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Revision as of 02:05, 7 January 2010

Link to my so-called blog

Hello and welcome to my User Talk page. You might enjoy my approximation to a blog, "Sayings of Chairman Pratt." --Vaughan Pratt (talk) 22:23, 8 September 2008 (UTC)

Welcome!

Hello, Vaughan Pratt, and welcome to Misplaced Pages! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers:

• The five pillars of Misplaced Pages
• How to edit a page
• Help pages
• Tutorial
• How to write a great article
• Manual of Style

I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~~~); this will automatically produce your name and the date. If you need help, check out Misplaced Pages:Questions, ask me on my talk page, or place {{helpme}} on your talk page and someone will show up shortly to answer your questions. Again, welcome!  --MarkSweep (call me collect) 23:39, 6 May 2006 (UTC)

math notation

Hello. Please note that in non-TeX mathematical notation, one should italicize variabels but NOT digits and NOT punctuation. That is consistent with TeX style and standard on Misplaced Pages. Michael Hardy 00:10, 7 May 2006 (UTC)

Preview

You may want to use the preview button and an edit summary, so that it is clear from article history what you are up to. Thanks. Oleg Alexandrov (talk) 03:01, 7 May 2006 (UTC)

Greetings

So Misplaced Pages is what emeritus professors do with their spare time these days, eh? (Except for Don Knuth, who is probably going to be spending his next three lifetimes finishing TAOCP.) Glad to have you here. You'll find the quality of the editors varies considerably, but the more experienced folk keep an eye on Misplaced Pages talk:WikiProject Mathematics. You can add it to your watchlist if you like. If you have any questions about Misplaced Pages stuff that's one place to ask; or I can try to help. It can be a strange and bewildering environment, but the mathematical parts seem a bit more sane than some of the rest.

I'll put your talk page on my watch list, so you can reply here if you like. --KSmrq 08:17, 8 August 2006 (UTC)

By the way, if you're going to be writing serious mathematics the following pages are relevant:

1. Mathematics Manual of Style
2. Misplaced Pages:WikiProject Mathematics/Conventions
3. Help:Formula
4. Misplaced Pages:Mathematical symbols
5. User:KSmrq/Chars

If my page of characters shows lots of missing character symbols, you may want to get a Unicode font with broad coverage, such as Code2000. Or, wait for the STIX Fonts Project release. --KSmrq 05:45, 9 August 2006 (UTC)

hyphen, minus, en dash, em dash

When preparing material for TeX/LaTeX in mathematics mode, we can type "3 - 2" using the character Unicode calls HYPHEN-MINUS (U+002D), which is typeset as a beautiful minus sign. Likewise, double and triple dashes in LaTeX text mode produce an en-dash ("–") and an em-dash ("—"). We don't have those automatic conversions in wiki text, but we do have a handy collection of "Insert" items below the edit window. It's easy to see when a hyphen is used instead of an em-dash, and en-dashes are mostly used for ranges (like dates and pages), so are a little less common. That leaves the minus. In the monospace font that I use (which I presume is typical), a hyphen and a minus look identical in the edit window. However, they look quite different on the presented page, "-" versus "−". Because of this, some people prefer to use an HTML named entity, "−", so there is no ambiguity.

I just thought I'd alert you to the issue, for the lazy purpose of saving me some cleanup work. :-)

In general, some mathematicians prefer to type entity names for special characters, while others would rather take advantage of the representation power of UTF-8. Use whatever you like, such as "∩" or "∩" (the UTF-8 character) for set intersection; the visual result in both cases is "∩".

We hope one day in the not-too-distant future to leverage the typographic power of MathML; that will be a happy day for the mathematics editors here and at other wikis, with much easier editing producing much prettier output. --KSmrq 02:33, 11 August 2006 (UTC)

First use of "Western Hemisphere"

At Talk:Western_Hemisphere#Modernity_is_when_precisely.3F you said, "Any sources pinning the origin of the concept down to a smaller interval than 1492-1624 would be very welcome!" I have replied there with a citation for 1494. Nurg 06:03, 9 September 2006 (UTC)

Discussion about renaming "Boolean algebra"

FYI, there is a discussion going on about renaming our article now named Boolean algebra. The discussion is being held at Talk:Boolean algebra#Revisiting naming. If this issue is of interest to you, you are welcome to contribute your insights and opinions.  --Lambiam 21:11, 14 June 2007 (UTC)

Elementary Boolean algebra

Hi Vaughan Pratt. You are off to such a great start on the article xxxxx that it may qualify to appear on Misplaced Pages's Main Page under the Did you know... Elementary Boolean algebra. Appearing on the Main Page may help bring publicity and assistance to the article. However, there is a five day from article creation window for Did you know... nominations. Before five days pass from the date the article was created and if you haven't already done so, please consider nominating the article to appear on the Main Page by posting a nomination at Did you know suggestions. If you do nominate the article for DYK, please cross out the article name on the "Good" articles proposed by bot list. Again, great job on the article. -- Jreferee 02:23, 4 July 2007 (UTC)

Relational algebra

Hi Vaughan,

since you are the author of some of the references in this article, you seem like the natural one to ask. It seems to me that the text fails to adequately distinguish between a certain system of equational logic, and its models. I'm particularly confused by the sentence about Boolean algebra bearing the same relation to P(S), for some arbitrary set S, that relational algebra bears to S×S. Does that mean that S×S is a model of the system of equational logic called "relational algebra", under some interpretation, and that therefore S×S is a relational algebra? That's my best guess, but I haven't digested it enough to do more than guess.

I'd like to get the wording cleaned up, not only to make the article clearer in itself, but to figure out which way to disambiguate the Boolean algebra link here. --Trovatore 09:00, 24 July 2007 (UTC)

My bad, should have been relation algebra, not relational. --Trovatore 18:32, 24 July 2007 (UTC)

My recommendation would be to replace the first two sections (definitions and axioms) with the simple definition of RA given near the end of the Examples section of residuated lattice. The current article suffers from long-winded definitions that give little insight, compounded with miserable notation. --Vaughan Pratt 04:42, 25 July 2007 (UTC)

More in the same vein now at Talk:relation algebra --Vaughan Pratt 22:40, 26 July 2007 (UTC)

Invite

Thank you for your recent contribution to a few logic articles. Have you considered joining the Misplaced Pages:WikiProject Logic? It is an effort to coordinate the work of Wikipedians who are knowledgeable about logic in an effort to improve the general quality and range of Misplaced Pages articles on logic topics. We at the project invite your participation and correspondence. Be well.

Gregbard 02:55, 25 July 2007 (UTC)

Reduct

Hi, Vaughan.

I noticed that you started working on this article, which someone else has already tagged for context, and for sources.

I'm not sure if you've seen it already or not, but the {{Underconstruction}} template can be useful for new articles. It produces a warning message to let other editors know you're still working on the article.

Just thought it might come in handy. Have a great day! DavidCBryant 14:59, 14 August 2007 (UTC)

Also, is pseudoelementary class about chemistry, sociology, theology, international law, or what?? I know the answer to that question, but does the person reading the article know? Michael Hardy 15:24, 17 August 2007 (UTC)

Sigh. Ok, fixed. --Vaughan Pratt 20:33, 17 August 2007 (UTC)

Wolfram's (2,3) controversy

I've moved this section to the "PSJ-VRP Dialog" section of the (2,3) Talk page as being a more appropriate place for it. --Vaughan Pratt 17:05, 6 November 2007 (UTC)

Hello again. I've been feeling a bit put out, criticised from both ends, but while I haven't caught up yet, your sentence ...approached the controversy by considering both sides (which unfortunately led some of those taking my side to assume he was taking the other)... really cheered me up. A small thing, perhaps, but thanks very much. Pete St.John 17:21, 6 November 2007 (UTC)

Actually I wasn't sure myself in the beginning but your questions did seem much better focused on the issues than those of the current crop of defenders of the proof, without whose obscure arguments this whole sorry mess could have been cleared up long ago. At this point it seems to me that enough opinions by those not on the official committee have been expressed that I for one am now going to step out of the debate and wait for any further word from the committee beyond the announcement last month of one its members that a proof has been accepted. I see my role in this as having been merely to argue that Smith's proof is insufficient to exclude LBAs from the class of machines falling into his proposed criterion for universality. Under the Rules and Conditions of the prize only the committee can judge the merits of Smith's criterion; whether any additional post-decision judging is necessary or appropriate is up to them. --Vaughan Pratt 17:47, 6 November 2007 (UTC)

Deletion of the Erdos Number categories

Recently the categories related to Erdos Number were deleted. There are discussions and debates across several article talk pages (e.g. the Mathematics WikiProject Talk page. I've formally requested a deletion review at this deletion review log item. Pete St.John 18:30, 7 November 2007 (UTC)

