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This work was published in “Nature Machine Intelligence“, the journal boycotted by pretty much everyone who matters in ML. Reflects poorly on the authors, regardless of the actual merits of their finding.
This work was published in “Nature Machine Intelligence“, the journal boycotted by pretty much everyone who matters in ML. Reflects poorly on the authors, regardless of the actual merits of their finding.
what's the reason it's boycotted? appeal to authority isn't very informative for those not keeping up with this stuff
By the way, Paul Cohen, who proved the independence of the Continuum Hypothesis, says that Godel did not express much interest in independence results (I think Godel believed in Platonism):
https://www.youtube.com/watch?v=VBFLWk7k1Zo
An article by Godel, taking a philosophical viewpoint about set theory and independence, is "The modern development of the foundations of mathematics in the light of philosophy":
http://www.marxists.org/reference/subject/philosophy/works/a...
Godel believed that for well-defined areas of mathematics, we can add more _intuitive_ axioms to make the theory decidable: The appropriate quote from the article: "I would like to point out that this intuitive grasping of ever newer axioms that are logically independent from the earlier ones, which is necessary for the solvability of all problems even within a very limited domain, agrees in principle with the Kantian conception of mathematics. "
Earlier quoted context omitted.
The reals are infinite. Float/double So, while I think your question is interesting and good, I don’t think integer size is a strong counterexample in support of a different conclusion.
float/double can store a subset of the rationals plus some other values which aren’t found in the reals
It's an absurd thing for GP to say integers aren't infinite (apparently talking about fixed width integer types) and then turn around and say float/double are infinite (talking about single precision and double precision floating point types).
Professor Peter O'Hearn (UCL Computer Science) says latest research findings on 'unsolvable' mathematical problems is “of a rare kind”, and will probably be important for the theory of machine learning.
Isn't all this press by the Nature publishing group just about hyping up one of its newer magazines that the larger research community is boycotting? By the way, Paul Cohen, who proved the independence of the Continuum Hypothesis, says that Godel did not express much interest in independence results (I think Godel believed in Platonism): https://www.youtube.com/watch?v=VBFLWk7k1Zo An article by Godel, taking a philos…
This work was published in “Nature Machine Intelligence“, the journal boycotted by pretty much everyone who matters in ML. Reflects poorly on the authors, regardless of the actual merits of their finding.
As someone who isn't in the know, I found this[1] Forbes article about the journal. Forbes portrays the opposition as opposing the fact that it's a closed access journal, but are there other points of contention that weren't reported in the article? [1] https://www.forbes.com/sites/samshead/2018/04/30/tech-giant-...
Where is mathematics in ML today? Most of that are happening under the hood and all algorithms are just a black box.
There's a very neat and often forgotten piece of math in learning, VC dimension (unrelated to venture capital): https://en.m.wikipedia.org/wiki/Vapnik–Chervonenkis_dimensio... Also, the reason why black box methods are such a big deal now is precisely because controlled/engineered methods turned out to be inferior (obvious example: image recognition; look no further than into the story of the dropout method and Alex…
[0] http://www.math.ucla.edu/~chernikov/teaching/Combinatorics28...
Isn't all this press by the Nature publishing group just about hyping up one of its newer magazines that the larger research community is boycotting? By the way, Paul Cohen, who proved the independence of the Continuum Hypothesis, says that Godel did not express much interest in independence results (I think Godel believed in Platonism): https://www.youtube.com/watch?v=VBFLWk7k1Zo An article by Godel, taking a philos…
Gödel proved the other direction of the independence of CH (and the Axiom of Choice), and had been trying to prove independence some years after that. He had actually succeeded in proving the independence of AC by 1943, and later said in an interview with Hao Wang that his methods could have probably been extended to prove the independence of CH by 1950, but he stopped working on it because he developed a distaste for the subject. In retrospect, Gödel wished that he had continued his work so that set theory progressed faster.
The article The Origins of Forcing by G. H. Moore in the proceedings of the 1986 Logic Colloquium is a good discussion of the relevant history.
> Godel believed that for well-defined areas of mathematics, we can add more _intuitive_ axioms to make the theory decidable: The appropriate quote from the article: "I would like to point out that this intuitive grasping of ever newer axioms that are logically independent from the earlier ones, which is necessary for the solvability of all problems even within a very limited domain, agrees in principle with the Kantian conception of mathematics. "
This line of research hasn't gone very well in practice since Gödel's time. It has produced a lot of interesting set theory, but has not really impacted mathematics at large.
Isn't all this press by the Nature publishing group just about hyping up one of its newer magazines that the larger research community is boycotting? By the way, Paul Cohen, who proved the independence of the Continuum Hypothesis, says that Godel did not express much interest in independence results (I think Godel believed in Platonism): https://www.youtube.com/watch?v=VBFLWk7k1Zo An article by Godel, taking a philos…
> By the way, Paul Cohen, who proved the independence of the Continuum Hypothesis, says that Godel did not express much interest in independence results (I think Godel believed in Platonism): Gödel proved the other direction of the independence of CH (and the Axiom of Choice), and had been trying to prove independence some years after that. He had actually succeeded in proving the independence of AC by 1943, and late…
> This line of research hasn't gone very well in practice since Gödel's time. It has produced a lot of interesting set theory, but has not really impacted mathematics at large.
What about Hugh Woodin's work? I agree that it has not had impact yet, but do you think it might lead along this suggested line?