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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 a

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.
- baddox 9y ago
  I find it odd that everyone is presenting the analogy as “humans is to understanding the final theory as dogs is to understanding calculus.” Why not just use “the final theory” for both second terms? In other words, do we expect a dog to ever understand the final theory of physics? Surely not. Do we expect a 2 year old human to ever understand the final theory of physics? Still, presumably not.

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.

baddox 9y ago
I find it odd that everyone is presenting the analogy as “humans is to understanding the final theory as dogs is to understanding calculus.” Why not just use “the final theory” for both second terms? In other words, do we expect a dog to ever understand the final theory of physics? Surely not. Do we expect a 2 year old human to ever understand the final theory of physics? Still, presumably not.