someone will find it entertaining. Always looking for any substantive commentary. I'd be incredibly interested to know if anyone thought there might be a way to model A^ using a neural network that satisfied the conditions in the paper. https://www.dropbox.com/s/uveu8eiq2snsojs/Sep12Noon.pdf?dl=0 https://www.dropbox.com/s/uveu8eiq2snsojs/Sep12Noon.pdf?dl=0
sukruh 4y ago
The brain is a biological organ, and like all other biological organs it has its limits. A human heart can only pump a certain amount of blood per minute. A human liver can only perform certain chemical reactions. The brains's limits in mental arithmetic or memorization are obvious, but is its ability to form and understand abstractions also limited? A dog will never understand how a credit card works. Are there concepts that our human brains are biologically incapable of understanding? Maybe some of the current philosophical questions like consciousness or the illusive appearance of free will are beyond our limits. I wish I knew more about computability, decidability, the Incompleteness Theorem etc to think further about this.
- astrobe_ 4y ago
  > Are there concepts that our human brains are biologically incapable of understanding As silly as it sounds: UFOs. Chasing UFOs with jet-fighters is probably as silly as a dog eating a credit card. To be clear, I don't imply that UFOs exist. Science says "I don't know" for the few serious cases that are still unsolved, and that's my answer too.
- andorov 4y ago
  We can't even fully understand chess (or even checkers), in the way that we can completely understand tic-tac-toe.
- inglor_cz 4y ago
  " The brains's limits in mental arithmetic or memorization are obvious" Those limits are pretty high up, though, given the incredible performances of math savants: https://en.wikipedia.org/wiki/Hypercalculia https://en.wikipedia.org/wiki/Hypercalculia Safe to say that most of us are nowhere near those limits.
skybrian 4y ago
It's interesting how much of an image can be missing if it gets the overall vibe right. I guessed immediately that these images were all computer-generated, but they still looked "okay." I certainly didn't notice that the bike had no handlebars, because there was a blob that could sort of be handlebars, maybe. And the missing limbs might just not be visible, maybe? In part, I think it sort-of-works because artists often make abstract images by leaving stuff out. A lot can be wrong with an image and it still gets "artistic license" if it looks painted? It seems similar to GPT-3 generated text, where if you skim it looks okay, but if you attempt to really understand the text, it's nonsense. (And it's similar for a lot of spam websites these days.)
guywithahat 4y ago
If anyone's interested in learning more about human intelligence I'd highly recommend the bell curve by Richard Herrnstein and Charles Murray. It basically follows the NLSY and looks at how IQ varies from person to person and how that impacts that persons life. The book itself is a bit old however that's still arguably the best, most comprehensive study we've done on IQ
HardlyCurious 4y ago
edmcnulty101 4y ago
Being that it's proven and we know for a fact that human intelligence is on a spectrum, why can't a baby be born with a 300 IQ. Given that Intelligence is not directly co-orellated with success....and tons of Mensa people are waiting tables and doing jobs requiring no advanced IQ. The real sad part is that there may be a baby with a 300 IQ who is trapped in a shitty dead end job by capitalism.

97 points by ColinWright 4y ago

mikewarot 4y ago

This is a duplicate of https://news.ycombinator.com/item?id=32799953 https://news.ycombinator.com/item?id=32799953

ColinWright 4y ago
I first submitted it at least a day ago, I think probably at least three days ago. Clearly it's been put into the "Second Chance" pool, because I did not resubmit this. Mods: You might want to merge the discussions. @dang

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?
  - 4y ago
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.

phkahler 4y ago

>> Soon I start to wonder about concepts that I don’t know exist: concepts whose existence I can never even suspect, let alone contemplate. What can I ever know about that which lies beyond the limits of what I can even imagine? I find it more interesting or even frightening to contemplate those differences among humans today. For those with an IQ in the 90's, what thoughts and concepts am I able to understand that they can't? And likewise, what am I personally not able to to grok that some of the smartest people can? Even within engineering and software I find that some practitioners have a hard time with some things I find easy, and I have a hard time with concepts others find easy. It may just be differing backgrounds, but what if these are differences in raw cognitive capability? Levels of abstraction seem real if not well defined.