If the argument is to help people find their Erdos number, an encyclopedia seems the wrong kind of resource for that. There should be a separate website for that sort of matchmaking. Is there some more encyclopedia-relevant reason to keep these categories? --Vaughan Pratt 02:18, 8 November 2007 (UTC)

• I gave my version of the reasons to reverse the deletion, at this subsection on the wikiproject:mathematatics talk page. However, reasons to reverse the deletion are not the same as reasons to have the category, exactly. I think it's more a matter of finding other people's number, than one's own (if that's what you meant), and that has more socio-political-historical interest than strictly mathematical interest. Part of the problem, IMO, is that Erdos Numbers are to some extent an object of mathematics (a metric on vertices of a graph) but more an object of mathematicians, the people.
• I'm interested in your comment "an encyclopedia seems the wrong kind of resource". That's similar to an objection raised by (my) opposition, so if you could elaborate it might help us (me) understand their case, the rhetoric of which has to date been disappointing (to me).
• I'm a little distracted as I have been formally accused with unethical "canvassing" practices, cf item at my Talk which has a link to the ANI item (I don't even know exactly what ANI is yet, but it's some kind of administrative process dealing with unethical conduct). I'm determined not to drop the Erdos Number issue just because of what I consider a personal, in fact ad hominem and technically inaccurate, accusation, but I'm spread a bit thin at this writing. Thanks again, Pete St.John 19:19, 8 November 2007 (UTC)

• User:Ramsey2006 wrote a good short answer to the question "why do we want Erdos Numbers in Wiki bios?" at the deletion review item. He's staying calm when some of us are getting a bit edgy. Pete St.John 21:36, 8 November 2007 (UTC)

Proof (at project page)

There's a discussion of proof (in workaday mathematics) vs formal proof (in an Axiomatic System) at the math project talk page, here. This may have bearing on the way Proof is explained in some articles. Remarkably easy to get confused and flustered when talking about basics we never think about :-) and I don't exclude myself. Pete St.John (talk) 20:23, 3 January 2008 (UTC)

Metalogic

There is a little confusion (to me, anyway) about metalogic vs logic, at categories for discussion; should the metalogic cat be kept, or merged with mathematical logic, etc. Pete St.John (talk) 20:52, 18 January 2008 (UTC)

Sandbox

/Sandbox

Boolean algebra task force

I'd like to invite you to participate in the Boolean algebra task force that I am forming. Despite the name, a task force is just an ad hoc subcommittee of a wikiproject to work on a particular issue. In this case, I think that our articles on various aspects of Boolean algebra, propositional logic, and applications would benefit from some big-picture planning of the organization of material into various articles. The task force would not require a great time commitment. The main goal is to work out a proposal for how the material should be arranged. A second goal is for the focus to remain interdisciplinary, including computer science, logic, and mathematics. — Carl (CBM · talk) 16:12, 28 January 2008 (UTC)

Willing and able. Great that somebody's taking the big picture here in an organized way. :) --Vaughan Pratt (talk) 18:11, 28 January 2008 (UTC)

I have to admit to a conflict of interest - the current organization is too complicated for me to understand where various information should be located. I didn't realize there was an ongoing discussion at Boolean algebra (logic) about the same problem. Maybe a little bit of centralized planning will help ease worries that material is being omitted in introductory articles, etc. — Carl (CBM · talk) 19:06, 28 January 2008 (UTC)

That's not so much a conflict of interest as an outsider (?) taking a high-level view of a problem that has got the active participants bogged down in the myriad details. No one has collected all the many Boolean-relevant articles in one place before, which is a great way of illustrating the scope of the problem and a good forum for suggesting various groupings leading to merges. (Given the big yawn with which Boolean algebra was largely greeted in Boole's lifetime, Boole would have been chuffed to see all this activity now.) --Vaughan Pratt (talk) 19:26, 28 January 2008 (UTC)

I am an outsider, I suppose, in that I haven't been active in the various discussions about the Boolean logic articles. My first goal is to get buy-in from the established participants, since I want to have a full range of viewpoints included in the discussion. — Carl (CBM · talk) 19:34, 28 January 2008 (UTC)

From my perspective your organization page makes a great start on that. Package it as an improved forum over the existing use of article talk pages, which aren't the greatest place for discussions of merges because it isn't clear which discussions belong in which talk pages. The tendency has been for there to be a single thread which moves around between talk pages but with an inertia that keeps it on any one talk page for a while. Boolean algebra (structure) hosted most of the discussion until the last month or so when it jumped to Boolean logic, StuRat's revival of his article. Your organization page presents the view from outer space, which could be neutral territory if no one shoots the satellites. --Vaughan Pratt (talk) 20:10, 28 January 2008 (UTC)

"super-recursive" algorithms

The interesting thing, perhaps, at Super-recursive algorithm is that the bold claims are made by an academic logician, published by Springer even. Otherwise this tastes the same to me as the (2,3) controversy. Currently however the discussion is perfectly calm, just a bit surreal. Pete St.John (talk) 16:38, 6 March 2008 (UTC)

Hi Pete. Looking at the article's history I see that it doubled in length in the last 24 hours due to the addition of a long and disjointed rant in bad English about confusions and illusions by User:Multipundit, is that what you're responding to? I'm aware of Mark Burgin's book by that title ("Super-recursive algorithms"). It's ranked at 1,736,232 by Amazon (cf. 107,236 for Wolfram's A New Kind of Science). Does Misplaced Pages have any articles about books ranked that low? And do any theoretical computer scientists besides Burgin use the term? As best I can tell it seems to be Burgin's made-up name for computability classes above Turing degree 0 such as the arithmetic and analytic hierarchies, which have been studied for many decades. No one besides Martin Davis seems to have found it worth their while to review the book, and Davis's highly negative review can summarized with two words, "crackpot literature." It's ok I suppose to have articles about (as opposed to on) crackpot subjects in Misplaced Pages provided there is sufficient controversy to warrant such an article (cf. Ann Coulter), but presumably not when the only people involved are the few who have uncritically taken the book at face value. If Martin Davis overlooked some genuine novelty in the book I would be interested in hearing about it. Meanwhile perhaps the article should abandon its elaborate pretense to be about a legitimate subject, which User:Multipundit's rant tends to undermine anyway, and be turned into at most a brief article commenting on the book, or simply deleted altogether. --Vaughan Pratt (talk) 05:33, 7 March 2008 (UTC)

Pete, I pursued my point about "pretense" a little further by pursuing the list of alleged hypercomputationalists Eberbach, Kugel, van Leeuwen, Siegelmann, Wegner, and Wiedermann given in the article's lead. While researching it I ran across Martin Davis's article "The Myth of Hypercomputation" which debunks the concept and some of its proponents. Siegelmann's claim to hypercomputation as something that can happen in nature would appear to rest on such illogic as "In nature, the fact that the constants are not known to us, or cannot even be measured, is irrelevant for the true evolution of the system. For example, the planets revolve according to the exact values of G, π, and their masses." I couldn't agree more with Davis's remark that "It is hard to know where to begin in criticizing this view of 'nature'." Siegelmann seems oblivious to such elementary facts about space that it is curved making the exact value of π irrelevant to cosmology beyond its first dozen or so digits, and seems to think that the laws of celestial mechanics are exact in the sense envisaged or at least modeled by Newton when quantum mechanics clearly indicates otherwise. The several articles by Eberbach and Wegner are dismissed by Cockshott and Michaelson in The Computer Journal 50 (2):232-247 (2007) with an article whose abstract reads "Wegner and Eberbach have argued that there are fundamental limitations to Turing Machines as a foundation of computability and that these can be overcome by so-called super-Turing models such as interaction machines, the {pi}-calculus and the $-calculus. In this article, we contest the Wegner and Eberbach claims." Peter Kugel merely repeats Roger Penrose's interesting but far from convincing hypothesis that artificial intelligence can never hope to compete with human intelligence because only the latter can compute more than a Turing machine. The only people on this list with actual results are Wiedermann and van Leeuwen, who establish the computational power of fuzzy Turing machines with some nice technical work that does not however contradict the Church-Turing thesis in the manner hoped for by proponents of hypercomputation. In short a few legitimate but not at all shocking results mixed in with a whole lot of crackpottery in much the same sloppy vein as the article. --Vaughan Pratt (talk) 07:25, 7 March 2008 (UTC)

Well I guess I was right in thinking you might be interested :-) No, the (remarkable) recent essay by Multipundit (whose username I admire) came after my note here; I only just read it. (Most of it.) The work described in the article sounds to me like pseudoscience (for want of a better term); and you've slam-dunked it, as far as I'm concerned. I may have too much respect for Springer (they have published so many so very good books) or maybe too high expectations. Anyway thanks for your reply, I'll link it at the article talk. Pete St.John (talk) 17:35, 7 March 2008 (UTC)

