User talk:EmilJ/Archive 2

Thanks for the tip
And for cleaning up the hyphens, dashes, and minus signs in the quadratic residue article (I'd swear that somewhere I read that &amp;ndash; was proper for formulas; I didn't even realize that &amp;minus; existed)

I can see the difference between – and &minus; by juxtaposing them; –&minus; the minus is raised a pixel or so higher. Subtle.

Thanks again.

Virginia-American (talk) 17:10, 1 April 2008 (UTC)

Probability of Solovary-Strassen primality test
The probability of the Solovay-Strassen primality test can be more specifically limited than 1/2. I will find the reference in the textbook that a math teacher of mine owns. Meanwhile, I have my own version (the math teacher made me re-calculate everything). It involves the use of Bayes' rule.

"To derive the probability of failure of the Solovay-Strassen Primality test, Bayes' rule is used. In this problem, event A will be the probability that n survives m number of trials and event B will be the probability that n is composite. So, the probability that a number n is composite given that it survives m number of trials is what we are looking for. P(A|B) (the probability that a composite number n survives m number of trials) is less than or equal to 2^{-m} because at most half of the numbers can be liars. P(A) is expanded and found below. P(B) is the probability of choosing a composite number. The probability of choosing a prime number is about $$ \frac{1}{ln n}$ $$ however, to increase our chances, we will discard the obviously non-prime, a.k.a. \textbf{even} numbers, doubling our chance to $$ P(\neg B) = \dfrac{2}{ln n} $$ Thus the probability of choosing a composite number is $$ P(B) = 1 - \dfrac{2}{ln n} $$ $$ P(A|\neg B) = 1 $$ since if n is prime the number of trials it can survive is infinite.

$$ P(B|A) = \frac{P(A|B)P(B)}{P(A|B)P(B) + P(A|\neg B)P(\neg B)} $$

$$ \leq \frac{2^{-m}(1 - \frac{2}{ln n})}{2^{-m}(1 - \frac{2}{ln n}) + \frac{2}{ln n}} $$

$$ = \frac{1 - \frac{2}{ln n}}{1 - \frac{2}{ln n} + \frac{2^{m+1}}{ln n}} $$

$$ = \frac{ln n - 2}{ln n - 2 + 2^{m+1}} $$

So

$$ P(B|A) \leq \frac{ln n - 2}{ln n - 2 + 2^{m+1}} $$

Does my probability still seem dubious?

--Heero Kirashami (talk) 22:44, 27 April 2008 (UTC)


 * You are seriously confused about what a probabilistic algorithm is, and how is its probability of failure defined. The statement "the probability of failure of the algorithm A is at most p" means "for every input n, the probability (over its internal coin tosses) that A fails to give the correct answer on input n is at most p". It does not involve any probability distribution on the inputs in any way. (One of the reasons being to rule out trivial "algorithms" like ignore the input and return "composite", which according to your definition correctly computes primality with the negligible error of 1/ln n.) So, while your computation might be correct (I did not check it), it is totally misguided, the number computed has nothing to do with the error probability of the algorithm.


 * Furthermore, the bound $$ \dfrac{ln(n) - 2}{ln(n) - 2 + 2^{m+1}} $$ as you inserted in the article uses a mysterious parameter m which does not appear anywhere in the article, and the bound is actually worse than the usual 1/2 (or 2-m with more trials and your notation) bound, as assymptotically $$ \frac{\ln n - 2}{\ln n - 2 + 2^{m+1}} \to 1$$ for $$n\to\infty$$. For future, note also the correct formating of $$\ln$$ in TeX. — EJ (talk) 11:39, 28 April 2008 (UTC)


 * However, note that the original calculations of an author much smarter and less confused than an eighth grader were correct. And he actually knew how to define the actual terms. I'm still somewhat confused about the terms, but I know how to do the calculations. If I can reference the book, then I will place it in the article. --Heero Kirashami (talk) 22:26, 28 April 2008 (UTC)


