User talk:Michael Hardy


Welcome to user-land! :-) (bwahahahah!) -- Tarquin 20:27 Jan 9, 2003 (UTC)


Autistic savants


My name is Jef Reinten; I recently read your comment in the discussion board for Autistic savants. You commented that you doubt the existence of mathematical savants because math requires a degree of ingenuity. This claim is only partially correct; there are no low functioning savants that demonstrate a truly creative approach to maths. However, savants have been encountered that demonstrate profound skills in arithmetical processes (Treffert D.A. (2000) Extraordinary people Bantom Press, London), but not the complex mumbo jumbo that you seem so into.

Should you wish to discuss this further I would be pleased to hear from you.

Hi, Michael,

We obviously share and interest in Archimedes and statistics.

Thanks for improving the explanation of Archimedes' theorem on the area of the parabola, and correcting my mistakes in the list of his books. I am writing from memory, since my copy of Heath is sitting on a shelf several thousand miles from me, so it's very good that there's someone out there to set me straight. -- Miguel

Just curious. Are you Michael Hardy from MIT, Michael Hardy from Texas (I found the two names on Google) or other Michael Hardy? wshun 00:49, 17 Aug 2003 (UTC)

I was at MIT for three years; I no longer am. I've never had an academic appointment in Texas. Michael Hardy 14:02, 17 Aug 2003 (UTC)

Here's why I think the content of "Generatics" is not taught anywhere. The

American Mathematical Monthly of the Mathematical Association of America is considered the magazine for college math teachers, who prepare HS and Middle School teachers. In 1979, when I started at Naval Research Laboratory, with an excellent library, I spent many lunch hours, sandwich in hand, searching copies of AMM from first issue to last for an article on this subject, even mention of Hamilton's vector form. Nada. I then. in 1979, sent a one page explanation of this. It was rejected as "too difficult" for their readers. Next year, in 1980, I sent essentially the same article. No rejection or even notice of my submission. In 1981, ditto, with a rejection, again "too difficult". In 1982, 1983, 1984, no rejection, no notice of submission. Then I started sending a two sentence letter about this. Never printed.Twice a year, until my retirement in 1990, 12 letters in all -- each a 2-sentence letter, only syntactically varied. Never printed. Somehow it is heresy. And no one will tell me why.jonhays 00:29, 22 Sep 2003 (UTC)

Your premises do not support the conclusion that anyone considers it "heresy". You have not demonstrated that the referee was wrong to call your article too difficult for that journal's readers. The individual topics you mentioned are standard parts of the curriculum, even if collecting them into a single topic under a single name is not. To imagine that the only reason anyone might reject your writings for publication is that they consider them heretical is to start to look paranoid. Michael Hardy 01:31, 22 Sep 2003 (UTC)

Hi - fab work on Boolos, Second-order logic (LONG awaited) and Cantor's Theorem and first uncountability proof. I added some bits and links to my stuff. There is still a confusion between the diagonal argument (which explicitly mentions the reals i think) and Cantor's Theorem (which simply says for any set S, P(S) > S). Not sure this is entirely clear.


Hi Michael. Good job spotting my error in the Markov property article! Ben Cairns 03:45, 18 Nov 2003 (UTC)

Hi Mike,

I finally got the chance to access Cantor's original paper (1891) containing the first version of the diagonal argument. Also found a useful link on the web to the German version (as edited by Zermelo) of the paper. It turns out that Cantor intended it as a general proof that for any M whatsoever, P(M) > M. He never mentions the reals or anything like that (though he mentions some consequences of the argument later in this short piece).

The consequence of this is that the "diagonal argument" article is introduced entirely wrong, in saying Cantor's proof is that the [0,1] is uncountable. That is of course a consequence of the proof, but the proof is mroe general than that.

Your piece on Cantor's theorem (which I edited) is however pretty much OK as it stands. Dean B.

I've nominated you for adminship. If you accept, please reply at Wikipedia:Requests for adminship. Maximus Rex 06:53, 1 Dec 2003 (UTC)

Hi Michael: two things...

  1. I've converted that Desargues' theorem PDF to a PNG and updated the page. It still needs some good alternate text, though, which I thought I'd leave to you (such geometry is not really my thing).
  2. Have you given up on the 'Show preview' option when editing pages? No wonder you've made 12K edits :) More seriously, doesn't this reduce the effectiveness of the Wiki?

Regards, Ben Cairns 02:02, 2 Dec 2003 (UTC)

Hi Michael. Would you mind having a look at User:Bjcairns/Probability? I have an idea to build a table of contents for people wanting to learn probability from the Wikipedia, and would greatly appreciate your input. I imagine some kind of pre- or proto-Wikibooks thing. (Any other probability people reading this are also most welcome!) Thanks, Ben Cairns 00:37, 5 Dec 2003 (UTC)

CHALLENGE PROBLEM. Doggle Company has a fleet of 10 vehicles: 4 vans, 3 small trucks, 2 big trucks, 1 sedan. What is the probability, ceteris paribus, that. at a given time, 4 vehicles will be in use? Please note that this is not the multinomial probability distribution , which samples distinguishable items from a distinguishable population. Rather, it samples undistinguished items from a distinguishable population. The answer is found at , which fills in a critcal gap in statistical literature. authored by User:Jonhays0, 03:12, 5 Dec 2003

You're now an administrator -- Tim Starling 00:32, Dec 6, 2003 (UTC)

Congratulations. If I had realised you weren't already one I would nominated you long ago. I know we have clashed on occasion but I am glad to see that someone who does so much good work on wikipedia is getting proper recognition. We could almost call you our editor-in-chief or at least proofwriter-in-chief. Good luck! Fear�IREANN 01:09, 6 Dec 2003 (UTC)

Thank you.
I promise to sentence three Wikipedians to burn at the stake for heresy (or maybe for hearsay) each week. Michael Hardy 01:44, 6 Dec 2003 (UTC)

Hi there. Congrats on the adminship - join the club! You were asking why "Penny" was capitalised in the chapter titles but not in the introductory chapter -- the reason is the articles' subject is "Penny" and the "English" or "British" is just a qualifier. "History of the English penny" was not my title for the article, as it had a more hierarchical name to match all the other denominations linked off "British coinage" but someone else took a dislike to it and renamed it... not my idea! Arwel 03:03, 6 Dec 2003 (UTC)

I've found a misplaced reference showing that "generatics" did not start with me in content,

only in name. The book, "Learn from the Masters", edited by Dwetz, Fauvel, Bekken, Johannsson, Katz (Mathematical Association of America, 1991), says on p. 286, "It was not until 1894 that J. Tannery introduced the arithmetic of rationals as pairs [vectors] of integers." (Jules Tannery (1818-1910), French, is cited ONLINE.)--In 1957, I received a grant from the National Science Foundation to organize the first NSF Workshop in Puerto Rico, planned for high math school teachers (some from States). I taught "Foundations of Mathematics". I was sent papers (later lost) from previous Workshops. One set described Tannery's work and Hamilton's formulation of complex numbers as pairs or vectors of reals. The formulator filled in by deriving integers from pairs or vectors of natural numbers. The latter shows how "the law of signs" derives from CLOSURE on DEFINED DIFFERENCES (DDs) of naturals : (a - b), s.t. subtrahend is not greater than minuend, hence, a natural number. Critical is multiplication law for DD. From standard multiplication algorithm, find that, for DDs, (a - b) * (c - d) = (a*c + (-b)*(-d)) + (a*(-d) + (-b)*c). Applying, 10 = 5*2 = (9 - 4)*(2 - 0) = 18 + (-4)*(2) + 0 = 10, hence, (-4)*(2) must act as a subtrahend -8, leading to "negative times positive equals negative" rule. Applying product rule to 30 = 6*5 = (9 - 3) - (7 - 2) = (63 + (-3)*(-2)) - (18 + 21) = (63 - 39) + (-3)*(-2) = 24 + x = 30, hence, x = 6 = (-3)*(-2), leading to "negative times negative equals positive" rule. This is forced by CLOSURE on DDs. However, in the "Generating arithmetic" article which I initiated, some one put in that CLOSURE is a concept from category theory, very advanceed math. Yet, the above book, on p. 260, says, "For Galois (1830), Jordan (1870), and even in Klein's "Lectures on the Icosohedron" (1884), groups were defined by the one axiom of closure. The other axioms were implicit in the context of their discussions -- finite groups of transformations." So CLOSURE goes back at least to 1830.Jonhays0

Ok... What is the reason to have a self-link? - UtherSRG 00:36, 3 Jan 2004 (UTC)

The reason is that the article is about the concept of a fixed point. Michael Hardy 00:41, 3 Jan 2004 (UTC)
Maybe I'm clueless, but that doesn't give me anything. Or is this just a pun? :) - UtherSRG 00:43, 3 Jan 2004 (UTC)
It's a useful pun in this case, because it is suggestive of the article's topic. It is instructive; it helps the reader remember the idea. Humor should not be included when it is gratuitous, but this instance of humor helps get the point across. Michael Hardy 00:47, 3 Jan 2004 (UTC)
Yup. I was clueless. It's a great pun. I've been doing this too long today. :)

In my mind multiple comparisons is part of analysis of variance but simultaneous statistical inference is broader, including things like confidence bands in regression.Cutler 20:34, 3 Jan 2004 (UTC)

I have no idea whether to put it here or not. I am still not very familiar with these systems, but I would want to say thank you, for your welcome and your advice. -Sothis

just want to say thanks for the many quality math articles you contributed. I enjoyed them extremely. Xah P0lyglut 14:06, 2004 Jan 7 (UTC)

Thank you. I'm glad someone's reading them. Michael Hardy 21:55, 8 Jan 2004 (UTC)

Mike, thanks for your interest in the Cox's theorem article. I've appended a comment about formatting to the article talk page. Best, Wile E. Heresiarch 23:51, 8 Jan 2004 (UTC)

Michael, thanks for the comments on L-S. I still had the other comment, to more with the internal conection between this, your article on Second-order logic, and the other on First-order logic. As follows:

My difficulty is what "first order" sentences are. It says under First-order logic that "first-order logic is strong enough to formalize all of set theory and thereby virtually all of mathematics." But it also says " It [FOL] is a stronger theory than sentential logic, but a weaker theory than arithmetic, set theory, or second-order logic."