Oops, I suppose I should have anticipated being linked to and adopted a tone more like that of Davis's review, sorry about that. That way everyone would have been happy including User:Multipundit who said of the review at Talk:Super-recursive_algorithm#Ungrouded_claims_and_false_information, "there is not a single negative word in the whole review." Oh well, there seem to be several cats out of the bag by now, one more shouldn't make much difference so one might as well be frank. I don't know about the book but your pigeonholing of the article as pseudoscience hits the nail on the head. The last sentence of the third paragraph of the pseudoscience article starting "Accordingly" seems particularly apropos here. The occasional injustice aside, good science speaks for itself, bad science has to be defended by its perpetrators. --Vaughan Pratt (talk) 22:42, 8 March 2008 (UTC)

Yeah sorry to link your talk, but you had written so much I didn't want to paraphrase it myself (remember I'm not a logician; I'm a programmer, with a background in combinatorics). In regard to your concern about Multipundit's PoV, I checked the contributions history and it seems definitely a Single purpose account. I brought this to the attention of CBM, here who has been following the article and is concerned with mathematical logic. Sometimes I wish for a broad ax but usually we have to settle for a scalpel, or even whitewash. Pete St.John (talk) 19:21, 9 March 2008 (UTC)

Does Penrose stand by the claim (badly paraphrased) that computers can't do what human brains do? In the 70's there was a big debate regarding chess and AI, "computers will never beat humans at chess because..." which I followed avidly, as a kid I was interested in both, and I advocated the machines. Now I hear similar things because computers don't yet play Go well (although machines today can give the equivalent of queen odds to machines of twenty years ago). It seems an eternal yearning. Do you know a reference for the Penrose quote? And incidentally, I had never realized the math Penrose (tiling?) was the brother of the chess Penrose; the game score in the article is, I think, an example of the opening named after him (the "Penrose-Tal Line"). Pete St.John (talk) 19:34, 9 March 2008 (UTC)

See the first sentence of The Emperor's New Mind, namely "Penrose presents the argument that human consciousness is non-algorithmic, and thus is not capable of being modeled by a conventional Turing machine-type of digital computer." --Vaughan Pratt (talk) 02:49, 10 March 2008 (UTC)

Pete, when you mentioned ad hominem in your response to User:Multipundit at Talk:Super-recursive_algorithm#An_exhibition_of_fallacies, were you referring to his accusing me of ignorance or his accusing me of making a personal attack? I take the former as a personal attack. And I see in Misplaced Pages:PA that a groundless accusation of personal attack itself constitutes a personal attack, which for my money makes us two for nil. It would be interesting to know whom he thinks I attacked personally, him or Burgin, and in what sense he considers the attack personal. For all I know both of them are great guys; certainly both have a very similar command of English (my apologies to whichever of them considers that a personal attack). --Vaughan Pratt (talk) 02:49, 10 March 2008 (UTC)

Talking of command of English, User:Multipundit seems unacquainted with the English phrase "such as" in his assessment at Talk:Super-recursive_algorithm#An_exhibition_of_fallacies of my characterization of the "super-recursive class of algorithms" (the term used in the definition) as "computability classes above Turing degree 0 such as the arithmetic and analytic hierarchies" as being "completely incorrect." The article starts out with "super-recursive algorithms are algorithms that are more powerful, that is, compute more, than Turing machines." Does User:Multipundit read what he writes?

I'd also be interested to know how not reading a book about a subject makes one ignorant of it. If that were true we'd all be ignorant of algebra until we'd read every book about algebra. Or is User:Multipundit of the opinion that the Misplaced Pages article leaves one in the dark about the subject? Unfortunately it does; fortunately I've read other Burgin publications about super-recursion that do a much better job of explaining it. --Vaughan Pratt (talk) 03:27, 10 March 2008 (UTC)

We seem somewhat to be in synch; I just responded to the "such as" point (it's easiest if the opponent is so angry as to use logic so slack as to be self-inconsistent within a paragraph, but really I don't want anyone to be angry) and the book vs paper thing (as you had mentioned that yourself earlier) before getting to this. But I don't recall which thing seemed most ad hominem, and such an item I'd prefer to let pass, on the "not get angry" point :-) Also it's the "compute more" in a context of, apparently, no result at all in observable time, that seems the most clearly in need of explanation, or to put it another way, the kookiest.

Be all that as it may, there are other (and better qualified in logic than I) editors watching, and they seem content that the article is not misrepresenting an idioscyncratic view as accepted science. So patience rules. I have sometimes wanted to take a Gatling to a roomful of freshmen but, OTOH, I'm pretty sure some of my professors have felt the same way about me. Ax fired me twice from one summer job, that's kinda...cool...or not. Pete St.John (talk) 04:39, 10 March 2008 (UTC)

I have nominated super-recursive algorithm for deletion. I see, at best, a "weak keep" argument. If the decision is "keep", the discussion will at least have helped establish a reasonable perspective for a proper article on the subject (which, if it were up to me, would be very brief, and as coldly dismissive as NPOV allows). Unfortunately, in the deletion discussion so far, there aren't very many contributors with the kind of background appropriate for assessment. Also, I don't see a whole lot of effort among them to sift the literature for any actual real peer reviewed article about the topic.

My own grasp of computing theory has faded somewhat. It's been almost 30 years since I learned what little computing theory I ever knew, at Eugene Lawler's knee. (I was a mere undergraduate in a course required for quals, actually the only undergrad, IIRC. But he didn't kick me aside dismissively -- far too nice a guy, and BTW why no Misplaced Pages article yet?). I don't think being a homework grader for the same course when it was taught later by Richard Lipton while he was at Berkeley counts much toward credentials in the field. Then again, Lipton didn't fire me either, so I maybe I was doing something right. At any rate, my contributions are open to the criticism that I'm out of touch, hopelessly dated, that I don't know about the latest, greatest, hottest, overarching paradigm in computing. "Paradigms" being so much more important than dull stuff like, y'know, proofs? Yakushima (talk) 17:11, 26 May 2008 (UTC)

Image copyright problem with Image:Bands.svg

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If you have any questions, please feel free to ask them at the media copyright questions page. Thanks again for your cooperation. Sdrtirs (talk) 04:46, 15 May 2008 (UTC)

Should be ok now. It's a self-made svg. I wanted to put the copyright info in when I uploaded it, and was expecting some help to pop up somewhere to guide me but this didn't happen so finally I gave up. A pointer to the procedure I should have followed so as to make this information pop up automatically would be appreciated. As it was I ended up just now simply editing the whole page of that figure and an earlier figure I'd done (for Heron's area formula), copying the whole of the latter to the former, and then making the appropriate changes. Very crude but it (hopefully) worked. --Vaughan Pratt (talk) 06:53, 15 May 2008 (UTC)

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Edits to your bio in re Pentium FDIV bug

I hope you consider this anecdote significant enough for mention. Maybe it's not. It's getting to be ancient history. If there was any "fallout" from Henry Baker's "Chernobyl", there's probably not much point in trying to do the accounting now, unless a recomputation of some number, somewhere, would net me a higher Social Security payout.

Perhaps I overestimate the significance of the Pentium bug because I'd had a similar experience, years earlier, at a company that used Weitek FP parts. (As Intel was itself was forced to, when its 387 FP effort ran out of time. IIRC, Intel later licensed Weitek's FP design for embedding in the Pentium chips.) On the basis of this bad experience, I sometimes like to claim "prior independent discovery of the Pentium bug -- even before there was a Pentium".

In 1985, over the course of a month or so while working for a company developing hardware and software for IC circuit simulation, I went from studying Newton's method for division (and exponentiation?) all the way down to EPROM burning of approximation lookup tables, following Weitek datasheets and instructions for lookup table development. It was the first time in years I'd done anything with calculus, and the effort was resulting in a chip I could personally plug into our company's FP accelerator board. To me this was Very Cool. I actually started having warm, fuzzy feelings about William Kahan, a prof at U.C. Berkeley who I'd always thought of as being overbearingly pompous about low-order bits so low that no sane computer scientist should give a rat's ass about them. But actually working with a product of Kahan's mind changed my mind. IEEE arithmetic was the Right Way, and he, more than anyone else, had led the charge on it. Low order bits: give a rat's ass!

Nice while it lasted, but ... late one night, it all went a little funny, as happens in startups (but also, it seems, in big companies like Intel.) One of our hardware engineers, while doing his own "testing", noticed some numeric "errors". He "corrected" these in the EPROM by changing the lookup tables. I tried to persuade him that the errors would just pop out even more significantly somewhere else if he messed with Weitek's prescription. He wasn't having any. And he was a hardware engineer, and this was hardware, and our VP of Engineering was a hardware guy. So I lost. Luckily (for the simulation market), it didn't matter anyway: the company went nowhere with its analog circuit simulation product.

