# User talk:Vaughan Pratt

## 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 Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers:

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 Wikipedia: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 Wikipedia. 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 Wikipedia 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 Wikipedia talk:WikiProject Mathematics. You can add it to your watchlist if you like. If you have any questions about Wikipedia 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. --KSmrqT 08:17, 8 August 2006 (UTC)

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

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. --KSmrqT 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, "&minus;", 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 "&cap;" 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. --KSmrqT 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.  --LambiamTalk 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 Wikipedia'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 (Talk) 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

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)

## 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

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 Wikipedia 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 Wikipedia 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 Wikipedia: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 Wikipedia 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 Wikipedia 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

Thank you for uploading Image:Bands.svg. However, it currently is missing information on its copyright status. Wikipedia takes copyright very seriously. It may be deleted soon, unless we can determine the license and the source of the image. If you know this information, then you can add a copyright tag to the image description page.

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)

## Image copyright problem with Image:BarsParams.svg

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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 $\wedge$ (\wedge) into ∧ and $\vee$ (\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 $\nu$ (\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)

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 Wikipedia'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: Cop × CSet 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 Wikipedia 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)

## Ordinal (number)

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

Thank you for visiting my User Talk page. You might also enjoy my approximation to a blog, "Sayings of Chairman Pratt." (I started out thinking I could keep this at the bottom of this page but grew tired of moving it back down after each new item was added below it.) --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 $\aleph_0$.

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 ω2. Picking up yet more speed, we arrive at ω3, ω4, … and then ωω. Getting into high gear we speed past ωω, ωωω, ωωωω, …, to arrive at ε0, the least ordinal α satisfying α = ωα.

Throughout this entire sequence, every ordinal has been countable, that is, its cardinality has been $\aleph_0$. 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 $\aleph_1$, which is the next cardinal after $\aleph_0$. There is a sequence of increasingly large ordinals as measured by their cardinality, denoted ω1, ω2, ω3, …, with corresponding cardinalities $\aleph_1$, $\aleph_2$, $\aleph_3$, …. The cardinality of an ordinal defines a many to one association from ordinals to cardinals, with all ordinals between ωi inclusive and ωi+1 exclusive having the same cardinality $\aleph_i$.

## 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)

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)
Neither of Gabriel Cramer's parents having a separate entry in Wikipedia, I've now unlinked them both from their son's article. --Vaughan Pratt (talk) 21:14, 7 July 2010 (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 H_color stimulates each cone cell, we must calculate the integral (with respect to w), over the interval [Wmin,Wmax], 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 H_color) to a particular perceived color (which is a single point in R^3_color). 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 R^3_color, 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)

I hope I'm not barking up the wrong tree, but: 1) I took a look at this section of the article we both worked on, and it strikes me as really not bad at all, if I do say so myself.
2) Yet I recently realized that the set of physical colors -- which I've long thought of as a *Hilbert space* -- is not really a Hilbert space. What it is, is the space of all measures on the set of wavelengths (which could if desired be restricted to the visible ones). This allows, e.g., a single wavelength to contribute say half the energy of a "physical color" but a range of wavelengths to contribute the rest of the energy. Another reason it's not a Hilbert space is that the contribution of each wavelength is never negative.
I believe the technical term for a "space of all probability measures" like this is a "Choquet simplex". But here there is an additional factor of (0,∞) to account for the total energy contained in the "physical color". (Alas, I don't know much about such things.)
I suspect this can be made to resemble, or be, a Hilbert space if one "takes logarithms" in a sense.Daqu (talk) 06:52, 5 September 2010 (UTC)

You're quite right about applicability of Choquet theory, which I had to look up just now, thanks for that pointer. What's needed I suppose would be convex regions of the affine counterpart of Hilbert space, projected onto R3color. This is essentially what happens in the CIE diagram, every color within which can be obtained as an affine or barycentric combination (linear combination whose coefficients sum to 1) of colors chosen from around the boundary, each of whose points corresponds to a single wavelength. The additional requirement that the coefficients be nonnegative creates a convex subspace of affine space coordinatized by its extreme points, uniquely so only when they are linearly (or rather affinely) independent, namely the interior of the CIE diagram. Any spectrum in Hcolor can be normalized to unit area (taking care of your concern about total energy), and the resulting values taken as the barycentric weights around the boundary to produce a point within the CIE diagram corresponding to the human-perceived color of that spectrum. The boundary of the CIE diagram being planar, its continuum many extreme points are far from linearly independent and therefore for any given color on the CIE diagram there are many spectra each serving as a different coordinatization of the same color. --Vaughan Pratt (talk) 19:27, 5 September 2010 (UTC)

