User talk:Michael Hardy/Archive1

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)


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. 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)


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)

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)


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)