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Turing Oversold?
121–130 of 311 posts
Re: Turing Oversold?
#122We've been over this. Gödel's mu-recursive functions were a poor model of computation because it's completely unclear how to physically implement the arbitrary-function minimization operator. So people didn't see how to build a machine that calculates this way. Similarly, there's no clear way how to mechanize lambda calculus. Turing Machines, on the other hand, were instantly obviously mechanizable. It was clear that…
"For example, it was claimed that Turing founded computer science.[...] Turing's 1936 paper provided the "theoretical backbone" for all computers to come." So your argument is, because it is unclear how to "physically implement the arbitrary-function minimization operator", Turing is the better "theoretical backbone" and has founded computer science?
I don't think it's important to quibble over who's overrated or underrated among these giants of math and CS who already get tons of recognition (I'm glad Schmidhuber brings many other historical names into the narrative).
However, yes, I do think that 'mechanization' or physical implementation is a crucial piece of Turing's contribution that is wrongly ignored in this article. And I think without mechanization, there is no CS as we understand it.
Re: Turing Oversold?
#123Earlier quoted context omitted.
"For example, it was claimed that Turing founded computer science.[...] Turing's 1936 paper provided the "theoretical backbone" for all computers to come." So your argument is, because it is unclear how to "physically implement the arbitrary-function minimization operator", Turing is the better "theoretical backbone" and has founded computer science?
Not OP, but I agree with them. The word computer means multiple things. In one sense it the abstraction of universal computation. Imagine a world where actual physical computers didn't progress to universal computation, but were stuck being purpose built to the present day. The field of computer science would be utterly different because they couldn't actually compute anything with their science. They could just disc…
The article writes about your point of general computation and purpose built computers:
"Likewise, Konrad Zuse never got a Turing award despite having created the world's first working programmable general computer 1935-41. [...] It was pointed out that none of the computers built during the 1940s were influenced in any way by Turing's 1936 theoretical paper, [...]"
Re: Turing Oversold?
#124Earlier quoted context omitted.
"For example, it was claimed that Turing founded computer science.[...] Turing's 1936 paper provided the "theoretical backbone" for all computers to come." So your argument is, because it is unclear how to "physically implement the arbitrary-function minimization operator", Turing is the better "theoretical backbone" and has founded computer science?
I don't think it's important to quibble over who's overrated or underrated among these giants of math and CS who already get tons of recognition (I'm glad Schmidhuber brings many other historical names into the narrative). However, yes, I do think that 'mechanization' or physical implementation is a crucial piece of Turing's contribution that is wrongly ignored in this article. And I think without mechanization, ther…
I can only repeat my comment from down:
"Likewise, Konrad Zuse never got a Turing award despite having created the world's first working programmable general computer 1935-41. [...] It was pointed out that none of the computers built during the 1940s were influenced in any way by Turing's 1936 theoretical paper, [...]"
Re: Turing Oversold?
#125We've been over this. Gödel's mu-recursive functions were a poor model of computation because it's completely unclear how to physically implement the arbitrary-function minimization operator. So people didn't see how to build a machine that calculates this way. Similarly, there's no clear way how to mechanize lambda calculus. Turing Machines, on the other hand, were instantly obviously mechanizable. It was clear that…
> I don't understand why Schmidhuber continues to ignore this crucial point.
It is difficult to get a man to understand something when his salary depends upon his not understanding it.
But wait a minute, you might say, facts are facts.
And if everyone had the time and resources to discover and digest every fact, your understanding would be the end of it.
But everyone doesn't have time and resources. To compensate, we rely on others to curate facts for us. When we encounter an internally consistent subset of facts that suits our ideals and our interests, we adopt that point of view.
There are infinitely many subsets of curated facts that can be presented as internally consistent. That's why there are so many different points of view.
What bearing does this have on Turing's role in computer science, and his latter day fame in a society which came to be defined by silicone logic?
The First Computers Were Human (and Mostly Women)
https://mjosefweber.medium.com/the-first-computers-were-huma...