## Wilson Riles

I thank you for spending time on Wikipedia. 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 Wikipedia 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)

Thanks for creating an article about Wilson Riles. It was sorely needed; he was one of the best-known people in California back in the day. I just finished working it up, adding some more references and wikfying it; feel free to show it to his daughter-in-law now! --MelanieN (talk) 01:01, 6 March 2012 (UTC)
P.S. Turns out there isn't an article about Bill Honig either. I'll put that on my to-do list. --MelanieN (talk) 01:01, 6 March 2012 (UTC)

Glad someone appreciated it at last! Thanks for the Wikification. Looking forward to something on BH. --Vaughan Pratt (talk) 08:39, 6 March 2012 (UTC)

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 Wikipedia 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)

Hello, Vaughan Pratt. This message is being sent to inform you that there currently is a discussion at Wikipedia: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)

Hello, Vaughan Pratt. This message is being sent to inform you that there currently is a discussion at Wikipedia: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)
In the meantime I got to wondering whether Wood's paper had indeed been ignored. So I looked through a few of the issues of Phil. Mag. following the one in which Wood's article appeared, and to my surprise found an article about ten times as long as Wood's little note refuting it in great detail. It was written by no less than Charles Greeley, then the director of the Smithsonian Astronomical Observatory and later secretary of the Smithsonian from the Depression to WWII. I also found another paper by Wood in the same volume of Phil. Mag. a few issues later claiming to shoot down yet another theory (unrelated to the greenhouse effect), which like his previous paper was rebutted, this time even more promptly. For more on this see http://boole.stanford.edu/wood . --Vaughan Pratt (talk) 04:55, 22 March 2010 (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 Wikipedia 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 Wikipedia.

VP: Wikipedia is wrong in lots of places, as I well know -- I've fixed many technical errors in my several years of editing Wikipedia 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 Wikipedia 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 [1], 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 Wikipedia 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 Wikipedia 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 Wikipedia: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.
Having had to defend WMC from quite recent attacks on him by some rather vicious AGW deniers, I was sufficiently annoyed by his summary judgment of a book on no apparent basis whatsoever as to feel that maybe I shouldn't be defending him after all. The only reason I didn't expand on my objection to his casual dismissal of Muller and MacDonald, leaving it instead as merely a "generalized statement," was that I felt I should stop at that point to give people a chance to reply before going into more detail. Unless WMC or Atmoz or someone else in their camp has something more concrete to say against M&M I would feel like I was flogging some kind of dead horse were I to expand on my objection.
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)
Yes, it's neat stuff. I wondered for years what "PROFSVD" meant on Gene Golub's license plate until my student filled me in. Now I can understand AI talks by the new generation of AI researchers, who apply all that technology in ways the old generation have no idea about, and can use it in my own speech research. --Vaughan Pratt (talk) 03:15, 7 January 2010 (UTC)

## Constructively speaking

Hi, I noticed on one of the talk pages that you may have an interest in constructive non-standard analysis. Your contribution would be welcome. Tkuvho (talk) 14:33, 10 January 2010 (UTC)

Hi, Tkuvho. Thanks for drawing my attention to this article. However I make it a rule only to contribute to articles I know something about, and I'm sorry to say that constructive NSA is above my pay-grade.
I would say however that the very need to redeem NSA by having to make it constructive in order to make it attractive mathematically is itself a strike against NSA. The benefit of topology as an approach to analysis is that one doesn't need to abandon one's classical nonconstructive outlook in order to understand it and explain it to students having a wide range of abilities. Any subject that depends on constructivity in order to make sense is going to appeal only to a few students, the rest will throw up their hands and move on to combinatorics or algebraic geometry or something that makes more sense to them. --Vaughan Pratt (talk) 17:23, 10 January 2010 (UTC)

