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
"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?
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.
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.
> 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?
> 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.
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).
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?
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.
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.
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.
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.)
> 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.
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.
>> 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.
> 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.
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.
>> 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.
> Amputees are not treated any less than athletes.
I see you don't understand meritocracy. Amputees can physically do less than athletes, therefore they deserve worse food, worse housing, and worse medical care, unless they can offset this defect in some other way.
It's almost blasphemous to do otherwise; if God has seen fit to punish them, your offsetting of that punishment shows a prideful disapproval of God's plan. God has made His judgment of the amputee clear, so it's actually your duty to reinforce that judgement. God has given us dominion over this world, and the responsibility to maintain it; we can do that better with athletes, rather than people who are missing limbs. Or secularly, we collectively maintain the world's wealth through our individual contributions. The mean athlete contributes more, the mean amputee contributes less, and what goes around, should come around. Workers, not shirkers!
I like to think of it as the reverse golden rule. Accept unto yourself that which you would have done to others. If you're worth less, eat less.
This sounds like an astoundingly appealing philosophy to one who is towards the top of this meritocracy pecking order, and utterly repugnant to anyone downward. It's so self-serving in that regard, that the "conflict of interest" in those who benefit in extolling it as the order for all...well, it makes the whole thing highly questionable. Is it the best way because it's the best way, or because it's best for you? It's really hard to see anyone who is on the wrong end of this system arguing for it, so in the end they would have to be subjugated? That rarely (never?) works out (if it can be considered a good thing to work out at all...), so it's clear to me that a hard-liner meritocratic system is never really going to work.
Let's give rewards equally to all; the builders, the creators, the criminals and the leeches. That is surely the best system of distribution. How cruel must you be to let another man have less than you? So we must take from those who labor and with a wisdom that they have not, re-distribute the fruit of society fairly to all. It is a unjust and wicked world, so let us take control and right the world's wrongs.
Von Neumann’s impact is at least an order of magnitude greater than Tao’s. No disrespect, he is a great mathematician. But the sheer breath of von Neumann’s impact is unparalleled. [1]
Why do we often implicitly consider the human cognitive capability as it is embodied in adult individuals' biological makeup to be immutable, now and in the future? Even a single existence proof of a method for cognitive enhancement would deal away with this frame.
Given the sheer amount of capital available for trial and error on (sometimes ridiculous like juicero) consumer products it's weird that so little of it is allocated to advance the biotechnology of human enhancement.
>> "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.
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.
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.
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.
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.
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...
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.
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.
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".
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.
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.
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.
>I strongly believe there is nothing I can't learn, eventually.
Well that's the crux isn't it? If some prodigy can learn QFT before the age of 13 they have a lifetime to go beyond those concepts. But if it takes you 50 years to learn you don't have enough time to go beyond that. That's a fundamental piece of intelligence, the speed you can lean at.
Which is why it is said that, if we do it right, we "stand on the shoulders of giants". E.g., we don't each need to reinvent calculus, Sir Isaac Newton and Gottfried Leibniz did that already...
Anyone who takes 50 years to learn QFT exists only in the imagination. Real people either learn QFT in a reasonable amount of time, or they don't understand it at all.
>>not the nature of his intelligence, but simply the depth of his mental stack.
Excellent observation
In an experiment on spiders that I found very enlightening, the experimenter placed some desirable food on one (small) platform, and the spider on another perch, and there was a 3D maze of links that the spider could use to get to the food, but only one proper path. The spiders sat for around two hours, then used the exactly correct path to reach the goal. The researchers figured that they were using their tiny memory to just grind through the options until they found the right path, then went for it.
I've found this fascinating and oddly inspiring ever since I read about the study; I'm sorry I can't find it now to link here.
Note that those would have been some species of Portia (jumping spiders), known both for their unusual visual acuity and extraordinary intelligence. Most spiders can't do that.
Right, and all digital computers are Turing Machines. See also Stephen Wolfram's Principle of Computational Equivalence[1].
