Richard Jernigan -> RE: Wave-particle duality (Sep. 2 2016 16:36:05)
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ORIGINAL: Piwin <snip> This is a relief. I was feeling pretty bad at not understanding the slightest thing about quantum physics, if only perhaps the odd zombie cat analogy. In the reddit discussion you posted, though I can understand conceptually what is meant by "excitation of a field", as soon as I try to map that on to "reality" I loose the little grasp I had to start with. A lot of it is simply that I am not conversant enough in mathematics to do as Feynman suggested and "follow the mathematics". I would ask this though: do you think that our understanding of the world is inherently limited by our "mental set-up", for lack of a better word? In other words, is there a point beyond which we simply won't be able to go, not merely because it is counter-intuitive to us, but because of our biological constraints? <snip> Your question prompts a couple of observations, though the length of your post implies to me that it raises a number of different questions. My observations here address only a part of your post. There are clearly limitations to the number of abstractions an individual can keep track of at once, and to the complexity of mental pictures that can be held in the imagination. This ability varies from one individual to the next, and can be cultivated through practice and instruction. But there are limits. People have responded to this in at least a couple of ways. One is through abstraction and generalization in mathematics. A relatively familiar example is the development of vector analysis. There is a famous book called "A Course of Modern Analysis" by Whittaker and Watson, published early in the 20th century. It contains not a single illustration. Furthermore there are page after page containing lists of equations, one for each dimension. A three-dimensional problem is discussed with numerous sets of three equations, one each for, say x, y, and z, even though the equations may differ only in the name of the dimension. Physicists and mathematicians in the latter half of the 19th century had begun to use a notation where all three dimensions were represented by a single symbol, called a vector. In fact, mathematicians soon realized that vector notation could very compactly represent calculations in an infinite number of dimensions. This abstraction and generalization has proceeded apace in the 20th and 21st centuries, enabling more and more complex entities to be represented by fewer and fewer marks on paper. There is no apparent limit to this progression. A second approach to outflanking human mental limitations has been the development of electronic computers. Their memories are vastly greater than human capacity for reading and writing data, and their calculations are extremely swift. There are even mathematical proofs that are embodied (in part) only in computer programs that produce and check gigabytes of data. Of course mathematicians debate whether it really is a proof, if only a computer can check it. These days great progress is being made in cascaded neural networks, the outputs of one level of electronic neural nets being input to successively higher levels. The networks are "trained" by being given inputs, and being told whether the outputs are right or wrong. After sufficient "training" the networks can fairly reliably arrive at the right outputs for novel inputs. This process (called "deep learning") mimics to some extent the learning processes of animals. Work on this is just beginning to bear significant fruit. It is a new focus of work in artificial intelligence, and a lot of money and effort are being put into it. The usual optimistic predictions are being made, but the limits of this strategy have yet to be identified. We read about self-driving cars, but I haven't run across any accounts of significant scientific applications, though it would seem obvious to try giving it a shot. As far back as the late 1960s I remember chatting over beer and enchiladas with a friend, who had been invited to address the International Congress of Mathematicians only a few years after getting his PhD, a tremendous distinction, one which was conferred only a few times in a century. He was speculating that a certain calculation could not be carried out because there were only a finite number of particles in the universe. But at that time, I think quantum computing had not seriously been considered. Certainly he and I were both unaware of its possibility at that time. The number of energetically achievable states of the individual particles is vastly smaller than the number of energetically achievable superpositions of states of numbers of particles, so I don't know what his evaluation would be today. Is there a limit to our ability to understand the universe imposed by the structure of our brains? I don't know. I think there is a sufficiently vast field of ignorance to keep us occupied for the foreseeable future. RNJ
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