chrsig 4y ago
> It may just be differing backgrounds, but what if these are differences in raw cognitive capability? Honestly, I think ignorance may be bliss. I loathe to think about what arrogance, bigotry, and manifestations of depression would pop up had we concrete ways to measure capability.
- anonporridge 4y ago
  Ignorance isn't a real option. If the truth is knowable, someone will find it eventually. The best you can do is opt yourself into ignorance. You can't opt everyone around you into the same ignorance. And by opting yourself into ignorance, you potentially create a competitive advantage for those who don't have the same hangups for facing ugly truths as you do.
- phkahler 4y ago
  >> Honestly, I think ignorance may be bliss. I loathe to think about what arrogance, bigotry, and manifestations of depression would pop up had we concrete ways to measure capability. That's why I find the idea somewhat frightening. But that is also what makes it a far more interesting (relevant) question.
barrysteve 4y ago
What difference would it make? We treat poor and rich as equals... or should. Amputees are not treated any less than athletes. These questions impose artifical beliefs as plausible theorems

sdenton4 4y ago

>> "What is truly stunning about the fact that modern science and mathematics are formulated through a sequence of marks is its exclusivity: nothing other than these finite sequences of symbols is ever found in modern mathematical reasoning." Well that's simply not true. We draw pictures all the time. But putting that aside... Written mathematics is a serialized form of mathematical understanding, meant to be decoded by other mathematicians. The understanding itself is often very non-textual, and the process of serialization and deserialization can be extremely difficult. And the reasoning process itself often proceeds in non-textual ways, prior to the process of serialization.

NoToP 4y ago
You kind of just described the language faculty as well.
- tgv 4y ago
  Everyday language is an entirely different thing. I don't think we can "serialize" maths at a speed of 3 symbols per second. I also think your OP is quite wrong. What (s)he calls serialization, is attempting to formulate and test an idea in a "proof language", where a successful and correct string determines the validity. A normal sentence has an entirely different use. Math is (much) more like programming than speaking.
  - kevinventullo 4y ago
    That said, much of modern mathematics is still fairly informal, with “the proof is left to the reader” implicitly showing up in nearly every written sentence for the sake of brevity.

ngvrnd 4y ago

“Wovon man nicht sprechen kann, darüber muß man schweigen.” L. Wittgenstein

eyeundersand 4y ago
"Whereof one can not speak, thereof one must be silent." (per google translate)

glitchc 4y ago

This refrain has been repeated through time immemorial, stretching as far back as the ancient Mediterranean, Chinese and Vedic cultures. They have consistently been wrong. Ergo, the conclusion I draw is that if there is a limit to human intelligence, we are not even close to it.

x86x87 4y ago
I believe that humans and human intelligence is pretty limited. We are overcoming our limitations by using abstractions and tools. People today are not significant smarter than people 5000 years ago. We just have better tools which allow us to create better tech which in turn allows us to create better tools. And we keep going.
lm28469 4y ago
Knowledge or intelligence ?

barrysteve 4y ago

Why would you ask this question and not bump into God? That concept of a living inside a computer simulation, asking if we can know the unknowable, even bumping into Marduk... is answerable by the divine. Though the parable about the ten ox was kind of cool. Hackernews loves to revisit the zen and the art of motorcycle maintenance in many different forms, yet the answer is always the same. The 'No thing' in the ten ox parable, in zen and the art, in this articles pondering about what is unknowable, is god...

brink 4y ago
Wholeheartedly agree. Our intrinsic existence with its beginning and its end is a contradiction, so I define God as "the unknowable thing that we came from", the "container of time and space". If it's reasonable to assume that there's consciousness down here, it's also relatively safe to assume that there's some form of more complete consciousness in the higher thing that we came from.
pessimizer 4y ago
Saying something is only answerable by the divine is just like saying that you refuse to answer something. The unknowable is not answerable by the unknowable.
gjm11 4y ago
If "God" is the answer to every question (or at least every sufficiently ultimate-sounding question) then I suggest it is not really a useful answer to any question. Frankly, what you say comes across to me as "How dare all these people talk about deep mysterious things without giving my preferred Answer To All Deep Mysterious Things?". Well, maybe your answer is wrong. Or maybe somehow more than one can be right. Or maybe there are in fact multiple Deep Mysterious Things that don't all have the same answer. Or maybe, as you clearly think is obvious, those other people are all wrong because the only right answer to any Deep Mysterious Thing is "God". But you might consider the following: if your current beliefs imply that anyone who asks questions like these should "bump into God", then the fact that someone asks questions like these and doesn't indicates that something in your current beliefs is wrong. Still more, the fact that (as you complain of in your last paragraph) people frequently ask such questions without "bumping into God".