## Nothing about Fourier or signal processing?

I've found nothing about Fourier in this article or in any of the articles bearing on climatology and the various atmospheric sciences. Why did Fourier invent spectral analysis, a fundamental tool of signal processing, and apply it to his study of heat transfer, if it is so irrelevant to the subject that no Wikipedia editor even mentions it in the context of heat? --Vaughan Pratt (talk) 18:00, 7 December 2009 (UTC)

If it's so important, why don't you put something in the article about it? WP:SOFIXIT. Wikipedia editors aren't omniscient-- we wait for experts to happy by and ask questions like yours. They we point out that it's a volunteer effort, so pitch in. SBHarris 18:29, 2 February 2010 (UTC)

## You are now a Reviewer

Hello. Your account has been granted the "reviewer" userright, allowing you to review other users' edits on certain flagged pages. Pending changes, also known as flagged protection, is currently undergoing a two-month trial scheduled to end 15 August 2010.

Reviewers can review edits made by users who are not autoconfirmed to articles placed under pending changes. Pending changes is applied to only a small number of articles, similarly to how semi-protection is applied but in a more controlled way for the trial. The list of articles with pending changes awaiting review is located at Special:OldReviewedPages.

When reviewing, edits should be accepted if they are not obvious vandalism or BLP violations, and not clearly problematic in light of the reason given for protection (see Wikipedia:Reviewing process). More detailed documentation and guidelines can be found here.

If you do not want this userright, you may ask any administrator to remove it for you at any time. Courcelles (talk) 01:18, 18 June 2010 (UTC)

## Speedy deletion declined: Carbon budget

Hello Vaughan Pratt, and thanks for your work patrolling new changes. I am just informing you that I declined the speedy deletion of Carbon budget - a page you tagged - because: Definitely needs fixing, but does not meet any criterion for speedy deletion. Use AfD to pursue deletion. Please review the criteria for speedy deletion before tagging further pages. If you have any questions or problems, please let me know. decltype (talk) 21:49, 2 July 2010 (UTC)

Ok, but I did review the criteria before tagging it. User talk:128.160.199.100, who says he's an oceanographer, had commented at the bottom of Talk:Carbon cycle that the page should be deleted as it was "just incoherent babbling." After reading the article I agreed, and so looked to WP:CSD to see which criterion best matched this description. It looked like db-g1 was the best match to "incoherent babbling" (which pretty accurately describes the article). If you disagree then could you please rewrite that criterion to clarify why this piece of "incoherent babbling" as the oceanographer called it does not meet the "patent nonsense" criterion. It sure looks like patent nonsense to me. Note that I wasn't tagging it for any of the eight excluded reasons (poor writing etc.). --Vaughan Pratt (talk) 23:47, 2 July 2010 (UTC)
Even if it doesn't hold water from an expert's point of view it consists of coherent sentences - that is, it didn't look like nonsense to any of the contributors who have previously edited the article (it has been around since 2008). A unilateral speedy deletion I would deem as controversial, and thus inappropriate. I really think AfD would be the best venue to pursue deletion. Alternatively, the article could be turned into a redirect (if a suitable target exists). This would almost surely be preferable to deletion. Regards, decltype (talk) 15:35, 6 July 2010 (UTC)
Ah, I see I should have drawn the distinction between deletion and redirection, I had been planning to delete the body but redirect the page to carbon cycle, which seems to be the commonest meaning of the term "carbon budget" (it's not a widely used term though it does appear a few places albeit not with a standardized meaning). See any reason not to do that? If I do the redirect and spot a worthwhile number or reference in carbon budget that's not already elsewhere in Wikipedia I'll merge it into the appropriate article. For the moment however I'll just put a merge tag on carbon budget. --Vaughan Pratt (talk) 18:24, 6 July 2010 (UTC)
No objections to that, it seems like a reasonable course of action. decltype (talk) 21:01, 7 July 2010 (UTC)
Ok, great, I'll wait a few more days for any objections to surface then merge. --Vaughan Pratt (talk) 21:09, 7 July 2010 (UTC)

## Proof (quality)

This is an automated message from CorenSearchBot. I have performed a web search with the contents of Proof (quality), and it appears to include a substantial copy of http://plumbot.com/Proof.html. For legal reasons, we cannot accept copyrighted text or images borrowed from other web sites or printed material; such additions will be deleted. You may use external websites as a source of information, but not as a source of sentences. See our copyright policy for further details. (If you own the copyright to the previously published content and wish to donate it, see Wikipedia:Donating copyrighted materials for the procedure.)

