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This seems to be a problem of constructing approximate mental models to explain "emergent" properties of complex systems composed of interacting simple elements

by hliyan 9y ago

This seems to be a problem of constructing approximate mental models to explain "emergent" properties of complex systems composed of interacting simple elements (such as atoms). I would like to think that such explanations aren't always necessary, so long as a computer simulation of the simpler (and well understood) elements can reproduce the emergent behavior. It seems to be a limitation of human working memory rather than some theoretical limit to comprehension.

incadenza 9y ago
I agree. To model any complex system, it only really requires that a person or a group of people understand, and are able to codify their knowledge the system for a given period of time. Just think of your average decently sized code base. There's enough complexity there such that any single human can't understand it at a given time, save for a very high-level explanation. Does this mean that we don't understand the code base? I don't know if that's the right way to think about it.
- lr4444lr 9y ago
  Except that there is no emergent property of code. It is the sum of its logical parts, no more, no less. Any emergent value requires our conscious design.
  - naasking 9y ago
    > Except that there is no emergent property of code. It is the sum of its logical parts, no more, no less Why do you think emergent properties are not the sum of their parts? If I may simplify, there are generally two classes of emergence, metaphysical and epistemic. The former claims that systems are more than the sum of their parts, that some magic happens when some combination of things are brought together. Few people in science or philosophy takes this position seriously. Epistemic emergence is more about what approach to use to learn about a system. Science is typically reductionist, and it's very successful. However, some properties would be difficult to discover this way because they are only observed in complex interactions between multiple entwined subsystems. For a simplistic example, consider a scenario where you know nothing about physics, but are given unlimited time and unlimited tools to separately test the properties of oxygen molecules, and hydrogen molecules. But, you can never test them together, only separately. Given these constraints, it seems virtually impossible to infer the property that H2O is transparent to visual light. But this property is easy to see when studying them together. Epistemic emergence would hold that we maybe couldn't learn everything about hydrogen and oxygen by studying them separately, or at the very least, doing so isn't always the most effective means to learn about them. But ultimately, the properties revealed of H and O belong to them, and aren't metaphysical.
    - lr4444lr 9y ago
      I only made the statement with regard to code. I don't dispute a different situation generally or the specific example of molecular optics.
      - naasking 9y ago
        And I asked for clarification. The rest of my comment describes the various positions on emergent properties. So which is it you intended? The fact that it's code we're talking about isn't relevant.
pdonis 9y ago
> I would like to think that such explanations aren't always necessary, so long as a computer simulation of the simpler (and well understood) elements can reproduce the emergent behavior. But that just switches the limit to the limit of our computing power. Which is a pretty strict limit. For example, we can't construct computer models to predict the properties of all the elements in the periodic table just from knowledge of the underlying laws of electrons, protons, and neutrons.
- worldsayshi 9y ago
  > we can't construct computer models to predict the properties [...] from knowledge of the underlying laws Hmm, or can we? This gave me the idea of trying to extract "emergent laws" using machine learning. There should be a way to build an AI that tries to find rules that approximate behaviour of complex systems. I'm sure there's lots of work on this already.
  - pdonis 9y ago
    *> This gave me the idea of trying to extract "emergent laws" using machine learning. This is not what I was talking about. I was talking about a case where we know the underlying laws (the electromagnetic and strong interactions), but the computer models that we would construct from those laws would take more time than the age of the universe to run on our current computers and give us useful output. Using computers to try and infer underlying laws, not currently known to us, from data is a different thing, and I believe there is indeed ongoing work in this area.
    - worldsayshi 9y ago
      But my point being that if we can construct approximations on top of underlying laws that are cheaper to run, then the outcomes of any complex model could be approximated.
- hliyan 9y ago
  I think we can, if we get to the layers below those particles. i.e. if we develop full mathematical descriptions of quarks and electrons, and the behavior of the four fundamental forces (strong, weak, electromagnetic and gravity), I think a computer simulation will be able to predict the macroscopic properties of any element.
sdenton4 9y ago
