User talk:Michael Hardy/Archive2

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

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.

Dbuckner

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)

One of the things that needs doing after your move of "History of computing" to History of computing hardware" is that some or all of the backlinks listed onWhat links here for "History of computing" will need to be manually changed. Just so's you know, I'm going to start at the bottom of the list, and work my way up. Cheers, Cyan 21:53, 3 Dec 2003 (UTC)

I have finished changing the links over. Cheers, Cyan 22:34, 3 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 http://members.fortunecity.com/jonhays/parprob.htm , 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! FearÉIREANN 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)

Re the Ginzburg-Landau theory page I pressed 'Save' before the page was finished by mistake - I immediately bolded the title and re-saved. -- GCarty 08:54, 11 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

Michael, thanks for you work in Holy Avenger, I really appreciated it. Would you care to take a look in the related articles Marcelo Cassaro and Erica Awano? Cheers Doidimais Brasil 18:45, Dec 14, 2003 (UTC)

Re binational solution, thanks for the advice on when to italicize - noted! -- ChrisO 22:45, 18 Dec 2003 (UTC)

Bolding Titles

Thanks. I'll be doing that. :-) -- Mathieugp 17:07, 19 Dec 2003 (UTC)

Hi Michael :) Care to merge edits between your new Leibniz notation with Leibniz's notation for differentiation? I'll leave it up to your good taste to the direction of merging, since there's a Newton's notation for differentiation and a Lagrange's notation for differentiation which I think should have a less complicated title... Dysprosia 00:01, 22 Dec 2003 (UTC)

Thanks for the <math> mode fix on H-alpha, etc. I knew it looked lousy but didn't know the html for \geq, only the tex. --zandperl 05:28, 31 Dec 2003 (UTC)

Where I have added "unwritten" articles, should I include them in list of statistical topics?Cutler 00:08, 2 Jan 2004 (UTC)

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)

Michael, just to say I had some comments on the L-S theorem article, which I have put in the "discuss" section. Cordially, Dean.

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

Moving content

I see that you moved the contents of the page that used to be at List of words that are nouns or adjectives when the accent is on the first syllable and verbs when on the second to the page that is now at Initial-stress-derived noun by a cut-and-paste operation. (Similarly for the talk page.) Please don't do this, as it splits up the page history. It's better to use the "Move this page" tool, which can be found at the side of each page. If you can't do move a page because there is a redirect where you want to move the page to, you can ask a sysop to delete the redirect first. (The deletion can be done immediately if it has no non-trivial history.)

More generally, if you do copy material from one page to another, you need to bear in mind that attribution of authorship needs to be preserved. If you paste other people's content into an article without indicating that it is not your own, it appears that you are contributing the material yourself, which is arguably plagiarism. Even if you do indicate that it is not your own, but don't say where you got it from, then authorship cannot be assigned to it, which is arguably an infringement of the terms of the GFDL. If you do say where you got it from, then authorship can be assigned to it by checking the edit history of that page, and the consensus seems to be that that's sufficient for the terms of the GFDL to be satisfied. Even ignoring all the legal stuff, I just think it's nicer to be able to work out who has written what. For one thing it saves you from getting the blame for other people's bad writing... ;) -- Oliver P. 07:55, 11 Jan 2004 (UTC)

I've replied at Talk:Factor analysis. Angela. 02:15, Jan 13, 2004 (UTC)

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 http://members.fortunecity.com/jonhays/parprob.htm , which fills in a critcal gap in statistical literature.jonhays 17:54, 17 Jan 2004 (UTC)

Thanks for typos.

I am sure that it is NOT k>0 in the VP inequality (something like k>1.4?) but I can't put my hand on the paper. Do you have a different source? I'm off working for a few days now.Cutler 13:49, 20 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 131.183.84.196 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
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:
A special case of the poission distribution is the exponential distribution, where the x parameter is 1:
- 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 , vary proportionally with the time elapsed, so it becomes 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 Aykaç and Carlo Brumat eds., 1977). -- Cyan 03:00, 2 Mar 2004 (UTC)~

Someone who thinks there is only one differential operators, called "the" differential operator, worked on this page.

I take it you're referring to me - would you rather I didn't? Dysprosia 10:47, 4 Mar 2004 (UTC)

Hello Michael. After my edit of Triangle you recommended:

When writing about a word rather than using the word to write about what it refers to, italicize it

That's not a Wikipedia rule nor even a convention,

Yes, it is.

afaik (enlighten me if I'm wrong). Most articles seem to use boldface at first mention of the topic.

That's a separate issue altogether. I never suggested using italics at first mention.