This message was placed automatically, and it is possible that the bot is confused and found similarity where none actually exists. If that is the case, you can remove the tag from the article and it would be appreciated if you could drop a note on the maintainer's talk page. CorenSearchBot (talk) 05:45, 6 July 2010 (UTC)

The direction of the theft is backwards, plumbot.com got that material from Wikipedia in the first place. --Vaughan Pratt (talk) 18:09, 6 July 2010 (UTC)

## Herding cats

It occurs to me, out of the blue and apropos of nothing in particular, to remark that editing Wikipedia requires all the skills of an accomplished herder of cats. Today everyone seems to be a Wikipedia editor, and satisfying them all can become a significant component of the overall editing process. Many would-be editors who are highly qualified in their area are easily put off by those with less than a tenth of their qualifications but with ten times the aggressiveness. I'm too thick-skinned myself to be easily put off that way, but I know some experts who have published dozens or even hundreds of papers in their area who just give up after being discouraged by a few wikilawyers who jump on them for violating who knows what arcane Wikipedia guidelines. It's really too bad the real experts are so easily put off contributing to Wikipedia. --Vaughan Pratt (talk) 06:38, 6 July 2010 (UTC)

## Proof (truth)

Where does the text in Proof (truth) come from? Did you write it yourself, or did you split it from another article? Regards, Theleftorium (talk) 09:34, 6 July 2010 (UTC)

Wrote it all myself. (I can claim some authority on the subject, having first learned about syllogistic proof from a book my high school swim coach lent me in 1960, studied it further in freshman philosophy in 1962, wrote my master's thesis in 1969 on translating Lewis Carroll's syllogisms into logic by computer, gave the first polynomial-length proof system for primes (showing they're in NP) in 1974, invented dynamic logic in 1976 and action algebra in 1990, taught a course on algebraic logic, CS 353, for twenty years, and am affiliated with the Symbolic Systems program as well as CS and EE. The many links in the article should suffice as the references, but I'm happy to either source or delete as appropriate any sentence you have doubts about or feel like challenging.) Vaughan Pratt (talk) 17:54, 6 July 2010 (UTC)
Please don't remove maintenance tags without addressing their concerns. Everything in that article may be true, but it is equally true that the article is unsourced. This is out of keeping with our policy on verifiability. Notwithstanding your credentials, we provide sources which our readers may use to verify material on their own; this is a necessary part of being an encyclopedia that anyone may edit. Other resources, such as Scholarpedia, which vet their contributors and provide peer review, may be able to rest on the authority of their authors, but we don't. It isn't about the accuracy of your material; it's about Wikipedia's policies. And the template serves a purpose. If you do not intend to add sources, the tag puts the article into a category which alerts other contributors that sources are necessary. The See also links are not usable as sources; Wikipedia articles do not cite other articles.
See also Wikipedia:Researching with Wikipedia, which may help to clarify both why the "See also" wikilinks do not count as sources and why sources are required. --Moonriddengirl (talk) 18:21, 6 July 2010 (UTC)

Since you decided to post some criticisms of me at Wikipedia talk:WikiProject Mathematics#Review needed at Proof (informal) to establish consensus, I have replied there. However, for future reference, user talk pages are the proper place for raising such concerns with other editors. Gandalf61 (talk) 19:00, 11 July 2010 (UTC)

