en User talk:Michael Hardy Archive3

Beta Distribution

Michael, I don't understand how to communicate with you directly regarding the change I made to the page on the Beta distribution, so apologies if this is not the correct place to do it. I thought that you were referring to the CDF, not the pdf. apologies. The pdf is straight, but the CDF obviously is not...

Separately, the formula for the entropy of the beta distribution from that RAND appendix has something wrong with it. They derived the formula under the assumption that alpha and beta were both >= 1. Thus, the formula is incomplete, because, in fact, alpha and beta are only restricted to be > 0. The beta(1, 1) = uniform must be entropy maximizing, but there should be some expression that indicates the entropy for alpha and beta in [0,1). The formula, as written, does not indicate that the assumption is that a,b >=1, and just plugging in numbers less than one will demonstrate that the formula on the page will have maximum entropy at B(0, 0), which is incorrect.

Actually it had not occurred to me that the cdf might have been intended. But yesterday, when I found that it said "the Beta function", I changed it, since the Beta function is actually neither the cdf nor the pdf; the Beta function is the normalizing constant (or its reciprocal, depending on which nomenclature you're using). It now says the Beta density function. So it should be unambiguous in saying which one is a straight line. I haven't checked the part about entropy yet..... Michael Hardy 18:34, 30 November 2006 (UTC)[reply]

Homogeneity afd

Would you mind taking a look at the afd for Homogeneity? It looks legit to me, but I don't know enough about the topic so say for certain. OhNoitsJamie ^Talk 22:43, 19 July 2006 (UTC)[reply]

Intransitivity

Thanks for your clarification! I will put more talk on the page's own talk page. Rp 15:26, 21 July 2006 (UTC)[reply]

Invitation to join Wikipedia:WikiProject Eastern Orthodoxy

Hi there! I've noticed that you've edited articles pertaining to the Eastern Orthodox Church. I wanted to extend an invitation to you to join the WikiProject dedicated to organizing and improving articles on the subject, which can be found at: WikiProject Eastern Orthodoxy. This WikiProject was begun because a need was perceived to raise the level of quality of articles on Wikipedia which deal with the Eastern Orthodox Church.

You can find information on the project page about the WikiProject, as well as how to join and how to indicate that you are a member of the project. Additionally, you may be interested in helping out with our collaboration of the month. I hope you'll consider joining and thank you for your contributions thus far! —A.S. Damick ^talk ^contribs 18:22, 24 July 2006 (UTC)[reply]

Bell polynomials

I may have totally missed the point, but the section numbering does not appear any different to me whether that heading is there or not, maybe whatever bug it was has been fixed? Martin 15:00, 25 July 2006 (UTC)[reply]

No, you're wrong. Look CAREFULLY at the section numbering. Without that header, it numbers a subsection as if it were a main section. Michael Hardy 15:02, 25 July 2006 (UTC)[reply]

Oh right, I see, that isn't a bug though, of course you can't start with a sub section when there is none to be a sub-section of. Personally I would consider it wrong now, as "Convolution identity" is now a sub of the "definition" which doesn't make sense to me, but I'll respect your wishes. Martin 15:10, 25 July 2006 (UTC)[reply]

"Convolution identity" can be considered an appropriate subsection of "Definition" because it introduces another characterization of the Bell polynomials, and, at least from the point of view of deductive logic, either of the two equivalent characterizations could be taken to be the definition. I'm going to think about how to edit the article to make this clear. Michael Hardy 17:56, 25 July 2006 (UTC)[reply]

radius of convergence

Alright, thanks for letting me know. Its unfortunate it wasn't corrected sooner. I still only have limited understanding of the math behind radiuses of convergence. Fresheneesz 20:42, 26 July 2006 (UTC)[reply]

License tagging for Image:HardyBlack+White.jpg

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Reference to Apostol

Michael,

The reference to Apostol may not have historic significance but reflects on a chronological order in which I have discovered the proof. In mathematics things are discovered and rediscovered all the time. I've no doubt Apostol would have cited a source of his proof, if he was aware of any. He did not.

I came across a proof in Kiselev's book that is virtully (logically, but not visually) the same as in Apostol's article years after I read Apostol's article. After this happened I have amended the page. Should I find additional information related to the proof, I would add aditional references.

Alex

P.S. Michael, for questions related to my site, I would ask you to use my forums - if you do not mind, of course.

The old book in which I read that argument had an illustration identical to the one in Apostol's article. I seem to remember an attribution to an ancient Greek. Michael Hardy 21:26, 30 July 2006 (UTC)[reply]

Michael, many thanks for the reference. I am going to amend the page.

Alex 12:01 9 Aug 2006 (EST)

Stub

Please don't delete stub tags without adding in relevant corresponding category tags (if they don't already exist in the article) -- especially if doing so would leave an article without any categories at all! AnonMoos 01:42, 31 July 2006 (UTC)[reply]

boundary value problem

You're using too many capitals in section headings. I did some downcasing. See Wikipedia:Manual of Style. Michael Hardy 22:59, 31 July 2006 (UTC)[reply]

I added by mistake them when copying over from another article, thanks for pointing it out. Rex the first ^{talk | contribs} 23:28, 31 July 2006 (UTC)[reply]

Template:Seeintro

Hi Michael. Re: Template:Seeintro, the correct response was to fix it, not to delete it. This is now done.

You seem stressed lately. I've seen several edits, where you seemed to react very sharply to things where a more moderate option was available. Too much Wikistress? We've all been there. :)--Srleffler 01:27, 1 August 2006 (UTC)[reply]

I remember that with the various obnoxious "otheruses" templates, it was actually impossible to case them to use lower case initial letters (that's one of several reasons why "otheruses" templates are generally a bad thing. That such a fix would be possible in this case was more than I realized. Michael Hardy 15:04, 1 August 2006 (UTC)[reply]

I actually prefer the first letter of an article name to be capitalized, when the text is referring to the article itself (as a title). In other words, I prefer "see Introduction to special relativity" to "see introduction to special relativity", because the text containing the link is talking about the Wikipedia article itself, not about the subject of the article.

The otheruses templates are well established and clearly preferable to using unique text each time, since they allow a common format to be maintained and easily updated.--Srleffler 10:58, 2 August 2006 (UTC)[reply]

To say "For other uses of honey, see ..." or "For other uses of personal lubricant, see..." or "For other uses of women, see..." is certainly not preferable to phrasing it intelligently instead. I style manual entry with examples for use in the several different scenarios that occur, followed by judicious editing with the "dablink" template, is far better than the obnoxious "otheruses" templates, which should all be deleted. Michael Hardy 16:14, 2 August 2006 (UTC)[reply]

I think that the idea of seeintro tag was brilliant. We just used it on evolution.--Filll 23:09, 12 December 2006 (UTC)[reply]

Links

See the reply on my talk page and do not hesitate to continue the discussion there. Kompas 21:05, 2 August 2006 (UTC)[reply]

Technical analysis

Wow, you seem to have edited 6 articles on my watchlist today plus you know something about stats! This suggests that you might want to check out some of the statistical claims in Technical analysis (see also the discussion page) Some of this stuff is just plain crazy, some of it is investments scams, some actually has some protoscience behind it, and there is some that might actually turn out to be science, but with all the claims and outright POV stuff, it is real hard for me to sort out.

Any help would be appreciated.Smallbones 00:52, 4 August 2006 (UTC)[reply]

Hello

Your personal image is slated to be deleted, and to save it from deletion, please place a copyright tag like {{GFDL-self}} . --Bhadani 13:15, 5 August 2006 (UTC)[reply]

Do you want the image to be deleted? --Bhadani 11:45, 9 August 2006 (UTC)[reply]

Fuck Profanity vs. Vulgarity

How is 'fuck' considered vulgarity but not profanity? Last time I checked it is more of a profanity (not religious profanity as in the original meaning) than of a vulgarity. While technically both terms have different origins, they have since come to mean generally the same thing. Although some people might argue that profanity refers only to the sacred, this is not the case in present day. Using my references (profanity,vulgarity, and vulgarism) you'd see my case in point. Please make a response to this post, not reposting it on my discussion because I rarely check it but will flag this to check to see when it is updated. Thank you. -- Stexe (17:09, 2006 August 7, User:71.225.125.176)

"Other uses" discussion

You were previously involved in discussions relating to whether the wording of templates such as {{otheruses}} should simply say "For other uses" as it currently does or should read differently. I've started a discussion on the issue at Wikipedia talk:Disambiguation#"Other uses" of what? and thought you might be interested. —Simetrical (talk • contribs) 02:59, 8 August 2006 (UTC)[reply]

Actually, I think "otheruses" templates should be abolished. They're incredibly obnoxious. Michael Hardy 17:34, 8 August 2006 (UTC)[reply]

UM

UM and U of M is a trademark of the University of Michigan ... I point to [[1]], also Michigan was the first school formed which was University of M********* (1817). --Jon Cates 20:43, 8 August 2006 (UTC)[reply]

Do you have any particular reason to think they were using the phrase "U of M" before the others? Michael Hardy 23:02, 8 August 2006 (UTC)[reply]

#1 The University of Michigan was formed more than 15 years before any of other U of M styled Universities in the United States

#2 The University has properly registered it as a trademark and wordmark as noted in my reference.

While other schools maybe styled as U of M or UM, these are stylations and not official trademarks such as it is in the University of Michigan case. The University of Michigan case goes beyond the concepts of colloquialism and is indeed legally protected.

--Jon Cates 23:19, 8 August 2006 (UTC)[reply]

What makes you think the others are not official trademarks? And, as I asked, do you have any particular reason to think the University of Michigan was using the phrase "U of M" before the others? You did not answer that. In the case of the University of Minnesota, it is not a mere colloquialism, but is used officially in many instances. Michael Hardy 20:10, 9 August 2006 (UTC)[reply]

Continuous-time Markov process

There are two categories of continuous time Markov processes: the continuous-time discrete-state m.p. (also called continuous time Markov chains) and the continuous-time continuous-state m.p. (I don't know any other name for them, the diffusion processes are a subset but there are others). In any case, someone wrote an article entitled 'continuous-time Markov chain', moving it to 'continuous-time Markov process' may have been unfortunate because the article is about discrete-state m.p. (see first sentence) i.e. about only one of the two categories I mentioned earlier. Encyclops 00:40, 9 August 2006 (UTC)[reply]

I am uncertain of conventions. It looked as if some people may reserve the word "chain" for discrete-time processes, but I could be wrong. Michael Hardy 21:43, 10 August 2006 (UTC)[reply]

Wikipedia:Manual of Style (headings)

Hello Michael,
Just noticed your recent addition to the above; by "other reasons" are you thinking of proper nouns and/or something else...? Perhaps some (links to) examples might help. Best wishes, David Kernow 05:18, 9 August 2006 (UTC)[reply]

Some people, writing about "the Prime Minister" or the like, capitalize it (while of course writing about "various prime ministers" with lower-case letters). I think there are also various other occasions. The main point should really be that one should not capitalize an initial letter of a word merely because it's in a section heading. Any other reasonable occasion to capitalize it should be allowed. Michael Hardy 21:40, 10 August 2006 (UTC)[reply]

Thanks for your reply. I'd appreciate your recalling and/or linking to examples of these reasonable occasions, as I can't think of any myself – I hope my mind has not gone blank! Whatever they are, I feel the "or other words that for other reasons should be capitalized" phrase would benefit from being made more specific. Regards, David 04:06, 11 August 2006 (UTC)[reply]

I just thought of one possibility – if you agree – viz. section headers that are (verbatim) quotes. I can't recall any examples already in use and perhaps it's a possibility that is best discouraged, but in lieu of any other circumstances, how about phrasing Capitalization's first sentence as "Capitalize (a) the first letter of the first word; (b) any proper nouns; and (c) if using a quote as a heading, any other words that are capitalized in the quote. Leave all other words as lowercase."...? Yours, David 04:16, 11 August 2006 (UTC)[reply]

Verbatim quotes are one such case. Another is this initial C: Was King Alphonse really a Catholic? Michael Hardy 16:45, 16 August 2006 (UTC)[reply]

Isomorphism class?

