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And that evidence is... an unproven theory, which itself is also heavily qualified?
by mumbisChungo 6y ago
And that evidence is... an unproven theory, which itself is also heavily qualified?
- ogogmad 6y agoAccording to the article, it rests on a plausible conjecture. I need to read further. [edit] According to the abstract of the paper referred to in the article (https://arxiv.org/abs/1902.10935 https://arxiv.org/abs/1902.10935) it rests on a "central conjecture in the area of network coding". Make of that what you will.
- mumbisChungo 6y agoFrom the abstract: >In this work, we prove that if a central conjecture in the area of network coding is true, then any constant degree boolean circuit for multiplication must have size Ω(nlgn), thus almost completely settling the complexity of multiplication circuits So, given an unproven assumption and also given that we are constrained to doing multiplication on a boolean circuit, this may be "perfect" in a sense. Seems like the title is mostly just clickbait.
- hinkley 6y agoYeah but in the backstory they also mentioned that Kolmogorov conjectured that the optimal solution was O(n^2). Conjectures aren't doing so hot in this area, it seems.
- ChrisLomont 6y ago>Conjectures aren't doing so hot in this area, it seems. For that one counter-example how many conjectures turned out to be true?
- timwaagh 6y agoAh but that's not what this game is about. It's about what you can prove. And conjectures are by definition things you can't prove yet. So the longer they stand and the more paths they block the more frustrating it gets.
- dogfoods 6y agoRTFA and find out!
- waynecochran 6y agoI would say most mathematical conjectures are stronger than most scientific theories. What I mean is that the conjectures are easily falsifiable (i.e., counter examples, if found, can easily be verified) and have been shown to be true for an enormous number of of cases. So unproven mathematical conjectures are not just "wild hypotheses."