We are narrative creatures, and have no problem constructing approximate mental models. The problem is building useful and correct models which can be used for prediction. The great thing about gravity is you can plug on a couple masses to an equation and know exactly what will happen. On the other hand, we have lots of short hand for what the brain is doing (eg, "memory") and lots of just so stories about how those things might work (eg, "like a stick of RAM"), but those stories rarely give a full picture of what's going on it help predict how to improve things - like remember, or cure Alzheimer's. For many complex systems, simple observation is a problem. With a brain, you can't observe things in fine detail without killing the host. So we can't see how local phenomena interact to create complex emergent behavior - observing the local means suppressing the global. And while we have big global observations from MRIs, and tiny local observations from cutting out individual neurons and applying electricity, there's a huge middle ground in between. Another problem is that global emergent phenomena can change the way the local systems behave... We tend to imagine knowledge progressing from the tiny systems or to the big systems, but we see feedback in the other direction too, for example through hormone release. Which, again, is difficult to observe when isolating tiny parts of a system.
da_chicken 9y ago
No, you're not thinking big enough. Think of it like this. You've got a dog. Your dog is very smart. She knows her name, she does tricks, she has a pretty apparent understanding several spoken words, tonal inflections, and body language, and can even catch a frisbee out of the air when you throw one. However, no matter what you do, no matter how hard you or she tries, your dog will never understand calculus. A dog is simply not capable of understanding what calculus is or what it is for or how it describes relationships of objects in Newtonian physics. There is a fundamental physiological limit to her intelligence, and topics like calculus are beyond it. Humans are much more capable than dogs. However, humans are still physical beings. As such, they have physical limits to brain size, and physical limits to brain activity. We also have a limited life span, so if something exists which might be comprehensible to a 200 year old human, we may never know it. It is most probable that there are concepts, topics, and systems that are simply too complex for human intelligence to understand even if we had access to the equivalent of a Calculus For Dummies. Worse, human brains are limited to their senses, and scientific understanding is contingent on both observation and repetition. A system can only operate on the data it has available to it. If something exists which either cannot be perceived or cannot be repeated, then we have essentially no capability of even knowing that we don't understand it. The fact that some of the most complex systems have been understood though abstraction, encapsulation, and modeling doesn't mean that all possible systems will behave that way or can be understood that way or, frankly, even that the knowledge we gain about systems that way can truly be called "understanding." How often do we say, "It wasn't until I experienced it myself that I understood"? As far as AI, well, we don't even know if they're capable of consciousness or sentience, let alone sapience. They may just be arbitrarily complex systems good enough to simulate human behavior and fool a Turing test. No, passing a Turing test doesn't mean you're conscious or sentient; it means you're not definitely non-sentient or inanimate. And if the basis of everything an AI knows is what they learned from us using algorithms we decided to give them, what does that mean they won't be capable of just because we're the ones that taught them? TLDR: The universe is not obligated to function in a manner comprehensible to human intelligence.
- libraryofbabel 9y ago
  I've always liked the dog analogy ever since I came across it in Stephen Weinberg's book Dreams of a Final Theory: "...it may be that humans are simply not intelligent enough to discover or to understand the final theory. It is possible to train dogs to do all sorts of clever things, but I doubt that anyone will ever train a dog to use quantum mechanics to calculate atomic energy levels." The impossibility of dogs doing Calculus is an equally nice example, but I think we could push the point further. Calculus is not only hard and unnatural for dogs; it is hard and unnatural for humans as well. There were anatomically modern humans equipped with culture and language for something like 30,000 years before even one of them understood calculus. It's truly extraordinary that this thing which was at the absolute limits of the human intellect in the 17th century is now taught routinely in high schools and colleges across the world, and used for such mundane purposes as building bridges or stock trading. Those inclined to optimism could read in this a story about how humans are not like dogs, because culture. (i.e.: "culture allows us to consolidate and simply the understanding of previous generations so future generations can build on it towards almost limitless horizons", etc.). But I'm a pessimist: calculus is still damn hard for nearly all human beings (just ask your average college student). Heck, I found it pretty tough to learn and I ended up getting a masters in math. And - to get back to the article - I'm not convinced that current topics at the edge of human understanding today (string theory, or whatever) are ever going to get 'mundane'. It takes many years of special training and extraordinarily single-minded dedication to even get to the current frontier of knowledge in these areas. At some point, as the article says, perhaps the math just gets too hard. Fortunately, just because the universe might not be comprehensible by humans (we never get to a successful theory of quantum gravity, or whatever) doesn't mean science itself will have a end. There's plenty to do in other fields.