There can be, and are theories that no one human brain can ever fully understand (like Quantum Mechanics) and yet we have developed them... no one person did, but they emerged from the combined work and brain power of many people and the tools they used, be those pure mathematics or (nowadays) Google, AI, computer proof assistants. That's why even Richard Feynman said no one ever really understands QM, one just kind of gets used to the way the math gives the right answers[2].
A single human brain could never have developed QM, but combine a large number of them and the right tools, and I don't see any reason why there should be "hard limits to knowledge" any more than there's a limit to what a turing machine can compute given enough time (and a long enough tape).
Turing machines were invented to demonstrate the limits of computation. QM is fully described by math, hence computable. Not sure what point you are making?
That the essential nature of reality eludes us is evidenced by the way in which we develop our own simulation of the universe via Artificial Intelligence.
Our models are a crude - albeit based on initially valid principles - representation of thought processes. While we can get interesting results from our cargo cultish approach to thinking [much like a cargo cult representation of an airplane can fly briefly if thrown off a cliff] we are clearly off course in our quest.
Our intelligence was developed through the senses, and this simple fact is not considered by those who make artificial intelligence. We do not feed our models with information from the senses. We use models to recognize images that were not acquired by the senses.
I work in an approach in which artificial intelligence is acquired through an evolutionary process, with sensors [image, acoustic, pressure, chemical] capturing -human - reality in real time, and processing it without having to solve a specific problem. In short, a model of reality recognition, in which each frame of reality is transformed into tensors, and each new frame is the result of the recognition and is weighted by the previous frame. That would be a closer mimicking of the human learning.
When - human like - intelligence emerges from this system, it can then be used for practical purposes.
You've essentially asserted that the human brain is turing complete. I don't disagree with you.
However, the problem that I see is computational time. Just like that 8bit computer, if your mind is sufficiently limited, you don't have the lifespan to learn certain things.
Which incidentally implies that there may, legitimately, be things that old people have learned that we are simply incapable of understanding before we reach old age.
>However, the problem that I see is computational time.
We arrived quickly to the conclusion that intelligence is mostly speed, that I think is the correct definition.
IQ tests have a time limit. Increase the limit, and anybody would increase their IQ score. With a infinite time limit, you likely would have an perfect IQ score. So what does an IQ test measure? it measures how fast can you complete a series of tasks, that is, it measures your speed, because intelligence is speed.
I've finished plenty of tests before time was up. The limit on time is NOT a limiting factor for most people, at least it wasn't when I went to school 4 decades ago.
I often finish tests long before the time limit is up, for a variety of reasons, but I can't think of any time where the results took that into account. Should it? (IMO yes, but that gets difficult to account for)
The notion of a "deep enough stack to keep the pointers to those context handy" depends on the complexity of what you're learning. If the task at hand has a large enough memory demand, then you might find yourself "swapping" to external storage too frequently, and someone with even a slightly better working memory might not have to -- they'll probably be able to learn much faster.
That being said, this is an opportunity, not a problem -- if they learned something, they can probably explain the concept to you much more efficiently and help you learn as well. Some of the best learning resources online are informally written blogs :)
This sounds wholy wrong to me. What do you mean there is nothing you can't learn? What about all of the states of a chessboard. Or even the best move of a given position. Humans will never compete with a computer in this capacity. We absolutely do not have an infinite space to store things in our brain
I certainly can learn all the rules of chess. I know most of them already. It's not unknowable. Knowing how things work is what I was talking about, not out-computing a computer.
