| > It isn't even clear what you mean by abstraction at all. I'm using abstraction in the sense of 'blueprint abstraction' from game theory. This is basically compression of the input to your learning algorithm. There exists lossless compression - perfect one to one abstraction. There is also lossy compression - given one compressed form it could be any number of uncompressed forms. Abstraction with error is then compression with error. What I was trying to prove and what I still believe to have proved is that some algorithms when given an input of unbounded size have the property of not terminating. What I then tried to show was that abstraction breaks the proof of non-termination, because it breaks the core assumption of diagnolization - that there is a one to one mapping. So the proof of non-termination doesn't hold. > I am familiar with virtually all the topics you are discussing, so you can skip the citations. I literally linked to a paper that used abstractions in the way I meant it. So maybe you should not skip citations? Clearly you don't know the fields as well as you think you do. > I find no coherence to any of your segues. It isn't a segue; it is what you asked for. I gave you a proof that unabstracted learning problems can terminate where abstracted problems terminate. > You are completely out of touch [2][3] This is such an ironic statement; here we were discussing what abstraction techniques we should teach when teaching computer programming and you're trying to complain that I'm the one who is out of touch when I say computers use abstractions. They definitely do. In fact, they use abstractions with error. |