Do you think there are things forever beyond our grasp?

[newjerseyrunner]

I read about a Bonobo named Kanzi today, who's learned how to make fire (with a little help from human technology) and I started thinking about our own evolution and wondering about the various levels of intelligence we had throughout.

I've always been interested in other primates and other intelligent animals in general and their relative intelligences. Koko the gorilla and Alex the parrot are really cool.

I also watched a documentary on the history of our own understanding of mathematics and how it evolved from the greek's word problem like world to the level we've taken it to now. It made me especially think about the fact that humans are terribly poor at coming up with new ideas but once those ideas are there, large numbers of people can expand on it. True genius and paradigm shifts were few and far between. And the difference between knowing math and understanding math.

I started wondering about much Kanzi could possibly understand. Not has the desire to understand or the attention span. Assuming an unlimited attention span, the desire to learn, and hell, an infinite amount of time, and the proper teaching methods, would there be a limit to her ability to understand abstract thoughts? I know all primates can do very simple pattern recognition, and abstract numeric thoughts. I'm fairly certain it could pick up addition and subtraction, and probably multiplication and division too. I think it could probably grasp that mathematical formulas can represent the physical world and I think she'd understand to some degree Newton's laws. But I don't think she could learn relativity or quantum physics. I think it's too weird and abstract.

Assuming that we omit the future possibilities of extending our intelligence with AI or genetic engineering, do you think there are concepts that some alien species has figured out that simply can't be taught to any human being no matter how intelligent? I'm positive that at least a handful of us could follow any mathematical formulas of any advanced laws that we don't currently know of, but that's not the same as actually understanding it.

I'm not talking about things we can't figure out because we can't test something, I'm talking purely about our ability to understand something.

Do you think we have limits, or is our mind flexible enough to adapt to learn anything given enough time? Thoughts?

 

[Dr. Courtney]

I think only humans really have the capability to grasp mathematics at the level of algebra, trig, and calculus.

It is unclear to me where the limit of human thinking ability might be. Much higher than we usually see, I suppose.

Perhaps the developments in the past 500 years are an indication of what might be possible in the next 500.

That's pretty impressive.

 

[Ryan_m_b]

Given that animals have clear limits I find it reasonable to believe humans do to. It seems unlikely that we've evolved to the point that our brains are theoretically capable of understanding anything given time. An interesting question is if we would be able to recognise a problem we can't understand.

 

[Dr. Courtney]

An interesting question is if we would be able to recognise a problem we can't understand.

You're not married, are you?

 

[newjerseyrunner]

Given that animals have clear limits I find it reasonable to believe humans do to. It seems unlikely that we've evolved to the point that our brains are theoretically capable of understanding anything given time. An interesting question is if we would be able to recognise a problem we can't understand.

That's a very interesting thought indeed. I can't quite answer that. I want to say that we'd be able to come up with the problem, but then again, if it's so abstract an beyond our understanding, would we even consider it a problem or is that just "how it is?"

You're not married, are you?

As someone who's getting married in December, this is my favorite response on PF yet.

 

[Ryan_m_b]

Lol no not married but appreciate the sentiment. Coming at this issue from another direction: it's actually very easy to think of things the human brain can't comprehend, at least at the first degree. Any system behind a very small number of interactions is virtually impossible to comprehend at once. For example: it's not possible to hold in your mind a dynamic metabolic reaction of several hundred different chemicals. But whilst that's a hard limitation we get round it through reductionism. Complex phenomenon are broken down into their components and sub components and we focus on learning them. Then after understanding those rules we gain insight into the larger system. This goes beyond individuals, a team of people each understanding a component of the system can be said to understand it at the collective level.

On that basis your question becomes is everything amenable to reduction?

 

[Dr. Courtney]

I once hypothesized that any system can only "understand" systems simpler than itself.

One might understand a simplified model of something more complex than oneself, but then one has only really understood the model.