I like your perspective, as well as some of the points other commentors have made in response to your own. However, there is one point you make that I disagree/question - is a physical skill and grace not also a form of knowing? The human body and brain are intrinsically connected "machines" (not a term/concept I love, but for want of a better one...) and so their knowing and learning must surely be tied together. But, larger than this yet so interconnected - is this aspect of our being not also where we experience our first limitations? And if so, then wouldn't that imply limitations to our purely cognitive experience? For example: I can swim (a physical skill), but due to pure bodily limitations (height, arm/leg span, etc.) will never be an Olympian (a physical achievement). Surely, you and I could be taught how to and practice as we would attempt to learn, but still likely never achieve the grace of a ballerina, possibly regardless of the age at which we begin. And so - how is it that this "failure"/limitation could not also be applied to the cognitive? Isn't also likely that our own intelligence could have similar limitations that we perhaps aren't even aware of, for how would we measure? Again, just positing some questions your comment brought to mind; in particular, I appreciate the idea of the depth of mental "stack" being the quality of measurement that matters in differentiating intelligence levels. And so now: to find the physical stack, which in this case is both metaphorical and real (for the weight lifters out there, anyway).
Except that if you started that old CPU 40 years ago a modern CPU would be developed years later and then started, then woild quickly overtake the depth to which your old CPU could have ground the problem to. Yes you can learn anything given time, but you will die before that.
I don't agree. It depends on your definition of "learning" and "knowledge", I guess, but I think there's a big difference between types of knowledge to be acquired, some of which simply cannot be achieved via computation.
For example, a person could probably easily devise an algorithm to compute what a "y" value must be for a given (x,y) pair on a coordinate plane by successively applying additions to each previous input (similar to how you would implement a fibonacci sequence). You could graph lines this way. But with an insight that this potentially infinite task can be represented so concisely as f(x) = mx + b will take all this work out of your hands... That's not something that you necessarily would ever learn by performing any amount of computation.
To achieve this insight, you have to have somehow risen above the level of base computation to an abstraction. For things that someone else has already figured out, sure, you could always expand on their work forever.
- 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.
> 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".
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.
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.
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.)
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
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.
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[ 3.4 ms ] story [ 155 ms ] threadMods: You might want to merge the discussions. @dang
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?
https://en.wikipedia.org/wiki/Evidence_of_absence
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?
> 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.
The hard problem of consciousness seems particularly suited to avoid the mechanisms that "we" "know" anything (e.g., objective evidence and the scientific method).
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?
My favorite example:
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.
> 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.
"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.)
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.
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.
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.
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.
That's why I find the idea somewhat frightening. But that is also what makes it a far more interesting (relevant) question.
These questions impose artifical beliefs as plausible theorems
The answers to these questions have real ramifications, treating them as artificial is how harm to real people happens.
I see you don't understand meritocracy. Amputees can physically do less than athletes, therefore they deserve worse food, worse housing, and worse medical care, unless they can offset this defect in some other way.
It's almost blasphemous to do otherwise; if God has seen fit to punish them, your offsetting of that punishment shows a prideful disapproval of God's plan. God has made His judgment of the amputee clear, so it's actually your duty to reinforce that judgement. God has given us dominion over this world, and the responsibility to maintain it; we can do that better with athletes, rather than people who are missing limbs. Or secularly, we collectively maintain the world's wealth through our individual contributions. The mean athlete contributes more, the mean amputee contributes less, and what goes around, should come around. Workers, not shirkers!
I like to think of it as the reverse golden rule. Accept unto yourself that which you would have done to others. If you're worth less, eat less.
[1] https://www.youtube.com/watch?v=8nt3edWLgIg&t=382s
Now, Terry Tao is a person of the same, if not greater caliber. A real, living 200 IQ genius.
[1]https://www.wikiwand.com/en/John_von_Neumann
I get that we aren't (yet) spoiled by availability of (gene or cellular) therapies uplifting our IQs, but hey, at least those mice were able to receive theirs: https://www.cell.com/cell-stem-cell/pdf/S1934-5909(13)00007-...
Given the sheer amount of capital available for trial and error on (sometimes ridiculous like juicero) consumer products it's weird that so little of it is allocated to advance the biotechnology of human enhancement.
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.
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.
(per google translate)
Ergo, the conclusion I draw is that if there is a limit to human intelligence, we are not even close to it.
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.
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...
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.
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".
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
"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
Processing power is useless without inputs.
Take for example Conway's Game of Life. Initial state is "perceived" from the seeder. From there it's a perception-less process.
They say Einstein ruminated ten years on relativity. Did he need much perception for his absolutely not useless result?