Yet under Second-order logic we have "second-order logic differs from first-order logic in that it allows quantification over subsets of a domain, or functions from the domain into itself, rather than only over individual members of the domain."

I have difficulty in understanding how "first-order logic is strong enough to formalize all of set theory and thereby virtually all of mathematics." But also that FOL by implication does not allow "quantification over subsets of a domain". These statements seem to contradict each other. If FOL does not allow quantification over subsets of a domain, how can it "formalize all of set theory and thereby virtually all of mathematics."?

Regards, Dean

Hi Michael, if the idea appeals to you, I'd like you to review Principle of indifference. If you choose to do so, and you see something that needs fixing but don't feel like doing it yourself, I'll be keeping an eye on the talk page. Cheers, Cyan 01:41, 15 Jan 2004 (UTC)

Talk:Covariance matrix

I put in my two cents at Talk:Covariance matrix -- SEWilco 19:29, 15 Jan 2004 (UTC)

List of statistical topics

Will do - thanks for pointing this out (and for supplying various links etc on the U-test page). seglea 00:14, 17 Jan 2004 (UTC) (Hedgerow statistician)

CHALLENGE PROBLEM. Doggle Company has a fleet of 10 vehicles: 4 vans, 3 small trucks, 2 big trucks, 1 sedan. What is the probability, ceteris paribus, that at a given time, 4 vehicles will be in use? Please note that this is not the multinomial probability distribution, which samples distinguishable items from a distinguishable population. Rather, it samples undistinguished items from a distinguishable population. The answer is found at , which fills in a critcal gap in statistical literature.jonhays 17:54, 17 Jan 2004 (UTC)

Borel's paradox

A recent addition, this article could undoubtedly use your expertise, if you're so inclined. (I am the original author.) -- Cyan 17:48, 27 Jan 2004 (UTC)

Claiming old edits of yours

Out of an off chance on reading Talk:Aluminum, I noticed a number of edits you probably made when you were logged out. If you like, you can claim the edits under if you still have access to that IP. Thanks, and HTH Dysprosia 09:04, 21 Feb 2004 (UTC)

Alright, do you have any sense of civility? Grow up! I see the picture you posted and I was a little surprised. I was genuinely expecting someone younger.

Poission distribution is not only parameterized continuously, but discribes the probability of events as they occur in continuous time. The events are discrete events, no doubt, But we are talking about their distribution, not the events themselves.

It is impossible to simulate processes that involve poission distributions to perfect accuracy on a turing machine. Turing machines can perform any discrete mathematical operation to perfect accuracy. Therefore, poission distribution is not discrete.

Perhaps you are speaking of some dogmatic naming convention. I don't give two sh!ts about this convention. I care whether the poission distribution is discrete or continuous in a meaningfull sense. The fact that the events that occur are discrete events does not make the distribution itself discrete.

The poission distribution takes two parameters. Neither of those parameters is more primal than the other. One of them is continuous, therefore, the distribution itself is continuous.

What is your problem? Do you need to take an anger/ego management class? This is ridiculous! -- Kevin Baas 01:00, 25 Feb 2004 (UTC)

Mr. Baas, you have been very rude on a number of occasions on talk pages, and that which you call my rudeness was in fact merely my description of the facts, plus my opinion that you often write unclearly.
You are confused about the Poisson distribution. Any Poisson distribution is a discrete probability distribution; the family of all Poisson distributions is parametrized by one non-negative real parameter. Your reference to "events as they occur in continuous time" suggests that you are confusing the Poisson distribution with the Poisson process. Indeed, we are talking about the distribution, not the events themselves. The support of this probability distribution is the set { 0, 1, 2, 3, ... } of non-negative integers; therefore, it is necessarily a discrete distribution.
You write that "It is impossible to simulate processes that involve poission distributions to perfect accuracy on a turing machine." But the same is true of all probability distributions, including a single coin-toss. You wrote: "Turing machines can perform any discrete mathematical operation to perfect accuracy." But they cannot simulate a coin toss. And you forget that the probability that a biased coin comes up heads can be a noncomputable irrational number, and that in no way diminishes the fact that the number of "heads" that appear -- either zero or one -- is a random variable whose probability distribution is discrete.
In your manner of writing about mathematics, you appear to consistently make matters more complicated than they really are.
That I do not follow conventions dogmatically is proved by the nature of some of my contributions to Neil Weiss's new book on probability, in which I argued at length in favor of some unconventional nomeclature that he ultimately adopted. I follow conventions in order to understand others and to be understood by others.
Your statement that "One of [two parameters] is continuous, therefore, the distribution itself is continuous." is utter nonsense; even the simple coin-toss random variable is parametrized by a continuous parameter.
And, moreover, as I said, there is just one such parameter, and it is continuous. You seem to have in mind that the family of Poisson distributions is parametrized by two parameters, and one is discrete! I know of no discrete parameter used to parametrize the family of Poisson distributions. Conventionally, this family is parametrized by one parameter λ (I do not insist on that particular letter) and the probability mass function is given by
<math>P(X=x)={\lambda^x e^{-\lambda} \over x!},</math>
where x ∈ { 0, 1, 2, 3, ... }.
"Continuity" of a parameter space in no way implies that a distribution belonging to the family is discrete.
You would both communicate and understand better if you if you learned conventional language instead of exhibiting a holier-than-thou contemptuousness of it.
You would both communicate and understand better if you were not so often so belligerent. Michael Hardy 01:50, 25 Feb 2004 (UTC)
I agree that there is turbelence and a million other processes involved in the flipping of a real coin, and that it would be quite inconceivable for a computer to simulate all of these processes. But that's boringly obvious. Why even mention it?
Perhaps "calculate" the probability would be a term that communicates my point better? The probability is a computable number. These probabilities can be manipulated and composed every which way, without involving random numbers, in what may be called a "simulation". The end result is a discrete probability distribution which is an exact solution, not an outcome or event.
However, a computer cannot produce an exact solution if the probability model involves a poission distribution.
If the coin is biased and the resulting probability is an uncomputable number, this implies that it was biased by an uncomputable number. But nondimensionalizing solves this problem. Essentially, we're not really concerned with "numbers" when we're talking about a computer. We're talking, rather, about finite states. So long as the problem can be coded by a finite number of states, it is discrete, and can be operated on by a turing machine.
The poission distribution is often represented in the form:
<math>P(x,\lambda)={\lambda^x e^{-\lambda} \over x!}</math>
A special case of the poission distribution is the exponential distribution, where the x parameter is 1:
<math>P(\lambda, t)={\lambda e^{-\lambda t}}</math>
- Kevin Baas 17:04, 25 Feb 2004 (UTC)
Here you are mistaken on several counts. (And you still give just one parameter λ.) You are wrong to call the exponential distribution a special case of the Poisson distribution. The Poisson distribution is a discrete distribution assigning a probability to each nonnegative integer. The exponential distribution is a continuous probability distribution that assigns a positive probability to every interval in the half-line (0, ∞). To say the exponential distribution is a special case of the Poisson distribution would mean that every exponential distribution is a Poisson distribution but not every Poisson distribution is an exponential distribution. That is false; the exponential distribution is not a Poisson distribution. As I said, you are confusing two different things with each other: (1) Poisson distributions, and (2) (more complicated) Poisson processes. A 1-dimensional Poisson process involves discrete Poisson distributions and continuous exponential distributions. The distribution of the number of "arrivals" in a given time interval is a discrete probability distribution; it is a Poisson distribution. The distribution of the waiting time until the next "arrival" after a given time is a continuous probability distribution; it is an exponential distribution, not a Poisson distribution. Every time I've taught probability I've warned students not to confuse these two things with each other, and almost always some of them do. So be more careful. Michael Hardy 20:05, 25 Feb 2004 (UTC)
Heh, you guys argue a lot.

I agree with Michael -- what he is saying is standard nomenclature. If either one of you was wrong, though, there's no need to throw words like "two shits" around to prove your point. :-)

I agree; as I said, Kevin Baas often seems very angry; I don't know why. Michael Hardy 02:17, 27 Feb 2004 (UTC)

The distribution just describes the probability P(X=x) of an event X=x happening. Usually the value of the variable is not considered a parameter

...and if it is so considered, it certainly does not parametrize a family of probability distributions. Each value of λ determines which probability distribution we're looking at. So the probability distribution is determined by the value of just one parameter. Michael Hardy 02:20, 27 Feb 2004 (UTC)
Perhaps this is where our problem of communication lies. Where you consider a probability distribution as parameterized, I consider the probability distribution in-itself. A "discrete" probability distribution is one that can be represented by a finite set of symbols, without recourse to any formulas, and is, likewise, a selection from a finite set of possibilities. A continuous one, on the other hand, does not meet these constraints. -- Kevin Baas 05:41, 28 Feb 2004 (UTC)

(at least I have never seen anyone talk about it that way). Certainly the final value of the distribution function depends on its parameters and on x, but "parameters" usually refers to the other values that characterize that particular distribution, e.g. for the binomial distribution you have n and p (the number of tosses, the probability of a success per toss).

Maybe that's the source of your debates? I guess you can refer to x as being the "argument" to the function, instead of a parameter of the function.

Finally, as to your examples, you can have various distributions depending on the situation is. As you mentioned, you can make a Markov process out of the poisson distribution (by making the Mean parameter, i'll call it <math>\lambda</math>, vary proportionally with the time elapsed, so it becomes <math>\lambda</math>t). Then the probability of the first success is exponentially distributed. That's a different distribution and it does depend on two parameters. (It's a special case of the Gamma distribution, if you want to say that.) The poisson distribution is one of the only distributions that has one parameter (the mean), because it describes pretty simple things. And yes, it is discrete.

PS: Aren't computable numbers those numbers that can be computed in a finite time? If so, I don't see why the probability of a binomial distribuion with parameters n and p is possibly non-computable. (This is to Michael, I guess.)