 

[newjerseyrunner]

Lol no not married but appreciate the sentiment. Coming at this issue from another direction: it's actually very easy to think of things the human brain can't comprehend, at least at the first degree. Any system behind a very small number of interactions is virtually impossible to comprehend at once. For example: it's not possible to hold in your mind a dynamic metabolic reaction of several hundred different chemicals. But whilst that's a hard limitation we get round it through reductionism. Complex phenomenon are broken down into their components and sub components and we focus on learning them. Then after understanding those rules we gain insight into the larger system. This goes beyond individuals, a team of people each understanding a component of the system can be said to understand it at the collective level.

On that basis your question becomes is everything amenable to reduction?

Basically yeah, your example is more a limitation on the human ability to remember than our ability to comprehend it. Not being able to keep track of something isn't the same as not being able to understand it. Each individual reaction can be calculated and the results extrapolated from there, we understand how to do that and why it works.

My question wasn't if you think there are things that can't be reduced, are there reductions that human being simply don't have the intellect to see, even if it were explained to us. If some being billions of years old came to you and described to you the laws of the universe as it knew them with it's eons of scientific method. We would have to learn it all gradually like children, but is there a point at which it would be like trying to explain relativity to an ant, or does our flexibility give us the ability to learn anything given enough time, previous knowledge, and experimentation with learning it?

I see no reason to believe that there aren't things beyond our grasp forever, not because it's not discoverable but because we lack the creativity to do it.

 

[DiracPool]

My question wasn't if you think there are things that can't be reduced, are there reductions that human being simply don't have the intellect to see, even if it were explained to us.

Looking over your posts I'd paraphrase your question as to one that seeks to identify the capacity of what the brain is able to achieve. Without having an exact mechanical (or quantum mechanical) model for how the brain works, then this is not possible to answer. But we certainly have limitations, no matter how smart we think we are. For example, we can't perceive 4 or 5 or 6 dimensions. That would seem to be a limiting factor due to our biology. But we can perceive 3 (spatial) dimensions. Why is that? That seems a limitation. And contrary to popular belief, non-human primates/ mammals do not have any confirmed capacity for any even rudimentary or "proto" grammatical construction or mathematical ability, even basic arithmetic. This is a long-running debate with many published studies, but no real progress has been made since the seminal article by Euan McPhail, so I refer you to that:

http://www.researchgate.net/publication/231885378_The_comparative_psychology_of_intelligence

As far as this statement:

I think it could probably grasp that mathematical formulas can represent the physical world and I think she'd understand to some degree Newton's laws.

Do you really believe that? Do you think a chimp has a concept of what a mathematical formula is? Do you think that a chimp, or a dolphin, or an African grey parrot for that matter is able to understand what F=ma means?

I see no reason to believe that there aren't things beyond our grasp forever, not because it's not discoverable but because we lack the creativity to do it.

We, as humans, have plenty of creativity, this is indeed what distinguishes us from all the animal life on the planet, but that doesn't mean that there are not things that are beyond our grasp forever. The sad truth is that, at the end of the day we are limited by our biology. But the good news is, though, is that we won't know what that limitation is because we don't have the capacity to understand it

 

[zoobyshoe]

Do you really believe that? Do you think a chimp has a concept of what a mathematical formula is? Do you think that a chimp, or a dolphin, or an African grey parrot for that matter is able to understand what F=ma means?

I also object to that kind of characterization, as in a recent article someone posted saying babies understand Newton's 3 Laws. What babies and animals sometimes grasp is more like, "When I do this, it does that." That's very rudimentary compared to being able to understand the phenomenon can be described as quantities governed by a formula. Indeed, the instinctual ability to sharpen the "this" that one does to control the "that" that results, without putting any numbers to it at all, is quite remarkable, but it is a different activity altogether than the cerebral abstraction that is F=ma.

 

[Oldfart]

A question that some of these posts seems to raise is: Might some animals be capable of understanding concepts which we humans cannot grasp? For instance, could it be that a microbe could develop ability to visualize five dimensions because this skill enhances its ability to survive?

 

[William White]

Do you really believe that? Do you think a chimp has a concept of what a mathematical formula is? Do you think that a chimp, or a dolphin, or an African grey parrot for that matter is able to understand what F=ma means?

can they understand the abstract meaning behind roman characters and mathematical symbols

obviously not
do (some) animal brains work in ways that allow them to process complex information to calculate and predict motion and forces of objects, the consequence of motion etc.

obviously yes

animals brains do very complex processing of physical "problems".there are lots of humans that have no concept of a mathematical formula or what F=ma is.