I think "isomorphism class of" is redundant in your last change to Robertson-Seymour theorem: a graph that is isomorphic to another is also a minor of that other, so a class that is downwardly closed is also closed under isomorphism. Or maybe I am missing something? (Liberatore, 2006). 00:08, 10 August 2006 (UTC)[reply]

OK, maybe my definition of "minor" was just a graph that could be formed by deleting vertices and contracting edges, but perhaps you define it as any whose isomorphism type can be arrived at that way. I'll go back and look at this again. Michael Hardy 21:41, 10 August 2006 (UTC)[reply]

Saint Benilde

Good day, i've reverted your edits to the De La Salle-College of Saint Benilde article. First of all, it was written on the Manual of Style that lead sentences in bold should not contain links but you've added one. Second, in the Philippines we pronounce Benilde as it is. Forcing the diacritics on it seems to be unneccessary and wrong for me. -- Mithril Cloud 10:38, 10 August 2006 (UTC)[reply]

I put the diacritics there only in order to bypass a redirect page. I don't know who wrote the article about the man of that name, but that's who put the diacritics in that article. I pronounce it as two syllables, the final "e" being silent, and with the accent on the second syllable. I've always spelled it without diacritics because my familiarity with Benilde-St. Margaret's School (coming from a time when I lived near it, and it was called Benilde High School) is how I first heard the name. Michael Hardy 21:33, 10 August 2006 (UTC)[reply]

The diacritics came in later after it was featured in the DYK. I've created and named the article using Benilde Romancon to make things simpler, but used Benilde Romançon on the article content since Romancon by itself already sounds different. We pronounce Benilde as two syllables and silent final e too, but without the sharp stress in the first e like the diacritic mark suggested. Thanks for the revised linking by the way. -- Mithril Cloud 08:11, 11 August 2006 (UTC)[reply]

Combinatorial enumeration

Greetings. I wonder if you would help find someone to expand the stub on Combinatorial enumeration, which is not all that useful in its present form, even cryptic, I would say. It needs a 500 word or so summary, perhaps taken from some source in the public domain. I would volunteer to write this myself but I do not feel qualified. Thanks! Zahlentheorie 16:31, 10 August 2006 (UTC)[reply]

I'm not really qualified to write an article of any appreciable length on this. But maybe I'll add a few things..... Michael Hardy 21:42, 10 August 2006 (UTC)[reply]

Howdy

		The Original Barnstar
		This barnstar is given to recognize particularly fine contributions to Wikipedia, and to let you know that your hard work is seen and appreciated. evrik 23:15, 10 August 2006 (UTC)[reply]

Thank you very much. Michael Hardy 22:45, 11 August 2006 (UTC)[reply]

Edit summary

When editing an article on Wikipedia there is a small field labeled "Edit summary" under the main edit-box. It looks like this:

The text written here will appear on the Recent changes page, in the page revision history, on the diff page, and in the watchlists of users who are watching that article. See m:Help:Edit summary for full information on this feature.

Filling in the edit summary field greatly helps your fellow contributors in understanding what you changed, so please always fill in the edit summary field, especially for big edits or when you are making subtle but important changes, like changing dates or numbers. Thank you. Your recent edit to Energetics was a good one (fixing the capitalization in a category), but it would have helped if you had included "Fixed capitalization" in the edit summary field. Thanks. TruthbringerToronto (Talk | contribs) 21:55, 12 August 2006 (UTC)[reply]

Gosh, I agree with that. Putting an edit summary is very helpful. :) Mathbot 06:16, 13 August 2006 (UTC)[reply]

Another request

Hey. Would you mind leaving summary comments when you edit an article? Thanks a bunch! -- Chris53516 18:16, 29 September 2006 (UTC)[reply]

Yo! Anybody there?? It's really friggin' annoying when you edit something and don't leave a summary. Do you mind? Chris53516 20:25, 11 October 2006 (UTC)[reply]

Hello. I suspect I write summaries about 50% of the time. I certainly have no intent to annoy anyone. Often whent the summary would take longer than the edit (e.g. adding a link or fixing a typo) I don't do them. Michael Hardy 20:28, 11 October 2006 (UTC)[reply]

Well hell, it drives me nutz. It seems like every page that I watch that you also edit, you come along and do like 2 - 10 edits and leave NO summaries for any or only a couple. If you're going to do a series of small edits, try to do them all at once rather than multiple. Or, if you HAVE to do a series of small edits, at least leave a final summary of what you did. Chris53516 20:46, 11 October 2006 (UTC)[reply]

Dammit! Use the friggin edit summary! What the hell???? Why do you continue to ignore it? – Chris53516 ^(Talk) 14:10, 17 November 2006 (UTC)[reply]

Edit summary usage for Michael Hardy: 69% for major edits and 43% for minor edits. Based on the last 150 major and 150 minor edits in the article namespace. There is progress. Mathbot 16:07, 17 November 2006 (UTC)[reply]

Yeah, but that's a lot of major edits without summaries. I could care less about minor edits. It is SO annoying when he comes along, edits a page like 4 or 5 times in a row, and leaves NO summaries of any of them. – Chris53516 ^(Talk) 16:11, 17 November 2006 (UTC)[reply]

TeX

I responded to your comment at User talk:Rainwarrior#TeX, regarding a small edit I made to Homogeneous coordinates. Perhaps you expected me to reply here. I was just wondering whether you specifically thought that what was there before ( R^2:(x,y) -> (x+a,y+b) ) looked better than what I changed it to ( $\mathbb {R} ^{2}:(x,y)\rightarrow (x+a,y+b)$ ), or whether you were just trying to caution me about the problems wikipedia sometimes has with inline TeX? (I do know of the problems, generally I find them bearable.) I personally thought that the former looked awful, and figured this was an improvement, but if you think it is not, I would like to know if you have any suggestions for an alternative. - Rainwarrior 01:46, 16 August 2006 (UTC)[reply]

Here's what looks better than what you changed it too, at least in the situations where TeX looks bad:

R² : (x, y) → (x + a, y + b)

I certainly would not have left it the way it was before your edit. Michael Hardy 01:50, 16 August 2006 (UTC)[reply]

Ah, okay. So your suggestion, then, is to use regular markup instead of inline TeX wherever possible? - Rainwarrior 03:17, 16 August 2006 (UTC)[reply]

Aside from personal words of wisdom offered here, I suggest consulting WP:MSM#Typesetting of mathematical formulas. --KSmrq^T 07:04, 16 August 2006 (UTC)[reply]

Thank you. - Rainwarrior 16:40, 16 August 2006 (UTC)[reply]

Serial Comma on Euler characteristic

I don't see any ambiguity with omitting the comma that you inserted here. the Manual of Style claims that there is no consensus on Wikipedia. Are you a particular proponent of it? — cBuckley (Talk • Contribs) 22:32, 16 August 2006 (UTC)[reply]

I prefer to use it. (Note also that I fixed an error--a lack of required spacing--in that same edit.) Michael Hardy 01:13, 17 August 2006 (UTC)[reply]

Experimental Study Group

I didn't delete it but it does meet the CSD A7 clause and thus that's what I tagged it as. Whispering^(talk/c) 22:33, 16 August 2006 (UTC)[reply]

Hey no big deal I made a mistake ok? No need to go ballistic. Whispering^(talk/c) 22:57, 16 August 2006 (UTC)[reply]

Well, I certainly did not "go ballistic". Michael Hardy 22:59, 16 August 2006 (UTC)[reply]

Nett weight and Net weight

You've made an assumption; I'd guess based on your country of origin.

Tomato, tomato, potato, potato? Let's call the whole thing off. --Dweller 09:00, 17 August 2006 (UTC)[reply]

Actually, I googled both spellings and found several hundred thousand occurrences of "nett" and tens of million of "net". Michael Hardy 18:24, 17 August 2006 (UTC)[reply]

thank you

Thank you for correcting spelling (eg eccentricity for excentricity) and beautifying formulas. It is much appreciated. Bo Jacoby 12:37, 17 August 2006 (UTC)[reply]

For other uses...

Thanks Michael, but my issue was actually more about the vertical alignment of the italicized notice with respect to the main body of the article. — RJH (talk) 14:25, 18 August 2006 (UTC)[reply]

Thanks!

Michael, I just wanted to say thanks for the work you do in WP. I keep running across your edits on the math pages that I work on, and you have fixed some of my errors in the past (and many <math> to html edits too!) I just want to say, I have enjoyed working "with" you on these pages. Thanks and keep up the great work! - grubber 21:59, 18 August 2006 (UTC)[reply]

Thank you. Michael Hardy 22:01, 18 August 2006 (UTC)[reply]

Yay, Michael rules! My name starts with M too, so there is correlation, and I do statistics also. [2] Mathbot 01:16, 19 August 2006 (UTC)[reply]

Hi

and thanks for checking in on some of my stubs which are still in the pipeline. The thing on singular values has been modified a bit and inserted into the singular value decomposition main article. Please have a look and see if it is OK. --KYN 22:25, 19 August 2006 (UTC)[reply]

Limit theorem

I've replied to your bizzare allegations at talk:limit theorem. Psychobabble 01:40, 21 August 2006 (UTC)[reply]

"Improving TeX"

I read your comments on "improving TeX". Agreed, Wikipedia's inline TeX abilities are a bit limited and can result in some ugly output. In the case of the specific filtration article that I edited, I wanted to make the style more uniform, as some parts of it had been in TeX and others in italicized text.

Generally uniformity of style is good. But using TeX in "display" and "italicized text" in inline notation seems preferable to me, because of the sometimes ugly output. —Preceding unsigned comment added by Sullivan.t.j (talk • contribs)

Also, please note that

One should italicize variables but NOT digits and NOT punctuation; this matches TeX style;
a blank space should preceded and follow "+", "=", "−", etc. In some cases it's a good idea to use the "non-breakable" blank space (so that no line-break will come between the two characters).

context-setting

I agree entirely with your comments re context and setting, and I'm going through my contributions now with them in mind. (We do seem to be racing each other to it, though!) Sullivan.t.j 22:14, 21 August 2006 (UTC)[reply]

Michael Hardy 21:55, 21 August 2006 (UTC)[reply]

Fraction style

Not that I know of. I looked through the style guide for stuff about fractions, but I couldn't find anything. I've been avoiding changing stuff where I didn't know what was going on, like math equations. Also it seems to me like music signatures should stay at 3/4, etc. On the other hand, stuff like "he went 7 1/3 innings without a hit" should definitely be changed, in my opinion. —Chowbok 19:14, 22 August 2006 (UTC)[reply]

I certainly agree with you about "7 1/3"; I wouldn't use that format for an integer part followed by a fractional part. Michael Hardy 19:16, 22 August 2006 (UTC)[reply]

Deletion policy

You were instrumental in deleting bio of Marion Cohen, an accomplished mathematician and author, and of Elaine Zanutto, yet what's with the one-line article on Dennis DeTurck? Why not wipe that? The articles on Herbert Wilf, John Allen Paulos, Doron Zeilberger, it goes on and on with males...why do you not delete them too? That is not what I would want. Why not keep and improve all the articles, men and women alike. Their achievements are comparable. MathStatWoman 18:01, 23 August 2006 (UTC)[reply]

No I was not. I had nothing to do with that deletion. Michael Hardy 18:03, 23 August 2006 (UTC)[reply]

User:MathStatWoman

She likes to piss people off, so just ignore her. If you talk to her too much, she'll start insulting you. I would stay away from her. Chris53516 18:22, 23 August 2006 (UTC)[reply]

Squaring the circle

I said finite when I should have said constructible. My bad. From pi "An important consequence of the transcendence of π is the fact that it is not constructible." My point is that that caption is a lie. Do you argue that point with me?? You say "In the first place, it is not claimed that illustrations are exact.". But doesn't "A square and circle with the same area." make, for all intents, that exact claim? Why bother with that caption. Do you think that you can create a squared circle with pixels? I doubt it. This is not about mathematics, it is about whether a caption in a lie or not.--Justanother 15:54, 24 August 2006 (UTC)[reply]

My points are:

It is indeed possible for a square and a circle to have the same area (the impossibility asserted by the theorem is not that that is impossible, but rather that the rule-and-compass construction is impossible.
Everybody knows that illustrations in geometry articles are ALWAYS approximations, whether made with pixels or with ink on paper. A theorem of geometry may say (paraphrasing) "This square has the same area as that rectangle", and accompany it with an illustration. The square and the rectangle as abstract mathematical objects do have EXACTLY the same area, and the square and the rectangle in the illustration in the book are approximations. Everyone realizes that they're obviously always approximations, so it is not a lie to say they have the same area. The assertion that two things have the same area is naturally understood to refer, not to the physical illustration, but to the abstract mathematical objects that they illustrate.

Michael Hardy 02:16, 25 August 2006 (UTC)[reply]

Hi. I appreciate your point of view. I am not a mathematician and I actually came to the article by way of the Timecube, which was referenced in another article I was reading. I had never encountered the "squaring the circle" and I found it interesting. The more we discuss, the more interesting I find it. My conclusion is while a square and a circle can, in theory, have the same area, there is NO way to represent that in the physical univers, not with ink or pixels nor with molecules or atoms or subatomic particles or whatever. That is pretty cool to me and I found that the caption detracted from my feeling of wonder. I think the simple caption "Squaring the circle" serves well. --Justanother 14:05, 25 August 2006 (UTC)[reply]

Inferential statistics - is terminology standard?