- Greg Magarshak 12:32, 26 Feb 2004 (UTC)

Because some numbers p between 0 and 1 are not computable. There are only countably many algorithms, after all. Michael Hardy 02:20, 27 Feb 2004 (UTC)
But the point is, Michael, that the number q between 0 and 1 is quite computable: it is q. The solution is a Godel number. -- Kevin Baas 17:57, 27 Feb 2004 (UTC)
I tried to give this comment the benefit of the doubt, but it doesn't make sense. "Most" (in the sense of cardinality, or in the sense of Lebesgue measure) numbers between 0 and 1 are not computable. Nothing stops "q" from being such a number. The statement about Gödel numbers appears to be nonsense; Gödel numbers are usually taken to be integers,
...What? Godel numbers are not integers. Godel numbers are elements of a set. Their symbolic representation is completely arbitrary.
but if one insists on some real-value Gödel-numbering system, the comment remains nonsense. The real parameter identifying a Bernoulli distribution need not be computable. Michael Hardy 00:56, 28 Feb 2004 (UTC)
My point is that you are thinking absolutely whereas the point of a computer is to think relatively; abstractly - such as abstract algebra. One can say, for instance, that the symbol "1" represents Chatin's constant, and then build axioms around that. (Too many axioms, and the system becomes logically inconsistent, too few and it is logically incomplete, and one can't have a complete and consistent system - this is what Godel proved.) Thus, yes, even though, starting from the standard system of mathematics, one cannot compute Chatin's constant, one can begin with a system that uses Chatin's constant as a basis, and Chatin's constant is thus quite computable. Ofcourse, one cannot construct from that system a combination of axioms that is topologically equaivalent to Chatin's constant, but that is irrelevant, we are still able to compute the value that we desire, in terms of our custom-tailored symbolic set. Is this clear? I feel I've stated it pretty unambiguously here. -- Kevin Baas 05:41, 28 Feb 2004 (UTC)

The above now seems clear, but that's no reason to call it a Gödel number. Michael Hardy 01:03, 29 Feb 2004 (UTC)

Guys, what I mean by computable here is that, given n and p I don't see what's so uncomputable about the Binomial distribution. Everything in the Binomial formula is computable. You can't stick a chaitin's constant anywhere in there. - Greg Magarshak 3/01/2004
The reason I am calling it a Godel number is because the entire theorem which involves Godel numbers is based on this view. Hence, the essay being entitled "On the formal incompleteness of Principia Mathematica and related systems". Indeed, any discussion of Godel numbers tacitly assumes this view. The reason to call it a Godel number is to invoke this context. Why else would one call it anything at all, if not to invoke a context? -- Kevin Baas 07:16, 29 Feb 2004 (UTC)

Re: I. J. Good and [1]. It may interest you to know that Bruno de Finetti did in fact refer to him as "Irving Good" in a "Farewell Lecture" delivered at the Istituto Matematico G. Castelnuevo on the 29th of November, 1976 (translated and published as Probability: Beware of Falsifications in "New Developments in the Applications of Bayesian Methods", Ahmet Ayka� and Carlo Brumat eds., 1977). -- Cyan 03:00, 2 Mar 2004 (UTC)~

Sugestion concerning the use of TeX on Wikipedia

On most browsers, TeX looks terrible when embedded in text, like this: <math>\int_0^1 x\,dx</math>. When it is "displayed", rather than embedded in text, it should be indented, like this:

<math>\int_{-\infty}^\infty 1\,dx</math>

and not like this:

<math>\int_{-\infty}^\infty 1\,dx.</math>

Michael Hardy 22:06, 8 Mar 2004 (UTC)

I agree with you. It looks better. Simple and elegant solution. -- Decumanus 22:16, 8 Mar 2004 (UTC)
But you can inline it like
<math>\int_{-\infty}^\infty1\, dx</math>
  which looks pretty good.
Herbee 11:58, 2004 Mar 16 (UTC)
On your browser, perhaps. On mine, Michael's original example looks perfectly fine; it's almost properly aligned and very nearly the proper size. OTOH, your "hackish" (no offense) alignment is completely misaligned! But it's all just coincidence, of course. On the machine I use at work, standard inline TeX looks awful. (I haven't checked this page on that machine.) This is why tinkering with the purely visual appearance of something on Wikipedia is not necessarily a good thing. BTW, before someone brings it up, one could argue that Michael's indenting of displayed TeX is not purely a visual choice, but also a somewhat semantic one. I mean, displayed math is indented (actually, centered) by default in TeX for a reason... - dcljr 21:20, 26 Jul 2004 (UTC)

Hello again, Michael. I noticed you adding an apostrophe to Descartes' theorem. That is an improvement in itself, but I had a reason to remain apostrophe-less. I have now added the complex Descartes theorem (as a section in the same article), but the two titles are now inconsistent. I've done what seemed best to me. What do you think?
Herbee 12:36, 2004 Mar 17 (UTC)

I think it's OK with the apostrophe in the title and with the one apostrophe-less section. Anyone looking for Descartes theorem with no apostrophe will get redirected appropriately. Michael Hardy 21:32, 17 Mar 2004 (UTC)

Michael, in the book "Proofs without words", there is another nice visual proof (using a circle) of Pythagorean theorem, attributed to "Michael Hardy",...any relation? Revolver 03:07, 19 Mar 2004 (UTC)

I seem to recall writing a proof of the inequality of arithmetic and geometric means that appeared under proof without words in the College Mathematics Journal; I suspect that is what you saw. Michael Hardy 23:57, 20 Mar 2004 (UTC)


Hi Michael, I'm interested in the fact you are the first contributer to the article iconostasis. It seems out of your main interest. Just curious, but can you let me know what makes you be interested in this field? Just an aesthetic interest or other? I study art philosophy and a would-be Eastern Orthodox faithful (Father David considers me unprepared to baptize yet now). KIZU 20:35, 20 Mar 2004 (UTC)

Partly it's just the esthetic appeal of polysyllabic Greek words. Although not a religious believer, I have also written on Wikipedia about some historical and technical aspects of Eastern Orthodoxy and Roman Catholicism. Michael Hardy 00:23, 22 Mar 2004 (UTC)
However, you know far less about the Orthodox Church than you think. For example, you installed the BLATANT LIE that the Orthodox Church cannot hold an Ecumenical Council without the participation of the Pope of Rome. What Orthodox Bishop taught you this? Where in Orthodox Catechism did you learn this? This claim is absolutely and outright false. It's the sort of thing that a Jesuit propaganda tract would promulgate.Dogface 22:47, 26 Mar 2004 (UTC)


It's seems like we are having a "little" Edit War on Newcomb's paradox. Ben insists that it IS NOT a paradox (he even putted a silly green box with an irony by David Hume -- see Newcomb's paradox history page). I yet talked to him but he doesnt want to hear me!

See the history pages on Newcomb's paradox and William Newcomb for more info

And please, edit this page, its more than 37k long --Dobrowsky Mdob 01:28, 22 Mar 2004 (UTC)

Newcomb's Paradox

Newcomb's paradox is not a paradox because reverse causation is defined in the problem. Please return the David Hume quotation. Bensaccount 04:05, 22 Mar 2004 (UTC)

Hi, I saw your note about not finding Insitute Professors. I put in a request to the MIT library to see if they can provide one. If they respond I will let you know. AJim 02:41, 27 Mar 2004 (UTC)

Michael, thanks for the articles on holomorphic and analytic functions, esp. the proof of holomorphic ==> analytic. Some classes don't make the distinction clear. Revolver 05:32, 1 Apr 2004 (UTC)

Thanks -- I'm glad someone's reading this stuff. Michael Hardy 00:55, 3 Apr 2004 (UTC)


thanks for your edit on statististical efficiency. Would you cast your eye over my recent Cochran's theorem? I ask because I'm trying to get my brain round it and I figure that writing a wiki article is the best way to learn.


Robinh 08:31, 5 Apr 2004 (UTC)

legal vs natural persons

Hi Michael. I'm not a legal expert; but, this is how it has been explained to me. I would be glad to be corrected.

Although a slave is in every natural sense a human being and fully a person, the law considered these people in a legal sense as 2/3 3/5 of a person. Likewise in abortion law, the issue of whether the unborn child is, in a natural sense, a human being, although not entirely irrelevant, is legally distinct from how the law regards the child. Unless legal status of personhood is recognized, natural personhood doesn't necessarily correspond with legal personhood. The same issues may come into play in euthanasia, if I understand them correctly. The person in a legal sense has standing before the law, which the person considered naturally does not have - so that I may by law (in my state of Oregon, for example) make provision to protect my doctor from prosecutiion for murder for putting my natural self to death. I think that this is what the paragraph was referring to, which spoke of a "non-correspondence between natural and legal" status of personhood. Mkmcconn 04:14, 9 Apr 2004 (UTC)

I've answered on your talk page. Michael Hardy 18:37, 9 Apr 2004 (UTC)
The concept of a legal person concerns "entities", not "organizations": organizations are entities, but so are people. Returning to the example, an unborn child is legally considered a person only so far as necessary to protect its rights should the child be born. If it is not born, then its personhood is not recognized by the courts, so that reparation for tortious damages cannot be sought on the child's behalf, unless the child is later born. The legal concept of personhood is involved here in a very clear way, as in the old case of slaves as well. The point is that whatever the courts recognizes as a person, is a person - regardless of whether that entity is naturally considered a person. And in a few strange cases, even natural persons are not always considered fully a person in a legal sense.
Michael, It seems to me that the only reason that the article does not deal with this issue directly, is because it is not written to do so; not because "legal personhood" is irrelevant to these issues. Mkmcconn 21:32, 9 Apr 2004 (UTC)

Perhaps legal personhood could deal with the issues you raise and legal personality (now a redirect page) with the "organizations" issue. It seems to me that when people use the phrase legal person or legal personality, they're always talking about organizations that the law treats in some circumstances as if they are persons. Michael Hardy 21:48, 9 Apr 2004 (UTC)

That's a good suggestion. And since "Legal person" almost always refers to organizations, it appears, [[legal personhood]] seems to be the appropriate place for the other concepts to be dealt with. A see also section can be added to the "legal person" article. Thanks for the interaction. Mkmcconn 22:56, 9 Apr 2004 (UTC)


Thanks for fixing up law of agency... --Rj 03:07, May 3, 2004 (UTC)

Mann-Whitney and other stats matters

Hi Michael-- thanks for fixing up the maths in the Mann-Whitney U test. I have just put up a page on the Page test, a little known but very useful generalisation of Spearman's rank correlation coefficient, which so far as I can see is otherwise undocumented on the web. The maths on that needs fixing, too, but I will get round to it eventually... More important, would you be able to have a look at the terminology etc? I am a user of stats rather than a statistician and there is always a risk I have committed a solecism. I'd be grateful.