 

[DiracPool]

can they understand the abstract meaning behind roman characters and mathematical symbols

obviously not
do (some) animal brains work in ways that allow them to process complex information to calculate and predict motion and forces of objects, the consequence of motion etc.

obviously yes

animals brains do very complex processing of physical "problems".there are lots of humans that have no concept of a mathematical formula or what F=ma is.

I'm not sure exactly what you are trying to say here...

 

[William White]

Animal brains are carry out very complex 'calculations'

 

[DiracPool]

Animal brains are carry out very complex 'calculations'

Ah, ok, thanks. Well, the brain doesn't know a calculation from a hole in the ground or a supermassive galactic black hole. So it does no calculating. It's a chaotic system that is just falling on physical laws to generate particular patterns that drive behavior and thoughts. The word "calculating" is a human created term relating to the uniquely human task of writing down and performing operations on written characters that we've also created. The "complex processing" you attribute to human or any other mammalian brain is no more intentionally sophisticated or directed than the pattern of rivulets than run off a hill during a rainstorm. Everything is just following the path of least resistance.

As far as your comment, "there are lots of humans that have no concept of a mathematical formula or what F=ma is," I beg to differ with you. I think most people understand at least that 1+1=2 and 2x2=4, in whatever language they speak, and understand that this implies some sort of weighted equality. A non-human animal has no concept of that.

As far as what F=ma means, any non-organically compromised Homo sapien sapien has the capacity to understand what that means, given the time and the effort to learn it. A chimpanzee will never understand it, no matter how much time and training you give it.

 

[mfb]

I also object to that kind of characterization, as in a recent article someone posted saying babies understand Newton's 3 Laws. What babies and animals sometimes grasp is more like, "When I do this, it does that." That's very rudimentary compared to being able to understand the phenomenon can be described as quantities governed by a formula. Indeed, the instinctual ability to sharpen the "this" that one does to control the "that" that results, without putting any numbers to it at all, is quite remarkable, but it is a different activity altogether than the cerebral abstraction that is F=ma.

That is also important for Kanzi. He can make fire using human tools, yes - but does that count as some deeper understanding of the concept of fire, or is it just following procedures humans showed him? He certainly does not understand it at a level we humans do - chemical reactions between the wood and oxygen in their air and so on.

I think most people understand at least that 1+1=2 and 2x2=4, in whatever language they speak, and understand that this implies some sort of weighted equality.

Most, but http://www.independent.co.uk/news/science/unlocking-the-secret-sounds-of-language-life-without-time-or-numbers-477061.html.

 

[zoobyshoe]

That is also important for Kanzi. He can make fire using human tools, yes - but does that count as some deeper understanding of the concept of fire, or is it just following procedures humans showed him? He certainly does not understand it at a level we humans do - chemical reactions between the wood and oxygen in their air and so on.

In fact, the majority of humans who make fire don't understand the chemical reactions. We know that people as mathematically sophisticated as the Greeks considered fire to be some kind of divine magic, stolen from the gods by Prometheus. The mere ability to learn "When I do this, it does that," can accomplish wonders way beyond our ability to understand what's happening.

 

[WWGD]

In fact, the majority of humans who make fire don't understand the chemical reactions. We know that people as mathematically sophisticated as the Greeks considered fire to be some kind of divine magic, stolen from the gods by Prometheus. The mere ability to learn "When I do this, it does that," can accomplish wonders way beyond our ability to understand what's happening.

Same goes today: you ( most of the population) drive a car , watch t.v., fly in planes, surf the web, use cellphones , use electricity in genera,l without understanding how any of it works.

 

[mfb]

In fact, the majority of humans who make fire don't understand the chemical reactions.

Sure, but there are humans that do. That's not my point. You can make fire with different levels of "understanding". Kanzi will not reach the level some humans reached.

My computer can show me millions of pages of text that contains a huge amount of knowledge - that does not mean the computer understands the text. It just repeats what humans wrote into it.