I have very vague memories that there was some hapless software guy at Intel who ran into a similar same wall of ignorance, and that he just left his defense as a report in Intel's bug tracking database, where it lay, ignored, until the fiasco. I'd like to substantiate this vague memory if possible, because it would make a great addition to Pentium FDIV bug. But so far I haven't had any luck. Yakushima (talk) 06:43, 3 June 2008 (UTC)

My understanding from conversations with various sources including Kahan is that Intel took due (but in hindsight insufficient) care to verify that their implementation of SRT was correct. I hadn't heard anything about a "wall of ignorance" at Intel being the root of the problem. Ignorance is everywhere, like nitrogen in the atmosphere: as 80% of the air, nitrogen acts as a great flame retardant/antioxidant (fires would burn furiously if the atmosphere was all oxygen) but few scoutmasters blame it for the inability of their scout troop to start a fire. --Vaughan Pratt (talk) 16:58, 4 June 2008 (UTC)

terra preta inappropriate banner

Thank you for having removed it from this article. Best regards Basicdesign (talk) 21:54, 15 June 2008 (UTC)

I removed it for lack of supporting documentation in the talk page. I do agree with the tagger however that that section needs some clean-up, in particular turning the kudos and acknowledgments into appropriate citations. I don't know enough about terra preta to do so myself. --Vaughan Pratt (talk) 19:33, 16 June 2008 (UTC)

Wedge or circ symbol for meet?

Hello Vaughan, I am replying here because of the long delay due to my inactivity. I am not aware that I ever made a change from \wedge to \circ (of course this would be a very strange thing to do, especially without discussion), so I suspect it's a technical problem. You mentioned my edits of 3 May at Lattice theory. On that day I changed many formulas from pseudo-TeX to plain Unicode, turning ${\displaystyle \wedge }$ (\wedge) into ∧ and ${\displaystyle \vee }$ (\vee) into ∨. In my browsers (Firefox and Internet Explorer on Windows XP, but with numerous special fonts installed) it seemed to be correct, and in my current browser (Firefox on Linux EeePC) it still looks correct. Does it still look wrong for you, or was it a problem with a defective font on a public computer? --Hans Adler (talk) 23:27, 21 August 2008 (UTC)

Hi Hans. Turns out the problem is with my laptop, which for some reason displays \circ where other computers display \wedge. These changes to Unicode incidentally are good---but are you also applying them to Greek letters? The Unicode for Greek ${\displaystyle \nu }$ (\nu) is ν (ampersand nu;) which looks like the letter vee on all the computers I've seen it on. Any idea whose fault that is? --Vaughan Pratt (talk) 22:46, 22 August 2008 (UTC)

I think that just depends on your choice of fonts. On my computer the two variants of nu are virtually identical in appearance. I would imagine that it's a problem with either low quality fonts or fonts that try to do sans-serif Greek letters. (Probably a sensible choice for the display of Greek text.) --Hans Adler (talk) 13:28, 15 September 2008 (UTC)

I would have thought it preferable when displaying Greek text to use a font in which Latin vee was distinguishable from Greek nu. --Vaughan Pratt (talk) 21:33, 15 September 2008 (UTC)

Sources about Yugoslav Wars

In my thinking Timeline of Yugoslavian breakup is OK --Rjecina (talk) 20:09, 8 September 2008 (UTC)

Actually I was looking for an article that ties the events together. Without some glue to make a coherent whole of this "article," trying to digest these scattered events is like eating trying to eat powdered milk without water. --Vaughan Pratt (talk) 21:53, 8 September 2008 (UTC)

Birkhoff's representation theorem

Vaughan — I just put together an article on Birkhoff's representation theorem (for distributive lattices) that you may be interested in, especially in conjunction with some of your old papers and with Boolean algebras canonically defined. Do you think it should be expanded to also include his representation theorem for Boolean algebras, or is there any other relevant material I may be missing?

I came to this subject from the knowledge space application — some people I've worked with are using this representation in actual software for evaluating the knowledge of high school mathematics students — and I also have an unpublished paper on rectangular cartograms where it comes up again, so it's not only logic where it's useful. —David Eppstein (talk) 23:30, 30 November 2008 (UTC)

Hi David. Thanks for bringing this to my attention. I'd completely forgotten about my promise last January at Talk: Stone duality to fix that article and was only reminded of it when I ran across it while trying to sort out where I thought your article should fit before responding to you. I tend to think of this theorem of Birkhoff as the finite part of Stone duality. From a pedagogical standpoint, one good trajectory for students of Stone duality is to understand first the finite case of the duality of Boolean algebras and sets, then extend that to distributive lattices (your article), then proceed to Stone's extension of these results to the infinite case. At some point, sooner rather than later in my view, the behavior of the associated homomorphisms should be pointed out, with plenty of examples. Your article is the ideal venue for that, although given Misplaced Pages's relatively fine granularity a separate article on that topic might be appropriate as it contains quite a bit of material, as well as providing very concrete motivation for the category theoretic view of these dualities. --Vaughan Pratt (talk) 19:15, 2 December 2008 (UTC)

To follow up on this, do you have any recommendations for references to the functorial version of the representation theorem? Along with being appropriate to include in the article here, this has actually come up in some of my research: I have an algorithmic application where one distributive lattice is a sublattice of another (with different top and bottom elements), I understand the partial order corresponding to the big lattice, and I want to find a description of the partial order corresponding to the smaller lattice. I'm not sure in this case whether it's better understood as an injective morphism from the small lattice to the big one, or a surjective morphism from the big one to the small one, but either way the representation theorem seems very relevant. —David Eppstein (talk) 02:36, 14 December 2008 (UTC)

The functorial version is the one needed to really appreciate the duality. One doesn't need the formal definition of functor to appreciate that to each embedding of a poset P as a subposet of Q, an injection f: P → Q, there exists its corresponding quotient of the distributive lattice Q* (the dual of Q) producing P*, a surjection f*: Q* → P*, and moreover to each quotient Q of poset P, a surjection f: P → Q, the corresponding embedding of the distributive lattice Q* in P*, an injection f*: Q* → P* (not that every morphism f need be either to be dualizable, every f dualizes).

There is an extremely elementary way of seeing this contravariant correspondence between morphisms (yes, that's a functor because it preserves composition, but one can sweep the functor itself under the rug and just talk about the correspondence between the morphisms as a bijection). The trick resides in grokking the meaning of the op in the homfunctor Hom: C × C → Set in a way that eliminates functors. Here's the trick. When you concatenate arrows f:X→Y and g:Y→Z as f;g (; is the converse of composition, i.e. f;g = gof) then f can be understood as stretching g "to the left". As such it is an action on any arrow of the same type as g, meaning in the same homset, namely C(Y,Z). This action of f therefore maps the set C(Y,Z) to C(X,Z).

Now regard the dual Q* of the poset Q as consisting of the monotone functions from Q to the two-element chain 2 (the schizophrenic dualizing object). Any monotonic map f: P → Q induces a map f*: Q* → P* which is a function mapping each monotone function g: Q → 2 to the monotone function f;g: P → 2 (or gof if we use the more standard notation). Once you understand the dual in terms of dual points (akin to group characters and functionals) in this way it becomes completely trivial to compute the duals of both the posets themselves and their morphisms.

Exactly the same method gets you back from distributive lattices to posets, using the same dualizing object now understood as a distributive lattice (it's schizophrenic). In that case the morphisms are distributive lattice homomorphisms, which the duality sends to monotone functions.

Chu spaces put all this on a footing that is completely independent of such specific categories as posets, distributive lattices, sets, Stone spaces, etc., via a mechanism that implements the above in a remarkably simple yet all-embracing way: the machinery for composing with dual points is implemented with matrix transposition! Couldn't be simpler! --Vaughan Pratt (talk) 00:01, 15 December 2008 (UTC)

That is illuminating, especially the part about viewing the distributive lattice as Hom(P,2). Are there references for this that I could cite in the Misplaced Pages article? —David Eppstein (talk) 00:16, 15 December 2008 (UTC)

Sorry, I don't have one. I derived the above account from Peter Johnstone's book Stone Spaces. Peter has his own standards of what constitutes an elementary explanation, which diverge from mine at about the point the external homfunctor starts to play a role. Let me ask on the categories mailing list if there's an explanation more like mine than Peter's. --Vaughan Pratt (talk) 05:03, 15 December 2008 (UTC)

In the meantime I've made an attempt at an explanation in Birkhoff's representation theorem#Functoriality. —David Eppstein (talk) 04:06, 16 December 2008 (UTC)

Oh, Stanley has it? That's great, I should have thought of him, he's been on top of algebraic combinatorics for ages. In that case you could cite Johnstone anyway (steal the reference from Boolean algebras canonically defined) but make Stanley your main reference.