At Wikipedia talk:WikiProject Mathematics#Review needed at Proof (informal) to establish consensus you now say "The link to Vaughan Pratt from User:Vaughan Pratt was placed there without my knowledge or approval. I neither knew nor cared why it was put there ...". And yet on May 7, 2006, the first version of your user page was created by User:Vaughan Pratt with contents "Link to Vaughan Pratt". This looks as if it was very much with your "knowledge and aapproval", unless you perhaps wish to claim that someone else was using this account at that time. If there is some inexplicable misunderstanding here, and you are not in fact Vaughan Pratt in real life (as many editors seem to believe) then you simply have to say so. Indeed, if you are not Vaughan Pratt then you are required to say so, as per this section of our username policy. Gandalf61 (talk) 23:41, 11 July 2010 (UTC)
I'm very sorry, Gandalf61, whoever you are in First Life, but I have run out of time to pursue your concerns, which appear to me to have degenerated from the unreasonable to the absurd. You started this by complaining about me at Wikipedia talk:WikiProject Mathematics#Review needed at Proof (informal) to establish consensus, most of which I simply ignored since I did not wish to start a war, but felt obliged to protest your most egregious complaint, your suggestion that I identify myself on Wikipedia with Vaughan Pratt rather than User:Vaughan Pratt, which unlike your other complaints is hitting below the belt. You have misrepresented my defense of myself with "Since you decided to post some criticisms of me at ..." when any reader of that page can see by going to the top of that section that you decided to post some criticisms of me at that page and I felt obliged to respond to the worst one while ignoring the rest. Note moreover that I would still be User:Vaughan Pratt, and would still be doing all the same edits I do, even if the page Vaughan Pratt had never existed. I feel your complaining has now degenerated into WP:wikihounding. I have no idea what you're referring to in the above, but I am aware of no revision page that bears out your claim. I certainly never put that link there myself. If you feel your concerns warrant troubling the authorities please raise them with them. --Vaughan Pratt (talk) 04:37, 12 July 2010 (UTC)
I don't have concerns - I simply wanted to put the record straight concerning some of the mistaken claims you were making about your edit history. Either you or someone else using your account put that link on your user page - I don't understand why you continue to insist otherwise. Anyway, the history of your Wikipedia posts is there for anyone to see, so I don't need to labour the point.
On reflection, I think it is possible that you may have misunderstood what is meant in context by "identify yourself". It simply means that you act and post on Wikipedia as if you are Vaughan Pratt in real life, and are happy for other editors to make that assumption about you. I could have said "claims to be Vaughan Pratt", but that might have been taken to imply that I was sceptical of that claim, which I am not. There is nothing wrong with identifying yourself with the subject of a Wikipedia article (as long as you are indeed that person) - on Wikipedia you are free to reveal or hide your real life identity as you choose. When I said that you identify yourself as Vaughan Pratt it was not a complaint or a criticism - simply a statement of fact - and there was absolutely no need for you to post a "defense".
Personally, I don't care whether you are Vaughan Pratt, the ghost of Albert Einstein, or the Great Panjandrum. I was (and continue to be) simply baffled by your bizarre attempts to deny the facts of the matter, which are both obvious and innocent. Gandalf61 (talk) 09:01, 12 July 2010 (UTC)
For most people not in a witness protection program or engaged in covert surveillance it is a blessing (or whatever) to be in Wikipedia, but not for editors, for whom it creates a conflict of interest and is therefore something of an embarrassment to the editor, though obviously not to others for whom it serves the same purpose as all biographical articles. (A similar situation arises for conference program committees, with some conferences not allowing the PC members to submit, some not caring, and a few even taking the position that if the organizers saw fit to put you on the PC then your paper can bypass the PC's review, which is not unreasonable in areas so small that most of those with anything worth saying on the subject are on the PC.) I am highly sensitive to that problem, and therefore to avoid any appearance of conflict of interest I have scrupulously stayed away from that page from the day I started editing on Wikipedia. Except in situations where people ask me for information they (not me) could add to that page, I try to act like the page simply does not even exist on Wikipedia. I identify myself on Wikipedia solely as User:Vaughan Pratt. It is therefore disingenuous for you to argue, on the ground that the Wikipedia editor User:Vaughan Pratt is the same person as Vaughan Pratt (which is not in dispute), that I identify myself on Wikipedia as the latter. If you as a Wikipedia editor were cursed with the same dual identity problem you would have a better appreciation for a distinction that I have consistently drawn in this unfortunate debate and which you have inexplicably turned a disingenuously blind eye to throughout.