by hliyan 9y ago

incadenza 9y ago

I agree. To model any complex system, it only really requires that a person or a group of people understand, and are able to codify their knowledge the system for a given period of time. Just think of your average decently sized code base. There's enough complexity there such that any single human can't understand it at a given time, save for a very high-level explanation. Does this mean that we don't understand the code base? I don't know if that's the right way to think about it.

lr4444lr 9y ago
Except that there is no emergent property of code. It is the sum of its logical parts, no more, no less. Any emergent value requires our conscious design.
- naasking 9y ago
  > Except that there is no emergent property of code. It is the sum of its logical parts, no more, no less Why do you think emergent properties are not the sum of their parts? If I may simplify, there are generally two classes of emergence, metaphysical and epistemic. The former claims that systems are more than the sum of their parts, that some magic happens when some combination of things are brought together. Few people in science or philosophy takes this position seriously. Epistemic emergence is more about what approach to use to learn about a system. Science is typically reductionist, and it's very successful. However, some properties would be difficult to discover this way because they are only observed in complex interactions between multiple entwined subsystems. For a simplistic example, consider a scenario where you know nothing about physics, but are given unlimited time and unlimited tools to separately test the properties of oxygen molecules, and hydrogen molecules. But, you can never test them together, only separately. Given these constraints, it seems virtually impossible to infer the property that H2O is transparent to visual light. But this property is easy to see when studying them together. Epistemic emergence would hold that we maybe couldn't learn everything about hydrogen and oxygen by studying them separately, or at the very least, doing so isn't always the most effective means to learn about them. But ultimately, the properties revealed of H and O belong to them, and aren't metaphysical.
  - lr4444lr 9y ago
    I only made the statement with regard to code. I don't dispute a different situation generally or the specific example of molecular optics.
    - naasking 9y ago
      And I asked for clarification. The rest of my comment describes the various positions on emergent properties. So which is it you intended? The fact that it's code we're talking about isn't relevant.

pdonis 9y ago

> I would like to think that such explanations aren't always necessary, so long as a computer simulation of the simpler (and well understood) elements can reproduce the emergent behavior. But that just switches the limit to the limit of our computing power. Which is a pretty strict limit. For example, we can't construct computer models to predict the properties of all the elements in the periodic table just from knowledge of the underlying laws of electrons, protons, and neutrons.

worldsayshi 9y ago
> we can't construct computer models to predict the properties [...] from knowledge of the underlying laws Hmm, or can we? This gave me the idea of trying to extract "emergent laws" using machine learning. There should be a way to build an AI that tries to find rules that approximate behaviour of complex systems. I'm sure there's lots of work on this already.
- pdonis 9y ago
  *> This gave me the idea of trying to extract "emergent laws" using machine learning. This is not what I was talking about. I was talking about a case where we know the underlying laws (the electromagnetic and strong interactions), but the computer models that we would construct from those laws would take more time than the age of the universe to run on our current computers and give us useful output. Using computers to try and infer underlying laws, not currently known to us, from data is a different thing, and I believe there is indeed ongoing work in this area.
  - worldsayshi 9y ago
    But my point being that if we can construct approximations on top of underlying laws that are cheaper to run, then the outcomes of any complex model could be approximated.
hliyan 9y ago
I think we can, if we get to the layers below those particles. i.e. if we develop full mathematical descriptions of quarks and electrons, and the behavior of the four fundamental forces (strong, weak, electromagnetic and gravity), I think a computer simulation will be able to predict the macroscopic properties of any element.