 

[zoobyshoe]

Sure, but there are humans that do. That's not my point. You can make fire with different levels of "understanding". Kanzi will not reach the level some humans reached.

Agreed. If you were able to teach a chimp to count, could you teach it to add? If you could, could you teach it to subtract? To multiply and divide? Suppose you could. Could you then get it to understand that non-objects, things like forces, can be quantified? Could you teach it to quantify and measure acceleration? The more sophisticated the concept, the less likely it seems a chimp could grasp it.

 

[zoobyshoe]

Same goes today: you ( most of the population) drive a car , watch t.v., fly in planes, surf the web, use cellphones , use electricity in genera,l without understanding how any of it works.

I myself do this all the time. I'm pretty sure computers operate by magic of some sort.

 

[eachus]

If you are deeply interested in the answer, take a course in Computability Theory. Prereqs usually include a few years of Calculus and some Computer Science courses, so you are unlikely to see many Psychology or Philosophy students there. :-(

The (very) short answer is that there are some answers that cannot be known. See Godel's Proof. For computations which are possible, there are various classes of difficulty which relate to the amount of (scratchpad) memory or the number of steps required to solve the problem. These classes are usually described in terms of the size of the problem description. For example, adding a list of numbers requires time proportional to the length of the list, and the memory required is proportional to the largest intermediate subtotal.

The third measure of difficulty, usually ignored in Computability Theory is the size of the algorithm required. Usually this is small compared to other memory requirements, but there are some algorithms that are pretty complex. (The proof of Fermat's Last Theorem for example.)

 

[WWGD]

If you are deeply interested in the answer, take a course in Computability Theory. Prereqs usually include a few years of Calculus and some Computer Science courses, so you are unlikely to see many Psychology or Philosophy students there. :-(

The (very) short answer is that there are some answers that cannot be known. See Godel's Proof. For computations which are possible, there are various classes of difficulty which relate to the amount of (scratchpad) memory or the number of steps required to solve the problem. These classes are usually described in terms of the size of the problem description. For example, adding a list of numbers requires time proportional to the length of the list, and the memory required is proportional to the largest intermediate subtotal.

The third measure of difficulty, usually ignored in Computability Theory is the size of the algorithm required. Usually this is small compared to other memory requirements, but there are some algorithms that are pretty complex. (The proof of Fermat's Last Theorem for example.)

Interestingly, though, there are programs (e.g., arcade games) with millions of lines of code, written by different people, that run in a relatively smooth way.

 

[mfb]

It took decades to figure out how to make programming standards to allow many different components to interact as smoothly as they do today. And this is still work in progress - programs get more complicated all the time. Nice visualization (connected things are older and newer versions of the same software).

No one knows the whole code of a recent "large" operating system. Just reading 50 million lines of code would take years at a rate of a few seconds per line - and reading everything once is certainly not enough to know it afterwards. A team was still able to put it together, as the task could be split up enough to make the subtasks possible for humans.

Similarly, no one can think of every detail of a 500+ page proof in mathematics at once. But a few experts can understand it step by step.

Are there tasks that cannot get split up fine enough? That's the question.

 

[zoobyshoe]

Here's a point the OP made that hasn't been addressed:

I also watched a documentary on the history of our own understanding of mathematics and how it evolved from the greek's word problem like world to the level we've taken it to now. It made me especially think about the fact that humans are terribly poor at coming up with new ideas but once those ideas are there, large numbers of people can expand on it. True genius and paradigm shifts were few and far between.

We tend to collectively credit ourselves with abilities that are actually only possessed by the few. You'll hear people saying things to the effect that humans came up with the theory of relativity, and other similar accomplishments, when it was actually only one human among billions who did. We confuse the ability to understand a concept with the ability to arrive at the concept in the first place. So, the human race as a whole (and perhaps the bonobo race as well) is actually ultimately limited by the quality and quantity of its geniuses.

 

[mfb]

We tend to collectively credit ourselves with abilities that are actually only possessed by the few. You'll hear people saying things to the effect that humans came up with the theory of relativity, and other similar accomplishments, when it was actually only one human among billions who did. We confuse the ability to understand a concept with the ability to arrive at the concept in the first place. So, the human race as a whole (and perhaps the bonobo race as well) is actually ultimately limited by the quality and quantity of its geniuses.