Michael, since you seem to be a statistician (or at least have more of a statistics background than me), could you take a look at Inferential statistics?

This article defines technical terms like "deduction distribution function" and "induction distribution function" that, according to Google, appear nowhere else on the web (at least, not with the same meaning). Furthermore, the author (User:Bo Jacoby) has a history of trying to promote personal nonstandard notations on Wikipedia.

Maybe it is perfectly all right in this case; as I said, statistics isn't my field. But the lack of corroborating hits on Google combined with the lack of references combined with the author's past behavior seems to warrant a closer look.

Thanks!

—Steven G. Johnson 16:26, 25 August 2006 (UTC)[reply]

Thanks for pointing this out.

The whole article is confused. I'll do more on it over the next few days. Michael Hardy 23:38, 25 August 2006 (UTC)[reply]

AfD Nomination: Marion Cohen

An article that you have been involved in editing, Marion Cohen, has been listed at Wikipedia:Articles for deletion/Marion Cohen. Please look there to see why this is, if you are interested in it not being deleted. Thank you.

I'm relisting this on procedural grounds as the original AfD was closed early. Espresso Addict 03:13, 26 August 2006 (UTC)[reply]

Reply on Wikipedia talk:Images

Hi,

It's been a long time since you posted that question on Wikipedia talk:Images (regarding the "high resolution" message), so I thought I'd drop you a note to let you know that I've responded to it. It doesn't seem that anyone has dealt with or discussed that issue, so perhaps it's still timely. -- Visviva 18:02, 2 September 2006 (UTC)[reply]

Thank you. I've done that edit now. Michael Hardy 18:06, 2 September 2006 (UTC)[reply]

RE: 0.999...

Hey there. Thanks for taking the time to respond. I guess my downfall here is that it is not something I remember learning in secondary school. Perhaps my curriculum was weak, or maybe I just didn't persue enough math classes (imaginary numbers in trigonometry class baked my noodle!). Another user also pointed out my ignorance. However, correcting ignorance is really what a project like this is all about, and if you look at the thread I started on the talk page, there seems to be a consensus forming that the title and the lead paragraph smack of argumentation and original research, which is misleading to the content of the article and was the source of my discomfort as it turns out. There seems to be some agreement that "Proofs that 0.999... equals 1" or simply "0.999..." would be a more appropriate and encyclopedic title. I'm sure we'd love your input. Chadbald 04:13, 5 September 2006 (UTC)[reply]

I like simplicity for a variety of reasons, one of which, as applied to article titles, is that a simpler title is more likely to be found either by a search engine or a human using common sense. So I'm inclined to think "0.999..." would be better. Argumentation is not always inappropriate, but I haven't looked closely at this article lately, so I won't endorse whatever is there now. When I said "everyone" I meant, essentially, everyone who takes all the math courses normally offered in secondary school. Michael Hardy 17:39, 5 September 2006 (UTC)[reply]

Your title change to Point source (polution)

Michael, the word "pollution" has two ells. So now the "point source" article has a mis-spelled title. - mbeychok 18:59, 5 September 2006 (UTC)[reply]

Yes --- one of my worse typos; I've fixed it now. Next I'll see what to do about links to those pages. Michael Hardy 20:42, 5 September 2006 (UTC)[reply]

Thanks

Wow, Michael, you've been a busy bee to say the least. Thanks for picking up those minor edits in the various articles in the Category:Air dispersion modeling. Also, thanks for resolving, I hope, the mess that the "Point Source" controversy was becoming.

I think that I have now corrected all of the pertinent links from "Point source" to "Point source (pollution)". By pertinent, I mean those that occurred in contexts concerning air and water pollution. Thanks again, - mbeychok 23:05, 5 September 2006 (UTC)[reply]

You really need to read the discussion at Talk:Point source

Michael, User:Srleffler is proposing to completely undo the excellent re-organization you made of Point source yesterday. In fact, he has already changed some of it. You really should chime in there and defend your work. I have done the best I could to express my disagreement with User:Srleffler, but I think you could do an even better job. - mbeychok 07:39, 6 September 2006 (UTC)[reply]

A[s] I keep repeating, several times every day, on Wikipedia, TeX looks very good when "displayed" but horribly ugly, almost to the point of illegibility in some cases, when embedded in lines of text.

I noticed your hard efforts in the history of Pfaffian. You're absolutely right; please keep repeating it! (Although we really shouldn't blame TeX, but rather texvc.) —Toby Bartels 23:05, 7 September 2006 (UTC)[reply]

Thank you and help please

Thank you for commenting that I need not leave Wikipedia, your help, and your emails, but this is what happened, and I am intimidated and frustrated:

I had truly planned to stop editing Wikipedia. Yet due to some kind words and encouragement from Wikipedians like you, I tried, timidly, to return.

This is what transpired: I always sign in, even when reading articles. I had been reading articles on the Riemann hypothesis and the zeta function, when I was alerted that there were messages on my talk page. There were several messages advising me not to stop editing and an offer to discuss the content of proposed new articles with other editors. Therefore, I decided to attempt to contribute again.

The response was that User: Chris53516 vandalized my discussion/talk page and sent me at least two messages (and I quote) that I was guilty of "dishonesty" (this was posted on a vandalized version of my discussion/talk page) and was a "liar" (posted on User: Chris53516's own page), simply because I had decided to contribute to Wikipedia again.

Moreover, I am not a "sockpuppet" nor a "sockpuppet master". I always sign in, and I always use the same user name. I do not at all appreciate this nomenclature on my user page; it is an insult, implying that I am using underhanded, sneaky means of editing via aliases. I do not do so. I share a computer and a network. Strangely, I have been accused of being the "sockpuppet" of people who have different IP addresses, whom I have never met. On Wikipedia, is it standard to be assumed guilty without proof? to be assumed guilty until proven innocent? to be assumed guilty without an attempt to be proven innocent?

Hence, it seems, that I am truly disliked on Wikipedia and that the way to settle disputes, for me at least, is to leave. If you think otherwise, look at what happened to my discussion/talk page, due to User: Chris53516 who was aided by User: Chan-Ho Suh in restoring my talk/discussion page. This is ironic since User: Chris53516 urges Wikipedians to "be nice". Hence, in my attempt to contribute to Wikipedia again, I have confirmation that it is indeed an unpleasant and frustrating experience, and ruled by those who have a different concept of "being nice".

However, I would like answers to my questions above, so I truly understand how Wikipedia operates.

To review and summarize, the questions I would like answered are these:

1. Should I not sign in when reading other articles, so that I do not see alerts that I have messages?

2. If it is acceptable for me to sign in when reading other articles, is it all right for me to re-join Wikipedia, even after I thought I would stop editing, after having been encouraged to do so by other Wikipedians?

3. If it is indeed acceptable for me to decide to edit again, am I really "dishonest" and a "liar" as per User: Chris53516?

4. Is it appropriate for Wikipedians such as User: Chris53516 and User: Chan-Ho Suh and others (anonymous) to vandalize my discussion/talk page by deleting favorable comments while adding their own verbiage including terms that, in my opinion, are insulting and, moreover, false?

5. Why am I being accused of "sockpuppetry" when it is not true, and cannot be proven simply because it is not true?

6. Why is the accusation of "sockpuppetry" displayed on my User page? I really do not appreciate this, especially since it is a false accusation.

7. What does "be nice" mean on Wikipedia, as User: Chris53516 recommends ? Does it include calling another Wikipedian "dishonest", someone who intends to "deceive", and a "liar" if that Wikipedian decides to return to Wikipedia and attempt to communicate with others via talk, or to edit an article?

8. Why had so many of my articles been deleted? So many of my edits reverted? Even when I supplied citations? (Some of the articles I started became quite lengthy, although they were intended to be concise, simply because of so many requests to establish importance of the subject, noteability, to provide more and more citations even after having supplied many, etc.)

9. If you do indeed answer my questions, and if I should respond to your answering me, shall I anticipate being called "liar", "dishonest", "sockpuppet" that I "deceive", etc (by other Wikipedians, of course, not by you!) Again, thank you.

But now you might have an idea why (a) I had decided to leave Wikipedia, and (b) was concerned about trying to re-join and edit again.

I suspect that this experience that I have had on Wikipedia has affected other Wikipedians, probably who are people with valuable information to contribute, but who have decided to stop creating articles or to edit because of similar experiences. This would lead to an incomplete and inconsistent encyclopedia, which is not what Wikipedia should be.

Sorry for the long message, but Wikipedia is an internet phenomenon, and these issues are important, to me and to others, including students in university, grade school, and high school.

Moreover, I had wanted to use my time to contribute actual content and learning more about the markup language: articles about topics in maths and stats, bios of persons, and other topics that interest me; i.e., spend my time on useful endeavors for Wikipedia, not being involved with disagreements nor wasting time on matters such as these.

Thank you again.

MathStatWoman 09:29, 9 September 2006 (UTC)[reply]

Recurring decimal

Hello. I read "infinitely" and "many times", rather than "infinitely many" and "times" and my observation was that "infinitely" seemed to contradict "many times", which I in my non-maths world would take to have a finite limit. For your excellent "infinite prime numbers" example — if I noticed the problem, I would have reworded as "infinite number of prime numbers". My amendment was for readability, and not a technical change. I could have use "repeats an infinite number of times" had I thought of it at the time. If you decide that is better, then please change my edit. Thanks for taking the trouble to discuss something I've done: my edits are small and usually of minor significance and it's nice to be noticed. Bazza 12:52, 14 September 2006 (UTC)[reply]

It sounds as if you read "repeats infinitely, many times", whereas it was intended as "repeats infinitely-many times". I wouldn't normally use a hyphen for such a thing, but in view of the potential misunderstanding you raise, I'm considering it. Michael Hardy 23:50, 14 September 2006 (UTC)[reply]

Improper Integral

Hi Michael Hardy. Regarding the article improper integral, and your edits to it. It's much appreciated. However, you may want to look in the history page to find the correct person with whom your comments should be directed. I actually took Calculus 1 as a summer course, and thought the two pictures would be nice. I didn't write the article. At any rate, thanks for your concern! Have a nice day :) Kareeser|^Talk! 02:00, 15 September 2006 (UTC)[reply]

Edits to Minnesota historical articles

Thanks for making corrections to some of the articles I've been working on. I'm a newbie and I appreciate the help. Appraiser Talk

template cquote

Hi Michael. I responded to your problem with a call to template:cquote [3] --Ligulem 10:47, 17 September 2006 (UTC)[reply]

Seems to work. Thanks! Michael Hardy 00:10, 18 September 2006 (UTC)[reply]

Thanks for TeX

Thanks for converting my crappy graphics to TeX on Student's t-test. I'm dumb and don't know how to do it. :) Chris53516 18:22, 19 September 2006 (UTC)[reply]

Often trying to emulate the examples of TeX in various articles may be the quickest way to learn TeX. Michael Hardy 19:55, 25 September 2006 (UTC)[reply]

Fibonacci

I gave up editing articles on Fibonacci numbers, the golden ratio and related subjects a while ago; it's too frustrating with all the nonsense so many people believe in and want to include. Niels Ø

One way of solving this problem is to replace false assertions NOT with correct assertions, but with those PLUS cited evidence and liberal explanations to back them up. Your assertion that the sequence was erroneously named after Fibonacci left me unsure whether you were saying Fibonacci was never aware of the sequence, or learned it from someone else, or discovered it independently but later than someone else, or what. That's nowhere near enough information to be convincing. When you give enough information, people will be sufficiently impressed and let it stand. Michael Hardy 20:24, 21 September 2006 (UTC)[reply]

Thanks for the reply. Really, I should have kept silent to begin with, as the problem is I don't have the energy to fight the misinformation properly. It's not a specifik Wikipedia problem; it's more like a world-wide conspiracy propagating second-hand misinformation. PS. I am not generally paranoid.--Niels Ø 06:48, 22 September 2006 (UTC)[reply]

The very first item that Google shows you when you search on "Fibonacci number" is the Wikipedia article. Just put the right information here and other sites and various experts will read it. Michael Hardy 20:25, 22 September 2006 (UTC)[reply]

American Gold Eagle

I have left you a response @ Talk:American Gold Eagle. --Kurt 06:12, 23 September 2006 (UTC)[reply]

Thanks...