sdenton4 9y ago

We are narrative creatures, and have no problem constructing approximate mental models. The problem is building useful and correct models which can be used for prediction. The great thing about gravity is you can plug on a couple masses to an equation and know exactly what will happen. On the other hand, we have lots of short hand for what the brain is doing (eg, "memory") and lots of just so stories about how those things might work (eg, "like a stick of RAM"), but those stories rarely give a full picture of what's going on it help predict how to improve things - like remember, or cure Alzheimer's. For many complex systems, simple observation is a problem. With a brain, you can't observe things in fine detail without killing the host. So we can't see how local phenomena interact to create complex emergent behavior - observing the local means suppressing the global. And while we have big global observations from MRIs, and tiny local observations from cutting out individual neurons and applying electricity, there's a huge middle ground in between. Another problem is that global emergent phenomena can change the way the local systems behave... We tend to imagine knowledge progressing from the tiny systems or to the big systems, but we see feedback in the other direction too, for example through hormone release. Which, again, is difficult to observe when isolating tiny parts of a system.

da_chicken 9y ago

No, you're not thinking big enough. Think of it like this. You've got a dog. Your dog is very smart. She knows her name, she does tricks, she has a pretty apparent understanding several spoken words, tonal inflections, and body language, and can even catch a frisbee out of the air when you throw one. However, no matter what you do, no matter how hard you or she tries, your dog will never understand calculus. A dog is simply not capable of understanding what calculus is or what it is for or how it describes relationships of objects in Newtonian physics. There is a fundamental physiological limit to her intelligence, and topics like calculus are beyond it. Humans are much more capable than dogs. However, humans are still physical beings. As such, they have physical limits to brain size, and physical limits to brain activity. We also have a limited life span, so if something exists which might be comprehensible to a 200 year old human, we may never know it. It is most probable that there are concepts, topics, and systems that are simply too complex for human intelligence to understand even if we had access to the equivalent of a Calculus For Dummies. Worse, human brains are limited to their senses, and scientific understanding is contingent on both observation and repetition. A system can only operate on the data it has available to it. If something exists which either cannot be perceived or cannot be repeated, then we have essentially no capability of even knowing that we don't understand it. The fact that some of the most complex systems have been understood though abstraction, encapsulation, and modeling doesn't mean that all possible systems will behave that way or can be understood that way or, frankly, even that the knowledge we gain about systems that way can truly be called "understanding." How often do we say, "It wasn't until I experienced it myself that I understood"? As far as AI, well, we don't even know if they're capable of consciousness or sentience, let alone sapience. They may just be arbitrarily complex systems good enough to simulate human behavior and fool a Turing test. No, passing a Turing test doesn't mean you're conscious or sentient; it means you're not definitely non-sentient or inanimate. And if the basis of everything an AI knows is what they learned from us using algorithms we decided to give them, what does that mean they won't be capable of just because we're the ones that taught them? TLDR: The universe is not obligated to function in a manner comprehensible to human intelligence.

libraryofbabel 9y ago
I've always liked the dog analogy ever since I came across it in Stephen Weinberg's book Dreams of a Final Theory: "...it may be that humans are simply not intelligent enough to discover or to understand the final theory. It is possible to train dogs to do all sorts of clever things, but I doubt that anyone will ever train a dog to use quantum mechanics to calculate atomic energy levels." The impossibility of dogs doing Calculus is an equally nice example, but I think we could push the point further. Calculus is not only hard and unnatural for dogs; it is hard and unnatural for humans as well. There were anatomically modern humans equipped with culture and language for something like 30,000 years before even one of them understood calculus. It's truly extraordinary that this thing which was at the absolute limits of the human intellect in the 17th century is now taught routinely in high schools and colleges across the world, and used for such mundane purposes as building bridges or stock trading. Those inclined to optimism could read in this a story about how humans are not like dogs, because culture. (i.e.: "culture allows us to consolidate and simply the understanding of previous generations so future generations can build on it towards almost limitless horizons", etc.). But I'm a pessimist: calculus is still damn hard for nearly all human beings (just ask your average college student). Heck, I found it pretty tough to learn and I ended up getting a masters in math. And - to get back to the article - I'm not convinced that current topics at the edge of human understanding today (string theory, or whatever) are ever going to get 'mundane'. It takes many years of special training and extraordinarily single-minded dedication to even get to the current frontier of knowledge in these areas. At some point, as the article says, perhaps the math just gets too hard. Fortunately, just because the universe might not be comprehensible by humans (we never get to a successful theory of quantum gravity, or whatever) doesn't mean science itself will have a end. There's plenty to do in other fields.