What you've written looks very good, that was quick! The one change I see right away that needs to be made is that the division of labor between Stone and Priestley needs to be divided more carefully. Priestley saw how to use Nachbin's idea of ordered topological spaces to make more intuitive the strange spaces that Stone came up with in 1937 for the infinite case of the duals of distributive lattices. However you allocate that credit, you could run it by Hilary for her reaction, she's still very much round and about and working on various projects. --Vaughan Pratt (talk) 04:48, 16 December 2008 (UTC)

Thanks. I should point out that the Johnstone reference has already been in the Birkhoff's theorem article for some time. —David Eppstein (talk) 05:24, 16 December 2008 (UTC)

Hyperbola

My exposure to hyperbolas was limited to high school solid geometry and analytical geometry and that was many years ago. So you have the benefit of the doubt. I only ask that you clarify for non-mathematicians your statements that make use of math concepts that are not familiar to non-mathematicians. Your later comments on my talk page clearly explain these concepts and I suggest you add those explanations to the article. However, this meaning of hyperbola does not belong in the introductory paragraph, but rather should come a few paragraphs later, in a separate sub section, after elementary hyperbolas are described. Greensburger (talk) 02:25, 14 December 2008 (UTC)

Regarding adding the explanations to the article, this seemed like an excellent idea so I did, thanks for that. I have some remarks about the addition on the article's talk page. Regarding what should be in the introductory paragraph, I honestly don't know. That the hyperbola is encountered in daily life essentially as often as the ellipse is not consistent with defining it as the result of cutting a cone, how often does anyone encounter craftsmen cutting away at cones? It's an ancient Greek packaging of the concept that has hung on like grim death and should be updated to better reflect the impact of the hyperbola in the real world. The two possibilities that do justice to the importance of the hyperbola without intimidating people are the connection with y = 1/x and its affine transformations, a curve that frequently arises in practical mathematics, and how circles look from certain angles, which even people with Cartesian plane anxiety can understand, even if like you they don't believe it at first. The other important ways the hyperbola impacts the world are harder to convey in a sentence or two. Conic sections however do nothing for the importance of the hyperbola and are best viewed as a way of thinking about how circles look in perspective. To reverse those roles is to let the tail wag the dog. --Vaughan Pratt (talk) 23:26, 14 December 2008 (UTC)

Gordon Plotkin reminded me last night of a third familiar occurrence of the hyperbola that can be easily described in a sentence, namely the shape of an open orbit, as with a slingshot or gravity assisted swing-by of a spacecraft around a planet, or a comet that enters the solar system only once, as opposed to a closed orbit which is elliptical. This occurrence appears only implicitly at the very bottom of the lead, namely in the reference to the Rutherford experiment where the orbits are on an atomic scale, are driven by repulsive forces rather than the attractive force of gravity, and despite being open orbits are not referred to as such (when repulsive forces dominate there are no closed orbits). --Vaughan Pratt (talk) 18:58, 15 December 2008 (UTC)

After contemplating it some more I decided that my concerns about conic sections could be overcome with one word, "traditional." As long as it's clear that this way of packaging them is merely a tradition, as opposed to having something else to recommend it as a definition (but it's great as a model of perspective projection), and the actual utility of the concept comes immediately after, I'm fine with starting out with conic sections.

Also it's started to dawn on me that something that's been completely obvious to me all my life, namely that circles can look like hyperbolas sometimes (we did a lot of geometry at Sydney University back when I was an undergraduate), is not at all obvious to some indeterminate but evidently large (99.9%?) fraction of the world. I just never thought to check with anyone before. So I guess people have to be gradually warmed up to that concept. (Retired professor James Calvert at Duke has been writing for decades that circles are only seen as ellipses, never hyperbolas, but after only a little resistance he agreed with "There are lots of curiosities in perception!")

So I now have a candidate for a new lead at Candidate new lead for hyperbola article that incorporates all of the foregoing, check it out. --Vaughan Pratt (talk) 05:04, 16 December 2008 (UTC)

Image of Vaughan Pratt

Hello Vaughan Pratt! It is a shame we have no picture of you for the Vaughan Pratt article. If you have a suitable one that is taken by you, or that you have the rights for, we could maybe add it to your article. The one at http://boole.stanford.edu/pratt.html would certainly suffice if it can be released for our use. EdJohnston (talk) 02:55, 14 December 2008 (UTC)

Heavens, that one's from the last millennium, taken before I retired. Let me try and cons up something more recent. If the decade isn't important I have some from the 1940's. --Vaughan Pratt (talk) 22:37, 14 December 2008 (UTC)

I uploaded just now, if that works. Took it this morning. --Vaughan Pratt (talk) 22:57, 22 January 2009 (UTC)

Added to the article. —David Eppstein (talk) 23:02, 22 January 2009 (UTC)

sandbox

Il Trovatore is right: drafts should not be in the (Article) namespace. I have moved New lead for ordinal number to User:Vaughan Pratt/sandbox and moved Candidate new lead for hyperbola article to User:Vaughan Pratt/hyperbola. I endorse the above request for photo - the one from the 1940s should go on your user page - as should the shameless links. — RHaworth (Talk | contribs) 10:47, 23 December 2008 (UTC)

Thanks, my mistake, normally I remember to put this sort of stuff in my sandbox. The hyperbola thing can be deleted as that's now the entire lead in the hyperbola article, feel free to do so (I'm a mere wikimortal and can only blank it, which I've done). I suspect one reason there's nothing on my user page except a link is that some kind people (mostly in the UK as far as I can tell) created an an actual article, which eventually I figured out I should link my user page to. Except for one instance where I briefly supplied my Erdos number before deleting it again, I have not touched that article and currently have no plans to do so in the future (who knows what new belief system my overtake my aging brain in the future). Anyone else in the world should feel free to hack it up as they see fit, I have infinite faith in the all-too-vigilant wikiguards to revert any vandalism within the nanocentury. By all means put the shameless link there yourself, annotated however you see fit, and I'll try to come up with a more current photo; I imagine interpolating between that and the 1940s ones could provide endless entertainment so I'll consider that too. --Vaughan Pratt (talk) 06:19, 24 December 2008 (UTC)

I deleted the hyperbola one for you. The usual method for getting the attention of someone who can delete pages from your user space is to put {{db-u1}} (with the double curly brackets) on them. The db templates request speedy deletion more generally; U1 is the code for user requests within your own userspace. —David Eppstein (talk) 07:52, 24 December 2008 (UTC)

Yet another shameless link to my so-called blog

Goodbye and thank you for visiting my User Talk page. You might also enjoy my approximation to a blog, "Sayings of Chairman Pratt." --Vaughan Pratt (talk) 22:23, 8 September 2008 (UTC)

copy of ordinal (to be deleted shortly)

In mathematics, an ordinal number, or just ordinal, is a transitive set of ordinals, or hereditarily transitive set. That is, every element of an ordinal is transitive and its elements in turn are transitive and so on down. The Axiom of regularity stops this recursion after finitely many steps, namely at the empty set.

The finite ordinals are 0 = {}, 1 = {0}, 2 = {0,1}, 3 = {0,1,2}, …. This is a consequence of two remarkable facts, that every element of a finite transitive set is itself a finite transitive set (so we can drop "ordinal" as a condition for membership in a finite ordinal), and only one set of each finite cardinality can be transitive, whence the finite ordinals can be identified with their cardinalities as per the foregoing enumeration.

It is evident for the finite ordinals that the successor of an ordinal α is α∪{α}. In fact this holds for all ordinals. We write α∪{α} as α+1.

The set of all finite ordinals is transitive and hence itself an ordinal. It is the least infinite ordinal, and is denoted ω. It is the canonical example of a countable set, and its cardinality is denoted ${\displaystyle \aleph _{0}}$.

Like the finite ordinals, ω has a successor ω+1, namely {0,1,2,…,ω}. That in turn has a successor {0,1,2,…,ω,ω+1}, and we can continue in this way until we reach {0,1,2,…,ω,ω+1,ω+2…} = ω+ω, denoted ω·2. Continuing faster we eventually reach ω·2+ω = ω·3. We could consider ω·3+1, but moving yet faster we arrive at ω·4, ω·5, and eventually ω·ω, denoted ω. Picking up yet more speed, we arrive at ω, ω, … and then ω. Getting into high gear we speed past ω, ω, ω, …, to arrive at ε₀, the least ordinal α satisfying α = ω.