...for the style/formatting alterations you made to Gleason's theorem and the RQM draft. As it happens, those links were my doing.

I hope you don't mind, I noticed a typo in the message you left on my talk page, which is repeated on your user page, so I reciprocated the favour and fixed it (your userpage copy, obviously!). Byrgenwulf 19:40, 25 September 2006 (UTC)[reply]

Perron-Frobenius theorem

you make a mistake in the perron frobenius article i think. please read discussion

I've responded at talk:Perron-Frobenius theorem. Michael Hardy 17:57, 26 September 2006 (UTC)[reply]

Exponents

Good work on Exponents (disambiguation). It was the first time I'd attempted a reorganization on that scale, and I was hoping for assistance from more experienced editors. I've learned from the edits you made, and for that I am grateful. Alex Dodge 18:46, 26 September 2006 (UTC)[reply]

Mathematician-stub

Hi Michael - I'm the one who added the mathematician-stub to the Isadore Singer article. It seemed to me that the stub was warranted, since just about everything in the article could be expressed in the infobox. Does the stub work to bring the article to people's attention who otherwise would not have noticed it (thereby fleshing the article out)? Thanks - Rglovejoy 20:17, 28 September 2006 (UTC)[reply]

I'm not sure whether it brings it to people's attention, but there's also a standard template asking people to expand the article, without calling it a stub. I think the "stub" label is over-used (especially when I find articles too long to read in an afternoon so labeled---not that this is one of those). I am inclined to use it only when by virtue of its brevity the article seems to raise more questions of a sort that are nearly obligatory to answer in the article, than it answers. I'm not sure I can state my practice very precisely. Maybe I can find some examples. Michael Hardy 20:21, 28 September 2006 (UTC)[reply]

Floating point page

The page floating point needs expert attention, and such experts are extremely rare. Based on your past contributions in this or related fields, I wonder if you could take a look. William Ackerman 22:09, 2 October 2006 (UTC)[reply]

Re:"doing what you want"

What I said on that discussion page was a jokey one line comment of no value. I am confident enough in my opinions of Rand and her little cult of personality that I don't feel the need to argue over them with every over-sensitive Objectvist I come across. Good Day. Finite 01:42, 4 October 2006 (UTC)[reply]

What about arguing about it with non-Objectivists or those who are not over-sensitive, such as me? The fact is, it would be stupid to say Objectivism is "based on doing what you want", since Rand clearly and emphatically rejected hedonism and was clear and explicit about her theory of ethics. Michael Hardy 01:51, 4 October 2006 (UTC)[reply]

Sorry about jumping on you there, my assumptions can make me look stupid sometimes. I've been burned trying to argue with them in the past. Well that "doing what you want" bit, it is not a belief Rand espoused she certainly seemed to practice it, what with the illicit affair and belief in extreme self-intereset. I suppose I was oversimplifying. I had just finished an arguement with an Objectivist in which she declared me an "Enemy of Mankind" because I disagreed with her politically. Guess I shouldn't have used Wikipedia as a vent. What would you call that? Aggravated Trolling Disorder? Sorry again. Finite 02:24, 4 October 2006 (UTC)[reply]

request your comment

Hi Micheal, (I'm asking you this because I've noticed you are quite assertive on these issues) there is a little confusion over whether articles about economic goods should have plural or singular titles (see Talk:Veblen goods). Though I have made a case for singular, I only really want to see some standardisation between them all. thanks Martin 10:36, 4 October 2006 (UTC)[reply]

Cantor Distribution

I came accross the Cantor distribution article and rewrote it from my head, and it looks like you are it's major contributor... I think it looks easier now, but I am not sure if it is correct. Do you care taking a look at it? --Lucas Gallindo 03:23, 5 October 2006 (UTC)[reply]

The word eventuate really exists in english (well, yankeeish english, according to De Quincey)! My native language is portuguese, and as as I know there is no equivalent to eventuate on most latin languages, thats why it sounded funny to me. Please don't get mad at me :)

The description is correct? If you think your explanation was easier to understand, I will put them both in there (I promise I won't use inline TeX this time, last time I was sleepy).--Lucas Gallindo 20:15, 5 October 2006 (UTC)[reply]

I'm going to return to the article later. I don't think we should just put in the two explanations that were there as the were written, but rather we should make them fit together well. Michael Hardy 20:21, 5 October 2006 (UTC)[reply]

Inverse Function Theorem

Hi Michael! I've asked a question on page Talk:Inverse function about Inverse function theorem. Would you be so kind to take a look at on it. Thanks: Mozó 15:21, 10 October 2006 (UTC)[reply]

Proofs of Fermat's theorem on sums of two squares

I am translating your Euler's proof into french. The first four steps are OK for me, but I have difficulties with the last one. I don't see why Since the $k$ th differences of the sequence $1^{k},2^{k},3^{k},\dots$ are all equal to $k!$ . Would you be kind enough to help me a little bit? Thanks Jean-Luc W a french contributor with no english account.

PS: I think there are two slight lack of precision in step 4. In case you are interested to know, I will be happy to communicate about.

I am not the author of that section. I did a serious of small edits on it in April---I think mainly linking to Brahmagupta-Fibonacci identity. Michael Hardy 20:37, 11 October 2006 (UTC)[reply]

To bad, but thank you any way. Jean-Luc W 83.204.158.232 22:13, 11 October 2006 (UTC)[reply]

WP:DBTN

or should I say Wikipedia:Please_do_not_bite_the_newcomers. Sheesh--Justanother 00:29, 11 October 2006 (UTC)[reply]

Though I guess you said that because you thought all I did was add the underscore when what I did do was change the link from ALL of recorded history to the Classical Antiquity period of the Greeks and Romans. While the article points out that there was some work done on the problem prior to that, am I correct in thinking that the "formal" "straightedge and compass" geometry approach is from that period, especially in light of the description of the problem as Euclidean in the third line of the article? In any event, DBTN still applies.--Justanother 00:39, 11 October 2006 (UTC)[reply]

OK, I'm guessing you're referring to this edit. I don't see how it's "biting" anyone to say that these underscores are not needed and their use sometimes makes people think they are, and that then they sometimes add them to visible links. If I fix a typo in a newly added paragraph, and summarize the edit by saying "typo", that in no way implies that all the person did was create a typo where none was before. It would never have occurred to me that anyone would interpret my words that way. Michael Hardy 20:33, 11 October 2006 (UTC)[reply]

This is funny. I think I am too sensitive from editing in the Scientology series and being chewed on from my first edit (laff). I misinterpreted your "sometimes make newbies think they're needed" - I thought you meant that newbies added unnecessary underscores (i.e. unnecessary edits) to feel needed. I see it the other way now, sorry for the mistake. But a good example of why it is best to mention upsets with another editor; often it is probably just a misunderstanding. Better we switch to Lojban, I guess. --Justanother 20:49, 11 October 2006 (UTC)[reply]

Thanks for following me around and cleaning up my droppings

Good to know that you're looking after things, as I find that as I mature I become increasingly imperfect. Your long change comments are also good for some entertaining reading; really, I mean it. Dicklyon 22:09, 13 October 2006 (UTC)[reply]

"radius" in history of pi

Ha! Didn't even notice that ... fixating on the typos and weird English. That's why people need editors. - DavidWBrooks 21:22, 16 October 2006 (UTC) ... but as an addendum, as I reread your comment to me, make sure you figure out which editor did what before you start tossing bullshits. - DavidWBrooks 21:25, 16 October 2006 (UTC) ... ah, no , wait, I had to read it again - but I finally figured out what you're saying, your insults were directed at the correct people. You know, adding extra punctuation marks doesn't really improve an argument. - DavidWBrooks 21:35, 16 October 2006 (UTC)[reply]

inline tex

i see your point that inline tex can be really fugly. a couple questions.

1) is this the way to reply?

2) shouldn't you put all math in math brackets and leave the display properties up to the server? or is this just a dry principal that we'll follow once the server suits our aesthetic desires?

3) currently, the article martingale talks about a stochastic process $X_{t}$ with no explanation of what that symbol even stands for. if you follow the link to stochastic process you find that it is an indexed collection of random variables for $t$ in some index set. but the definition of continuous martingale makes no sense if you don't mention that $t$ is in $\mathbb {R}$ or $\mathbb {R} _{\geq 0}$ or whatever it is. Since the $\mathbb {R}$ symbol won't display except in comically large font, what do we do? —Preceding unsigned comment added by Sam Coskey (talk • contribs)

1) Yes, although a reply on your talk page would also do it, since I put your talk page on my watchlist for the time being. But note that you should sign your comments on talk pages by putting four tildas (~~~~) at the end; that causes your user name and the time to appear when you save your edit.

2) For now we have an unpleasant situation, not as bad as it used to be just after TeX became available on Wikipeida (at the beginning of 2003, I think). If you write e^{x then the e appears aligned with the letters preceeding and following it. But if you write $e^{\int x^{2}\,dx}$ , then (at least on all the browsers I've used) the whole expression gets centered so that the e is too low, and the whole expression is (again, at least on all the browsers I've used) ridiculously too big. When TeX is used in the normal way, as opposed to the way it's used on Wikipedia, none of these problems occurs. It's also no problem when TeX is "displayed", thus:}

\int _{-\infty }^{\infty }1\,dx>3.

3) I've written things like R³; I've seldom if ever used "blackboard bold". I agree that in martingale it should be stated explicitly that t represents time. Michael Hardy 17:57, 17 October 2006 (UTC)[reply]

Michael, thanks for your editing comments notating your edits to the statistical completeness article. I have seen inline cases which get ugly and then proceed to revert them to simpler html markup much as you did, but it never occurred to me til now that not all browser settings give the same rendering and some others might still see ugly inline rendering. As the simpler markup still looks good for reasonably uncomplicated content and seems quite understandable, I will note your example in the future. Baccyak4H 19:29, 6 November 2006 (UTC)[reply]

Thanks

Thanks a bunch for calling me a "dishonest idiot". Henning Makholm 20:44, 17 October 2006 (UTC)[reply]

Well I guess more than one person can be sarcastic. It's not easy to be patient with someone who leaves us guessing what he might have meant, even after he attempts some explanatory comments, about a matter that he says admits mathematical proof. That which admits mathematical proof can be expressed precisely, and vague touchy-feely language is abusive to the reader. Michael Hardy 23:00, 17 October 2006 (UTC)[reply]

Regarding your comment

"In estimation of covariance matrices, I describe what seems to me to be a surprisingly subtle and elegant application of linear algebra. I have no idea who originated it; I seem to recall that it is in Morris Eaton's book on multivariate statistics, and I suppose it is in lots of others. In that argument you find out why it is sometimes better to view a scalar as the trace of a 1×1 matrix than as a mere scalar and then to apply certain matrix decompositions to it."

An alternative route is to put the Wishart distributions straight away as a function of eigenvalues.

The minimisation then ceoms from the scalar inequality A<G (or is it the other way round?) where A and G are the Arithmetic and geometric means (in this case, of the set of eigenvalues)

I think this is spelled out in the book I did a long time ago - mARDIA/kENT/bIBBY

Eigenvalues make multivraiate analysis a lot easier - they also tie in with the geometric meaning. (Eaton did a good book on this too!)

Johnbibby 10:40, 18 October 2006 (UTC)[reply]

Hello. Thank you. On amazon.com, I find this: Graphical Models in Applied Multivariate Statistics (Wiley Series in Probability & Statistics). Is that the one you're referring to? Michael Hardy 23:29, 19 October 2006 (UTC)[reply]

Zeta distribution (case s=1)

Hi Michael,

Can you provide me some references about the case s=1 of the Zeta distribution? I am interested in its relation with density of integers that you mentioned. Thanks.

I think I may have first seen that in Gian-Carlo Rota's book on probability, published only by MIT's Copy Technology Center. He used it as the textbook for his undergraduate course on probability. It was to be published by Birkhauser eventually. He died before that could be finished. Last I heard, one of his colleagues was working with Birkhauser on it, but I don't know the status of the project. I think I know another good place to look, but I don't remember the details. I'll let you know if I find it..... Michael Hardy 23:46, 19 October 2006 (UTC)[reply]

Thank you

These probability articles you created are excellent. They are mathematically precise and comprehensive while still being accessible to the average reader and to the inexperienced mathematician. —Centrx→talk • 02:50, 19 October 2006 (UTC)[reply]

Thank you. Michael Hardy 15:05, 19 October 2006 (UTC)[reply]

Beta-binomial

Michael,

Do you know if there is a problem with the Beta-bionomial page ?

