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by ben_w
1038 days ago
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Mostly I agree with you, but > However, we can enumerate all the things that we create can do. Not really, no. Even before AI, "Turing Complete" makes things extremely hard to enumerate; see Busy Beaver numbers for how small a system can be and still outside our ability to fully comprehend — needing to use up-arrow notation because exponentials aren't big enough is always good for a laugh. |
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You example of the Busy Beaver numbers, which was a recent interesting read, is a good example of what I was trying to point out. We have a definition and even if we cannot enumerate each number, we discuss and think about these in a rational way. At the moment, I am quite interested in Computer Algebra Systems (of which there are a variety) and I find it interesting just how limited these systems are and just how difficult it is to program into them the capabilities that humans use to solves various problems. The various discussions have been quite enlightening.
Mathematics is an interesting subject and I think shows up the intractability of ever getting that highly feared singularity.
All artificial computing systems are limited in ways we are not. Your "Turing Machine" example is one such case. The Halting Problem being a class example.
I think that far too often, we fail to recognise that what we create is not that great. We often stand in awe of the things we make without comprehending that these things are a very poor reflection of what is around us and what we ourselves are.
Every time some hype comes about these artificial stupidity systems, I look at my youngest granddaughter and see in her, capabilities that far exceed anything that we have created. Even my old buck of a goat demonstrates capabilities far, far in excess of anything we have created in all of our computational systems.
As I have said elsewhere here, we have to be careful that we do not cede control of our lives to systems that we think are more than they really are - systems that are limited, fragile and prone to failure.