Throughout this entire sequence, every ordinal has been countable, that is, its cardinality has been ${\displaystyle \aleph _{0}}$. However one cannot infer from this that every countable ordinal is ω. To see this, consider listing all infinitely many even numbers first, and then continue by listing the odd numbers. Then 1 is preceded only by even numbers, but there is no even number immediately before 1 because there is no largest even number. So unlike the usual enumeration of the natural numbers, in which every number but 0 has a predecessor, this enumeration is structurally different, that is, it is not order isomorphic to ω. Instead it is order isomorphic to ω+ω = ω·2, because the set of even numbers standardly ordered is order isomorphic to ω, and likewise the odd numbers.

Furthermore we have not come close to exhausting the countable ordinals: ε₀+1 is countable, and so on. To get past the countable ordinals requires a new insight.

Every ordinal is linearly ordered by inclusion, for example 2 < 4 because {0,1} is a subset of {0,1,2,3}. This linear order is in fact a well-order, that is, every nonempty set of ordinals has a least element. Hence for every predicate that is not false of all ordinals, there exists a least ordinal satisfying that predicate. Furthermore no two ordinals are order isomorphic, and every well-ordered set is order isomorphic to some ordinal, whence the ordinals can serve to encode the order types of all well-ordered sets however large.

There exist uncountable ordinals, whence by the foregoing there exists a least uncountable ordinal, denoted ω₁. The cardinality of this ordinal is denoted ${\displaystyle \aleph _{1}}$, which is the next cardinal after ${\displaystyle \aleph _{0}}$. There is a sequence of increasingly large ordinals as measured by their cardinality, denoted ω₁, ω₂, ω₃, …, with corresponding cardinalities ${\displaystyle \aleph _{1}}$, ${\displaystyle \aleph _{2}}$, ${\displaystyle \aleph _{3}}$, …. The cardinality of an ordinal defines a many to one association from ordinals to cardinals, with all ordinals between ω_i inclusive and ω_i+1 exclusive having the same cardinality ${\displaystyle \aleph _{i}}$.

thanks

I've only just come across your long comment at Talk:Sokal affair. Thank you for the effort, it is rare on WP to see an extended thought, which is somewhat frustrating as there are many considerable virtues to the WP concept, but seeminly almost as many inapposite traits. On the whole, I think it's worthwhile, but I seeing you comment has encouraged me greatly that it may improve.

Your comment above saying Goodbye is, if accurate, a considerable disappoint to those hopes it seems. I will regret it greatly, now that I've come across your work. I'll leave a note at your 'so-called blog' saying more or less this, just in case, if possible. ww (talk) 06:19, 26 February 2009 (UTC)

Hi Ww, thanks for the positive feedback. I've been meaning to make my "blog" more interactive but am still stuck in 1995 technology there. My "goodbye" is in reference not to my departure but to that of the reader leaving my page---maybe a better phrasing would be "drop in again sometime." --Vaughan Pratt (talk) 08:37, 26 February 2009 (UTC)

Hello Sir

Being a renown computer scientist, this fellow computer science/business undergraduate asks you your advice. Which major would you recommend? I love to travel and work with computers. Is there anything you can recommend me? And sorry for posting such a random question. Have a good day! --DarkKunai (talk) 04:37, 6 April 2009 (UTC)

The (2,3) thing

Prof. Pratt, regarding your note at my talk, I've been inactive for over a year. Partly because I seem unable to relate to a demographic among non-science editors that I can't identify, much less understand; example being the deletion of the "Erdos Number" category from bios of mathematicians. But there is some PoV that is very influential here, but which I just don't understand at all.

So I'm not much help anymore. I skimmed the latest (quite a bit!) on the (2,3) talk page. Feel free to email me; I care, even if I feel, well, helpless. In this case, I have some sense of the motivation of the opposing camp (business promotion is perfectly natural) so it seemed imaginable to have a meaningful dialog. But I don't see convergence behaviour. Pete St.John (talk) 19:32, 30 April 2009 (UTC)

Cramer's Paradox

OK, my stub version of Cramer's paradox has been released. We shall see how many things User:Charles Matthews finds wrong with it (LOL). Encyclops (talk) 06:37, 1 May 2009 (UTC)

That's great. One less red link in Gabriel Cramer (one down, two to go). --Vaughan Pratt (talk) 04:04, 2 May 2009 (UTC)

(7 months later) Only one red link to go: Anne Mallet Cramer. If there's no likelihood of her achieving notability then she should simply be unlinked. Any comments? --Vaughan Pratt (talk) 05:47, 20 December 2009 (UTC)

Mathematics of color perception

Dr. Pratt -- I just took a new look at the article that we both worked on, and found this paragraph:

"Finally, since a beam of light can be composed of many different wavelengths, to determine the extent to which a physical color C in Hcolor stimulates each cone cell, we must calculate the integral (with respect to w), over the interval , of C(w)*s(w), of C(w)*m(w), and of C(w)*l(w). The triple of resulting numbers associates to each physical color C (which is a region in Hcolor) to a particular perceived color (which is a single point in R3color). This association is easily seen to be linear. It may also easily be seen that many different regions in the "physical" space Hcolor can all result in the same single perceived color in R3color, so a perceived color is not unique to one physical color."

I don't know who wrote this passage, but a physical color is normally represented as a single *point* (not "region") in the Hilbert space of physical colors -- that is the whole point of using a Hilbert space. To go into detail that is not currently in the article: This Hilbert space may be thought of as having as basis vectors each individual spectral color (to a standard intensity). Then vectors in the Hilbert space correspond to square-summable combinations of these basis vectors -- i.e., an arbitrary light of finite total energy. I solicit your opinion on this, but my plan is to change instances of the word "region" in the above quote to "point".

Thanks in advance.Daqu (talk) 15:18, 20 August 2009 (UTC)

The person to bring that up with would be the one who made the region edit, namely User:Tom Lougheed on 07:24, 4 July 2007. He may be thinking ahead to where a region of Hcolor is associated to a point in R3color, but then he should be saying that a single point in R3color corresponds to a single region of Hcolor, meaning many different points in Hcolor. Also "to a particular" should be "a particular" (one "to" too many). --Vaughan Pratt (talk) 19:46, 20 August 2009 (UTC)

Wilson Riles

I thank you for spending time on Misplaced Pages. But in the future, would it be possible to add a reference to articles you create? Very short stubs like that are usually CSD. Kind regards. Calaka (talk) 06:20, 23 August 2009 (UTC)

Sorry about that, I was doing it in a bit of a rush during lunch -- I was sitting next to his daughter-in-law and wanted to show her the Misplaced Pages article on him---was embarrassed when I discovered there wasn't one (hardly a Californian hadn't heard of him during the 1970s) so I did the best I could under the circumstances with the plan to get back to it when I got home. Hope it looks a bit better now. --Vaughan Pratt (talk) 16:50, 23 August 2009 (UTC)

questions about medicinal clay

Dear Vaughan,

Thank you for taking an interest in the medicinal clay article. I was the one who created and developed it, but then took a leave from it after it became the subject of some rather unfriendly (at least IMHO) editing on the part of certain users. They didn't improve the article, but it seems to the contrary...

I'm sorry that your long and thoughtful contribution and commentary on the Talk:Medicinal_clay page did not receive a quick reply from me as yet. But now I'm coming back to this subject again, and I would like to address your insightful comments soon in some detail.

(Actually, I've been doing quite a bit already in a closely related subject -- the article about Montmorillonite clay, where I've recently added a whole 41 refs about the medicinal use of Montmorillonite! There was a similar opposition there as well, I should add, on the part of some of the same users...)

In any case, thanks again for your contribution, and I hope you're still interested in the subject. Dyuku (talk) 05:58, 3 September 2009 (UTC)

Hi Dyuku. Yes I'm still interested, particularly since it bears on health which is starting to emerge as the biggest drain on the economy. However the role of medicinal clay seems fairly limited and straightforward as I understand it: it simply supplements the liver's role in mopping up toxins. I still don't understand how the toxin-laden clay is excreted however: does it bypass the liver, or go through the liver which somehow ignores it, or give the liver something more to deal with, or what? Anything else worth knowing about medicinal clay in general?