I don't like the looks of bold italics, it's ugly. This is similar to Gratuitous Capitals, on which I happen to agree with you. Literary traditions frown upon such practices.
—Herbee 23:19, 2004 Mar 6 (UTC)

Bold italics should be used when simultaneously introducing the title of an article which happens to be something that should be italicised. For example, in Hoop Dreams, the first instance (and only the first) of _Hoop Dreams_ is both bold and italics; this is correct -- it is bold because it's the first use of the article title; it's italicised because film names are italicised. All future uses are just italicised. Revolver 02:59, 19 Mar 2004 (UTC)


Sugestion concerning the use of TeX on Wikipedia

On most browsers, TeX looks terrible when embedded in text, like this: . When it is "displayed", rather than embedded in text, it should be indented, like this:

and not like this:

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
  which looks pretty good.
—Herbee 11:58, 2004 Mar 16 (UTC)

Thank you for your work at my article Myths over the GDR. Because of my older Englisch Knowledge its not possible for me to make the article better. Can you help ? 212.82.249.40 17:12, 10 Mar 2004 (UTC)

Arc length + Rectifiable curve

I think they both should be redirected to curve

What do you think? Tosha 03:48, 15 Mar 2004 (UTC)

On beat, music, you added a bit that says "In particular, it can and often does take the form referred to above, caused by alternating constructive and destructive interference of sound waves", referring to the rhythm of music. what did you mean by that? we can't think of any music that uses interference between two frequencies to mark the rhythm. it has probably been used once or twice in experimental music, but is at best very rare. i moved it to the talk page for now. - Omegatron 13:32, Mar 16, 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)

Iconostasis

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)

Hi,

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)

Spaces after headers

Please follow Wikipedia:Manual of Style (headings) convention in not introducting spaces after headers, which should be removed. Dysprosia 00:01, 23 Mar 2004 (UTC)

I wrote about this on the discussion page for Wikipedia:Manual of Style (headings). I proposed changing that rule. Nobody has yet replied! If you reply on that page, I'll read carefully. In the mean time, you have not addressed the issues that I raised there. Michael Hardy 02:32, 23 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)

Hello. I'd like to thank you for cleaning up some of the changes I made. I looked at your user page and read you were a mathematician. I am only a highschool student, and I am not familiar with LaTeX or standard formatting procedures, i only use it for lab reports. Do you mind giving me some pointers other than the ones listed in your "TeX in Wikipedia" section? I dont want to be a nuissance Sreyan 00:21, 1 Apr 2004 (UTC)

Hello. How TeX appears on Wikipedia probably depends on what browser you're using. I haven't thought through this question systematically, but often TeX looks bad embedded in text and good when "displayed", like this:
That's as much as I can say quickly. Michael Hardy 02:39, 1 Apr 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)


Sorry for my mistake editing your 0^0 page. The usage seemed very strange and it looked for all the world like a typo :-) (is this a typical undergraduate mistake I ask myself...)

Regarding MACs, it was one of my first edits around here, hence me not fixing all the other links. Really, it doesn't matter whether it's at lowercase or capitalized, but I'll be sure to point out the difference in the article (the difference is that capitalized is an ANSI standard, and lowercase refers to the general type). CryptoDerk 02:21, Apr 5, 2004 (UTC)


Hi

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.

best

Robinh 08:31, 5 Apr 2004 (UTC)

>As I often point out, on Wikipedia, TeX looks good in "displayed" math but >often looks very bad when embedded in text. I've switched to alternative >notation in interpretability logic. Michael

Michael, that's great, thanks a lot! I tried LaTeX but it was real trouble. Kntg 25 Apr 2004

Pythagoras

Actually, that wasn't my edit; an anon added that earlier. I just cleaned the grammar and such. I hadn't heard of it myself, but my last experience with geometry was years ago, and so I left it in. If it's a mistake, by all means remove it. Meelar 01:25, 9 Apr 2004 (UTC)

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)

TeX and the haversine formula article

Thanks for your comments on the mathification I made of the haversine formula article. -- pne 12:32, 13 Apr 2004 (UTC)

Deleting Vandalism

If you come across a page like Ascender, don't blank it. Instead add {{msg:delete}} to the top of the page and then list it onWikipedia:Speedy deletions. Thanks. Guanaco 23:21, 19 Apr 2004 (UTC)

re: Galton-Watson process

Hi. I'm glad to see someone adding to Galton-Watson process; I'm going to remove the stub notice (although at some point I'd like to see some of the math, with iterated probability generating functions and all that, added; I'll do that if I get around to it before someone else does). Michael Hardy 17:12, 28 Apr 2004 (UTC)

PS: Your link to "surnames" didn't work because "surnames" is plural! The article is title surname, with the singular. Generally plurals are not used in Wikipedia article titles except when writing about something that should normally be thought of in the plural. I'm going to create a redirect page with the plural "surnames". Michael Hardy 17:12, 28 Apr 2004 (UTC)

Good thinking. Unfortunately I'm not a primarily mathematician but a biologist though I do know quite a bit about population genetics. It does seem to me though that many of the maths articles in Wikipedia are either mind boggling because they jump into the maths at too high a level, or don't include any at all, which is just as bad. Oh well, here's to the future... Duncharris 09:07, Apr 30, 2004 (UTC)

Ferdinand von Lindemann

All right, thanks for taking care of that for me. I just think it's sometimes a little awkward to title a page by a person's full name, as opposed to a more conventionally used shorter form. Everyking 21:45, 1 May 2004 (UTC)[reply]

Clerical Celibacy Article

Thank you for correcting my edit. I endeavour to use the best language I can for article edits, but sometimes I fail. Gilgamesh 23:08, 2 May 2004 (UTC)[reply]

Agency

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

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