Thanks Charlesmartin14 23:12, 19 October 2006 (UTC)[reply]

Well, I did some editing to bring it into conformance with some Wikipedia style conventions, and moved it to fix the misspelling of the title. I haven't yet looked at the content much, but I will soon. Michael Hardy 23:47, 19 October 2006 (UTC)[reply]

Your minor formatting edit to Manifold Destiny

Please do not appear to legitimize edits such as those by Mikeeverest1 by doing minor edits like the one you did. This editor has been on a crusade to insert WP:BLP violating material into Sylvia Nasar and also Manifold Destiny. I see no evidence that these charges of racism against Nasar is anything more than cooked up allegations by a few bloggers on the Internet and doubt there is any reliable source that would substantiate such insertion. --C S (Talk) 02:40, 23 October 2006 (UTC)[reply]

Inverse Gaussian

Michael,

Thanks for the welcome and the comments. I hope this is the correct etiquette for replying.

I don't understand the "inverse" entirely either - perhaps my comment was a little hasty, but I wanted to improve on the old one. My new reference to Rausand and Hoyland has a discussion on the topic. It's certainly not a multiplicative inverse. I think it's more a "conceptual" inverse only: the gaussian deals with distance covered in unit time in a Brownian motion process, while the Inverse Gaussian describes the time to cover unit distance. I would need to check the references in R and H to be sure. NickMulgan 02:30, 24 October 2006 (UTC)[reply]

Thank you for your assistance on the DYK

Thank you for your assistance on the Samuel Cate Prescott article. It earned a DYK yesterday. I really appreciated it! Chris 12:38, 24 October 2006 (UTC)[reply]

Today's featured article

Just wanted to let you know a featured article you worked on, 0.999..., was featured today on the Main Page. Tobacman 00:32, 25 October 2006 (UTC)[reply]

Reversion in linear regression

Thanks for correcting my naiive edit to linear regression. I have a suggestion for the article to prevent others from making the same mistake I did: define b in an equation, so something like: b = beta_hat = equation for estimating beta

then

a = alpha_hat = equation for estimating alpha (using b)

but I'll leave it up to you, because you obviously know the page better than I.99of9 11:25, 25 October 2006 (UTC)[reply]

irrational number

If the definition I put up is incorrect, why is it in the introduction? I didn't write anything new up there, I just rearranged it. As it stands, the page real number says that a real number is the irrationals + the rationals. But the page irrational number says that an irrational number is the reals - the rationals. So now the intro contains a circular definition, and an incorrect one. So... we should do something about that. Fresheneesz 21:18, 25 October 2006 (UTC)[reply]

"the page real number says that a real number is the irrationals + the rationals"

It certainly should not say that in a way that makes it appear to be a definition. Michael Hardy 22:41, 25 October 2006 (UTC)[reply]

I think part of what you're missing is this: rational number is NOT defined as a number whose decimal expansion, or expansion in some other base, terminates or repeats. That's what I was calling a persistent meme that is not taught in math courses. Michael Hardy 22:48, 25 October 2006 (UTC)[reply]

Well if the reals shouldn't be defined like that, that page needs some sort of rearrangment, cause the page sure seems to imply that its the definition. And btw, i'm *not* missing that rational numbers aren't terminating or repeating decimals. I know that, and never said they were.. so.. i don't get why you're coming to that conclusion.. Fresheneesz 23:10, 25 October 2006 (UTC)[reply]

Well, actually they are, but that's not generally taken to be the definition, and for good reasons. But if you're not missing that point, then why did you write that in the edit that I criticized? Michael Hardy 02:21, 26 October 2006 (UTC)[reply]

Otheruses

Offensive? How? Your dablink says the same thing as the otheruses template. — Omegatron 22:37, 27 October 2006 (UTC)[reply]

I think I covered this ground a very large number of times. See template talk:otheruses.

Then discuss it there. Wikipedia:Don't disrupt Wikipedia to illustrate a point — Omegatron 23:58, 27 October 2006 (UTC)[reply]

As you can see, I have discussed it there. Sufficiently, I think. I certainly have not "disrupted Wikipedia to illustrate a point"; I just did a routine edit and stated why I did it in the summary. Probably three or four times a day for a couple of years I've replaced the "otheruses" template with the "dablink" template and probably about half the time have said in the summary that I was purging an "offensive" or "obnoxious" or "odious" template. Michael Hardy 01:22, 28 October 2006 (UTC)[reply]

I replied. I don't know if you ever read my reply. But I remain puzzled. It is as if you were accusing me of disrupting Wikipedia. You also seem to think I was trying to illustrate some particular point. I don't understand what makes you think that. I edited that article in order to improve the article. My edit did improve the article. What point is it that you think I was trying to illustrate? And what makes you think so? And in what way could that particular improvement to that particular article have been "disruptive"? Michael Hardy 01:06, 30 October 2006 (UTC)[reply]

I'm looking through that talk page, the template's edit history, and other discussion pages, and you've been consistently rude and uncivil in your campaign to "abolish" the otheruses template. Then, when no one agrees with you, you edit several articles per day to get rid of the template you personally don't like? In spite of a wide-spread consensus to continue using it? Using combative edit summaries with words like "offensive" or "obnoxious" or "odious" (the only reason I even noticed your actions)? That's called disruption, and you're obviously doing it to make your point about how "stupid", "execrable", or "incredibly obnoxious" the template is. How is that helping the encyclopedia? How is that promoting a cooperative community? Please read through Wikipedia:Civility and Wikipedia:Don't be a fanatic.

I've reworded the template to address your concerns. — Omegatron 01:54, 30 October 2006 (UTC)[reply]

I am NOT doing it in order to make any point. It is not disruptice. I edit to improve articles. There is a widespread consensus to support George W. Bush (among those who support him). There is a widespread consensus that astrology is the most important of the sciences (among those who think that). It is certainly not true that nobody agrees with me, but what if it were? That does not mean my expression of that view is "disruptive". Michael Hardy 02:01, 30 October 2006 (UTC)[reply]

your edit to Ocular ischemic syndrome

Hi, the edit summary for your recent edit to Ocular ischemic syndrome is somewhat offensive, at least to me. >> (A dog does not "refer to" an animal that barks (unless the dog speaks).) << Out of place and totally unnecessary for such a small edit, I would say. EyeMD ^T|C 12:11, 29 October 2006 (UTC)[reply]

It explains my edit. I keep coming across articles like that one that say things like "A dog is a term that is used to describe an animal that barks" instead of "A dog is an animal that barks". What is it that offends you about it? I could have omitted any edit summary, but that offends some people; several have said so. Why is it out of place if it simple says what I did and why? Michael Hardy 01:02, 30 October 2006 (UTC)[reply]

TRS Article -- Proposed Revert

Hi Michael. I propose a revert of the capitalization changes to the Telecommunications Relay Service article. I've posted my discussion on the talk page —Cliffb 07:49, 31 October 2006 (UTC)[reply]

Buoyancy

Talk:Buoyancy#Archimedes_discovered_buoyancy_in_his_bathtub?? Paul Beardsell 13:22, 31 October 2006 (UTC)[reply]

Assistance on mathematical formulas on Thermal death time

The reason I am leaving you a message is that I am in the process of working on Thermal death time and I am having problems on how to properly put in mathematical equations in this article. Can you please assist me on this? I would greatly appreciate it. Chris 14:54, 1 November 2006 (UTC)[reply]

Thank you for your help on the equations on this article. They look good and I greatly appreciate it. Chris 16:08, 3 November 2006 (UTC)[reply]

Quadratic integral

I just read one of the silliest comments I've seen in a while: "Is this really copyrightable?... It's just math." Are photographs really copyrightable? They're just photographs, not paintings. Tell you tell what: tell me whether this looks copyrightable to you. Michael Hardy 18:49, 2 November 2006 (UTC)[reply]

In order for copyright to be applicable, some sort of creative aspect is required. Your treatise indeed is copyrightable, but what about the proof? Are you saying that nobody else can prove this theorem without paying you royalties? What if I were a mathematician and somehow came up with the exact same proof on my own without even knowing about the existence of yours and then I published it -- would you sue me for copyright infringement? Your comment is in reference to quadratic integral, in which I asked that if anyone who was an expert in the subject were to write this article, wouldn't it come out basically the same? How many ways are there to derive a quadratic integral? howch e ng {chat} 19:09, 2 November 2006 (UTC)[reply]

Collimated light

An old discussion. Would you mind looking at the article's talk pages? I realized that it is unclear whether the concept refers to what's happening in either of the two situations: 1) the distance of the viewer (or imaging element) is large compared to the diameter of the lens used to view the object, giving practically parallel point-to-lens rays, or 2) the diameter of the object being viewed is small compared to the diameter of the lens used to view the object, giving practically parallel object-to-lens rays. Santtus 21:33, 5 November 2006 (UTC)[reply]

Dear Michael,

I've started a page called the Virtual classroom, where everybody is both a student and a coach, at my Esperanza subpage. It's a general learning environment for honing, fine tuning, and improving Wikipedia skills. We are currently comparing the user interfaces through which we make use of Wikipedia. I'm sure everyone there would be most interested in reading about how you navigate and edit Wikipedia. Please stop by and share your methods. The Transhumanist 06:05, 7 November 2006 (UTC)[reply]

Thank you for your help

Thank you for your help on the Thermal death time article. It earned a DYK yesterday. I really appreciated it! Chris 14:22, 7 November 2006 (UTC)[reply]

You're quite welcome. Michael Hardy 03:09, 9 November 2006 (UTC)[reply]

Bayesian information criterion

Hi, I am trying to clear up some confusion around the articles Schwarz criterion (and redirect Bayesian information criterion) and Schwartz set. Are you familar with the details of Bayesian information criterion sufficiently to be able to tell whether the article Schwarz criterion should be renamed? John Vandenberg 01:19, 9 November 2006 (UTC)[reply]

Moved from user page

Hi, sorry for the intrusion; I don't yet know how to put a message on your "my talk" as you did for me. Thanks for your improvements to Fisher's method; take a look at it now. I'm having a problem with a guy User:Lgallindo who keeps trashing the Sample size page I wrote; it's linked to his sampling page but is sufficiently different from it (not to mention immediately useful) to let it exist on its own. The engineers in our consulting firm use those N=... formulas often, so I think it's a useful and informative page by itself. -- hardy@sed.ara.com

Moved. -Slash- 06:40, 10 November 2006 (UTC)[reply]

Rank-and-file

I don't know why you deleted the Kinman/Dils reference from this entry, maybe because you haven't heard of the band or that they just weren't as big as the Rolling Stones or something?? :-) I just copied and pasted back what was previously there, though the phrase "next vehicle" sounds awkward to me.

I deleted it because at that time the article was not a disambiguation page, and the appropriate way to write about that band was to put it into a separate article, possibly called "Rank and File (band)", with a notice at the top saying:

For the band, see Rank-and-File (band).

or

For other meanings of this term, see rank and file (disambiguation).

or something along those lines. Michael Hardy 00:55, 12 November 2006 (UTC)[reply]

Your edits to Linear regression

You might want to try your edits again; this time looking at what you change carefully. What you modified didn't make any sense if you read it carefully. – Chris53516 (Talk) 14:30, 13 November 2006 (UTC)[reply]

Thanks

Hi Mike,

Thanks for letting me know about the capitalisation according to the manual of style. That is something new I learnt from you in Wikipedia. Cheers. -- Ch e z ^{(Discuss / Email)} 01:39, 14 November 2006 (UTC)[reply]

Euclid's Pythagorean theorem proof

Hi - Can you add labels for some more points and a few more lines to Image:EuclidsProof.png so Euclid's proof can be explained at Pythagorean theorem? I'd suggesting adding points S at the bottom right of the larger square, T as the right-most point (diagonally opposite Q in the smaller square), U as the bottom left of the larger square, and V as the left-most point, and then adding lines QS, PT, and QU, and RV. The substance of the proof is (with these labels) triangle QRS is identical to triangle TRP, the "R-side" portion of the PR square has twice the area of triangle QRP, and the smaller square has twice the area of triangle TRP. Hence, the QR square has the same area as the smaller portion of the PR square (and, similarly the PQ square has the same area as the larger portion of the PR square). Thanks. -- Rick Block (talk) 19:19, 25 November 2006 (UTC)[reply]

Completing the square

I am puzzled by your questioning the relevance of the new section I added to completing the square. It is relevant because it is about completing the square. And it explicitly says so. If you think that's incorrect, why don't you say that, rather than acting as if you haven't read the new section. Michael Hardy 03:43, 26 November 2006 (UTC)[reply]

OK, I see you want an edit war, expressing your arguments ONLY in edit summaries. Articles should demonstrate, when possible, that topics are broader than what the reader was taught in school as a child. This is one such case. Michael Hardy 03:46, 26 November 2006 (UTC)[reply]

I've requested third opinions at Wikipedia talk:WikiProject Mathematics. Michael Hardy 03:51, 26 November 2006 (UTC)[reply]

I do not want an edit war. I want additions like this to be supported by consensus before they are added. This addition is not directly related to the point of the article. Broadness is fine (although the proof you provide is not terribly broad). Math with no apparent purpose is not (i.e. why should we care that you can prove that 1/x + x >= 2 ? And why should that go in this article?). I don't think it adds anything of substance to the article, and it makes the article more confusing (at least to me). IF there were consensus, I would not object. Thank you for putting out the request. Michaelbusch 03:54, 26 November 2006 (UTC)[reply]

I'm not sure what you mean by "additions like this". Do you mean simply any addition whose relevance someone questions? The addition alone is not very broad, but the article as a whole PLUS the addition is broader than the article WITHOUT this addition. In mathematics, the purpose often comes "later".