I have added it to the list of statistical topics. Do you think we should have a subsidiary list of statistical significance tests?

seglea 01:36, 5 May 2004 (UTC)

Capital Letters In Headlines Suck

Please stop worshipping capital letters like this

I couldn't agree more. I try to neutralize capital letters myself whenever I see them (though, since English isn't my primary language, I sometimes hesitate). Keep up the good work (with the capital letters and with everything else). - Fredrik (talk) 18:05, 3 Jun 2004 (UTC)

Capitalization in Mathematics (please, not mathematics)

Ohhhhhh... this is definitely a ridiculous aesthetic issue... Imagine, what would happen when we start writing code in Wikipedia more diligently: Is there a reason on engaging into a war of coding styles? Some will argue that we must not use GNU-indentation but Java-indentation; that pascal-casing is better than camel-casing. XML-documentation or Javadoc-documentation? Ahhhgrrr...


  • G�del's first incompleteness theorem
  • algebraic geometry

what's next?

  • P = Np instead of P = NP

I don't really, really, really, mind; this is not a very important issue, but I do mind about it. The subject essence is still there in the article. But this is starting to turn ridiculous.

I concede that there are cases of frivolity... I was "wondering" wether I should write Non-Logical Axioms instead of Non-logical axioms. I chose the later, simply because there is no great sacrifice in acknowledging that sticking with the style of the former string would be just childish (I also understood that Non-logical Axioms has no better value as a title than its purpose.) On the other hand, pieces of work and subject fields are more proper nouns than mere descriptions of human activities:

  • Little Jon loves studying Algebraic Geometry on Sundays.
  • Little Jon loves doing Gardening on Sundays.

The first one is (must) almost sacredly be capitalized, while the second sentece would be arguably ridiculous (with all due respect to Gardeners). I do appreciate grammatical and spelling corrections (that is at least one of the good things of this Wiki-Wiki or whatever).

  • Carl is studying Little Jon's Law of Large Green Bananas.
  • Carl is studying little Jon's law of large green bananas.

Where is the point here? I prefer the former and would reprint my paper if it appeared as the later.

There is also something that I whould like you to consider: go and pick any of the Springer Verlag books. Theorems that can be referred to by anthing other than Theorem 5.14 are capitalized: not only in Pythagorean Theorem and Borel-Cantelli Lemma, but we also have the Closed Graph Theorem and the Binomial Theorem. And... ohhh yeah,

  • Real Algebraic Geometry


  • Holomorphic Foliations in Banach subspaces of codimension 1

appear as such in every single time you can read them.

--[[User:Irr�ti�nal|irr�ti�nal]] 03:06, 20 Aug 2004 (UTC)

Statistical ensembles


Here's a suggestion to make the statistical ensemble article more consistent with the quantum statistical mechanics article. Two important operational notions on ensembles are

  • Testing statistical equivalence of ensembles
  • Probabilistic sampling from ensembles A, B with probability p 1- p to form the convex combination of ensembles.

Since in the quantum mechanical case, ensembles are modelled by density operators this is a cleaner approach to the pure-state mixed-state dichotomy.

Moreover I like to think of the concept of ensemble as being itself operationally defined in the following sense: there is some laboratory procedure for producing systems which are instances of this ensemble. By repeating this laboratory procedure we obtain a sequence of systems X1, X2 .... Xk... Exactly how this sequential ensemble defines a state might be left out of the article, but here is an explanation: A sequential ensemble defines a state by the time average of measurements: e.g. for each observable A (for the reader's refernce this is discussed in the article quantum logic) we obtain a sequence of measured values (e.g. by observing a dial on a gauge) Meas(A, Xn). The time average

<math> \sigma(A) = \lim_{N \rightarrow \infty} \frac{1}{N} \sum_{k=1}^N \operatorname{Meas}(A, X_k) </math>

Of course there is a kind of ergodicity assumption here, but for explaining the operational meaning of ensemble I think this is good enough. Using Gleason's theorem this is given by a density operator S:

<math> \sigma(A) = \operatorname{Tr}(A S) </math>

In fact, we only need to know this for A a quantum question (in the sense of Birkoff von Neumann Mackey) i.e. a self-adjoint projection.

Whaddya think?

CSTAR 03:45, 12 Jun 2004 (UTC)

Hasse diagram

I think you miss the subtlety of the point I added at Hasse diagram. The fact is that one need not define the structure of the diagram in terms of a cover relation, but can bypass this and just do so in terms of the relation itself and omit self-loops. Perhaps it is more common to define the structure in terms of a cover relation, and perhaps it is "better" in some way to do this, but do you think it is best to leave the point out about bypassing the cover relation entirely - as it is possible to do so, is it not? Dysprosia 13:59, 15 Jun 2004 (UTC)

I think you're the one who's missing the point and making things too complicated. I've responded on your talk page. Michael Hardy 20:16, 15 Jun 2004 (UTC)
You see, this is the way I was originally taught re the diagrams. Either they have cocked up, or I've cocked up somewhere - there may have been some other restrictions - I'll have to look into it. Dysprosia 22:07, 15 Jun 2004 (UTC)
Ok, I think I've found the problem. Presumably in your "over-crowded" diagram you ignore the requirement of only representing an edge between a vertex and its immediate predecessor, this, of course, is necessary also.
That's what the cover relation is!!

I still think that having to write it in terms of introducing another relation is a little cumbersome.

You mean calling it by a different name, the "cover relation", rather than saying "only representing an edge between a vertex and its immediate predecessor", is what makes it too cumbersome for you?

I have something in mind for the page - it would be nice to be as explicit as possible and perhaps introduce why we use a cover relation because of this, but I'd be interested to know what you think. Dysprosia 22:18, 15 Jun 2004 (UTC)

Replied at my talk page. Dysprosia 22:29, 15 Jun 2004 (UTC)
Done. I hope you don't find too much at fault with what I've done. Dysprosia 01:49, 16 Jun 2004 (UTC)
I've just rearranged it a bit, putting the long discussion after the easy part. Michael Hardy 01:53, 16 Jun 2004 (UTC)
That seems to me to be a little odd - should we not motivate (and also mention) the ideas and concepts before we use them? Dysprosia 01:56, 16 Jun 2004 (UTC)
Depends on context. In this case I don't see why any motivation is needed, since this seems like a perfectly obvious way to view a finite poset. And the definition and pictures make the matter really simple, whereas the section titled "motivation" seems much less so. Michael Hardy 20:54, 16 Jun 2004 (UTC)
You might not see why it is needed, but someone else may find it useful. As it stands, the article introduces "y covers x" without any explanation in the first paragraph, and gives examples of Hasse diagrams, thus, without any explanation on how to derive them, and then explains everything after the fact. That does not make for a well constructed article, in my opinion. If you are then thinkign about adding some explanation in the first few paragraphs, then why not just explain why Hasse diagrams are useful, and why they are constructed in this manner, as I have done so? Dysprosia 05:06, 17 Jun 2004 (UTC)
Any objections to putting it back the way it was? Dysprosia 12:21, 19 Jun 2004 (UTC)
I'd rather not, since the definition and examples seem so simple and easily understood; I would not want to give the impression that the topic is a lot more complicated than it really is, by implying that the definition and examples cannot be understood without all that other material coming first. (This is not to say that there should be no other material, of course.) Michael Hardy 22:37, 20 Jun 2004 (UTC)
All right, but the way the text is structured currently cannot stand. I shall try and fix it. 22:41, 20 Jun 2004 (UTC)

Where did the page go?

Special:Undelete/Single_photon_emission_computerized_tomography: the log shows you, at 01:19, 25 Jun 2004, moving it to '''Why SPECT?''' Similar to X-ray Computed Tomography (CT) or Magnetic Resonance Imaging (MRI), Single Photon Emission Computed Tomography (SPECT) allows us to visualize functional information about; the resulting redirect page was, as you might expect, severely broken. The long title to which you moved it still shows up in the full-text search results, but following the link takes me to a non-existent page. Do you know what happened? —No-One Jones 06:14, 25 Jun 2004 (UTC)

No, I don't -- that's why I asked the question. So far no one's answered, as far as I know. Michael Hardy 20:44, 29 Jun 2004 (UTC)

Re log-odds: yes, my mistake, sorry. Log-odds is the same as logit, not a difference of logits. [2]. I'll move note over to logit. -- hike395 15:28, 25 Jun 2004 (UTC)


I still don't care to learn trig, and have forgotten all I ever knew, but bravo on What is trigonometry used for? That's a great article. jengod 00:15, Jun 26, 2004 (UTC)

Math tags are nice, but...

