Timeline for Can we define an "empirically generic" real number?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 13, 2018 at 22:24 | comment | added | Zsbán Ambrus | See also Gro-Tsen's related blog post madore.org/~david/weblog/… “Qu'est-ce qu'une machine hyperarithmétique ?” (in French, 2015-11-16), which tries to introduce the notion of empirically random and empirically general numbers to a broader audience. | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Jul 19, 2014 at 22:12 | comment | added | Gro-Tsen | I'm sorry my original formulation of the question was very messy and unclear. I tried reformulating it (starting from "edit/clarification") in a manner that I hope is clearer and less sweeping. | |
| Jul 19, 2014 at 22:06 | history | edited | Gro-Tsen | CC BY-SA 3.0 |
try to clarify the question and make it less informal by offering different formulation
|
| Jul 19, 2014 at 6:48 | review | Close votes | |||
| Jul 20, 2014 at 1:35 | |||||
| Jul 18, 2014 at 19:21 | answer | added | Robert Israel | timeline score: 2 | |
| Jul 18, 2014 at 19:16 | answer | added | Bjørn Kjos-Hanssen | timeline score: 4 | |
| Jul 18, 2014 at 18:35 | comment | added | usul | @EvanJenkins, agreed -- what I mean to say about $\pi$ and $e$ is that although they (seem to) pass "empirical" tests of randomness, they don't pass "algorithmic" tests of randomness. | |
| Jul 18, 2014 at 18:30 | comment | added | Evan Jenkins | Maybe I'm the one who's misreading, but it seems that Gro-Tsen is saying that π and e are emphatically not random, but rather that they (conjecturally) pass "empirical tests" of randomness, such as normality, while they fail empirical tests of genericity. | |
| Jul 18, 2014 at 17:34 | comment | added | usul | Or if perhaps you are not familiar with the field of algorithmic randomness (?), then I think it essentially answers your question. It is hard to tell from your post because you touch on most of the fundamental ideas/motivations of algorithmic randomness, but you don't mention it and you talk about how e.g. $\pi$ is "random", when it is definitely not algorithmically random. Sorry if I misunderstood though. | |
| Jul 18, 2014 at 17:29 | comment | added | usul | Can you be more specific in contrasting your "generic" numbers to Martin-Lof random numbers? As I understand it, you simply take the definition of Martin-Lof random and change "measure-0" to "meager". But since we understand a lot about algorithmically random sequences, it would be very helpful to understand more about how your notion differs. (Also where it comes from or where it is defined if you did not come up with the definition?) | |
| Jul 18, 2014 at 16:57 | comment | added | Joel David Hamkins | I like the topic, but your question is sweeping. In addition, it uses vague undefined terms such as "natural" and "empirical", and I expect that not everyone agrees with the claims you make about these notions. (For example, it seems quite reasonable to me for some to reject the idea that $e$ and $\pi$ are random in any truly robust sense, in light of the fact that they are computable numbers.) Perhaps you could focus the question on a more specific mathematical inquiry? | |
| Jul 18, 2014 at 16:39 | history | asked | Gro-Tsen | CC BY-SA 3.0 |