 * You see, the problem is not so much with the computation, but with your interpretation of the result. What you thus need to check is not the name of the book, but the actual formulation of the statement, and its meaning in the context. Given your own admission of being "somewhat confused about the terms", I will not hesitate to revert any addition which is at odds with standard and well-known facts abut the algorithm. — EJ (talk) 11:03, 30 April 2008 (UTC)


 * However, I have read through it carefully and so I have found the source. If you would like to check it, fine. However, even additions that are "at odds with standard and well-known facts ab[o]ut the algorithm." may be correct. As Cryptography: Theory and Practice, by Douglas R. Stinson, states, (I'm quoting this directly but re-phrasing will be necessary for the article) "If we have run the algorithm m times, what is our confidence that n is prime? It is tempting to conclude that the probability that such an integer n is prime is $$1 - 2^{-m} $$. This conclusion is often stated in both textbooks and technical articles, but it cannot be inferred from the given data." Thus, I do believe it contradicts commonly referenced facts about the distribution. However, just because everyone else assumed the world was flat didn't mean it actually was.


 * Thus, the computation is correct (and, given that m will be defined as the number of trials, completely sensible; further, it is not n, but m which is going to infinity, so it is still approaching zero, and further it does matter whether $$ 2^{-m} $$ is better, it matters which one is correct); however, his formulation of the statement was essentially the same as mine. Thus, I think that my result is correct. I am willing to reformat it so it matches with the article. However, I will wait for your "approval." If you need proof, then go find a copy of Cryptography: Theory and Practice, Second Edition, by Douglas R. Stinson, (If you go to Books_on_cryptography you can find its ISBN, but you can probably find a friend or someone with it, or try a library), and go to page 178 (Or "The RSA Cryptosystem and Factoring Integers"). --Heero Kirashami (talk) 00:01, 7 May 2008 (UTC)


 * Probabilistic algorithms and their probability of error are mathematical objects with an exact definition, which you can find in any standard textbook on computational complexity (e.g., Papadimitriou). It has nothing to do with anybody's confidence in anything. Confidence is a subject of psychology, not computer science. It is a proved mathematical fact that the probability of failure of the Solovay–Strassen algorithm is at most $$\varphi(n)/2n$$ for every n. It is likewise a hard mathematical fact that this bound is optimal, there are many inputs n which attain the bound: 1729, 2465, 15841, ... (in general, any Carmichael number n such that 2(p &minus; 1) | n &minus; 1 for every prime divisor p of n). You cannot argue with it any more than you can argue with 1 + 1 = 2, so what you say about flat world is just babbling nonsense. Finally, it makes no sense to say that "it is not n, but m which is going to infinity". In theory, it is customary to compare randomized algorithms using just one round (i.e., m = 1). In practical applications, both parameters are of course bounded, but m behaves as a constant much more than n does (m is usually a small number like 5 to 10, whereas n has hundreds of bits).


 * Your derivation above makes it clear that you are not computing a bound on the failure probability of the algorithm, but the conditional probability of pronouncing prime a uniformly randomly chosen composite integer in [1, n]. Actually, that's still not quite correct, as you introduced for no good reason another complication by excluding even numbers. (Why? Why not exclude also multiples of 3? Or 5? etc?) So, the actual description is that it is supposed to be a bound on the probability of pronouncing prime a uniformly randomly chosen odd composite integer in [1, n].