The <math> tags are nice, but we probably want to refrain from using it whenever there is a reasonable substitute. The pictures not only cost bandwidth, but also hurt the eyes when mixed in-line. Also, I think it is good to respect other people's styles and let them use their own style of spacing, numbering, and such.
Peter Kwok 18:50, 2004 Jun 29 (UTC)

I'm surprised that you're addressing this to me, since I have done dozens of edits that I summarized by saying that although TeX looks good in "displays", it often looks terrible on Wikipedia when embedded in lines of text; in those edits I changed TeX to alternative notations. I think I am the foremost proponent of the point of view that you've been urging. (Although I've been notably less fastidious about this after the most recent new server was put in place, since TeX now gets centered rather than lifted above the line.) Michael Hardy 20:41, 29 Jun 2004 (UTC)

Well, no offence, but recently I couldn't help but notice that your name appeared in a bunch edits (e.g. subadditive function, Lubell-Yamamoto-Meshalkin inequality, etc.) unrelated to the correctness or accuracy of those articles. In some places, I feel that your addition of <math> tags were not necessary. Perhaps having a little toleration to other people's style would be good? It is almost like I am not even allowed to put the "in mathematics" part at the end of the first sentence and have to be corrected. While I understand that we all should respect each other's right of editing, I just feel that some of those edits were overdone and are counterproductive in the sense that it creates frustration and doesn't add value. I won't blow the whole thing out of proportion here. Just wanted to let you know where I stand.
Peter Kwok 00:33, 2004 Jun 30 (UTC)

I do not edit without intending to make the article better. "A k-set" is better than "An k-set" for obvious reasons. Putting "In mathematics," at the beginning is better than putting it after the concept being defined for two reasons: the latter interrupts the sentence, and in many cases the reader should be given the appropriate context first. Definitions should not say "is called", e.g., "An animal that barks is called a dog" is inferior style to "A dog is an animal that barks." I don't know why those edits would create frustration. I do know why I would expect them not only to add value, but to be perceived by readers as adding value.
I am very strongly opposed to the idea that only correctness and accuracy matter. The sort of edits I mention above add comprehensibility and memorability. Those who think smoothly flowing style does not matter as long as the semantic content is correct and accurate are very wrong-headed in that regard, in my view. Michael Hardy 22:37, 30 Jun 2004 (UTC)

No one is going to argue about grammar and spelling with you. My main problem is that your sense of "style superiority" is rather personal and unconvincing. I have already stated the reason why I disagreed with your choice, so I won't repeat them here. From where I see it, you are not making the articles better— you are just making other people write like you. And I strongly believe that kind of attitude doesn't help promote respect and cooperation among users.
Peter Kwok 15:07, 2004 Jul 1 (UTC)

I can't find the part where you explain why you disagreed with any of my particular choices. Putting in mathematics at the very beginning helps users who follow a link to an article without having any idea whether it's about stamp-collecting or religion or detective novels or botany, so that they don't have to wade through what to them may be incomprehensible technical language before finding out that it's mathematics. On a number of occasions I have started reading an incomprehensible sentence only to find out at the end of a long first sentence or even later that it's about characters in some novel I've never heard of, and I don't like that. If attending to that kind of editing is not your strong point, why not just leave it to others and concentrate on what you know, instead of taking personally something that is not? I don't think that it's just my own personal taste that says that
Chatoyancy is a term used by gemologists to refer to an optical phenomenon in which etc., etc.....
is not as good as
In gemology, chatoyancy is an optical phenomenon in which etc., etc.....,
and not only because the first sentence above is more complicated than it needs to be. Michael Hardy 19:37, 1 Jul 2004 (UTC)
PS: As far as your comment about "not making articles better" is concerned, I don't think it's unfair to mention that I've added more solid content to Wikipedia's math articles, both in the form of a very large number of new articles and in the form of additions to already-existing articles, than all but perhaps four or five other Wikipedians, if that many. See the list of new articles I have created at User:Michael Hardy. Michael Hardy 19:54, 1 Jul 2004 (UTC)

Introduction to articles (Style)

Hi, I have read your conversation with Peter Kwok and I totally agree with you. I think your edits on the style of exisiting articles are very good and greatly increase the comprehensibility of the articles. Personal style is nice and all but someone needs to keep the style (design) of the articles consistent.

But enough of the compliments here is my question: How do I write the introductory sentence in an article on mathematics if I want to say

  1. The article is on mathematics
  2. Denote the subfield of mathematics the article belongs to
  3. Denote the name of the object I describe in the article

For example an article on Triangular matrices.

In linear algebra, a subfield of mathematics, a triangular matrix is a special kind of matrix blah,blah.

This sound ok, but I would like to have the more general category (mathematics) before the subfield (linear algebra) so focus of the sentence narrows down as the reader progresses through the sentence.

Any ideas ? Or is there already some sort of convention in wikipedia ? MathMartin 11:21, 1 Jul 2004 (UTC)

Thank you for the vote of confidence.
In several articles on combinatorics I've written "In [[combinatorics | combinatorial]] [[mathematics]]". Maybe "In the [[mathematics | mathematical]] discipline of [[linear algebra]], a triangular matrix is ..." would do it. Michael Hardy 19:58, 1 Jul 2004 (UTC)

I've hopefully improved the article. Is it more comprehensible? Dysprosia 09:38, 2 Jul 2004 (UTC)

Replied at my talk page. Dysprosia 09:36, 4 Jul 2004 (UTC)

Hasse diagram: pictures

Your pictures in the article on Hasse diagrams are fine, but their encoding (jpg) is rather unfortunate. Pictures that only contain huge areas of single colors can nicely (and lossless) be compressed as png's. I hope you still got the (xfig??) sources. Just export them as PNG and they will be much smaller and of much better quality. I added some more pictures to the page -- just compare their size and look (they were resized with The Gimp, so there is some grayskale interpolation which makes the files bigger ;-) --[[User:Markus Kr�tzsch|Markus Kr�tzsch]] 01:04, 8 Jul 2004 (UTC)

civic religion

Your are right. I intend to add patriotism (and so on) later, after I had improved the page; it will be quite long at the end, it really already is. I appreciate your comments though, its nice to get some input. Anywho, stop by Causes of World War II and give me your opinion there as well. Thanks--naryathegreat 02:48, Jul 15, 2004 (UTC)

Also, Civic religion is a better term than state religion, which is something else, as the article points out. And I hope that you would take some time to evaluate the premise before you added those nice little comments to the page. I don't appreciate comments like "it reads like somebody's high school project". There is also already an article on patriotism and nationalism. I think I'll add a paragraph that talks about pattriotism and nationalism, but civic religion seems to be a term that lends itself to an extreme, not in the same was as civil religion, which might be what you are describing (that page does not cover my topic).--naryathegreat 02:53, Jul 15, 2004 (UTC)

Scratch that--the comment was by another user, i just didn't notice it, sorry. You were a lot kinder than I gave you credit for.--naryathegreat 18:18, Jul 15, 2004 (UTC)

Nope. You can't just redirect a page because you don't like it or because you disagree-you need more discussion than that. So it's back, and this time, I've saved it so it will be easier to replace--you need to be careful, you can easily offend people with quick and rash actions like these.--naryathegreat 21:19, Jul 17, 2004 (UTC)

I didn't think it was quick and rash; it was after several days of discussion in which it seemed that various interested parties gave their views. Michael Hardy 21:23, 17 Jul 2004 (UTC)

There isn't near enough input to do that. Second, I see no way that you can accurately describe this type of extreme on that page (which I already have a low enough opinion of). It lends itself to benign forms of patriotism and such...not cult of personality extremes. And I have looked at the Cult of personality page, and it seems to already be long enough and have some good info. I just didn't see how I could fit this into that page without causing a big argument. And I wanted to avoid that. However, some of us seem to do that either way. This is why Wikipedia is coming apart at the seams. Dear me, another year and its gone...--naryathegreat 21:29, Jul 17, 2004 (UTC)

Hyperbole at its most hyperbolic. No, it's just an argument about one article. For every article that's argued about like this, a thousand others are being built steadily. Michael Hardy 21:34, 17 Jul 2004 (UTC)
... and how much input is enough? It doesn't seem as if the number of people interested in this article is huge. Michael Hardy 21:35, 17 Jul 2004 (UTC)

Then I don't understand why you care.--naryathegreat 21:38, Jul 17, 2004 (UTC)

Because the number of people whose interest it may engage later may be much larger, and because there are also those who read but do not edit. Michael Hardy 21:40, 17 Jul 2004 (UTC)

D(X) is used in Russian mathematics books extensively, maybe in English it is never used. In any case, the page obviously lacked a designation for variance, σ2 is commonly used, but is very inconvenient if you consider more than one variable. I don't mind your change, but let me assure you that I have not ever met var()/Var() until a few years ago and always saw and used D().

Paul Pogonyshev 21:53, 17 Jul 2004 (UTC)

Oh. OK. Thanks. -Stevertigo

OK, fine. -Stevertigo 21:09, 19 Jul 2004 (UTC)

Rest, residue, and remainder

(From merism) --- I don't use that one myself, but you are right; I have seen it. Smerdis of Tl�n 02:29, 21 Jul 2004 (UTC)

Yes, since you asked, I am in fact a lawyer. A smalltown lawyer, fortunately. Smerdis of Tl�n 18:39, 21 Jul 2004 (UTC)


Probabilistic foam. -SV 16:47, 29 Jul 2004 (UTC)


Dear god, the whole categorization scheme is a mess. People went off willy nilly and created whatever category made sense instead of trying to use some established categorization scheme, or even discussing them much. I put that in that category pragmatically as the category that discussed that kind of issue currently, not to say it was correct or anything. - Taxman 22:04, Jul 29, 2004 (UTC)

Imaginary unit TeX markup

What TeX markup do you use for the imaginary unit ? I have used <math>\mathrm{i}</math> in trigonometric polynomial. Is this the correct way to do it ? MathMartin 13:42, 5 Aug 2004 (UTC)

I've been accustomed to writing it like this:
Michael Hardy 21:29, 6 Aug 2004 (UTC)

I recently found the following version in a textbook and like it better because i does not look like a variable


And no need to duplicate your answer on my talk page. When I post a comment on someone's talk page I usually put a watch on the page. MathMartin 22:46, 6 Aug 2004 (UTC)

Names of World Countries in Greek

Here is a list of the countries of the world in Greek. The names are not in English, but their internet domains are; e.g., Φιλιππίνες (Filipp�nes) is PH which is the Philippines.