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mikewarot 4y ago

If we use Flowers for Algernon[1] as a model for reasoning about levels of intelligence, what's really different about Charlie as he progresses through the story is not the nature of his intelligence, but simply the depth of his mental stack. Once you have access to external means of storing context and knowledge, and a deep enough stack to keep the pointers to those contexts handy, you can slowly, but surely, grind through anything. It's possible (but silly) to set up an 8 bit based IMSAI computer with access to terabytes of disk space, have it emulate a 64bit CPU with loads of RAM, and grind through DALL-E... the state space of a 64bit CPU with all of its registers is well within the 64k address range of the S-100 bus. I strongly believe there is nothing I can't learn, eventually. Physical skills and grace are another matter, but learning is something I think is unlimited for most people, if they're curious about the subject. [1] https://www.sdfo.org/gj/stories/flowersforalgernon.pdf https://www.sdfo.org/gj/stories/flowersforalgernon.pdf

ColinWright 4y ago
There's an interesting bit in Chocky[0] where Matthew, Chocky's "host", (hereinafter "M/C") asks his father, on behalf of Chocky: "Why do cows stop?" M/C has noticed that the cows have seen the farmer open the gate to let them through hundreds of times, and they seem to want to go through, but seem unable to work out how to open the gate for themselves. M/C argues that intelligence shouldn't be limited, and you should just be able to build and build and build forever. But the cows don't seem able to do that. In Pure Maths we know that we can have strictly increasing sequences that are unbounded above, but we can also have strictly increasing sequences that are bounded. How do we know intelligence (by analogy) is the former, and not the latter? More, some sequences grow incredibly slowly, and maybe we are limited in practice even if not limited in theory. [0] https://en.wikipedia.org/wiki/Chocky https://en.wikipedia.org/wiki/Chocky
- aatd86 4y ago
  Very nice way to put it. Quite clever. The other thing is that there is a dependence on physical perception. Even if one has exceptional raw processing power, if one has no data to apply it to, intelligence can't express itself. To a degree, we are only intelligent because we exist i.e. we perceive. Processing power is useless without inputs.

renewiltord 4y ago

Thoughts that come to mind as I read: - why has increased energy availability stopped increasing cognitive ability in the massive leaps it used to? - I definitely know there are things that I struggle to grok that a few people rapidly do, and there are things that I rapidly grok that others fail to - and often this appears monotonically so general intelligence appears real - is modern intelligence just the result of sufficiently diverse training? i.e. do we have similar brains to our ancient ancestors just with far superior stimulation? - I suspect that all sorts of models will arise from the same base machine (our brains) scaled up (more neurons with more density and more energy). It's likely that physical constraints - energy use, mother birth canal - are bigger determiners since we have decoupled high intelligence from gener survival now - I find the simulation discussion tiresome. It seems masturbatory because it is so indulgent but does not advance thought. No one ever provides future hypotheses that are useful from a sim perspective or future thought experiments that go anywhere or testable experiments. I think the sim theory is a philosophical dead end and we'll conclude that one day. - If new cognition is needed, is it possible from the brain scale-up I mentioned before? Or is it like an aleph0 to aleph1 transition? I suspect there is a Turing completeness to cognition - in that there are some base laws which makes access to all math possible. - however, if scale-up is possible and if math is all accessible, we could imagine set-sets who are specialized optimized intelligence. Does the general absence of these imply that we haven't yet decoupled general intelligence from individual outcome? - I don't think direct experimentation on the limits of our intelligence will yield any outcome. I do think that we will eventually invent either biological or electronic super intelligences and this will likely result in conclusions that reveal something here. - I do notice that on psychedelics I become more susceptible to the idea that there is some greater truth out there that I'm just barely missing but considering that I never produce anything from that - perhaps this Missing Greater Truth feeling is actually a lesser form of consciousness - I.e. it's what you get when you leave intelligence and full consciousness behind. It's what bootstraps things. Anyway, I subscribe to that side because I find a slightly losing-myself feeling when I attempt to fully chase the "ideas I can't hold" concept.

