Do you think there are things forever beyond our grasp?

[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

 

[zoobyshoe]

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

What would be your preferred definition?

I think Diracpool's point was that the brain does not do what it does by crunching numbers any more than weather shifts and changes by crunching numbers. He believes brain activity is best described by chaos theory rather than likening it to, everyone's favorite analogy, a computer.

Also: good point about the robots. They're getting better faster than people are aware of.

 

[Stephanus]

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

Wow

 

[zoobyshoe]

Wow

Yeah, it's a little scary. Robocops and Terminators don't seem like quite so much of a stretch after you watch stuff like that.

 

[OCR]

What would be your preferred definition?

The one that's...

..."the" dictionary definition...

Any that would apply...
http://www.merriam-webster.com/dictionary/calculate

Any good one should do. Personally I favor Merriam-Websters. When in doubt, check for agreement among many dictionaries.

I, however, favor Wikipedia, again...

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

 

[laplacean]

It's very interesting to think about mathematics that humans would be unable to grasp. Especially considering with how abstract much of our current mathematics is. Makes you ponder what the human mind is truly capable of, and if there is an absolute threshold at some point. If we knew that we had a defined limit in terms of comprehension and understanding as a species, it would be a very sad day for all scientists.

 

[zoobyshoe]

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

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.

The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to the vague heuristics of calculating a strategy in a competition, or calculating the chance of a successful relationship between two people.

-wiki

DiracPool is clearly using it in the sense I've put in bold type. That's "the" dictionary definition I think would apply to this discussion.

His contention (if I'm not mistaken) is that the human brain as a whole entity can perform calculations, but the processes by which it does that are not, themselves, calculations.

 

[Ryan_m_b]

Regardless of how the brain calculates things unconsciously it is still an unconscious process. The fact that I can catch a thrown ball with relative ease does not grant me an thorough understanding of ballistics. It might give me an intuitive one but human intuition can be incredibly misleading. As an example this page shows how medieval scholars believed cannonballs acted in flight, flying straight at the angle shot before dropping straight down.

 

[William White]

Regardless of how the brain calculates things unconsciously it is still an unconscious process. The fact that I can catch a thrown ball with relative ease does not grant me an thorough understanding of ballistics. It might give me an intuitive one but human intuition can be incredibly misleading. As an example this page shows how medieval scholars believed cannonballs acted in flight, flying straight at the angle shot before dropping straight down.

But its still a mental process. And it is still a process that IS a manifestation of intelligence, of emergent behaviour.

Intelligent animals are much more able to predict motion and act accordingly than less intelligent animals. Or rather, there are animals whose brains have evolved to do the mental calculations required to predict motion.

A border collie can intercept and catch a thrown ball, predicting where it will be. This mental ability emerged. Many animals cannot do it, no matter how hard you try to train them.

Maybe those "scholars" should have actually looked at the ball? They did not use intuition, they were simply wrong (bizarrely).

 

[zoobyshoe]

But its still a mental process. And it is still a process that IS a manifestation of intelligence, of emergent behaviour.

Intelligent animals are much more able to predict motion and act accordingly than less intelligent animals. Or rather, there are animals whose brains have evolved to do the mental calculations required to predict motion.

A border collie can intercept and catch a thrown ball, predicting where it will be. This mental ability emerged. Many animals cannot do it, no matter how hard you try to train them.

Maybe those "scholars" should have actually looked at the ball? They did not use intuition, they were simply wrong (bizarrely).

I think you're grossly overestimating how much intelligence it takes to negotiate the environment. Consider the locomotion of the paramecium, which is a single cell organism. That is: it has no brain or nervous system by which to calculate anything:

Paramecia propel themselves by whiplash movements of their cilia, which are arranged in tightly spaced rows around the outside of their body. The beat of each cilium has two phases: a fast "effective stroke," during which the cilium is relatively stiff, followed by a slow "recovery stroke," during which the cilium curls loosely to one side and sweeps forward in a counter-clockwise fashion. The densely arrayed cilia move in a coordinated fashion, with waves of activity moving across the "ciliary carpet," creating an effect sometimes likened to that of the wind blowing across a field of grain.[11]

The Paramecium spirals through the water, as it progresses. When it happens to encounter an obstacle, the "effective stroke" of its cilia is reversed and the organism swims backward for a brief time, before resuming its forward progress. If it runs into the solid object again, it will repeat this process, until it can get past the object.[12]

It has been calculated that a Paramecium expends more than half of its energy in propelling itself through the water.[13] Its method of locomotion has been found to be less than 1% efficient. This low percentage is, nevertheless, close to the maximum theoretical efficiency that can be achieved by an organism equipped with cilia as short as those of Paramecium.

https://en.wikipedia.org/wiki/Paramecium#Movement

 

[zoobyshoe]

A border collie can intercept and catch a thrown ball, predicting where it will be. This mental ability emerged. Many animals cannot do it, no matter how hard you try to train them.