--Chris 00:45, 16 Aug 2004 (UTC)

Thanks. Michael Hardy 00:57, 16 Aug 2004 (UTC)
No prob. BTW, I found an even better page! --Chris 08:25, 16 Aug 2004 (UTC)

The business and economics forum

Anouncing the introduction of The Business and Economics Forum. It is a "place" where those of us with an interest in the business and economics section of Wikipedia can "meet" and discuss issues. Please drop by: the more contributors, the greater its usefulness. If you know of other Wikipedians who might be interested, please send this to them.

mydogategodshat 19:12, 26 Aug 2004 (UTC)

TeX style guide

Hi, i would like to start a TeX style guide. People like you and Mat cross corrected my TeX but I guess after some time you get bored to point out the same mistakes all the time. Aside from the TeX style there could be advice how to name variables so the wikipedia math articles are consistent (e.g. <math>\gamma</math> for a curve because it is the c in the greek alphabet). Is there already such a page in wikipedia ? Do you know of any style guide outside wikipedia or is the correct TeX style just an oral tradition ? Where would I put such a page ? Thanks. MathMartin 10:18, 27 Aug 2004 (UTC)

Hello. I think I could contribute a number of things to such a style guide, but I'm not prepared to actually start the thing. Michael Hardy 22:17, 28 Aug 2004 (UTC)
I started a page at User:MathMartin/TeX_Styleguide. Not much content yet. I will treat it as a repository for informal style hints. If it grows big enough I will think about merging it into Wikipedia:WikiProject_Mathematics. You are of course very much invited to contribute as I really appreciate your style tips (TeX and English). I believe mathematics is not so much about discovering facts but about clarifying problems until the solutions becomes apparent (ala the late Wittgenstein). Therefore clear and precise language is very important for me. MathMartin 23:09, 2 Sep 2004 (UTC)


You Asked About My Capitalization. I'm Not Sure What You Mean Exactly... PERhaps yOU CouLd Give Me a Link? *hahaha* No, seriously, I don't want to be randomly capitalizing stuff. Please point out where I did and I'll cut it out. Thanks!--SFoskett 19:03, Sep 1, 2004 (UTC)

Storage area network and fibre channel are articles I recently moved, as are some to which they link. I don't remember which among them you originated. Michael Hardy 19:08, 1 Sep 2004 (UTC)
As I just spelled out in Talk:Storage area network, these terms are always capitalized in the industry. Despite what the rest of the world may think, lots of computer terms get capitalized, and that IS the standard. Perhaps Wiki has some other area for discussing this? In the mean time, I intend to return the capitals to those articles.--SFoskett 19:11, Sep 1, 2004 (UTC)
nice. a "capital" addition to "food-borne infections" Sfahey 22:56, 1 Sep 2004 (UTC)

How's 'bout this: Wikipedia_talk:Manual_of_Style#Capitalization_of_computer_terms --SFoskett 13:56, Sep 2, 2004 (UTC)

Statistics lead section

I've proposed a new lead section for the Statistics article. See Talk:Statistics#My attempt at article lead section and my comment immediately above that one. Comments welcome. - dcljr 19:38, 2 Sep 2004 (UTC)

Orthogonal polynomials

Thanks for the response. Dysprosia 01:22, 6 Sep 2004 (UTC)

More TeXnical questions

Can you explain why in Tikhonov regularization#Generalized Tikhonov regularization there are two formulas in LaTex form between math containers, but one gets typeset as

<math>\|Ax-b\|_P^2 + \alpha^2\|x-x_0\|_Q^2</math>

while the other is rendered in HTML?

<math>x_0 + (A^T PA + Q)^{-1} A^T P(b-Ax_0).</math>

is it just due to their complexity? (by the way, that is how it appears on this page as well with the browser and settings I am using now). Also, I had attempted to keep to a convention of using bold x vectors and italic A matrices. Should we not do the same in the pseudo TeX bits? using mathbf for vectors? It would still look a bit inconsitent. Ideally I would like to do it in such a way that it all works when everyone has switched to a browser that renders MATHML well without needing to fix everything by hand. Billlion 13:51, 6 Sep 2004 (UTC)


This is a brief answer off the top of my head; I'll ask my mom (who's born in Greece) for details later. But I'm pretty sure that Ellada is the colloquial modern Greek word for the country, generally used in conversation any time the country name is needed. Ellas is an older word for the country, these days with an almost poetic ring to it. It might have something to do with the use of Katharevousa up until the 1970s; I think Ellada may be a dimotiki word. --Delirium 19:11, Sep 7, 2004 (UTC)


I will not get mad, Mr. Hardy, as some people might, but take a look at my 0/0 page now. You were absolutely right. I have changed it. --Afuller2028 23:43, 9 Sep 2004 (UTC)

Great circle distance

The diameter is lesser at the poles, making the radius of curvature greater. Check out the remark in the GIS FAQ referenced in the article. Also, if you look at the image of the oblate spheroid it's obvious that you get larger distances than on a sphere near the poles and smaller ones near the equator. Fuzzy Logic 21:04, 13 Sep 2004 (UTC)

Oh ... I was hasty; it did say "... of curvature". Michael Hardy 21:11, 13 Sep 2004 (UTC)

"Paradoxical" nature of 0/0

I'm writing something up, eventually I'll get done, and I'll let you have a look at it. It's only a paradox in the same sense as "What happens when an irresistable force meets and immovable object?" is a paradox. At some stage in their learning, most people find the idea of subtracting 10 from 6 mind-boggling. The Greeks minds' boggled at irrationals. I still don't feel that imaginary and complex numbers are intuitive. 0/0 is paradoxical because people believe that you should be able to divide anything by anything and come up with "the" answer.

Take a crowd of people who have no more than high-school math and ask them "what's the batting average of someone who has never been to bat?" Most of them will say "zero." If you say, "well, why not 1.000 since they've never missed" a few people will see there's something puzzling. If you say "But the batting average could equally well be 0.500 or 1.500 or -2.00 or 10000.000" they won't get it. It needs to be explained. As I say, when I've got something written I'll let you know. [[User:Dpbsmith|Dpbsmith (talk)]] 22:32, 17 Sep 2004 (UTC)

More on 0/0

(Written to User:Barnaby dawson and copied here).

What you've done is very good. I'm actually experiencing sibling-rivalry-like pangs because I started working on this—you can see what I've got on User:Dpbsmith/temp—but what you've got is much more straightforward and to the point. I might come back and polish it sometime. What I've written myself currently has too much in it about numbers and intuition and not enough about 0/0.

I think you should definitely copy what you have to a temporary location somewhere in case the 0/0 page does get deleted. I'm not sure where this material should go. It could go in Division by zero or Indeterminate form or possibly on a new page, Zero divided by zero. I'm going to put these comments on Michael Hardy's talk page, too, and see if he has any thoughts.

Actually, I have a technical question for Michael Hardy. It's one of the things that has hung me up a bit. What is the most correct answer to the question "What is the value of sin(0)/0?" I guess the question is, what is the meaning of "sin(0)/0"? If it means the value of sin(0) divided by 0, then the answer is "indeterminate" or "NaN" (not a number), as I don't believe 0/0 is part of any definition of "number" that has ever been proposed. On the other hand, if it means "the limit of sin(x)/x as x approaches zero," the answer is not indeterminate at all, it is 1. It just "feels wrong" to me to say that sin(0)/0 is indeterminate, though; I feel that it "is" 1. Thoughts?

An explanation as to why certain mathematical terms have been defined in the way they have is not necessarily without merit. We must remember that those who are reading our encylopedia may not have a degree in mathematics as you and I have. For those who have not studied mathematics the material on the page "indeterminate form" does not explain why 0/0 is regarded as undefined. We should also be open minded enough to understand that some people may have a different notion of what a function is than we do. To explain to these people why indeterminate forms are regarded as such we must do more than discuss a few limits. I would point out that the space of analytic functions on riemann surfaces is an alternative intuitive way of viewing functions and many people will start with a similar intuitive notion of a function (they need not understand riemann surfaces or the complex plain to have some similar intuitive notion). The links given at the bottom of the page are interesting further reading for people interested in foundational issues. I archived the original text before the revert and I am going to put up a new page using this text: zero divided by zero. I should point out that the decision on the page cannot be read as a decision on the rewrite as the voting after the rewrite was 4 to keep 1 to delete. Barnaby dawson 10:12, 20 Sep 2004 (UTC)

LaTeX question

Hi, do you know how I can produce diagonal dots pointing upwards ? Like <math>\ddots</math> but mirrored on the horizontal axis. Google didn't know or would not tell me.MathMartin 13:41, 22 Sep 2004 (UTC)


Since you seem to be Wikipedia's resident mathematical articles expert, I was wondering whether you would mind possibly adding in TeX to Srinivasa Ramanujan some formulas he came up with? It seems unfortunate that on a page about someone who came up with some very unusual and remarkable formulas that we don't see any at all. --Lowellian 07:34, Sep 23, 2004 (UTC)

So did your response mean you were going to work on Ramanujan or that I should go find someone else? Oh, by the way, please post on my Talk page, not my User page. --Lowellian 22:00, Sep 23, 2004 (UTC)

Okay. Happy editing on whatever you work on instead. --Lowellian 22:06, Sep 23, 2004 (UTC)

Headings that suck

I have noticed quite a few occasions when you have dealt to headings that stink something awful. Take a look at 3-19 Shooting Incident which I think lacks, um, just about everything. I'm sick of being bold around here. You interested in fixing it? Cheers Moriori 04:18, Sep 24, 2004 (UTC)

Examples of contour integration

Let me explain the reasoning for what I have done.

It is not the best idea to centralize all examples relating to a certain topic in one isolated page. I am sure that you are aware that it is not true that the only way to calculate contour integrals in complex analysis is by means of the residue theorem. I had moved the example you refer to, to Residue theorem. I had not removed the content completely, and have not made a judgement call to the example content as I think you may have thought I have done ("but it's good example").

Having examples placed in that article that deals with the topic serves a greater benefit to readers in that there is, immediately, an application of the residue theorem (or whatever the example deals with) in that article, and they need not have to click around just to see this. Observe further that an example that deals primarily with the Cauchy integral formula is placed at that article, and not at an isolated examples page, where it is more inaccessible.

Do you not agree with me that it is better to keep examples specific and appropriate to certain topics, and thus keep these examples with their respective topics?

Your point about the redirect however is pertinent, I will rewrite Examples of contour integration to reflect the fact that these examples are elsewhere. Dysprosia 06:29, 25 Sep 2004 (UTC)

I've restored the example again. I think you've missed the point.

I'm sorry, I wasn't aware that there was some point to get. If there is some sort of underlying point to get, as I see it, is that examples that deal with a certain topic should be placed in the article's page. I don't understand your objection to this.