 * Should it be mentioned in the article? No, I say. Neither the fact that it appeared as an example in some book, nor the fact that you were able to recompute it yourself, make it notable for inclusion in an encyclopedia. For one thing, there is no explanation why anyone should be interested in a parameter with such a ridiculously complicated description. Much more importantly, the appearance of the bound in the article would suggest the impression that it is a realistic estimate, which is completely false. The actual probability is much, much smaller. This is due to the fact that the number is equal to $$\frac1{1+2/(p\ln n)}$$, where p is not the usual (maximal) probability of error of the algorithm, but the average probability of error taken over uniformly random (odd) integers in [1,n]. This p is significantly smaller than 1/2. For a trivial bound, it is less that $$3/\pi^2\approx 0.304$$ (for m = 1), because $$\varphi(n)/n$$ is $$6/\pi^2$$ on average (see totient, or any textbook on number theory). For a stronger bound, Damgård, Landrock, and Pomerance give several bounds (e.g., $$p<(\log n)^{3/2}\frac{2^m}{\sqrt m}4^{2-\sqrt{m\log n}}$$ for m = O(log n), $$p<\tfrac17(\log n)^{15/4}2^{-(\log n)/2-2m}$$ for larger m) on the average probability of error of the closely related Miller–Rabin algorithm (see that article for an exact reference). (The point to observe in the somewhat complicated expression is that the bound is exponentially small not only in m, but also in log n.) I am not aware of such a bound being published for Solovay–Strassen (presumably because nobody gives a damn about the Solovay–Strassen algorithm any more, as Miller–Rabin is better in all respects), but the similarity of the two algorithms and their analysis strongly suggests that a bound of similar growth rate should hold for Solovay–Strassen as well.


 * So, apart from your bound being hardly useful, it is also highly misleading, as it is badly suboptimal. I thus cannot agree with putting it in the article. If you want to make yourself useful, you can search a library to find out whether there isn't a published paper extending the Damgård, Landrock, and Pomerance results to Solovay–Strassen after all (though it does not look very promising), instead of keeping pushing your bound. — EJ (talk) 10:45, 9 May 2008 (UTC)


 * Found it myself, it's actually in one of the reference of the DLP paper: Erdős and Pomerance show that the average probability of error of Solovay–Strassen (and even Fermat) is $$\exp(-(1+o(1))\log n\,\log\log\log n/\log\log n)$$ (for m = 1). I'll put it in the article. — EJ (talk) 13:49, 9 May 2008 (UTC)


 * Seeing as we have reached an agreement, you should put it in as I am still partly confused, and you can probably write it a lot better than I can. And it's definitely true, too, that no one gives a damn about Solovay-Strassen because Miller-Rabin is so much faster, with an equal or better probability of...working (that's the best I can say). And even though I have no idea what the heck your number is, I don't disagree because it's probably for the general case (I think) instead of just for odds and also I am not too good with algebraic manipulation when there's so many logs. It's great that we've both grown as mathematicians, then! Thanks! For me, it would probably take...15,000 years to look through papers! --Heero Kirashami (talk) 06:10, 13 May 2008 (UTC)

notice, but please explain why you disagree with the proposed deletion in your edit summary or on its talk page.

Please consider improving the article to address the issues raised because, even though removing the deletion notice will prevent deletion through the proposed deletion process, the article may still be deleted if it matches any of the speedy deletion criteria or it can be sent to Articles for Deletion, where it may be deleted if consensus to delete is reached. --  Darth Mike  ( join the dark side ) 14:11, 5 February 2009 (UTC)


 * Whatever, I don't care. I just tried to disambiguate info on two different people mixed up in Andrew Robertson. — Emil J. 14:15, 5 February 2009 (UTC)

AfD nomination of Andrew N. Robertson
I have nominated Andrew N. Robertson, an article that you created, for deletion. I do not think that this article satisfies Wikipedia's criteria for inclusion, and have explained why at Articles for deletion/Andrew N. Robertson. Your opinions on the matter are welcome at that same discussion page; also, you are welcome to edit the article to address these concerns. Thank you for your time. --  Darth Mike  ( join the dark side ) 03:06, 6 February 2009 (UTC)

Stop inserting your lunatic pseudoscience
it is not ok to use such a language EmilJ. What I did was to help people to understand i easier since it is confusing to use sqrt(-1) as in 'proper use' section of the article. this is neither pseudoscience nor lunatic. i is a definition and one can define things different than other people, this is not pseudoscience but just a different idea. you may not open to different ideas but that doesn't allow you call other people as 'lunatic'. we are trying to share information as well as ideas here

by the way, I talked to Quaeler and settled the issue.. (Ati7 (talk) 13:18, 17 February 2009 (UTC))


