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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

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.

Don't forget memory. Intelligent processes are also a rather involved development of the state of the agents memory.

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?

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).

[1] https://en.wikipedia.org/wiki/A_New_Kind_of_Science#Principl...

[2] https://www.youtube.com/watch?v=aAgcqgDc-YM

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?

>>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.

Most ape-like creatures couldn't either. Until the one's that could took over the planet one day.

I live in fear of the day the spiders figure out how to topple humanity. You know they're just sitting there, grinding through the options…

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).

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)

By your answers I can see that you both didn't get a very high score on those tests.

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.

>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...

[Edit typo: of/if]

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.

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 :)

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.

Edited for clarity

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.