This example is almost too complicated to appear on the page titled residue theorem; it's too complicated to be the first example on that page,

I disagree, I think it illustrates it adequately. If you however think it is indeed too difficult, it doesn't mean that the example needs to be isolated - it only means that a simpler example should perhaps be provided (which I'm sure should not be difficult), along with the more in-depth one.

The examples for this page are not supposed to explain what the residue theorem says, but rather how to use it for certain kinds of integrals and sums.

Which is all the more reason it should be on the residue theorem page - what better place to put an example of the application and use residue theorem on the residue theorem page! Dysprosia 01:34, 26 Sep 2004 (UTC)

But the residue theorem is not the only method involved. The point is that these are examples of how to reduce otherwise intractable integrals or sums often involving only real functions to tractable integrals along contours in the complex plane. That is not the main point of the article titled residue theorem. And some examples appropriate for the page in question would not cite the residue theorem at all! For some of the contour integrals, the heart of the matter is the limiting process rather than the residue theorem. Those would not be appropriate for the residue theorem page, but would fit in nicely here?

May I ask what has been your experience with this topic other than on Wikipedia? Michael Hardy 01:45, 26 Sep 2004 (UTC)

Of course it's not the only method involved, but I am sure that you agree that its use is the turning point of the example there. I could rewrite your example to not use the residue theorem and just use the Cauchy integral formula and then place it on the Cauchy integral formula page as a relevant example. I am also sure that you yourself can see this. What is key to what I am saying is that we should not isolate examples that deal with using various methods all on one page.

I think the problem here is your intended purpose of the "Examples" page. I think that there can be a much more fruitful article listed as "Methods of evaluating contour integrals" or the like, which deals with the process of evaluating contour integrals in general and is not just a holding page for a collection of disparate examples, which is suggested by the title of the "Examples" page.

If you're willing, let's make some headway on such a new page, which would deal with the general method, then redirect the "Examples" page to this new page. Does this sound like a reasonable solution to you?

May I ask what has been your experience with this topic other than on Wikipedia?

I don't wish to disclose that in such a public manner, here. What is important here is that I do know the relevant material, and that's all that should matter. Dysprosia 03:15, 26 Sep 2004 (UTC)

Better now? Dysprosia 03:47, 30 Sep 2004 (UTC)

Perhaps, except that it's been altered so that's it's about altogether different topic from one I intended

I thought your intent was to illustrate the method of evaluating contour integrals by example? Like I've mentioned before, my recast was more to emphasize this and not just be a holding page for a collection of examples.

That leaves the question of what to do about the links to this page.

I'll go through and fix them up if need be, later today. Dysprosia 01:08, 1 Oct 2004 (UTC)

I thought your intent was to illustrate the method of evaluating contour integrals by example?

No. My purpose was not to illustrate how to compute these things; if that had been my purpose, the example I put there would have been given a much lower priority; I would have used it only after a series of simpler examples, each intended to isolate some specific aspect of technique. That is one reason why I asked about your experience with this kind of thing; I suspected you hadn't really done much of this and therefore failed to understand the purpose. The purpose was to illustrate by example how the evaluation of integrals along closed contours in the complex plane can be used to find integrals along the real line or sums involving only real numbers. Michael Hardy 21:09, 1 Oct 2004 (UTC)

Michael, I'm getting a little annoyed here. If you would have read Methods of contour integration, you would have seen such gems as
These contour integrals are often used to evaluate integrals of real-valued functions along intervals on the real line, that cannot readily be found by methods involving only real variables.
the contour follows the part of the complex plane that describes the real-valued integral,
follows the part of the complex plane that describes the real-valued integral as chosen before (call it R)
, then we can directly calculate R.
The article (Methods of contour integration) does deal with how the evaluation of integrals along closed contours in the complex plane can be used to find integrals along the real line. It does so by demonstrating the various methods of evaluating these contour integrals. Do I need to further spell it out by moving the page again to something like Methods of contour integration used to evaluate real valued integrals?
Perhaps instead of insulting me by insinuating that I have no experience with this kind of thing you instead read what I'm trying to do and maybe help out by editing so the article is acceptable to you, too, instead of continually reverting to your previous version of the article elsewhere. Does this sound reasonable to you? Dysprosia 02:14, 2 Oct 2004 (UTC)

OCA Autocephaly

I'm adding this on the off-chance you're still interested in a question you asked on my talk page several months ago. I'm only an occasional contributor here and don't check it very often so I just noticed it now, but I figured better late than never. My apologies.

The issue with OCA autocephaly is that it was granted unilaterally by the Moscow Patriarchate. This would appear to be legitimate since the American Metropolia, as it was then known, was part of the Russian Church. However, Constantinople is promoting the theory that they and they alone has the authority to grant autocephaly and that therefore the OCA's autocephalous status is not valid. I'm not sure what they base this theory on, frankly, since historically that's simply not how it's worked.

The result is that the Slavic Churches generally recognize OCA autocephaly and the Hellenic Churches generally don't. There's little practical effect. Since as far as Constantinople is concerned the OCA is still part of the Church of Russia, the OCA primate's name doesn't appear in their diptychs. Were there to be a Pan-Orthodox council of some kind no OCA bishop could attend without controversy unless he appeared as part of the Russian delegation. But the OCA is in full Eucharistic communion with all the other Churches including those where its autocephaly is unrecognized. This is an administrative issue more than anything else.

There's no doubt a great deal of ulterior motive going on here. The native flock in Constantinople itself is reduced to a few thousand souls; barely enough to keep the place running. The lion's share of their income come from their American parishes. Money is also an issue for other Old World Churches in impoverished areas with substantial American flocks, such as Antioch. Were they to recognize OCA autocephaly, they would also perforce recognize it as the legitimate Orthodox Church of America and could no longer canonically justify their own presence there even were they to employ the mightiest of weasel words. Recognition would therefore seriously jeopardize their income stream. It's hard to blame them since left to their own resources they wouldn't have much, but it does leave the American Churches in a canonical mess.

Disclaimer: I belong to an OCA parish. Although my original remark was in the interest of NPOV, I have made no attempt to be such here. --Csernica 02:29, 29 Sep 2004 (UTC)


Okay, thanks for reassuring me about Northwest Angle. Three cheers for new maps. Thanks. jengod 02:38, Sep 30, 2004 (UTC)

Imaginary colors

Hi, yeah the "complimentary" was a typo. Although I believe the meaning of "complementary color" in the fashion world is more or less "complimentary"... Overall, the complementary color article would be scientifically superseded by an adequate complementary wavelength article. The guts of this is already laid out in the (my) dominant wavelength article. The information worth keeping at complementary color would be the historical/social stuff: painting primary/secondaries, fashion meanings, etc.

Imaginary colors: not my forte but it's good for my education to try to explain it, so I'll give it a shot. The canon is the textbook Color Science (and more recent variations) by Wyszecki and Stiles. I don't know what your background is, so forgive me my pedagogy.

If you check out International Commission on Illumination, you'll see the CIE 1931 representation of human perceivable color space (for the "standard observer"). The short story on imaginary colors is simply that anything outside the horseshoe shape is an imaginary stimulus; you can assign it coordinates in the color coordinates system, but it cannot actually be evoked in the human eye; it's "bluer than blue" or "redder than red", etc. This is a pretty trivial point; the more interesting question is "why would we care about imaginary stimuli?".

If you take a second look at the CIE diagram, you can tell immediately that this is an important question; look at the axes that the horseshoe shape is plotted on. These are not axes of real primary colors; the point 0,0 in the CIE x,y system is outside the range of perceivable colors. Weird! Why would the CIE parameterize their color space based on imaginary axes?

Okay, here's where primaries come in: as you can see at gamut, no three primaries are going to define a gamut triangle that covers the entire horseshoe of possible human perceivable colors. This often comes as a surprise to math types since the human visual system is based at the input level on a set of three detectors. It seems like if we could just pick one light spectrum that stimulates only the blue cone, one spectrum for red, and one spectrum for green, then of course we could stimulate the cones in any combination and thus produce any possible perceivable color; since the human color system starts with a parameterization of light spectra into three variables, shouldn't we need only three different primary stimuli to cover the entire space? The problem is that there is no spectrum that stimulates only the green cone, so it isn't possible to get the necessary three pure basis functions for generating all possible greens.


You can see this from the cone response functions in the plot at right. This plot shows the response amplitudes of the three cone types to pure monochromatic light stimuli of varying wavelengths. As you move along the x-axis, you are stimulating with different pure wavelengths (basically going through the rainbow spectrum from indigo to deep red). If you think about it, you can see that there is a problem in the area around 500-600 nm. For the red and blue primaries it's a no-brainer; you pick wavelengths at the extremes of the spectrum that only stimulate these cones individually, giving you maximal linear combinatorial flexibility. But what are you going to pick for your green primary color? Something around 500, where you get mostly green response, followed by red, followed by blue, or something around 600 where you get red response followed by green response? If you pick 500 for green primary, then you won't be able to recreate 600 with your three primaries because you won't have any way of getting green without adding blue, which you don't want for 600. If you pick 600 for your green primary, you won't be able to recreate 500, because your green primary always has too much red in it.

As a math type, you could probably state this as a linear algebra, dependent systems sort of conflict (in fact, if you can do this off the cuff, I'd like to hear how you'd describe it), but I'm not gonna get into that :). What the visually minded (myself) can see is that on the horseshoe CIE diagram, the greens problem reads out really nicely as the impossibility to cover the horseshoe with a (contained) triangle; you can cover the red and blue ends of the space pretty well with the corners of a triangle, but because of the bulge around the green perimeter, you aren't gonna be able to do justice to that area of the spectrum no matter what primary (triangle corner) you pick there.

In practical color science, there are ways to get experimental measurements defining only the green cone response. For example, you pick a green primary at 600 and then ask how much red must be subtracted from the stimulus in order to recreate 500. How this subtraction is calculated practically has to do with color matching experiments and we don't need to get into it. The point is, now we can cover the entire perceivable color space with RGB primaries, it just requires negative primary coefficients sometimes. This is ugly, but it's functional, so one version of the CIE horseshoe shape is actually plotted on RGB coordinates with part of the visible area extending into the negative coordinates (mostly for R but a little bit for G too).

