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A formula for the nth digit of πœ‹ and πœ‹^n

arxiv.org

111–120 of 143 posts

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#111
post #98

Earlier quoted context omitted.

> And depending on journal I don't even get to reject it for that as long as the science is sound. and you shouldn't. As long as it is somewhat legible, forcing people who are not native English speakers to conform to another language 100 % in order for their science to be published is horrendous. There was a time 300 years ago, where great thinkers who did not speak French or German could not publish their thoughts…

The goal of publishing is that others can read your work. If it's badly written it will be hard to understand, and extra hard for non-natives.

actually, sometimes "native" English is much harder to read for non-natives than a non-native writing, due to 1. less vocabulary, and 2. more straight forward sentence structure.

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#112
Is there a physical limit to how many digits of pi can ever be computed/represented in the universe?

For example, let’s say we need one atom for each digit of pi that we want to store, the max limit of digits of pi would be something like the total number of atoms in the universe, minus the atoms required to compute and store the digits.

Has that been studied/calculated?

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#113
post #110
post #53

Earlier quoted context omitted.

"Published" in this context is short for "published to a journal" or more completely for this thread "gone through the full edit cycle you would expect from a paper published to a journal". For example, https://arxiv.org/help/jref says: > When a article is published, the author may wish to indicate this in the abstract listing for the article. For this reason, the journal reference and DOI (Digital Object Identifier)…

I understand what it means, which you could have seen by reading my comment carefully. My point is that this publication process is of little value these days.

I believe you when you say you understand, but your first sentence was "If you can download it from arxiv, it is published." Which is precisely what GP was responding to.

Furthermore, this thread started with someone complaining about the lack of polish which the publication process can provide.

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#115
post #109

Earlier quoted context omitted.

There is definitely a difference between "public(ly available on arxiv)" and "published (in a peer-reviewed journal)". Depending what I want to do I may prefer on or the other for my work as a researcher.

Sure, but if the paper is never published in a journal, and just exist as a pdf on arxiv forever, you won’t treat it any different than if it was published. You’ll still ignore it if it looks crap, still read it if it looks promising, still tell your friends about it if it has interesting results, still cite it etc. In short, it doesn’t matter much if the paper was formally published.

The "doesn’t matter much" is, I think, the crux of the matter.

commandlinefan's earlier negative aside concerned language quality.

IMO, I think people hold peer-review journal published papers to a (slightly?) higher language quality standard than what may be the first of several preprints. And I think anamexis was pointing out that difference.

As Wikipedia says: "The immediate distribution of preprints allows authors to receive early feedback from their peers, which may be helpful in revising and preparing articles for submission." https://en.wikipedia.org/wiki/Preprint

I expect that may include identifying and fixing typos.

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#116

It is all curious, but it seems that procedure that calculates the n-th digit using some other functions that require O(n) calculations (i.e. Bernoulli numbers) is not that exciting, as it's just a speedup comparing to a naive calculation (maybe a big one but still). Although because pi is a transcendental number maybe it is impossible to have an algorithm to return the n-th digit in O(1) operations? Does anyone know…

The interesting question is: are there real numbers whose N-th digit provably cant be calculated in O(N)?

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#117

It is all curious, but it seems that procedure that calculates the n-th digit using some other functions that require O(n) calculations (i.e. Bernoulli numbers) is not that exciting, as it's just a speedup comparing to a naive calculation (maybe a big one but still). Although because pi is a transcendental number maybe it is impossible to have an algorithm to return the n-th digit in O(1) operations? Does anyone know…

The interesting question is: are there real numbers whose N-th digit provably cant be calculated in O(N)?

Even better: there are (well defined) real numbers whose N-th digit provably cannot be computed at all.

https://en.wikipedia.org/wiki/Chaitin%27s_constant

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#118
post #53

Earlier quoted context omitted.

"Published" in this context is short for "published to a journal" or more completely for this thread "gone through the full edit cycle you would expect from a paper published to a journal". For example, https://arxiv.org/help/jref says: > When a article is published, the author may wish to indicate this in the abstract listing for the article. For this reason, the journal reference and DOI (Digital Object Identifier)…

Don't abbreviate unless you have great confidence that everyone hearing or reading your words shares the same dictionary.

And this is not the case here?

I mean, there's always going to be today's 10,000 [1] who doesn't know what, say, "VB.NET"[2][3] means.

[1] https://xkcd.com/1053/

[2] https://news.ycombinator.com/user?id=kwhitefoot

[3] https://en.wikipedia.org/wiki/Visual_Basic_(.NET)

But explaining or footnoting everything defensively, rather than pointing out misconceptions as they arise, seems excessive.

Further, someone may deliberately use a minority definition in order to stress a philosophical point. One valid viewpoint is that a publication is a publication is a publication. A preprint, a blog post, or a peer-reviewed journal publication should be given equal weight as being "published." I'll call this position #1.

Another valid point is that some works are incomplete, and may go through multiple drafts before reaching the final, "published" form, which it's best known by, and is likely the most polished of the versions. I'll call this position #2.

Often people want feedback, and one way to get feedback is by publishing a preprint. (There are others. I recall reading of a mathematician, about a century ago, who would first publish in his home country, and native language, to get friendly feedback from colleagues, before publishing in English. He's cited for his later publication.)

Someone who holds position #1 might fully understand that I use the dictionary with position #2, and still deliberately use position #1 in order to popularize that #1 dictionary. The difference isn't one of confusion or lack of knowledge, but one of viewpoints.

Let me be clear - I'm not saying that that's the case here. Instead, my example is meant to show it's not necessarily so simple as "shares the same dictionary" or not.

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#119
There is nothing of note here. This paper should be in 'general math', not number theory. You need to know the Bernoulli numbers in order for this to work, which is more computationally difficult than computing pi. So what. Yeah, Plouffe is a famous person in computer science and math, but this does not measure up to the hype. It reminds me of the stuff i tinkered with in high school when i first learned infinite series ..but not publishable-level, sorry.

Re: A formula for the nth digit of πœ‹ and πœ‹^n

#120

It is all curious, but it seems that procedure that calculates the n-th digit using some other functions that require O(n) calculations (i.e. Bernoulli numbers) is not that exciting, as it's just a speedup comparing to a naive calculation (maybe a big one but still). Although because pi is a transcendental number maybe it is impossible to have an algorithm to return the n-th digit in O(1) operations? Does anyone know…

exactly. this paper is trivial, sorry to say.
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