 * You most definitely did not help people to understand i easier, you rather inserted there two sentences mixing up various unrelated concepts in a way which did not make the slightest bit of sense. Minus sign is not any "property of a number", it is an operator taking one number to another. i is not a property of any number either (property of which number, I wonder?), nor is it an operator. It is a number itself. Saying "it is not a scalar entity" again makes no sense, as a scalar is a member of the base field of a linear space, and we are not talking about any linear spaces. (And if you take a linear space over the complex numbers, it has i as a scalar.) Your statement "'i' is an unit, not a value" is likewise absurd, as a unit is by definition a number whose norm (i.e., absolute value) is 1, thus any unit is automatically also a number (if number is what you mean by "value", otherwise it's meaningless). Sorry, but in my book, gibberish combining random mathematical terms in nonsensical sentences is pseudoscience. The reason why "square root of minus one" may be confusing has nothing to with any scalars, units, or whatnot, it is simply a consequence of the fact that square root is not a univalued function. — Emil J. 13:40, 17 February 2009 (UTC)


 * minus sign has three different usage as you can see in Plus_sign and as you said, first usage is subtraction. however, second usage is not substraction, not operator as well. it tells you that it is a negative number. and being negative is not about scalarity or magnitude. without minus sign, the number still has magnitude. that's why I used 'property', to mention that i should be more like as a symbol, not a value.
 * if you take i as sqrt(-1), then yes i is a scalar in a linear space over the complex numbers. what I am saying is that minus itself is not a number but -1 is a number. similarly, i itself shouldn't be a number, whereas i1 is a number. and again similarly, meter is not a value but a unit, whereas 1mt has a value
 * again, I am not talking about the reason for confusion about "square root of minus one". what I am saying is that if you define i as a value, you will have trouble as happened in that false proof of 1 = -1. anyway, thanks for sharing info. apparently, we don't understand each other and talk something else:) (Ati7 (talk) 14:24, 17 February 2009 (UTC))

Wikifying math-subjects
I'm sorry I hadn't noticed the wiki places a real apostrophe. It was maybe careless, but certainly not intentional. Would it be an option to replace x'z + y'z with xz + yz in order to maintain the same outcome, namely xy + yz, and using wiki-syntax instead of HTML? Dr. Breznjev (talk) 17:47, 18 February 2009 (UTC)


 * Well, the outcome looks the same, so I suppose it is OK. Whoever created the original formatting presumably did it for semantical reasons (it's not a single bold-face string "xy", but a variable "x" multiplied by another variable "y"), but I think that's not important enough to worry about. — Emil J. 17:54, 18 February 2009 (UTC)

Reference Desk Regulars
Thank you for all your contributions to the Wikipedia Reference Desk! In recognition of your work I have added your name to the list of Reference Desk Regulars. If you would prefer not to be listed, please let me know or simply remove your signature. Thanks again, and happy editing! –  7 4   09:57, 19 February 2009 (UTC)

Logical connective
I found your formulations of the properties to be much better. I am still wondering if there isn't something more to absorption, because it looks just the same as "dual". That one had been without a description for a while. Be well, Pontiff Greg Bard (talk) 16:08, 23 February 2009 (UTC)

Taken off Talk:Ω-consistent theory
You wrote:
 * I am happy that you are happy. Yes, superscripts, subscripts, different fonts, etc. are all sensible possibilities for notation of sorts. However, the trouble is that none of them is quite standard, so whatever usage you choose would require an explanatory note.


 * As for the default sort: the choice obviously depends on the theory. It is natural for the natural numbers to be the default sort in a theory of arithmetic, but not in other theories. For instance, in set theories or class theories the natural default sort is the sort of sets. And since you seem to be interested in subsystems of second-order arithmetic and their proof theory, note that set theory does not just mean ZFC, it applies equally well to Kripke–Platek and its extensions. — Emil J. 12:44, 3 March 2009 (UTC)

I guess the point about notation means that many-sorted logic is useful to Wikipedia only for rather niche articles. I'd say that subscripts is most widely used, I think due to a preference in theorem proving, but it has the problem with not indicating the sort of free variables.