sinenomine 4y ago
I like the questions, esp. this one: > If new cognition is needed, is it possible from the brain scale-up I mentioned before? Or is it like an aleph0 to aleph1 transition? I suspect there is a Turing completeness to cognition - in that there are some base laws which makes access to all math possible. There is indirect evidence from multiple studies of ML models and animal intelligence pointing in the direction of "scaling up is good for intelligence, if your system isn't limited by global connectivity too much". If you want to know more, see https://www.gwern.net/Scaling-hypothesis https://www.gwern.net/Scaling-hypothesis and Haier's The Neuroscience of Intelligence.

peterweyand 4y ago

To anyone interested I wrote a small paper on this and I'm looking around for commentary. It's mostly a philosophy paper, but it considers AI as well. I then go on to discuss moral and ethical questions. Here's a link to the latest draft. I don't know that it will ever be good enough to be an academic paper, but maybe someone will find it entertaining. Always looking for any substantive commentary. I'd be incredibly interested to know if anyone thought there might be a way to model A^ using a neural network that satisfied the conditions in the paper. https://www.dropbox.com/s/uveu8eiq2snsojs/Sep12Noon.pdf?dl=0 https://www.dropbox.com/s/uveu8eiq2snsojs/Sep12Noon.pdf?dl=0

sukruh 4y ago

The brain is a biological organ, and like all other biological organs it has its limits. A human heart can only pump a certain amount of blood per minute. A human liver can only perform certain chemical reactions. The brains's limits in mental arithmetic or memorization are obvious, but is its ability to form and understand abstractions also limited? A dog will never understand how a credit card works. Are there concepts that our human brains are biologically incapable of understanding? Maybe some of the current philosophical questions like consciousness or the illusive appearance of free will are beyond our limits. I wish I knew more about computability, decidability, the Incompleteness Theorem etc to think further about this.

astrobe_ 4y ago
> Are there concepts that our human brains are biologically incapable of understanding As silly as it sounds: UFOs. Chasing UFOs with jet-fighters is probably as silly as a dog eating a credit card. To be clear, I don't imply that UFOs exist. Science says "I don't know" for the few serious cases that are still unsolved, and that's my answer too.
andorov 4y ago
We can't even fully understand chess (or even checkers), in the way that we can completely understand tic-tac-toe.
inglor_cz 4y ago
" The brains's limits in mental arithmetic or memorization are obvious" Those limits are pretty high up, though, given the incredible performances of math savants: https://en.wikipedia.org/wiki/Hypercalculia https://en.wikipedia.org/wiki/Hypercalculia Safe to say that most of us are nowhere near those limits.

skybrian 4y ago

It's interesting how much of an image can be missing if it gets the overall vibe right. I guessed immediately that these images were all computer-generated, but they still looked "okay." I certainly didn't notice that the bike had no handlebars, because there was a blob that could sort of be handlebars, maybe. And the missing limbs might just not be visible, maybe? In part, I think it sort-of-works because artists often make abstract images by leaving stuff out. A lot can be wrong with an image and it still gets "artistic license" if it looks painted? It seems similar to GPT-3 generated text, where if you skim it looks okay, but if you attempt to really understand the text, it's nonsense. (And it's similar for a lot of spam websites these days.)

guywithahat 4y ago

If anyone's interested in learning more about human intelligence I'd highly recommend the bell curve by Richard Herrnstein and Charles Murray. It basically follows the NLSY and looks at how IQ varies from person to person and how that impacts that persons life. The book itself is a bit old however that's still arguably the best, most comprehensive study we've done on IQ

HardlyCurious 4y ago

edmcnulty101 4y ago

Being that it's proven and we know for a fact that human intelligence is on a spectrum, why can't a baby be born with a 300 IQ. Given that Intelligence is not directly co-orellated with success....and tons of Mensa people are waiting tables and doing jobs requiring no advanced IQ. The real sad part is that there may be a baby with a 300 IQ who is trapped in a shitty dead end job by capitalism.