I really liked this post; it puts modern computing into an interesting perspective.
I think the perspective of physics is also interesting to add, because I think it really shows how fundamental the idea of computation is. According to modern physics, everything is computation; every physical interaction, whether it’s between two elementary particles, or between two people shaking hands, is computation. As you mentioned, it was mathematically proven by Alan Turing that there is a type of machine, now called a Turing machine, which can compute anything that can in principle be computed, which therefore supposedly includes all of physics. All our laptops and other modern computers are Turing machines, so our laptops, in principle, are capable of computing anything physical, including a human brain. The question is, how practical is it to do a given computation?
Computing the movements that a grain of sand makes over the course of one second would take a laptop aeons to compute, let alone computing in real time what goes on in a human brain. However, in practice you don’t usually need to do an exhaustive computation to get the result you want. For example, you can program your laptop to calculate the result of 1+1, but you can also simulate your physical laptop while it is computing 1+1 to get the same result (hopefully 2). However, the latter would waste an extreme amount of computation you don’t need to do. Similarly, the relevant outputs of the human brain might be calculated with much less computation than it takes to simulate an entire physical human brain. In fact, artificial neural networks appear to do just that, meaning that the physical brain appears to “merely” physically implement the virtual equivalent of our artificial neural networks.
Some people have countered by saying that many important processes in the human brain have been abstracted away in artificial neural networks, but it is not clear that these processes are part of the fundamental computations that lead to the results we care about, instead of simply supporting the physical implementation of these fundamental computations. Some other people, such as Roger Penrose, have even claimed that human brains do processing that is not computable and therefore cannot be computed even using a Turing machine, in turn implying that such uncomputable processes are possible in nature, which is counter to modern physics’ understanding of nature.
I will point out that while there are some things that can never be computed (the last digit of Pi or e come to mind) there are also classes of these problems that can be calculated “close enough for all practical purposes”. If it was not for that consideration, we would be missing a lot of great engineering feats.
I really liked this post; it puts modern computing into an interesting perspective.
I think the perspective of physics is also interesting to add, because I think it really shows how fundamental the idea of computation is. According to modern physics, everything is computation; every physical interaction, whether it’s between two elementary particles, or between two people shaking hands, is computation. As you mentioned, it was mathematically proven by Alan Turing that there is a type of machine, now called a Turing machine, which can compute anything that can in principle be computed, which therefore supposedly includes all of physics. All our laptops and other modern computers are Turing machines, so our laptops, in principle, are capable of computing anything physical, including a human brain. The question is, how practical is it to do a given computation?
Computing the movements that a grain of sand makes over the course of one second would take a laptop aeons to compute, let alone computing in real time what goes on in a human brain. However, in practice you don’t usually need to do an exhaustive computation to get the result you want. For example, you can program your laptop to calculate the result of 1+1, but you can also simulate your physical laptop while it is computing 1+1 to get the same result (hopefully 2). However, the latter would waste an extreme amount of computation you don’t need to do. Similarly, the relevant outputs of the human brain might be calculated with much less computation than it takes to simulate an entire physical human brain. In fact, artificial neural networks appear to do just that, meaning that the physical brain appears to “merely” physically implement the virtual equivalent of our artificial neural networks.
Some people have countered by saying that many important processes in the human brain have been abstracted away in artificial neural networks, but it is not clear that these processes are part of the fundamental computations that lead to the results we care about, instead of simply supporting the physical implementation of these fundamental computations. Some other people, such as Roger Penrose, have even claimed that human brains do processing that is not computable and therefore cannot be computed even using a Turing machine, in turn implying that such uncomputable processes are possible in nature, which is counter to modern physics’ understanding of nature.
I will point out that while there are some things that can never be computed (the last digit of Pi or e come to mind) there are also classes of these problems that can be calculated “close enough for all practical purposes”. If it was not for that consideration, we would be missing a lot of great engineering feats.