Default sort: I should have put a smiley after my remark, which was based on punning natural as in number with the natural sort of choice. Quantification over real numbers I guess is more common than quantification over the naturals.

Kripke-Platek set theory: yes, that was the thought that led me to think of subsystems of second-order arithmetic.

I don't suppose there is much more worth saying on these topics, so I'll just say hi to one of the small band of Wikipedians who has published on the calculus of structures. &mdash; Charles Stewart (talk) 14:52, 3 March 2009 (UTC)


 * Well, hi. I don't think that there's much more to be said on this topic either. — Emil J. 16:09, 4 March 2009 (UTC)

Messing with references
The bot is randomly changing the order of references without any adequate reason, see e.g.. — Emil J. 10:55, 27 March 2009 (UTC)
 * As far as I can see (in the first 10 minutes) in this edit they are re-arranged into numerical order, which is part of WP:AWB general fixes. Rich  Farmbrough 12:04 27  March 2009 (UTC).

TeX link in Greek
Thanks for fixing he [el:Tex] link. I gave up fixing it as the bot just adds it back to the subpage. Will this stop it?

SimonTrew (talk) 14:35, 30 March 2009 (UTC)


 * I do not know the logic used by the bot, but I guess that it adds interwikis to articles which link back to the article in question, so let us hope that it will eventually realize that el:TeX/Προσωρινό was deleted and the correct name is el:TeX. — Emil J. 14:55, 30 March 2009 (UTC)

Current events
Please keep a civil tone and assume good faith. It is not another editors responsibility to correct your errors and your tone does nothing to help the project. Tomdobb (talk) 16:52, 1 April 2009 (UTC)


 * Are you kidding me? It is you who failed to assume good faith. I mentioned a well-publicized event widely reported in media, as well as in our pages like NATO, Members of NATO, etc. If you felt it needed a source, you should fix it by adding one (it takes about a 5 seconds with Google news), not revert it. — Emil J. 17:04, 1 April 2009 (UTC)
 * The guidelines for current events state all news items should be sourced. If an event is well-publicized, then you should have a source ready when you add it. Other editors can't be held responsible for your errors. Please follow the guidelines to avoid issues in the future. Tomdobb (talk) 17:10, 1 April 2009 (UTC)
 * I've gone ahead and filed a Wikiquette alert about this. Tomdobb (talk) 17:19, 1 April 2009 (UTC)


 * Be my guest. If you do not have anything better to do than bullying other editors, that's only your problem. — Emil J. 17:23, 1 April 2009 (UTC)


 * So you broke a rule, you were politely informed of it, and instead of simply fixing the problem you responded with an insult. Looking at this page, I see that you have been making a habit of interacting antagonistically with other editors.  That's a bad path to go down if you want to accomplish anything here.  Regards, Looie496 (talk) 18:37, 1 April 2009 (UTC)

Interpretability
You're quite right, thanks for fixing that. BrideOfKripkenstein (talk) 15:35, 4 May 2009 (UTC)

Janos Komlos
At least you could have waited a few days. Kope (talk) 15:21, 13 May 2009 (UTC)


 * Waited for what? Naming an article with a parenthetical disambiguation when the base name does not exist is simply wrong. — Emil J. 15:26, 13 May 2009 (UTC)

Sabotage!
There goes my cunning plan of getting the anon to at least understand and state the problem correctly ;-). --Stephan Schulz (talk) 15:28, 18 May 2009 (UTC)


 * I'm not so sure that the anon is responsible for the insufficient statement of the problem. Anyway, the question is quite weird. I for one haven't got the slightest idea what circles and squares have to do with the two arctans, except that the results happen to be the same. — Emil J. 15:57, 18 May 2009 (UTC)