If I can support you against the opposition let me know. Special interests on Misplaced Pages are always a pain to deal with. Be grateful you don't have to deal with the HMOs and drug companies, that's where the real money is today---unless you're a Clarence Darrow you don't stand a prayer against them, if you did longterm care would be the last of your worries. --Vaughan Pratt (talk) 07:25, 3 September 2009 (UTC)

Wolfram's (2,3) spillover

I've made a little effort to figure out this issue because it's also mentioned in more "prime time" articles like Turing machine#Universal Turing machines and Universal Turing machine#Smallest machines besides the dedicated article where I just saw you had some beef with (on its talk page). There's a discussion of how to (concisely) deal with the various notions of universality at Talk:Turing machine#Small UTMs, Wolfram stuff, and (not knowing you edit here until right about now) I had a conversation with User:CBM where I tried to make some sense of the long FOM discussion of 2007. Your input would be appreciated. Pcap ping 21:29, 17 September 2009 (UTC)

Oops, sorry, just noticed this (I think, how'd I miss it?). What sort of input could I help with? Or is it too late now? --Vaughan Pratt (talk) 00:24, 15 November 2009 (UTC)

Better later than never

		The E=mc² Barnstar
		For all your contributions to various articles on Boolean algebra and related topics. Pcap ping 21:51, 17 September 2009 (UTC)

WikiProjects that may be of interest to you

Perhaps you could add WT:COMPSCI and WT:WPMATH to your watch list. Occasionally, discussion on dealing with important articles in these areas happen on those WikiProject talk pages. Admittedly, the Math WikiProject has more active participants. Thanks, Pcap ping 22:01, 17 September 2009 (UTC)

Request for comments

Hello, Vaughan Pratt. This message is being sent to inform you that there currently is a discussion at Misplaced Pages:Wikiquette alerts regarding an issue with which you may have been involved. Thank you.
—Apis (talk) 12:29, 14 November 2009 (UTC)

Discussion on Solar Greenhouse

Vaughan,

I basically agree with what you are saying on about the article Solar greenhouse on the talk about, but many of your comments are not about the article, and are instead about Apis. I think you'd be more effective in getting towards an improvement of the article if you were careful to keep your comments on the talk page to the content of the article. Even if you are insulted stupidly, it can be best to walk away from that and return the topic to the article. If you think user behavior does need to be addressed, you could comment on the user's talk page or pursue various other channels to address it, as Apis is apparently starting to do regarding your comments. Thanks for caring about getting the page right!Ccrrccrr (talk) 22:12, 14 November 2009 (UTC)

Excellent advice, thanks. Next time I find myself tearing my hair out I'll try to follow the "tearing out hair" protocol, if I can remember it. There should be a link at the top of every talk page to help people like me who normally have no occasion to use it and therefore have no clue where to find it. It is much easier just to type that sort of thing in place; if others want to move it to a more appropriate place I have no objection, Pete St. John once did that to some of my concerns and I had no objection then.

Would Apis object strenuously if I struck out the offending parts of my talk page contributions to that article? --Vaughan Pratt (talk) 00:06, 15 November 2009 (UTC)

Yes, although not strenuously, but I fail to see what that would accomplish. A better place to start would be to refrain from making further personal attacks.
—Apis (talk) 12:43, 16 November 2009 (UTC)

Wikiquette alert

Hello, Vaughan Pratt. This message is being sent to inform you that there currently is a discussion at Misplaced Pages:Wikiquette alerts regarding an issue with which you may have been involved. The discussion is about the topic User:Vaughan_Pratt. Thank you. Dmcq (talk) 18:54, 16 November 2009 (UTC)

greenhouse effects

Hello again, Vaughan!

I've been reading about atmospheric greenhouse effects recently, and then stumbled upon some of your discussions in this area. Are you aware of the following recent publication?

Gerhard Gerlich, Ralf D. Tscheuschner, Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics. Int.J.Mod.Phys.B23:275-364,2009 http://arxiv.org/abs/0707.1161v4

Here's from the abstract,

"The atmospheric greenhouse effect, an idea that authors trace back to the traditional works of Fourier 1824, Tyndall 1861 and Arrhenius 1896 and is still supported in global climatology essentially describes a fictitious mechanism in which a planetary atmosphere acts as a heat pump driven by an environment that is radiatively interacting with but radiatively equilibrated to the atmospheric system. According to the second law of thermodynamics such a planetary machine can never exist."

Among other things, the authors claim that the conventional explanation of what takes place in the real-life glass greenhouse is wrong...

What do you think about it?

Cheers, --Dyuku (talk) 00:44, 20 December 2009 (UTC)

Hi Dyuku. Good to hear from you again.

Why is anyone interested in this paper? This is the same sort of rubbish that people upload by the minute to Youtube and debate by the hour on Amazon discussion groups. Evidently arXiv has been targeted in the same way, which is too bad other than being a nice exercise for students to identify the problems with the junk submissions. This one must surely set something of a record in that regard.

If you need a professional opinion ask any reputable meteorologist. If you want I can tell you a hundred things wrong with this paper, but I'm not a meteorologist so my opinion won't carry much weight. (I was however trained to M.S. level in separate programs in each of pure mathematics and physics, have supervised several EE students, and have operated a company building computers for SOCOM USN for some years, quite apart from my publications in computer science, logic, and algebra, so I'm not completely unfamiliar with this sort of technical material.) --Vaughan Pratt (talk) 05:41, 20 December 2009 (UTC)

Dear Vaughan,

Did you miss that this article was published in a peer-reviewed journal? (It was uploaded to arXiv prior to that, and was critiqued for a long time before being accepted at Int.J.Mod.Phys.) These are the people who take the Wood Experiment seriously, and I saw you dealing with this recently. So I thought you'd be interested...

You don't need to tell me a hundred things wrong with this paper, just one or two would do! :) --Dyuku (talk) 20:55, 20 December 2009 (UTC)

Ok, here are two.

1. Those who may not be physicists but who are at least familiar with the norm in scientific writing will immediately recognize this article as a hatchet job on established science, both from its hyperbolic language and from its novel attacks on Tyndall and Arrhenius. The attacks are easily shown to be false (not to mention scurrilous), but even if they weren't their novelty would demand confirmation by some other attacker.

2. Those who are physicists will find G&T's argument that greenhouse warming violates the 2nd law of thermodynamics laughable. The relevant effects and analogies can be computed wave-theoretically but for conductive and radiative interactions of this kind the statistics is more readily seen when expressed in terms of particles.

  The only significant difference between the atmosphere and a blanket as a thermal insulator is the ratio of phonons to photons in each. Increasing greenhouse gases in the atmosphere increases the number of collisions experienced by photons on their journey from the planet. Increasing the number of blankets on a bed increases the number of collisions experienced by phonons on their journey from the bed. Since both types of particles obey Bose-Einstein statistics, any argument showing that more greenhouse gas has no warming effect leads to the same conclusion for more blankets.

  G&T are pulling the wool over the eyes of innocents. I have no reliable conjecture as to what is behind the acceptance of this paper, politics being something of a mystery to me. --Vaughan Pratt (talk) 09:06, 21 December 2009 (UTC)

---

  Incidentally who were you referring to with "These are the people who take the Wood Experiment seriously?" The editors of this particular journal, or physicists in general? Actually either one would be surprising to me: I would have thought Foundations of Physics would be a more likely place to find Wood supporters.

  It occurs to me that we may be seeing a minor variant of the Newton effect. Newton looked for the diffraction effect that Huygens' wave theory of light would predict, failed to see it, decided light consists of corpuscles instead, and a century of physicists agreed with Newton until Thomas Young proved Newton wrong by showing that diffraction happens on a smaller scale than Newton anticipated. Here Wood looked for the heating effect in greenhouses that one would expect if Fourier, Tyndall, and Arrhenius were right, failed to see it, decided the effect is insignificant, and a century of physicists agreed with Wood.

  This analogy falls down in one small but important detail. In the 1960s when I went to school in Australia, and my wife in the US, we were both taught that the window material in greenhouses increased their temperature significantly. Had Wood's view prevailed by the 1960s this would be like students being taught half a century after Newton that light is a wave. Evidently Wood's experiment failed to convince the community, who by then would surely have been well calibrated on the magnitudes involved for all commonly encountered greenhouse-effect substances whether solid, liquid, or gas (certainly Tyndall and Arrhenius were) and therefore one imagines did not take Wood's experiment seriously.

  And rightly so. Wood made no attempt in his paper to reconcile his experimental observations with what theory would predict. If he had he would have realized that the effect works for greenhouses as for the atmosphere, with thicker glass (corresponding to higher CO2 levels) and less thermally conductive materials such as acrylic (corresponding to methane instead of CO2) both raising the temperature. And not by insignificant amounts. With 3/32" glass the greenhouse effect in glass produces a warming of approximately a degree centigrade, as Wood observed. With 3/8" acrylic my experiments have been demonstrating gains of 20 C.

  The big difference between 18th and 20th century physicists in the Newton-Wood analogy is that the former believed Newton over Huygens while the latter believed Tyndall and Arrhenius over Wood. The recent shift to Wood a century after his experiment is hard to explain (why is only Wood's experiment mentioned today but never the community's response to it back then?) but definitely wrong other than within the very narrow parameters Wood allowed himself, namely thin glass. Arrhenius's formula is not about a fixed level of CO2 but about the logarithmic dependence of temperature on level, which Wood did not address at all in the context of greenhouses. Nor did he experiment with any materials except glass and rock salt, understandable since plastic had not yet been invented. Had he used plastic instead of glass his results would have been very different on account of plastic's significantly lower thermal conductivity (which becomes inconsequential for materials that pass infrared since that creates a leakage path that bypasses conduction). Plastic is therefore better suited than glass to greenhouses for which solar heating is deemed desirable (there are other ways of heating greenhouses when additional warmth is needed but solar is surely the greenest).