Anyway, we'll see what the math community thinks. Michael Hardy 04:01, 26 November 2006 (UTC)[reply]

Elmo?

You don't happen to be the Michael Hardy that went to Elmo?? I noticed you edited my Makaravank Monastery article (nicely) and wondered... --RaffiKojian 04:19, 27 November 2006 (UTC)[reply]

I'm not the one. And actually, I did only one very minor edit on that article. Michael Hardy 04:37, 27 November 2006 (UTC)[reply]

UMN

It is always known as UMN not U of M . This is what I always knew living in Minnesota. Look at the school webaddress and everything associated with the school. UMN not U of M. 155.31.213.189 20:39, 30 November 2006 (UTC)[reply]

You're a total total ignoramus. "UMN" is used ONLY in domain names. Just google "U of M", in quotes, and you'll see inumerable University of Minnesota references (and also U of Michigan and U of Manitoba, etc.). I regularly get emails address to University of Minnesota employees with the subject-line "U of M Brief". Parking lots owned by the University of Minnesota have signs saying "U of M contract lot #37", etc. The university bookstore's various notices say "U of M Bookstore". Freeway exits on Interstate Highway 94 direct drivers in Minneapolis to "U of M". The Univerisit of Minnesota Alumni Association frequently calls itself the "U of M Alumni Association". I could cite hundreds of similar examples. Please stop being stupid and dishonest. Michael Hardy 20:56, 30 November 2006 (UTC)[reply]

Some evidence:

I regularly get emails address to University of Minnesota employees with the subject-line "U of M Brief".
Parking lots owned by the University of Minnesota have signs saying "U of M contract lot #37", etc.
The University of Minnesota bookstore's various notices say "U of M Bookstore".
Freeway exits on Interstate Highway 94 direct drivers in Minneapolis to "U of M".
On the University of Minnesota's "onestop" web page at http://onestop.umn.edu one finds "Search U of M People".
At the University of Minnesota's School of Statistics weekly colloquium, the speaker used a computer terminal that comes with the room; at the bottom of the screen anyone who looked at the fine print could read "Connected to UofM Wireless".
As I walk past the University of Minnesota's Transporation and Safety Building on Washington Avenue, I see signs informing me that the "U of M Police Department" is located there.
- Now I observe that the University of Minnesota Police Department's web page at http://www1.umn.edu/police/index.html has a small button in one corner that says "search U of M" and another that says "U of M Home".
Look at the web site of the University of Minnesota Bookstore at http://www.bookstore.umn.edu/include/aboutus.html: "The Bookstore serves U of M students, faculty and staff with..."
Google "U of M Police Department" (in quotes). Look at the first ten items. One is about the University of Memphis; all the others are about the University of Minnesota; Michigan is not mentioned among the first ten.
Look at the University of Minnesota Libraries' web page at http://www.lib.umn.edu. Among other things, you can click on "Libraries at the U of M".
Google "U of M" itself (in quotes). Among the first ten items, five are about the University of Minnesota, three about the University of Michigan, one about the University of Memphis, and one about the University of Manitoba. Not surprising, given that it seems rather obvious based on casual observation that the University of Minnesota uses the "U of M" abbreviation in an official way more often than do any of the other universities that do that (Michigan apparently in second place).
OK, try "U of M Medical School" (in quotes). Of the first ten items, seven are about the University of Minnesota and three about the University of Michigan.
Walk around the U of M campus in Minneapolis. Count instances. An alert person will quickly find hundreds.

To be continued.... Michael Hardy 23:36, 30 November 2006 (UTC)[reply]

AvErAgE and OvEr

Hey, if you're going to "fix" capitalization in a short article, you might want to do it all through the article. The article has a complicated history, and as I recall it there were good reasons for all the caps. I don't remember what they were, and I don't think it's very important today. What's important is avoiding half-way work, and of course, being CoNsIsTent. ;-) Lou Sander 02:01, 2 December 2006 (UTC)[reply]

---

Health Wiki Research

A colleague and I are conducting a study on health wikis. We are looking at how wikis co-construct health information and create communities. We noticed that you are a frequent contributor to Wikipedia on health topics.

Please consider taking our survey here.

This research will help wikipedia and other wikis understand how health information is co-created and used.

We are from James Madison University in Harrisonburg, Virginia. The project was approved by our university research committee and members of the Wikipedia Foundation.

Thanks, --Sharlene Thompson 18:00, 4 December 2006 (UTC)[reply]

We noticed that you are a frequent contributor to Wikipedia on health topics.

That I was a frequent contributor on health topics is certainly more than I suspected. Michael Hardy 20:28, 4 December 2006 (UTC)[reply]

Style corrections

Thanks for your edits to my recent additions to the George Boolos and Adrian Piper articles. I guess I need to read the Wikipedia style manual.

Robert Rubin —The preceding unsigned comment was added by Roberterubin (talk • contribs) 15:19, 9 December 2006 (UTC).[reply]

Article in need of cleanup - please assist if you can

The article Acoustics, to which you have helped contribute, has been flagged as requiring cleanup.

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image Headscratcher

Hey Michael Hardy, I was wondering if you could take a look at J. B. S. Haldane. Specifically, why does "Image:Haldane.jpg" result in that dorky team mascot in the page, but on mouse-over the popups show the intended photograph of JBS (or arguably his dad, but either way better than some errant accipiter)? Cheers, Pete.Hurd 04:12, 12 December 2006 (UTC)[reply]

No idea. I suspect something in the template rather than in the article itself. Michael Hardy 04:35, 12 December 2006 (UTC)[reply]

OK, thanks Pete.Hurd 05:19, 12 December 2006 (UTC)[reply]

Article in need of cleanup - please assist if you can

The article Apriori algorithm, to which you have helped contribute, has been flagged as requiring cleanup.

If possible, we would appreciate your assistance in cleaning up this article to bring it up to Wikipedia's quality standards. If you are unsure what the nature of the problem is, please discuss this on the article's talk page.
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2-D Gaussian

Hi Michael,

Re: Gaussian_function

It was interesting that you considered the formulation

f(x,y)=Ae^{-\left(({\frac {x-x_{o}}{\sigma _{x}}})^{2}+({\frac {y-y_{o}}{\sigma _{y}}})^{2}\right)}

harder to understand than the current one

f(x,y)=A\exp \left(-\left(a(x-x_{o})^{2}+b(x-x_{o})(y-y_{o})+c(y-y_{o})^{2}\right)\right).

The second one enables me to visualize the gaussian because there is a direct interpretation of the sigmas. I work mostly in biology and use this function a lot and express it in this manner.

Any how, I'm going to add the previous formulation too to the equation you now have. If you have a strong objection to that we can discuss it.

thanks Kghose 23:05, 14 December 2006 (UTC)[reply]

You just put two identical TeX displays here. Your example is misleading, because it incorrectly suggests that there are no other 2-dimensional Gaussian functions, i.e. that there are none that have an xy term. Michael Hardy 23:07, 14 December 2006 (UTC)[reply]

Hi Michael thanks for pointing out the identical TeX displays. You must have been pointing it out as I was correcting it. As an example I don't think it necessarily has to show the most general case. the xy term of course allows us to change the "axes" of the spread. However, as an illustration of the shape of a 2-D gaussian the first example is simpler. How about I add a note to the second formulation saying that it is a more general formulation of a 2-D gaussian ? Thanks Kghose 23:11, 14 December 2006 (UTC)[reply]

Hi Michael, I've made some changes to the article. As a minor point I moved the image back to the left because this staggers the two images on the page and that should look better. The long formula breaks the para, but it should be possible to make the layout a bit better Kghose 23:21, 14 December 2006 (UTC)[reply]

Hi Michael, regarding the puzzle on your page, is the idea the difference between having plus as a binary and a unary operator? Kghose 23:27, 14 December 2006 (UTC)[reply]

Liquid state machines

Hi Michael,

I see the Liquid state machine article has been renamed to Liquid-state machine. It is my experience that the common usage in the field is without the dash. Perhaps it should be changed back to avoid confusion?

thanks Kghose 23:38, 14 December 2006 (UTC)[reply]

Responded on the IP talk

Since I hadn't (yet) added the banner that said I did that, I'm letting you know that I, erm, do that.
152.91.9.144 05:54, 18 December 2006 (UTC)[reply]

I'd have had no idea at all what you're talking about if I hadn't looked at the edit summary you added to this comment. I've been editing here for somewhat over four years, and as far as I know, edits done in sections with titles have always had the section title as the default edit summary. Are you referring to something else? Michael Hardy 06:04, 18 December 2006 (UTC)[reply]

Math and comprehension

The nature of a general purpose encylopedia is that the subject be made available to non-experts. If the subject can not be made available to non-experts, it should not be in wikipedia to begin with! My late father was a mathematics professor and he liked to say that he can tell if a person is a real expert in a field because a real expert can explain a topic they are an expert in a few sentences to laymen. --- Safemariner 06:13, 18 December 2006 (UTC)[reply]

If the subject can not be made available to non-experts, it should not be in wikipedia to begin with!

I agree that articles should explain things to non-experts, but in this case non-experts means mathematicians who don't know that particular area of mathematics. Some things about many areas of mathematics can be explained to non-mathematicians, but it is unreasonable to ask that in the particular article you mention. That doesn't mean it shouldn't be here. By that standard, tens of thousand of mathematics articles written by perhaps thousands of mathematicians will have to get deleted from Wikipedia. You're going to lose that argument. Michael Hardy 06:18, 18 December 2006 (UTC)[reply]

I am not trying to argue for wholesale deletion but for wholesale improvement. I really hope that I do not lose that argument. I am hoping that Mathematicians do not think that they do not need to follow the guideline for overviews at http://en.wikipedia.org/wiki/Wikipedia:Lead_section#Provide_an_accessible_overview . I do not think it is an onerous request for me to ask that Mathematicans follow the guidelines, especially: "Where uncommon terms are essential to describing the subject, they should be placed in context, briefly defined, and linked" --- Safemariner 06:41, 18 December 2006 (UTC)[reply]

Also, you may want to give other editors a chance to add context when requested if you can not improve the article yourself rather than just delete the context tag. Deleting a context tag after just a day is a rather abrupt measure. --- Safemariner 07:10, 18 December 2006 (UTC)[reply]

The only case where I recall deleting the "context" tag that you added recently was where I had just edited the article to provide the needed context. That was Abel's theorem. In its present form that article can be understood by anyone who's had calculus---thus a very very broad audience. The missing context was only the failure to tell the other readers at the outset that mathematics was the general subject area. I am among the strongest proponents of inclusion of that information. One of my favorite examples of the occasion for that information at the beginning is the article titled schismatic temperament. If you think of the usual meanings of the words schismatic and temperament, it sounds as if it's an article about a psychiatric disorder. But it's actually about musical tuning. I edited the article to provide that information at the beginning. I think that gives enough context to tell the reader that those who know nothing about musical tuning might not be able to expext to understand the article. Michael Hardy 19:02, 18 December 2006 (UTC)[reply]

My request is to ask that editors follow this simple rule in the overview: "Where uncommon terms are essential to describing the subject, they should be placed in context, briefly defined, and linked". --- Safemariner 02:44, 23 December 2006 (UTC)[reply]

Let me give you some context. Mathematics is a broad and deep field, and much current research is remote from all but a small number of people actively working in the specialty. For example, graduate students in one department had a revealing guideline for when it might be worthwhile to attend a guest lecture: if you can understand any two consecutive terms in the title, you may be able to learn something. It is simply not possible to make every article broadly accessible, not even by defining terms. We sympathize with the goal, and we would like to achieve it, for ourselves as well as a wider audience. But for some of our topics we are lucky if anyone understands it well enough to write an article at all, much less try to explain it to a non-specialist.