Mapa v Seznam států a mezinárodních organizací podle postoje k nezávislosti Kosova
Asi jsem natvrdlý, ale proč jste vyměnil mapu? Resp. proč považujete Vámi dodanou mapu - informačně chudší a zdůrazňující pouze jednu z relevantních skupin států - za NPOV? Jann 15:30, 20 May 2009 (UTC)


 * Ta mapa není informačně chudší, protože jediná dostupná informace o dané situaci založená na ověřitelných objektivních faktech je zda daný stát formálně uznává Kosovo či nikoliv. Ono rozdělení neuznávajících států do pěti nebo kolika skupin není informace, ale pustá spekulace, daná místní interpretací různých kusých zpráv v mediích, a je nutně věcí názoru a POV. Na cswiki jste si toho možná nevšiml, protože tam needituje mezinárodní komunita, ale na enwiki, odkud mapa File:Kosovo relations.png původně pochází, vedlo její použití k nekonečným debatám o tom jak a proč má ta která země být vybarvena a k revert wars (viz archívy Talk:International recognition of Kosovo), což mimo jiné vyústilo ve fork na dvě verze, File:Kosovo relations.png a File:Kosovo relations2.png. Na konec komunita dospěla k názoru, že jediný neutrální způsob, jak situaci vyřešit, je použít novou mapu která se striktně drží faktů, tj. File:CountriesRecognizingKosovo.png. (Podobné dvoubarevné mapy se mimochodem používají i pro jiná sporná teritoria, viz International recognition of Abkhazia and South Ossetia a Foreign relations of the Republic of China) Další nepřímý důsledek je, že ty šestibarevné mapy jsou od té doby v podstatě neudržované (přesněji řečeno, s výjimkou očividných updatů když nějaká nová země uzná Kosovo edituje Kosovo_relations.png pravidelně pouze uživatel Avala, který prosazuje silně prosrbský POV). Použití této mapy na české wiki je proto dost zavádějící. — Emil J. 17:01, 20 May 2009 (UTC)

Functional completeness
Re your edit comment here – there was a good reason I didn't do this: I don't know where to look this up, and didn't have enough time to figure it out on my own and be sure it's correct. Unless I am doing something wrong, it's a straightforward but tedious exercise. Do you have a source, or an idea where to find one by any chance? In any case thanks for doing this. --Hans Adler (talk) 20:39, 2 June 2009 (UTC)


 * No, I do not have any source, I checked it by hand while fixing the relevant section in the logical connective article. If that is your concern, I still do not understand why you think that sets of size at most 2 are OK, but not the larger ones: if anything, the whole list should go, since we have no source for the smaller sets either. Note that the list you pasted there was incorrect to begin with, three sets were missing. — Emil J. 09:36, 3 June 2009 (UTC)


 * I think formally sets of size at most 2 are not OK, either. But as I hinted above, like you I felt the need to make the list complete and would have done my own original research if I had had the time; in my opinion uncontroversial original research for presentational reasons is a good thing. Concerning the incompleteness – I replaced a confusing table with 16 entries by a list with 15 entries, so I should really have noticed.
 * While looking up some things for this comment, I just realised that the Wernick reference in the article comes very close to what we need. His result (on the last page) needs only some little corrections to account for his slightly stronger notion of completeness. --Hans Adler (talk) 10:27, 3 June 2009 (UTC)


 * Sounds good, thanks for looking it up. — Emil J. 11:01, 3 June 2009 (UTC)

Treaty of Lisbon
Thank you for the improvements you made in the section about Czech Republic, but I am afraid you deleted all what came after it (for example, now there is nothing about Germany, which until yesterday was there). —Preceding unsigned comment added by 83.217.131.237 (talk) 03:33, 10 June 2009 (UTC)


 * I have no idea what you are talking about. Here's the diff of my edits:. As you can see, I did not touch the German section at all. — Emil J. 09:44, 10 June 2009 (UTC)

Yes now I see it again. I think that my iexplore version had a problem this morning, sorry for the mistake. —Preceding unsigned comment added by 212.221.24.162 (talk) 10:16, 10 June 2009 (UTC)