If Einstein wouldn't have come up with the concept of relativity (special and general), someone else would have. Might have taken some years more, but it was just a matter of time. Like most discoveries, it was not the work of a single person - the Michelson-Morley experiment had been done, the Lorentz transformation existed already. Einstein put it together to a consistent framework and later generalized it to include gravity - with mathematical tools that existed before.

 

[zoobyshoe]

If Einstein wouldn't have come up with the concept of relativity (special and general), someone else would have. Might have taken some years more, but it was just a matter of time. Like most discoveries, it was not the work of a single person - the Michelson-Morley experiment had been done, the Lorentz transformation existed already. Einstein put it together to a consistent framework and later generalized it to include gravity - with mathematical tools that existed before.

But my point is: the percentage of people who could have conceived of SR (or any revolution in understanding) is extremely low. What percentage of the people alive at the time do Michelson, Morley, Lorentz, Einstein, (and Poincarre) represent? The percentage of people who can understand it, once it was arrived at, is vastly higher. Billions of people understand Newton's 3 Laws today, but between Aristotle and Newton (about 2000 years), no one arrived at all three and understood their importance.

 

[WWGD]

But my point is: the percentage of people who could have conceived of SR (or any revolution in understanding) is extremely low. What percentage of the people alive at the time do Michelson, Morley, Lorentz, Einstein, (and Poincarre) represent? The percentage of people who can understand it, once it was arrived at, is vastly higher. Billions of people understand Newton's 3 Laws today, but between Aristotle and Newton (about 2000 years), no one arrived at all three and understood their importance.

Right, George Soros and I are millionaires; we have an average net worth of $600 million. We are, as a whole, rich. ;) . I have heard it called " The Royal We".

 

[mfb]

With an estimated $24.2 billion for George Soros, that means $23 billion debts for you? ;)

But my point is: the percentage of people who could have conceived of SR (or any revolution in understanding) is extremely low.

Sure. Luckily, one is all we need.

 

[WWGD]

Ultimately I think our information society does play that role of "distributed computing" , where problems are dealt with by a lot of people simultaneously and often broken down into pieces that are more easily digestible than the original one. And sheer repetition to the same concepts, given the constant flow of information, helps the break down process at an individual level: after you have been exposed to the same idea 50 times, by either watching it on TV, listening to it on the radio, or through conversation/internet, seems to help the process of breaking the idea down. I think Steve Wolfram addressed this in his ANKOS book.

With an estimated $24.2 billion for George Soros, that means $23 billion debts for you? ;)
.

Student Loan$$

 

[William White]

what we can achieve - intellectually - depends upon the defintion of "we".

Evolution of humans by natural and sexual selection may, due to civilisation, society, medicine, technology, - for all intents and purposes - have stopped. The "fittest" human babies are not the only ones reaching reproduction age, as would have been the case hundreds of thousands of years ago when homo sapiens evolved. We have created a civilisation where the 'rules' of natural selection do not apply. Those having the most children are not necesarily the "fittest". There does not appear to be the pressure to select big brains capable of abstract problem like there was solving half a million years agoso what can "we" achieve.
1) IF humans evolve, and the evolution favours greater intellectual skills, who knows? evolution in future society may favour more vicious humans rather than thoughtful ones. But consider the intellectual difference between the great apes - between humans and chimps. What could an evolved human mind that is as far removed from us as we are from other apes acheive?

2) If humans do not evolve, but merge with technology, there could be as much difference between us and that future technology enhanced humanity as there is between us and other apes. Already, many complex systems - circuits for example - are designed and tested by the previous generation of machines.3) so it all depends on whether humans can survive long enough to achieve 'everything'. Its certainly a popular sci-fi scenario that sufficently evolved (either naturally or technologically) beings are indistuingushable from what we would consider gods.

 

[eachus]

Interestingly, though, there are programs (e.g., arcade games) with millions of lines of code, written by different people, that run in a relatively smooth way.