However, the negative numbers are ugly, and make calculations harder (in turn making color technology more computationally demanding). Therefore, the standard CIE horseshoe is plotted on XYZ coordinates, a linear transformation of RGB that moves the visible area out of the negative ranges. So the XYZ coordinates are a transformation of real RGB primaries into more convenient, imaginary primaries.

Whew, that was a lot longer than I expected. Hopefully it was helpful. Let me know if you have more questions. Maybe a discussion like this will eventually become an article... So little time... --Chinasaur 03:22, 5 Oct 2004 (UTC)

Heartful Thanks

Michael, please accept my gratitude for the nice and perfect work you did in the Romanian Orthodox Church article. Much appreciated! And also your clean tidy pages, articles, and even driving licence are appreciated :O). We certainly need more of your candid, true editors like you! This was the ORIGINAL Wiki spirit, and with you I see it's not agonizing. Many thanks - irismeister 18:54, 2004 Oct 10 (UTC)

Thank you; I'm glad someone appreciates these things. Michael Hardy 19:29, 13 Oct 2004 (UTC)

Could have been worse

At least I didn't write "konsensos" Dogface 04:00, 13 Oct 2004 (UTC)

Gian-Carlo Rota

Hi, Mike! I don't know whether you've seen saw my suggestions for possible improvement at Talk:Gian-Carlo_Rota—especially the one that I didn't withdraw. If you haven't, I'd appreciate it if you'd take a look. —JerryFriedman 18:54, 13 Oct 2004 (UTC)

Margin of error

Hi, Michael. You may have noticed that the article made feature status, and I wanted to officially thank you and give you credit for starting the article and making valuable edits. I also recently changed some of the opening equations, and I wanted to ask your opinion about the display here. I am wondering if there might be a more visually appealing or appropriate way to list three similar formulas. Of course, your other comments and edits are always welcome, as well. Best, Andrew (Fadethree) 21:43, 13 Oct 2004 (UTC)

I made some edits and a reply at Talk:Margin of error. I always appreciate your edits, Michael. Also, I'm not sure how to edit the blurb, but if you'd like to update the main page blurb to reflect our edits to the opening, that would be great. Additionally, you'll note that I added a clearer MarginoferrorViz.png image, which the main page is not yet reflecting. Only if you have time, of course. Best, Andrew (Fadethree) 2:05, 19 Oct 2004 (UTC)
Never mind, I figured it out. Best, Andrew (Fadethree) 4:35, 19 Oct 2004 (UTC)

Hi Michael - I made the disambig as a result of the talk page discussion on whether it was a polling specific term - I was sort of hoping that someone who knew more than me on this would add usages in other fields - it used to link to something else that escapes me for a moment, but someone took it off saying it was not quite the same thing. Take a look and see if you can find the appropriate things to link to. Thanks for noticing, Mark Richards 18:15, 23 Oct 2004 (UTC)


Hi. I am searching for people interested in computer science and math. I found you via the history of the Boolean algebra article. I had a look at your userpage and understood that you have an interest in these areas, so I thought you might be interested to get invited in a new computer science project (not in wikipedia). See User:Npc/List. Thanks. Npc 21:06, 17 Oct 2004 (UTC)

Generalized Fourier series

Is there a reason for using \varphi instead of plain \phi? Dysprosia 03:00, 26 Oct 2004 (UTC)

It looks better and is less likely to be mistaken for <math>\varnothing</math> or <math>\emptyset</math> Michael Hardy 20:20, 26 Oct 2004 (UTC)

Infinite Monkey Theorem

I'm sorry, I don't understand. To quote the Manual of Style, "Use bold italics in the first sentence only for terms that would be italicized even if they were not set in bold, for example, book titles (this does not mean only terms that are always italicized; whether a word or phrase is italicized or not depends on context)." Infinite monkey theorem is not normally italicized. Regardless, the word "The" should not be capitalized at all. Andre (talk) 19:56, Oct 27, 2004 (UTC)

Name impersonator

User:MichelHardy looks like his username is designed to impersonate you, but it could be a coincidence. →Raul654 04:38, Oct 28, 2004 (UTC)


I agree it's a mess. Since I don't think any use is the clear winner (in the real world as a whole), I'd be OK with moving the MIT/computer slang stuff (I don't think it would work to try and separate those two, they are so deeply intertwined) to something like hack (technology slang), and turn hack into a redir to hack (disambiguation). Of course, then we'd have to go fix every page that references hack, but that's probably a good idea anyway, I'd expect that more than a few are to the wrong "hack" anyway. Noel 02:53, 29 Oct 2004 (UTC)

Question you might be well suited to answer

Wikipedia:Reference_desk#Question_transferred_from_Eikonal_equation_in_Gemotrical_optics, thanks it's way out of my league to even decide if it is a valid question. - Taxman 16:28, Oct 29, 2004 (UTC)

Accuracy dispute on Canon (fiction)

Before you put an accuracy dispute on any article it's a very good idea to triple-check your own accuracy. Your changes to the article relegated the definition of "canon" in fiction to a rather ironic "Some say", while you replaced it with the definition of "canon" as it would apply to Biblical canon. But that is why we have one page for Canon (fiction), one for Biblical canon, and a disambiguation page that tells you which is which. Your dismissive comment that what was there before your changes "looks as if it was written by popular-fiction types who know ONLY popular fiction" really begs the question of why they should not be trusted to write the article on canon in fiction. Who are you proposing as a better authority on the subject? -- Antaeus Feldspar 02:12, 1 Nov 2004 (UTC)

It is certainly not true that the definition I gave would apply only to the Biblical canon. Michael Hardy 02:33, 1 Nov 2004 (UTC)
Since you moved the discussion to my page, that's where I've responded. -- Antaeus Feldspar 17:09, 1 Nov 2004 (UTC)

Thank you

Thank you for your recent edit to the Mung Bean article. you are apparently one of the quiet strivers for excellence. Thanks for being a good example.Pedant 22:45, 2004 Nov 1 (UTC)

Infinite Monkeys

I added the Molson Canadian ads as it was for the 'pop culture' section of the article. Looking over the page again it would be better suited as part of the paragraph leading with Simpsons information, but I still feel its relevant as it was a huge national advertising campaign in Canada for a major product, and the whole focus on the ads was "an infinite number of monkeys at an infinite number of typewriters will eventually define all that is Canada."

Bacterial growth

If the number of bacteria is increasing exponentially, and each bacterium is reproducing at maximum rate, then the rate of increase can be increasing exponentially, no problems at all. RobertStar20 22:38, 2 Nov 2004 (UTC)

If what was meant was the each bacterium separately is reproducing at maximum rate, then the article is very unclear. Moreover, if each bacterium separately is reproducing faster at time t than at any other time, then one would expect slow per capita growth a later times, and therefore the growth rate is not exponential. In exponential growth, the per capita growth rate remains constant. If that varies, then growth is not exponential. Michael Hardy 22:46, 2 Nov 2004 (UTC)
If all the individual bacterium are separately reproducing at maximum rate, then the whole colony is at its maximum rate at that point in time, i.e. it is incapable of reproducing any faster. However, I agree that the per capita growth rate at later times will be slower, so it is indeed not technically exponential. Looking at the exponential growth page, maybe the logistic function is what it really is... but isn't this a bit too mathematical perhaps? We need a word which means increasing at an increasing rate, but not necessarily exponentially. As for the graph being incorrect, it's a log y-axis, so an exponential curve will become straight... if only it were actually exponential :-). [Unrelated question: do your comments on this page automatically appear on my talk page or what?] RobertStar20 23:20, 2 Nov 2004 (UTC)

Atomic orbital

I see you've cut back my liberal use of the <math>...</math> tag at Atomic orbital in favor of "italic" Wikitax and HTML subscripts. I used the formatting that I did not because of a masochistic attraction to unwieldly formatting, but rather because of a desire for consistency. Browsers may happen to render the two identically, but we shouldn't abuse this situation. --Smack 04:34, 3 Nov 2004 (UTC)

P.S. You seem to know a bit on this subject, so I'd like to ask for your assistance. I'm trying to reconcile this article with the pre-existing Electron configuration. The latter is quite a mess, and most of it should be deleted and replaced with more relevant, fresh content. I can do the writing and the deleting, but first someone needs to salvage a few juicy higher-mathematics tidbits and place them in Atomic orbital, preferably without disturbing that article's present simplicity and accessibility to the uninitiated. I'm marvelously unqualified to do this, and you seem to be marvelously qualified. Could you do this? --Smack 05:05, 3 Nov 2004 (UTC)

P(0) is NOT required to be proved, sorry...

Yes, you are right. I mistook the explanation for this in the talk page for transfinite induction to imply it was understood to mean that P(0) was proved by any induction step, which was wrong, of course. The similar wording in the other articles about m.i. didn't cause me to recheck my logic...

Good thing reverting is fairly easy and likely only to produce a better result...

Mark Hurd 09:23, 4 Nov 2004 (UTC)

Metropolitan / Archbishop

There are in the Orthodox Church actually only 3 ranks to the priesthood. Bishop, Presbyter, and Deacon. All other titles are honorary based sometimes on the length of service of the priest, and sometimes the prominance of his territory (See). The various jurisdictions within the church have different traditions as to how they dispence these titles. In the Greek tradition any bishop who holds an ancient See is called Metropolitan even if that see is a small villiage. Archbishop is usually reserved for the lead bishop in a national church unless it happens to be Jerusalem, Constantinople, Alexandria, Russia, or Antioch; in which case its Patriarch (Or Pope). I have never heard of a Metropolitan Archbishop though its perfectly possible one of the jurisdictions provide this position. In any case, the most ancient patriarch, Metropolitan, or Archbishop are still equal in rank to the lowliest bishop over the smallest congregation except perhaps in adminstrative duties.


Category:Probability distributions

Just wanted to say hi. I've made a few changes recently to several articles in and you caught a number of bloopers, for which many thanks. I was wondering if it makes sense to aim for a common structure for all the articles on probability distributions. So far I've tried to imitate to some degree the presentation of normal distribution. What is a good place to discuss issues that are common to a set of articles like this? Category talk:Probability distributions? --MarkSweep 01:01, 6 Nov 2004 (UTC)