  Incidentally you may be interested to know I'm currently constructing a computer-controlled lab to run more comprehensive and accurate experiments under a wide range of conditions, with parameters playing the role in greenhouses that various levels of various greenhouse gases play in the atmosphere, along with other parameters such as length of day (relevant to non-circadian artificial illumination of greenhouses and to cosmology), thermal mass, rate of convection, etc. More data will permit a more accurate assessment of the extent of the analogy between greenhouses and the atmosphere. One can compute these in principle from theoretical considerations, but the computations are sufficiently complex as to benefit from experimental corroboration, which may expose modeling errors; besides, the public puts more faith in experiment than theory and rightly so. (Being a theorist is not the same thing as being unaware of the limitations of theory.)

  I'll be in a position to solicit public comments once I've collected enough data to draw conclusions beyond the mere observation above that thickness and material play a role. For now all I have that's worth saying about the lab is that it's under way. --Vaughan Pratt (talk) 16:40, 21 December 2009 (UTC)

Hello, Vaughan,

Here are a few notes on what you wrote above.

You wrote:

Incidentally who were you referring to with "These are the people who take the Wood Experiment seriously?" The editors of this particular journal, or physicists in general?

I'm talking about Gerlich & Tscheuschner. They quote the whole big passage from Wood in their paper, and wholly agree with him. Wood actually had doubts about the atmospheric greenhouse effect, in his time already! Read the paper.

VP: Ah, I misinterpreted the referent of "These." Yes, I'd read enough of the G&T paper to see that they are as much fans of Wood as they are opponents of Tyndall and Arrhenius.

You wrote:

a century of physicists agreed with Wood.

Not at all. As far as I know, everyone ignored Wood. But now, even Misplaced Pages accepts that "actual greenhouses do not function in the same way as the atmospheric greenhouse effect does."

The distinction between the greenhouse effect and real greenhouses

VP: Sorry, I should have been clearer that I was writing a fairy tale analogy at that point. If you look at the paragraph immediately following, starting "This analogy falls down in one small important detail," you'll see that I'm well aware that everyone ignored Wood.

You wrote:

the effect works for greenhouses as for the atmosphere

You're wrong here, I'm afraid. So here I agree with Misplaced Pages.

VP: Misplaced Pages is wrong in lots of places, as I well know -- I've fixed many technical errors in my several years of editing Misplaced Pages articles and so far I would estimate fewer than 1 in 100 of my edits have been reverted (not counting those that have merely been improved on). The more important question here is whether Wood is correct. Do you have any reason whatsoever, besides this very brief paper by Wood reporting on a single experiment, with nothing to back it up (such as someone subsequently saying they agreed with Wood) except for the fact of publication, to think that the greenhouse effect is not significant for windows? If the entire theory of anthropogenic global warming were based on a total of three temperature measurements at two places, one of which was discarded because the outcome did not agree with the experimenter's theory, with the experimenter then saying self-deprecatingly "I do not pretend to have gone very deeply into the matter, and publish this note merely to draw attention to the fact that trapped radiation appears to play a role in preventing the planet from freezing," would you then go ahead and swear by anthropogenic global warming? I certainly wouldn't, I would say that until the experiment was shown to be repeatable AGW was rubbish. Bear in mind that for each minute Wood invested in his experiment Tyndall invested days. Then consider that G&T seek to deny Tyndall any credit for his hard work while holding up Wood as a great scientist for essentially no work at all by comparison. Wood was a great physicist; so was Newton; does that make either of them infallible?

I also think there's a bit of a general misunderstanding here... Nobody is about to deny that Earth's atmosphere acts as a bit of a thermal insulator. Which reduces the swings in temperature between day and night, for example. So atmosphere acts as a buffer.

VP: I agree about the misunderstanding, which is more than just a "bit." I strongly disagree with your next sentence however: most if not all reputable meteorologists would deny that the atmosphere without its greenhouse gases acts as an insulator. It was Tyndall who first wrote that if the Earth's atmosphere were deprived of its greenhouse gases the Earth would freeze over. So are you claiming, as G&T are obliged to do, that Tyndall (and hence Arrhenius) was wrong? That would be a much more interesting discussion than this G&T paper. (Without asking him, what would you predict William M. Connolley would say would happen to the Earth's temperature if all the greenhouse gases were removed from it leaving just the nitrogen, oxygen, and argon?)

But this buffer/insulator also _reduces_ the temperature during the day, besides keeping it up at night.

VP: That's very interesting, where did you see that? In the following two scenarios, which would end up with the higher surface temperature at noon? (a) The Earth is slowed down to rotate once every 2400 hours instead of 24 hours, without changing the atmosphere. (b) The whole of the Earth's atmosphere is removed without changing how fast the Earth rotates.

As you can probably guess, I'm somewhat of a skeptic in regard to AGW, as it's commonly defined. And I don't see it in any way, politically, as a Left vs Right issue. For example, here's a good article from a veteran leftist author you may be familiar with.

Alexander Cockburn, Turning Tricks, Cashing In on Fear, DEC 18, 2009

http://www.counterpunch.com/cockburn12182009.html

The article is about Climategate, certainly a notable scandal.

VP: Well, if you can quote Misplaced Pages to prove I'm wrong, may I return tit for tat here? To quote from the article on Cockburn, In contrast, Cockburn's position on global warming is consistent with views usually held on the right. He believes the phenomenon has not been proven to be caused by humans, citing the statements of Dr. Martin Hertzberg that rising CO2 levels are a symptom, not a cause, of global warming, which Hertzberg asserts is the result of natural, predictable changes in the Earth's elliptic orbit. In fact, Hertzberg is a semi-retired explosives expert who does not claim to be a climatologist. Ironically, of the many arguments made by Hertzberg listed at , the one he actually gets (almost) right, namely the direction of the causal arrow in the ice core record between CO2 and temperature, is precisely the one Misplaced Pages picks as (presumably) an instance of a right-wing view. This is backwards: in fact climate scientists today view the rise not as an indication of CO2-induced warming but rather as the result of a dramatically large positive feedback, so they would meet Hertzberg halfway on that point. I should add that Hertzberg also gets one other point half-right, namely the one about the ocean, since this too participates in a strong positive feedback, one that we'll see quite dramatically as soon the current thinning of the arctic ice reaches its vanishing point, which will be a discontinuous and therefore massive trigger. However he's completely out to lunch on the rest of his long laundry list of failings of climate science, which as Misplaced Pages correctly infers put him on the political right on AGW.

For quite a while now, I had some doubts about the atmospheric greenhouse effect. And then I discovered Gerlich & Tscheuschner article, which was quite refreshing...

VP: So you didn't have any problem with its non-scientific judgmental tone then? How did it compare in that regard with other papers you've read in scientific journals of comparable quality? And did you accept G&T's reasoning about the 2nd law of thermodynamics? And what was the basis for your own doubts before you read G&T?

All the best, --Dyuku (talk) 00:19, 22 December 2009 (UTC)

Hi Dyuku. I've interleaved my replies (7 of them) inline with your responses, each in the form of one paragraph prefixed with "VP:". If any of them are unclear I'd be happy to expand on them as needed. Cheers, --Vaughan Pratt (talk) 03:58, 22 December 2009 (UTC)

From JDC

Hi Vaughan Just discovered you are a Wiki Editor too. Regards John D. Croft (talk) 23:07, 29 December 2009 (UTC)

Only since 2006. I see from your talk page that you've been one since 2005. You twigged faster than me. Cheers, mate. --Vaughan Pratt (talk) 00:54, 30 December 2009 (UTC)

Climate change articles are under probation

Thank you for your contributions to the encyclopedia! In case you are not already aware, an article to which you have recently contributed, Hockey stick controversy, is on article probation. A detailed description of the terms of article probation may be found at Misplaced Pages:General sanctions/Climate change probation. Also note that the terms of some article probations extend to related articles and their associated talk pages.

The above is a templated message. Please accept it as a routine friendly notice, not as a claim that there is any problem with your edits. Thank you.

I absolutely agree with you that the level of discourse on those pages has descended quite a bit below optimal, but generalized statements about the illogic we've come to expect routinely from the AGW denier community are a step in the wrong direction.

On a more personal note, the day I figured out how to apply PCA to my own research was one of my happiest in the last few years. - 2/0 (cont.) 02:05, 7 January 2010 (UTC)