Danny Hillis wrote about Richard Feynman:

"He was always searching for patterns, for connections, for a new way of looking at something, but I suspect his motivation was not so much to understand the world as it was to find new ideas to explain. The act of discovery was not complete for him until he had taught it to someone else."

Which connects us to a story relevant to our topic. --KSmrq^T 12:23, 23 December 2006 (UTC)[reply]

Inferior/superior limit example

Thanks for the important notation fix - I guess I was a bit dazed.

--Trevorgoodchild 02:48, 20 December 2006 (UTC)[reply]

source?

In fact, all mathematical problems are stated primarily in words,^{[verification needed]} but students unskilled in mathematics often fail to realize that.

You put in this "verify source" statement. I thought this assertion was self-evident. Can you think of some alternative way of stating a math problem besides using words? I've been teaching math for a quarter of a century and I don't know any. The notion that it is otherwise is merely a mental pathology that happens when people who'd rather not understand math are required to fake it. Michael Hardy 02:53, 21 December 2006 (UTC)[reply]

Well, it isn't self-evident.

For starters, you can ask maths questions without words, by adding a questionmark to the relationship to be proven or the value to be calculated, etc.

ax² + bx + c = 0 ⇒ x = ?

Similarly, you can use ≟

Also, stating the questions like "Prove <...>", "Calculate <...>", "Derive <...> from <...>", "Integrate <...>" doesn't make a problem a word problem.

Most problems one encounters are economics problems, physics problems, and the like. After studying the real world, defining quantities and modelling it into an equation, it becomes a maths problem. Even if every maths problem had its roots in a real world problem (which is not the case, a lot of mathematicians toy with maths for the fun of toying with maths alone), that doesn't make them word problems. Indeed, sometimes entirely different word problems result in exactly the same maths problem.

I'm not saying that mathematics isn't useful, but it's a tool to make abstract thinking easier. When you are posing a problem like "Calculate the wavelength of the decay from the n=1 to the n=0 state for hydrogen", you're posing a physics problem, not a maths problem. One that would possibly not be solvable without math, but none the less.

I'm also not saying that solving a maths problem is just about manipulating symbols, but it has nothing to do with words. Indeed, most thinking hasn't - well, apart from linguistics.

Therefore, I have serious doubts about the statement I tagged, and ít needs good sourcing, from a trustworthy, peer-reviewed, and hopefully freely available source.

Regardless of how long you have been teaching math, even if you were an ancient sage from the Golden Age of Mathematics, I would still want verification - WP:V is a policy, not an option. Shinobu 04:00, 21 December 2006 (UTC)[reply]

Disambiguation

Why? --Emc² (contact me) 17:16, 22 December 2006 (UTC)[reply]

I'm not sure I understand what you're asking. It seems as if you're asking why I removed a notice from hypothetical question that says hypothetical redirects to that page. The reason is of course that hypothetical no longer redirects to that page. Michael Hardy 19:26, 22 December 2006 (UTC)[reply]

The edit summary can help in these cases. :) Oleg Alexandrov (talk) 20:26, 22 December 2006 (UTC)[reply]

Area of a disk

You brought the sorry state of “area of a disk” to the attention of mathematics editors. It is a minor service article which may not warrant a great deal of attention, but I gave it some nevertheless. More honestly, I completely rewrote the article. I trust I left it better than I found it. I still have one more piece I may add, which is presently in the form of interactive SVG declarative animation. (I began it previously as an illustration for pi.) Unfortunately, support for this method of animation is poor, so I'm not sure how (or when) I'll proceed. Anyway, since you said little about what kind of fixes you wanted, you can't complain if it didn't turn out as you hoped. (Well, you could complain, but I probably won't invest much more time in the near future.) I can still see aspects to improve; perhaps others will be inspired to jump in. Do let me know if I've made any egregious blunders. Otherwise, enjoy. --KSmrq^T 09:01, 27 December 2006 (UTC)[reply]

Hello. It looks enormously better now! I've some a few further edits and I think I might add another proof. Michael Hardy 23:37, 27 December 2006 (UTC)[reply]

Thanks, glad you like it. Frankly, its previous state was so miserable that I could have replaced the whole article with the tiny calculus proof and left it better. I notice you seem to be a traditionalist; I, too, was tempted to start with Archimedes, but my impression is that students today are not accustomed to geometric arguments. Besides that, the integral generalizes nicely to higher dimensions. But either order is fine with me. --KSmrq^T 00:31, 28 December 2006 (UTC)[reply]

Snare technique

I've added the "{{prod}}" template to the article Snare technique, suggesting that it be deleted according to the proposed deletion process. All contributions are appreciated, but I don't believe it satisfies Wikipedia's criteria for inclusion, and I've explained why in the deletion notice (see also "What Wikipedia is not" and Wikipedia's deletion policy). Please either work to improve the article if the topic is worthy of inclusion in Wikipedia, or, if you disagree with the notice, discuss the issues at Talk:Snare technique. You may remove the deletion notice, and the article will not be deleted, but note that it may still be sent to Articles for Deletion, where it may be deleted if consensus to delete is reached, or if it matches any of the speedy deletion criteria. Brad Halls 20:33, 27 December 2006 (UTC)[reply]

Hmm...

Remember time zones. -- tariqabjotu 03:20, 30 December 2006 (UTC)[reply]

From Sr13

I read your correction in the maths a while ago...thanks for the reminder! Sr13 (T|C) 02:45, 4 January 2007 (UTC)[reply]

Barnstar for your outstanding work on statistics articles

		The Original Barnstar
		I award you this barnstar in recognition of your continued work on statistics articles. Just about every statistics article I look at has some important contributions by you. Keep up the good work! Zvika 08:13, 5 January 2007 (UTC)[reply]

Thank you. Michael Hardy 22:49, 5 January 2007 (UTC)[reply]

Debits and Credits

... I'm moving this to talk:debits and credits. Michael Hardy 01:22, 9 January 2007 (UTC)[reply]

Shambala

I noted that you made a minor change to Shambala (song). After writing an article like that, it always makes me smile to see someone besides a bot has paid a visit. House of Scandal 11:57, 8 January 2007 (UTC)[reply]

Law of Large Numbers

Hello, Way back in March 2004 you added the following to the Law of Large Numbers: In probability theory, several laws of large numbers say that the average of a random sample from a large population is likely to be close to the average of the whole population. I have moved the word "large" from in front of the word "population" to in front of the word "sample". Please correct if this is in error. Regards JS 07:28, 10 January 2007 (UTC)[reply]

Variance

Hi, I added two introductory section to the variance page, because it was labeled as "too technical". Would you care to take a look? This is my first contribution to Wikipedia, so I'm not sure that the style is appropriate. Also, given your other contributions, I can imagine that you find my contribution not "mathematical" enough. This is intentionally, because I think that the topic is likely to be visisted by non-mathematicians. I also added more mathematical stuff about the variance of sums and variance decomposition, and a shorter proof for the unbiasedness. Do you think that the label "too technical" can be removed? How should that be done?

Thanks, JulesEllis 03:23, 15 January 2007 (UTC)[reply]

99/100 apples

Hello Michael,

There is currently an example on the law of large numbers page that say has 99 out of 100 apples being counted. I think this is misleading as it suggests LLN works because most of the population has been counted. In reality I believe LLN will work even if 0.001% or less are counted, as long as the sample is "large". Blue Tie wants to retain the example. If you agree the example should be deleted or changed (for example, making it 99 out of 10,000), please do so. Thanks! JS 19:53, 17 January 2007 (UTC)[reply]

Thanks for your attention to the LLN article, Regards JS 22:13, 17 January 2007 (UTC)[reply]

Hayward Fault Zone (information entropy)

Please do not contribute to information entropy by deleting material appropriate to the article. If you think (as stated) that it belongs (somewhere) in the article, then place it appropriately. Thanks, Leonard G. 04:08, 18 January 2007 (UTC)[reply]

Margin of error up for FAR

Margin of error has been nominated for a featured article review. Articles are typically reviewed for two weeks. Please leave your comments and help us to return the article to featured quality. If concerns are not addressed during the review period, articles are moved onto the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Remove" the article from featured status. The instructions for the review process are here. Reviewers' concerns are here. Jeffpw 06:56, 18 January 2007 (UTC)[reply]

Zariski surface

(copied from USER_TALK:Blaxthos)

At Wikipedia:Articles for deletion/Zariski surface, you wrote

Delete Sorry guys, hate to be the lone dissenting voice, but this article is promoting original research. It's unforuntate that often times Wikieditors are asked to voice opinions on conceps we have little experience with, which makes it truely difficult to sift what's accepted in the applicable community from what is being promoted as a new construct or theory.

The initial author of the article, user:r.e.b. is a world-renowned professor who knows very well what's accepted in the applicable community. How did you conclude that it's original research? Your comments assert that, but you don't attempt to give any reasons for thinking so. Michael Hardy 00:59, 21 January 2007 (UTC)[reply]

For one, I believe that the author of the article is also the proponent of the theory. WP:COI not withstanding, even if he is a world-renowned professor who knows very well what's accepted in the applicable community he is still promoting his own theory via Wikipedia. Apparently he has published some literature arguing for acceptance of his ideas, however every single reference I can find has traced back to his own writing. I think the main issue here is WP:Verifiability and his self published theory -- his repeated thumbing of nose at the community (or so it has seemed) probably didn't help, but I believe the problem is simply third party reviews. However, judging from the AfD, it looks like my opinion is in the minority, so it shouldn't make a difference either way. ;-) /Blaxthos 02:50, 21 January 2007 (UTC)[reply]

No, he's not. You're confusing two different people with each other. Piotr Blass is NOT the initial author of this article. Richard Borcherds is. Michael Hardy 02:51, 21 January 2007 (UTC)[reply]

Comment Is the erroneous belief that Piotr Blass is the initial author of this article the only point against it, or is there something else? Michael Hardy 02:56, 21 January 2007 (UTC)[reply]

Did, or did not the creator of the theory contribute significantly to the article? Is there any research available that is peer reviewed and unconnected to him? /Blaxthos 03:02, 21 January 2007 (UTC)[reply]

Did, or did not the creator of the theory contribute significantly to the article?

No---I think he died in 1986 and Wikipedia did not exist until six years ago.

But I think your question is irrelevant anyway. A Wikipedia article is not "original research" for purposes of the Wikipedia policy forbidding that, if everything in it has been published in scholarly journals before it appeared on Wikipedia.

And even if the creator of the theory wrote the whole article after its substantive claims were published in journals, that's no reason to delete it. Michael Hardy 02:30, 22 January 2007 (UTC)[reply]

Regarding the Posthumous dab page

Hello, you and I appear to have different ideas on how to apply Wikipedia's MoS formatting guidelines for disambiguation pages. For what it's worth, my particular concerns are that, since a dab page's only purpose is to direct readers to other articles, the introductory definition is not really needed (and somewhat redundant with the Wiktionary link). Also, the guideline recommends that entries "should nearly always be sentence fragments", and I don't see a need to ignore that guideline in this case.

Would you object if I tagged the page with a {{disambig-cleanup}} tag, so that interested third parties can take a look? --Muchness 23:15, 22 January 2007 (UTC)[reply]

I have no objection to such a tag.

Pages should be be comprehensible. Related definitions should not be made to look disparate. Michael Hardy 02:57, 23 January 2007 (UTC)[reply]

Thank you, I'll go ahead and tag it. I tend to edit dab pages strictly by the letter, but of course it's better to allow a certain amount of flexibility if it benefits the page. Regards. --Muchness 16:44, 23 January 2007 (UTC)[reply]

List of formulae involving π

It got AfD'd! I'm so upset.... It's partially my fault, because I mentioned it as an example of a good "list" article in a different AfD and the "delete" voters there nominated it (to prove a point). Perhaps you could offer your opinion, since you edit it a lot and seem to be a mathematician. --N Shar 06:36, 25 January 2007 (UTC)[reply]

Image copyright problem with Image:St_anthony_falls_Oct_2005.jpg

Thanks for uploading Image:St_anthony_falls_Oct_2005.jpg. The image has been identified as not specifying the copyright status of the image, which is required by Wikipedia's policy on images. If you don't indicate the copyright status of the image on the image's description page, using an appropriate copyright tag, it may be deleted some time in the next seven days. If you have uploaded other images, please verify that you have provided copyright information for them as well.