If you do study computability theory, you will find out that there are total functions and partial functions. A total function will always return a (valid) answer when called with valid parameters. Where possible programmers try to write such code. But there are some problems where only partial functions are known. These will never return an answer in some cases. (In other words the computer will grind away forever, and not find a valid answer.)

It turns out that determining whether a function is complete or partial is itself a partial function. (See the Halting problem.) Good software engineers run their code against a theorem prover. Sometimes you want a program to not halt, say the main loop in avionics code for a fighter jet. So sometimes you want a function that always halts, other times you want to prove your program doesn't halt. It's the ones in the middle that shouldn't ship, but too often do.

If you want to see a software engineer run away gibbering, say that the theorem prover doesn't work on your program, it just sits there "doing nothing." Oh, and if you do need to create perfectly correct code, stay away from C, C++ and related languages. it is possible to write good code in C. The issue is that many library functions return either a pointer or a number (which is an error code). Aha! You think I'll provide a "wrapper" function which handles the error codes. But that wrapper will probably include longjumps which are even harder on the theorem prover. And anyway you really do want the theorem prover to "look inside" the library functions to prove that no errors will occur. How many malloc() calls are there in your code?

 

[mfb]

3) so it all depends on whether humans can survive long enough to achieve 'everything'. Its certainly a popular sci-fi scenario that sufficently evolved (either naturally or technologically) beings are indistuingushable from what we would consider gods.

It is not limited to science fiction. If you could bring a modern computer (or similar devices) to the world of 1800 or earlier, you could easily convince the people that it is magic. Don't forget a power supply if the device does not run with batteries.

 

[zoobyshoe]

Sure. Luckily, one is all we need.

Right, but we're limited to the abilities of that one.

 

[William White]

Ah, ok, thanks. Well, the brain doesn't know a calculation from a hole in the ground or a supermassive galactic black hole. So it does no calculating. It's a chaotic system that is just falling on physical laws to generate particular patterns that drive behavior and thoughts.

Well, I'm glad you have dsolved the great mystery of emergent behaviour.

You might like to think that a pack of wolves hunting is of a different order of brain operations as writing down on a piece of paper.

I disagree. Its the same thing - the brain making sense of the world and making complex predictions with a purpose - just at a different level.

I think most people understand at least that 1+1=2 and 2x2=4, in whatever language they speak, and understand that this implies some sort of weighted equality. A non-human animal has no concept of that.

Many animals can count.

As far as what F=ma means, any non-organically compromised Homo sapien sapien has the capacity to understand what that means, given the time and the effort to learn it. A chimpanzee will never understand it, no matter how much time and training you give it.

non-organically compromised? what does THAT mean? Why is it impossble to talk straight?

Do you mean learning disabilities?

There are plenty of humans with learning disabilities; plenty that are far less capable intellectually than a chimp. They are still humans. That is what I meant.
The descendents of chimpanzees might understand it in 500,000 years. The common mother of you and a chimp did not understand it either. Intelligence emerges. Its a scale and we are somewhere along it. All that distinguishes us from other animals is where we are on the scale.

 

[William White]

It is not limited to science fiction. If you could bring a modern computer (or similar devices) to the world of 1800 or earlier, you could easily convince the people that it is magic. Don't forget a power supply if the device does not run with batteries.

well yes, that was Arthur C Clarkes thought experiment wasn't it?

But I don't really mean that sort of things.

More like the processes humans reserve to gods: creation of life forms, habitats etc.

 

[mfb]

More like the processes humans reserve to gods: creation of life forms, habitats etc.

Lightning, flight, knowing what happens anywhere on Earth right now, creating new elements, walk on Moon? Destroying a city in an instant?
We can do things today that were the responsibility of gods not that long ago.

In terms of artificial life, there is progress.

 

[William White]

Yes, but I was thinking more along the lines of a genesis type scenario - creation rather than destruction.

Its an interesting though experiment - a supremely intelligent entity with the technology to create entire worlds

 

[OCR]

non-organically compromised? what does THAT mean?

Lol, I think that might mean... a really stupid rock ...

non-organically compromised

Yes, basically, "humans with learning disabilities".