Well that's the crux isn't it? If some prodigy can learn QFT before the age of 13 they have a lifetime to go beyond those concepts. But if it takes you 50 years to learn you don't have enough time to go beyond that. That's a fundamental piece of intelligence, the speed you can lean at.
[Edit typo: of/if]
Excellent observation
In an experiment on spiders that I found very enlightening, the experimenter placed some desirable food on one (small) platform, and the spider on another perch, and there was a 3D maze of links that the spider could use to get to the food, but only one proper path. The spiders sat for around two hours, then used the exactly correct path to reach the goal. The researchers figured that they were using their tiny memory to just grind through the options until they found the right path, then went for it.
I've found this fascinating and oddly inspiring ever since I read about the study; I'm sorry I can't find it now to link here.
There can be, and are theories that no one human brain can ever fully understand (like Quantum Mechanics) and yet we have developed them... no one person did, but they emerged from the combined work and brain power of many people and the tools they used, be those pure mathematics or (nowadays) Google, AI, computer proof assistants. That's why even Richard Feynman said no one ever really understands QM, one just kind of gets used to the way the math gives the right answers[2].
A single human brain could never have developed QM, but combine a large number of them and the right tools, and I don't see any reason why there should be "hard limits to knowledge" any more than there's a limit to what a turing machine can compute given enough time (and a long enough tape).
[1] https://en.wikipedia.org/wiki/A_New_Kind_of_Science#Principl...
[2] https://www.youtube.com/watch?v=aAgcqgDc-YM
Our models are a crude - albeit based on initially valid principles - representation of thought processes. While we can get interesting results from our cargo cultish approach to thinking [much like a cargo cult representation of an airplane can fly briefly if thrown off a cliff] we are clearly off course in our quest.
Our intelligence was developed through the senses, and this simple fact is not considered by those who make artificial intelligence. We do not feed our models with information from the senses. We use models to recognize images that were not acquired by the senses.
I work in an approach in which artificial intelligence is acquired through an evolutionary process, with sensors [image, acoustic, pressure, chemical] capturing -human - reality in real time, and processing it without having to solve a specific problem. In short, a model of reality recognition, in which each frame of reality is transformed into tensors, and each new frame is the result of the recognition and is weighted by the previous frame. That would be a closer mimicking of the human learning.
When - human like - intelligence emerges from this system, it can then be used for practical purposes.
Edited for clarity
However, the problem that I see is computational time. Just like that 8bit computer, if your mind is sufficiently limited, you don't have the lifespan to learn certain things.
Which incidentally implies that there may, legitimately, be things that old people have learned that we are simply incapable of understanding before we reach old age.
We arrived quickly to the conclusion that intelligence is mostly speed, that I think is the correct definition.
IQ tests have a time limit. Increase the limit, and anybody would increase their IQ score. With a infinite time limit, you likely would have an perfect IQ score. So what does an IQ test measure? it measures how fast can you complete a series of tasks, that is, it measures your speed, because intelligence is speed.
That being said, this is an opportunity, not a problem -- if they learned something, they can probably explain the concept to you much more efficiently and help you learn as well. Some of the best learning resources online are informally written blogs :)
For example, a person could probably easily devise an algorithm to compute what a "y" value must be for a given (x,y) pair on a coordinate plane by successively applying additions to each previous input (similar to how you would implement a fibonacci sequence). You could graph lines this way. But with an insight that this potentially infinite task can be represented so concisely as f(x) = mx + b will take all this work out of your hands... That's not something that you necessarily would ever learn by performing any amount of computation.
To achieve this insight, you have to have somehow risen above the level of base computation to an abstraction. For things that someone else has already figured out, sure, you could always expand on their work forever.
- 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.
> 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 and Haier's The Neuroscience of Intelligence.
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
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.
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.
Those limits are pretty high up, though, given the incredible performances of math savants:
https://en.wikipedia.org/wiki/Hypercalculia
Safe to say that most of us are nowhere near those limits.
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.)
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.