For more information on using images, see the following pages:

This is an automated notice by OrphanBot. For assistance on the image use policy, see Wikipedia:Media copyright questions. 10:38, 26 January 2007 (UTC)[reply]

The information is there and is conspicuous and has been there as long as the page has existed. Michael Hardy 19:06, 26 January 2007 (UTC)[reply]

You know you're talking to a bot, right? — Omegatron 19:53, 26 January 2007 (UTC)[reply]

Product rule

I see the error now, but how would you propose illuminating the seemingly magical step in the usual proof? Keeping in mind the proof's audience is largely high school students... --Shamilton 05:17, 27 January 2007 (UTC)[reply]

It can be done via an illustration. Maybe I'll put one there at some point.... Michael Hardy 00:21, 28 January 2007 (UTC)[reply]

Done. Michael Hardy 23:10, 30 January 2007 (UTC)[reply]

Noncentral F-distribution

I didn't know Wiki had a Statistical independence page until you linked it. Nice edit. Steve8675309 03:26, 28 January 2007 (UTC)[reply]

Complex conjugate root theorem

See my recent post to the AfD, withdrawing the nom. You are right, it's not a corollary of the FTA, even though the textbook and WP articles I checked all asserted that it was. That assertion, however, makes no sense, and I should have trusted my logic rather than "authorities." As for the article itself, it looks a lot better, as usual for articles you have edited. --N Shar 00:14, 31 January 2007 (UTC)[reply]

Article in need of cleanup - please assist if you can

The article Autistic savant, to which you have helped contribute, has been flagged as requiring cleanup.

If possible, we would appreciate your assistance in cleaning up this article to bring it up to Wikipedia's quality standards. If you are unsure what the nature of the problem is, please discuss this on the article's talk page.
If you do not want to receive bot-generated messages on your talk page, please consider using the nobots template on your user talk page

FYI: iNic at the article on the St. Petersburg paradox

Possibly of interest to you:

User talk:Luna Santin#Problem brewing at St. Petersburg paradox

—SlamDiego 22:39, 8 February 2007 (UTC)[reply]

bypassing redirects

I saw you systematically work on bypassing redirects. You obviously have good intentions, but there is a guideline that explains that this is a little more damaging than helpfull. trespassers william, an impressed newbie.

That page says:

In particular, there should never be a need to replace [[redirect]] with [[target|redirect]].

That is idiotic! If an article misspells a person's name in a link, so it goes to a page that redirects to the correct spelling, I should just leave the misspelled name in the article??

People who write Wikipedia policies using the words "always" or "never", especially when emphasized like this, are almost (ha!) always being similarly stupid. Michael Hardy 00:27, 12 February 2007 (UTC)[reply]

see reply on my talk page (is this crossposting automatic?) trespassers william 14:24, 12 February 2007 (UTC)[reply]

Just curious

Why would you want to waste your effort trying to fix up an article (Inductive symbol) which is likely to be deleted anyway? JRSpriggs 07:42, 23 February 2007 (UTC)[reply]

Help

Could you take a look at the edits by User:Woollymammoth on Regression analysis? You examined his edits on another article, and it would help if you looked at the other one too to make sure everything is in line. By the way, you might want to archive your talk page; it's getting pretty big. — Chris53516 ^(Talk) 00:49, 25 February 2007 (UTC)[reply]

Talk:Regression analysis

Dear Dr. Hardy: What an incredible range! That 3rd star warms me in your attempting to make subjects accessible to the lay person (even in Econ., as I can attest).

Which brings me to Talk:Regression analysis#Proposed lead, my effort to reach the general reader (curious but with little background). I wonder if you or someone you could recommend would be willing to do one of the following:

Indicate whether the proposed lead would be an improvement or not as to the current lead.
Edit the proposed lead so as to satisfy (1) and replace the current lead.
Write a lede that fills in what the the proposed lead attempts to do.

Thank you for your assistance. My efforts to Edit the current lead have been reverted repeatedly with no substantive reasons given (IMHO), despite repeated requests for such over the course of the past week. My thanks. --Thomasmeeks 22:58, 26 February 2007 (UTC)[reply]

I hope that the above is ready for the article now, Dr. Hardy. Question: Isn't a small letter n more usually used for the sample size in stat., while a small or large k is more commonly used for the number of parameters in a regression? (The Wiki regression articles of course use n for the the number of parameters.) Thanks. Thomasmeeks 23:11, 5 March 2007 (UTC)[reply]

Hello. Sorry not to reply earlier. I think I've more frequently seen the lower-case n, and that is my preference, but both conventions are used. Michael Hardy 02:42, 6 March 2007 (UTC)[reply]

Thank you. Sorry I didn't follow. Just to be sure, the lower-case n is more common for the sample size? Thomasmeeks 03:29, 6 March 2007 (UTC)[reply]

Generalized continued fractions

Hi, Michael!

Thanks for cleaning up the notation in this article. I appreciate it.

This edit fixed some mistakes I made back in December. I'm not sure what to say … I must have been sleepy. :-( I probably used ctrl+c and ctrl+v to copy and paste an expression like ''x''<sub>''i''</sub>, then put digits in place of i and forgot to take the apostrophes out. Thanks for fixing it!

This edit also cleaned up some errors, but I didn't introduce them into the article. Another editor, Glenn L, was responsible for that bit of the article.

On the distinction between x_even and x_even, I'm not real sure what's right. I've never seen that particular notation in a book, so I just made it up on the spot because it seemed informative. I thought about expressions like x₂ and also x_i, and finally decided to italicize the word "even" because it was made up of letters, not numbers. But then, it wasn't really a variable, either. Anyway, I don't much care which way it appears, but I did want to point out this edit, where I modified the last occurrences of x_odd and x_even (at least, I think they were the last ones) to conform with the convention you had established with your earlier edits.

Thanks for all your good efforts, Michael! ;^> DavidCBryant 23:56, 26 February 2007 (UTC)[reply]

Spectrum

Hi, I reverted Spectrum to a version from two weeks ago, which was an article on the history and use of the word, rather than a dab page. The overwriting of the article (by another editor) was inappropriate on several policy/guideline grounds. In the process, I may have eliminated some of your edits that could add to the article. I apologize for this. Please see if the current article addresses your concerns, or needs modification. --Srleffler 03:28, 1 March 2007 (UTC)[reply]

"INCREDIBLY STUPID"

Could you please tone down your edit summaries? The FAR process has enough drama as it is. Melchoir 20:12, 1 March 2007 (UTC)[reply]

Perhaps, but when someone says Columbus crossed the Atlantic in 1992, eight years after the Macintosh computer was introduced, it's hard to assume they were sober when they wrote it. Michael Hardy 20:14, 1 March 2007 (UTC)[reply]

Yes, and a sober editor will be able to delete such a statement without shouting. Melchoir 20:24, 1 March 2007 (UTC)[reply]

Kriging

Hello!

I've originally visited the kriging page several months ago, looking for useful information (Specifically, I wanted to implement kriging in a Fortran program to interpolate unordered elevation data). The page struck me as being chaotic and going off at a tangent; little specific information on the kriging technique was provided, but there was a lot of vituperative wrangling against geostatistics.

I complained on the talk page and waited a long time for the article to improve. I revisited the article periodically, read the talk page and related user talk pages closely (JanWMerks and Merksmatrix in particular), and came to the conclusion that the reason the article is so wretched is because it is under continuous attack by a father-and-son team of cranks, who disrupt any constructive work with their own unsubstantiated agenda.

In order to give bona-fide editors like you more breathing space, I recommend that this matter be given due process under Wikipedia:Dispute resolution. Specifically, I propose that a request for help be filed under AMA Requests for Assistance, as a first step. Perhaps the Advocate will be able to guide us in the steps that need to be taken to stop the disruptive behavior. My ultimate goal is Article probation. I am fed up with the cranks. Aren't you?

Please let me know what you think at my talk page. I sent this message to Hike395, Michael Hardy, Vsmith, SCmurky, Antro5, Nvj and Berland, as these names appear a number of times in the discussions. Freederick 16:08, 2 March 2007 (UTC)[reply]

Survey Invitation

Hi there, I am a research student from the National University of Singapore and I wish to invite you to do an online survey about Wikipedia. To compensate you for your time, I am offering a reward of USD$10, either to you or as a donation to the Wikimedia Foundation. For more information, please go to the research home page. Thank you. --WikiInquirer 21:43, 3 March 2007 (UTC)^{talk to me}[reply]

Lobby 7

On the merits of the picture, I felt Lobby_7.jpg was (1) duplicated by Mass_av_77.jpg with regard to showing the same building, (2) was somewhat overexposed with the light through the windows, (3) did not really convey the details, scale, or impact of the room. The fact that the pictures on the right seem to run into other sections is a problem, so I chose to remove this picture based on the (lack) of merit as well as the length of the thumbnail. I like the east-looking from west campus picture because it does an adequate job of placing MIT within a larger geographical context as well as presenting a different perspective from the rest of the "gee-whiz" Neo-Classical and post-modern building pictures. I welcome any contributions you might have as I have neither the equipment nor the skill to take good pictures. Madcoverboy 05:41, 4 March 2007 (UTC)[reply]

I'm nominating "Binomial (disambig)" for deletion

Please note: I am nominating Binomial (disambig) for deletion.
You are shown in the history as having edited this page.
If you wish to object, check the details by clicking the link above.

Regards, JohnI 09:44, 6 March 2007 (UTC)[reply]

Coprime

Hi, Michael!

Just a short question. In page coprime we can find this:

The integer b has a multiplicative inverse modulo a: there exists an integer y such that by ≡ 1 (mod a). In other words, b is a unit in the ring Z/aZ of integers modulo a.

I think it is a kind of confusion. This would be better:

[...] In other words, b as a member of the ring Z/aZ of integers modulo a is an invertible element in Z/aZ.

Am I right? Thanks: Mozó 20:43, 9 March 2007 (UTC)[reply]

Well, it is standard in certain contexts to call invertible elements of rings "units". Whether it's the best for expository purposes may depend on context; I'm not sure I want to commit myself to it or against it right now. Michael Hardy 02:19, 11 March 2007 (UTC)[reply]

spelling

Hello. I notice you're doing lots of spelling corrections. Are you following a policy of always preferring American spelling to British spelling (as when you changed rigourous to rigorous)? Michael Hardy 23:13, 9 March 2007 (UTC)[reply]

Hi Michael, no I'm definitely not (intentionally) changing British English to American English or vice versa. I did check this one when adding the rule to my bot, and my dictionary doesn't have an entry for 'rigourous'. Just there, I checked the OED to be sure, and it had rigourous as a variant spelling, but AFAIK it's not the standard in either the UK or US. Since there's this uncertainty, I'll remove the rule. Cheers, CmdrObot 23:19, 9 March 2007 (UTC)[reply]

User talk:Michael Hardy/Archive3

Homogeneity afd

Invitation to join Wikipedia:WikiProject Eastern Orthodoxy

radius of convergence

License tagging for Image:HardyBlack+White.jpg

Reference to Apostol

Stub

Template:Seeintro

Links

Technical analysis

Hello

Fuck Profanity vs. Vulgarity

"Other uses" discussion

UM

Continuous-time Markov process

Isomorphism class?

Saint Benilde

Combinatorial enumeration

Howdy

Edit summary

Another request

TeX

Serial Comma on Euler characteristic

Nett weight and Net weight

thank you

For other uses...

Thanks!

Hi

Limit theorem

"Improving TeX"

context-setting

Fraction style

Deletion policy

Squaring the circle

Inferential statistics - is terminology standard?

AfD Nomination: Marion Cohen

Reply on Wikipedia talk:Images

RE: 0.999...

Your title change to Point source (polution)

Thanks

You really need to read the discussion at Talk:Point source

A[s] I keep repeating, several times every day, on Wikipedia, TeX looks very good when "displayed" but horribly ugly, almost to the point of illegibility in some cases, when embedded in lines of text.

Thank you and help please

Improper Integral

Edits to Minnesota historical articles

template cquote

Thanks for TeX

Fibonacci

American Gold Eagle

Thanks...

Exponents

Mathematician-stub

Floating point page

Re:"doing what you want"

request your comment

Cantor Distribution

Inverse Function Theorem

WP:DBTN

Thanks for following me around and cleaning up my droppings

"radius" in history of pi

inline tex

Thanks

Regarding your comment

Zeta distribution (case s=1)

Thank you

Beta-binomial

Your minor formatting edit to Manifold Destiny

Inverse Gaussian

Thank you for your assistance on the DYK

Today's featured article

Reversion in linear regression

irrational number

Otheruses

your edit to Ocular ischemic syndrome

TRS Article -- Proposed Revert

Buoyancy

Assistance on mathematical formulas on Thermal death time

Collimated light

Dear Michael,

Thank you for your help