Why is it impossble [sic] to talk straight?

Correctly articulated, it should be... organically uncompromised ...

Its an interesting though experiment - a supremely intelligent entity with the technology to create entire worlds

https://en.wikipedia.org/wiki/Superintelligence

https://en.wikipedia.org/wiki/Artificial_general_intelligence

 

[WWGD]

Yes, but I was thinking more along the lines of a genesis type scenario - creation rather than destruction.

Its an interesting though experiment - a supremely intelligent entity with the technology to create entire worlds

Like someone who writes computer games, each with its own rules?

 

[BobG]

Many animals can count.

I think this statement comes with many qualifications. Many animals can identify small numbers of objects without having to count - as can humans. That's generally limited to very small numbers from around 2 to 5 (with 3 or 4 being the most common by far).

Very few animals can take things a step further by counting a small number of groups, with each group consisting of a small number of objects. For most, their "counting" would be severely limited. They might know they have three groups, but if two of the groups had three and one of the groups had two, would they know they have 8 instead of 9?

Combining groups where the groups don't necessarily contain the same number of objects and coming up with a correct total is another step up and I think there are going to be very, very few animals that can do that, if any.

Lots of animals have a logarithmic sense of numbers - i.e. they can figure out a group has about twice as many objects as another group, etc. They really suffer in making precise counts of a large number of objects.

The effect is still very close to counting - at least some animals can figure out approximately how many objects they're looking at - but I don't think there are any animals that count the way humans do. In fact, if you look at the earliest counting systems, which were mostly base 5 (plus, perhaps, another base added in), I think human counting is something learned; not an inherent capability that a human raised in isolation would be likely to come up with on their own.

 

[Hector Mata]

Given that animals have clear limits I find it reasonable to believe humans do to. It seems unlikely that we've evolved to the point that our brains are theoretically capable of understanding anything given time. An interesting question is if we would be able to recognise a problem we can't understand.

I agree with this. However, it may be the case that our limit, wherever it is, is nevertheless sufficient to understand "real" problems, i.e., the ones Nature will throw at us (physics, chemistry, biology, etc.) and the ones we create (economics, politics, etc.).

I'm not a neuroscientist or anything, obviously, but also I imagine that there's a certain threshold of computational power that, once reached, is enough for solving pretty much anything the Universe throws at us, plus other problems we make up in our minds (i.e., pure mathematics), plus allowing us to pursue creative and aesthetic endeavours such as art. Maybe chimps and other smart animals are below this threshold. And of course, as the poster above also implies, maybe we're short of this threshold too, and there may be puzzles that we haven't even noticed are there and never will, because of our own limits. Or maybe we're exactly at the point where we can notice there's a problem, but can't grasp it well enough to solve it (i.e., attempts at unified field theories). Very interesting!

 

[BobG]

I think only humans really have the capability to grasp mathematics at the level of algebra, trig, and calculus.

It is unclear to me where the limit of human thinking ability might be. Much higher than we usually see, I suppose.

Perhaps the developments in the past 500 years are an indication of what might be possible in the next 500.

That's pretty impressive.

I think it's important to look at why developments in the last 500 years have been so much faster than during most of human history, and why developments have been so much faster in last 100 or so years than during the previous 400.

Some posts talked about groups of people can create something that an individual could never create. I think the same sort of applies to developing ideas. The more people that work on a given problem, the more likely a quick solution will be found. And the better our communication system has become, the quicker ideas can be spread to large groups of people.

At some point, there's going to be a threshold where ideas are being spread "fast enough" that communication improvements don't significantly increase our rate of development. I wouldn't say we're necessarily at that threshold, since a large percentage of the population of the Earth is still left out of the game. Nearly instantaneous communications only applies to the developed world.

But I also don't consider it a given that our rate of development will always increasing. At some point, we'll develop at a somewhat constant rate, even if that rate is much higher than we used to.

How to tell if there is an upper limit? If the rate of development starts to actually decrease, then it's probably because we're approaching that upper limit?

