Questions about the hard limits of human intelligence
aeon.co
aeon.co
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.
"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.
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?
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...
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.
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.
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.
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]
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 :)
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
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.
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.
That's why I find the idea somewhat frightening. But that is also what makes it a far more interesting (relevant) question.
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.
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.
These questions impose artifical beliefs as plausible theorems
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.
The answers to these questions have real ramifications, treating them as artificial is how harm to real people happens.
Now, Terry Tao is a person of the same, if not greater caliber. A real, living 200 IQ genius.
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?
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.
The hard problem of consciousness seems particularly suited to avoid the mechanisms that "we" "know" anything (e.g., objective evidence and the scientific method).
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.
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.)
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.
(per google translate)
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
- 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.
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...
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".
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.
Mods: You might want to merge the discussions. @dang
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.
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.