Turing, in addition to stating an ontology of computing, dared to invite the question, what is the difference between a computer and a human?
Re: Turing Oversold?
#126Being the first one to claim a formal proof to a theorem is not the most important thing. What's really important is to prove things that improve our understanding, which both Goedel and Turing have done, in the fields of logic and computing respectively.
Re: Turing Oversold?
#127Earlier quoted context omitted.
I'm not advocating telling lies. Sometimes we simplify, and doing so can be perfectly appropriate. Unfortunately that does open the stage for nitpicking and pedantry.
Story telling is how our society has transferred information since we started to communicate-- understanding the map is not the territory, nor should it be. A beautiful narrative can convey important kernels more efficiently than endless minutiae-- Awareness of this is important and elaborations are helpful for those interested in the details. I'm reminded of, "The Glass Bead Game," which discusses an academic societ…
Arguably our storytelling was an efficient hack in an age before writing. A story is a very high-overhead, low SNR way of communicating kernels of truth, but it's robust over time, so it allowed transfer and accumulation of knowledge across societies and generations.
But then we've invented and perfected writing, developed symbolic languages and notations (e.g. math, musical), long-duration storage media for text, and eventually networked digital computers. In terms of communicating and preserving knowledge, stories are pretty much the worst possible option you can choose.
We're comfortable with narratives because we didn't have anything else for hundreds of thousands of years. Stories are pretty much hardwired into our brains. But that doesn't make them the right choice, now that we've figured out much better alternatives.
More than that, I'm personally suspicious of stories being used in communication. There's no good reason to use them, and there's plenty of bad ones - it so happens that what makes a good story robust over time is the same thing you need to manipulate people into believing lies and shut off critical thinking.
Re: Turing Oversold?
#128I feel like it's really weird to call what Gödel was doing computer science.
I feel that computer science is really the wrong word. It's like calling astronomy "telescopy", to paraphrase Dijkstra.
"Computation" would have been a more felicitous term for the field, but that ship has probably sailed.
Re: Turing Oversold?
#129Name me a single mathematician - or honestly a single scientist or thinker ever that didn't stand on the shuolders of giant
Re: Turing Oversold?
#130Earlier quoted context omitted.
Computably countable is also a correct term. In line with this approach to computability theory: http://math.andrej.com/asset/data/synthetic-slides.pdf It shows that the unsolvability of the halting problem follows from: - The computable uncountability of N^N, which can be proved using an identical argument to the one Cantor used to prove the set-theoretic uncountability of N^N. - The computable countability of the p…
I don't doubt that the term is in use, and I understood what you meant. But it's not listed among seven (!) synonyms for computably enumerable on Wikipedia, and more the point, the slides you linked to also don't contain that term. However, that's not the point I wanted to make. I wouldn't like calling it computably countable even if everyone else did, simply because it gives the wrong intuition about subsets.
> the slides you linked to also don't contain that term
The term "countable" is used in the slides, where it means computably enumerable. The adjective "computably" is used when there's a need to distinguish set-theoretic notions from similarly behaved computability-theoretic notions. Otherwise the meaning of the term "countable" can be context-dependent.
> it gives the wrong intuition about subsets
In constructive logic, a countable set can contain an uncountable subset. The misleading intuition (in the context of non-classical logics) is based on classical logic where countability is a statement about the size of a set. Whether you think constructive logic is a good way of explaining computability theory is another question, but it's certainly a viable way of doing it.
It's like how the term "line" can mean something different in hyperbolic geometry from what it means in Euclidean geometry. You could argue that it might mislead people about the nature of parallel lines, but that's why hyperbolic geometry is not Euclidean geometry. Another example is using "multiplication" to refer to an operation on matrices, which might make people think that AB=BA when that usually isn't true. Mathematics is all about re-using terms and pointing out that there are differences.
[edit]
Admittedly, the slides do use the term "enumerable" as well, so that's another option. When there's a possibility for confusion with set theory, you can say "computably enumerable" as you suggested.
[edit] Made lots of edits. Hopefully, that's it.