Maybe. It could be a little like farming. The amount of crops a farm can grow is limited by some critical resource, but then you find a way to provide that resource and realize the Earth can sustain a much larger population than was originally estimated. But then you find you can improve things only so far because you hit another limited critical resource. Once you solve that problem, you hit another limit. And so on. Your progress undergoes constant bursts of improvements interspersed with constant flat spells with little improvement.

In other words, better communications solved one of our problems, but that can only improve things so far. Once the development rate slows, perhaps we'll discover what "new" limit is affecting our development rate, solve it, and undergo some new burst of development, etc.

Does there really have to be a physiological limit, though? It's well known that humans can artificially increase their physical performance in athletic events with performance enhancing drugs. That may not be looked at very favorably, which means developing even better performance enhancing drugs will be slowed, but the idea of artificially improving both physical and mental performance with drugs may be viewed more favorably in the future (as long as they don't carry the same serious side effects as drugs such as steroids).

There has to be some limit, somewhere, but that ultimate upper limit could be incredibly far into the future (assuming, of course, that our future actually stretches out very far).

 

[mfb]

Agriculture was developed about 10000 years ago. In terms of evolutionary timespans, this is nearly nothing. The same brain architecture that allowed simple agriculture is sufficient to build the ISS. Those massively differ in complexity. I don't see a reason to expect a critical limit soon.

It also raises the question why this timespan is so short:
- had humans the necessary brain capacity for agriculture long before, but just didn't have the right conditions or the right idea? Then we could catch up with a limit at any point.
- is there some critical threshold that suddenly allows to understand much more complex things? The brain equivalent of a turing-complete computer? Then a limit might be very far away.

There is an indication that a limit exists for our current human brains, however: education takes longer and gets more specialized compared to the past. A few hundred years ago, a scientist could be an expert in several areas at the same time. Today, a scientist can be an expert in a few narrow subfields - and it still takes significant time just to keep up with new developments. For progress, you need at least a few experts per subfield, so specialization has a limit, and time for education is limited by a human lifespan.

 

[Stephanus]

Do you really believe that? Do you think a chimp has a concept of what a mathematical formula is? Do you think that a chimp, or a dolphin, or an African grey parrot for that matter is able to understand what F=ma means?

I don't know about dolphin and parrot, but for a chimp or monkey to 'calculate' how to jump from one branch to another, they somehow 'calculate' their body mass, Earth's g, the strength of the branch, the distance.
Isn't it the one that triggered brain capability in ancient primate before they came down from the tree to the savannah?

 

[mfb]

I don't know about dolphin and parrot, but for a chimp or monkey to 'calculate' how to jump from one branch to another, they somehow 'calculate' their body mass, Earth's g, the strength of the branch, the distance.

In the same way small children do when they are supposed to predict something, or hit something with a thrown object, or perform similar tasks. I would not call this "calculate".

 

[Stephanus]

In the same way small children do when they are supposed to predict something, or hit something with a thrown object, or perform similar tasks. I would not call this "calculate".

Really? Try to build a robot with vision sensor, and grab a branch in a tree and jump to the other branch. Even Asimov will be clumsy at that task. But that's how nature works I think. I read that in the future the computer will use genetic material.

 

[mfb]

Try to build a robot with vision sensor, and grab a branch in a tree and jump to the other branch. Even Asimov will be clumsy at that task.

That's exactly my point - if animals (including humans) would actually try to calculate it with formulas, we would have the same problems as robots do.
Animals do not calculate how to jump, we make a good guess.

I read that in the future the computer will use genetic material.

This is completely unrelated to the discussion.

 

[Stephanus]

That's exactly my point - if animals (including humans) would actually try to calculate it with formulas, we would have the same problems as robots do.
Animals do not calculate how to jump, we make a good guess.
This is completely unrelated to the discussion.

Good point. Okay, so F = m.a is out for chimps, dolphin and parrot.

 

[OCR]

Try to build a robot with vision sensor...

Well, OK...

​

It's not that big of a jump... to the next branch.

... we would have the same problems as robots do.

Those being... ?

​

We need to "define" calculate somewhat better...

https://en.wikipedia.org/wiki/Calculation
https://en.wikipedia.org/wiki/Algorithm
https://en.wikipedia.org/wiki/Heuristic