Regarding this link you keep attributing to me, you seem to have overlooked that the link appears on both sides of the editing you pointed me at, showing that I could not have placed it there on the occasion to which you refer. I am certain I did not insert such a link, and was surprised when I saw it there since I had no idea how it could have got there.
Normally I don't go snooping around in other people's user talk pages in order to wikihound them, but on this occasion I looked at yours and noticed that there was refreshingly little discord, suggesting you don't normally allow yourself to be drawn into so heated a dispute. Finding this puzzling, I reflected on the events leading up to this dispute. It began with my article Proof (truth), which I'd previously been developing over some months in my user space until I felt it was about right. Almost as soon as I put it in article space people like Michael Hardy and you with their own ideas on the matter, without any discussion or prior warning at all on the article's talk page, immediately started making what they felt were the appropriate repairs to problems they saw. Not noticing that logic was a subcase of the article, MH moved it to Proof (logic), which can be done without administrative intervention but cannot be undone without it since it would overwrite the redirect. Disagreeing that "evidence" described premises, a point on which the mathematical community appears to be split roughly 50/50, you fixed that problem, again without consultation, by moving the article yet again, to Proof (informal), and deleting everything in the article to do with mathematical and logical proof (two forms of proof that themselves are quite different from each other as the article has noted from the outset), when in retrospect there was a very simple fix to satisfy the 50% that objected to the word "evidence:" just add "or argument". The article is now back to its original title and scope and is developing nicely, but the battle to make that happen took some time. In view of your role in adding to my work, it adds insult to injury to disparage the additional work you caused me as being attributable to my wikiholism.
Normally when my edits are reverted I don't redo them but instead raise the issue on the talk page. I did this in the case of your wholesale deletion of the mathematical and logic section of Proof (truth), but pointed out in doing so that your deletion made it harder for people to evaluate the situation and that I would soon put that material back. Time being of the essence in that situation, I only waited a short while for your response before putting it back. In view of the fact that the material was in such a state of flux due to your removal and my replacement, and that the material would end up suitably edited once a consensus had been reached, the preferable state for that material during any such discussion was "in" rather than "out" so it could be seen and evaluated.
The tendency of over-zealous editors, when they see some edit they feel is inappropriate, to decide they know better and revert it, has discouraged many experts from contributing to Wikipedia. Donald Knuth complained to me that when he tries fixing problems in algorithm and combinatorics articles he immediately gets reverted; the famous category theorist Michael Barr has made the same complaint. In Michael's case I asked him to send me the desired edits, which were perfectly reasonable, and I made them for him, being more experienced at dodging the bullets flying around the warzone that zealotry has made of Wikipedia.
I hope this clarifies my concerns, and I'm sorry that what started out as what you evidently perceived as a perfectly innocent revert of an uninformed edit that was "clearly" inappropriate somehow managed to escalate in this way. It would be helpful if Wikipedia encouraged its editors to be more circumspect about their reverts by not shooting first and asking questions later. It would save an awful lot of strife, and eventually the less thick-skinned experts might feel more comfortable contributing their expertise. --Vaughan Pratt (talk) 18:15, 12 July 2010 (UTC)
Yet again you insist that you did not place the Vaughan Pratt link on your user page ("I am certain I did not insert such a link"), ignoring the obvious and incontrovertible evidence to the contrary in your user page history (Hint: look at the very first entry in that history, the edit with which you created your user page on May 7, 2006). Very bizarre - almost delusional. Taken together with your logorrhoea, your persistent name dropping, and your obsessive insistence on your "expert" status - well, you certainly have an unusual personality.
But you are right about one thing - I do indeed prefer to avoid unproductive disputes. So I am done here. Gandalf61 (talk) 08:19, 13 July 2010 (UTC)
I'm sorry you feel that way, but I see no need to reply in kind, as the dismissive manner in which you've expressed your opinions throughout the whole of this exchange, starting from your very first sentence in Wikipedia talk:WikiProject Mathematics#Review needed at Proof (informal) to establish consensus, speaks for itself. You have left no stone unturned in looking for reasons to insult or disparage me, including interpreting my defending myself against your most egregious insult as criticism of you, even though I have turned a blind eye to the many other insults too petty to warrant response. You have not made a serious effort to adopt the sort of neutral tone that can help dissipate such tensions, instead continuing a barrage of gratuitous insults that cannot possibly help defuse things. I have refrained from saying so directly until now because I thought it would be counterproductive, but apparently it makes no difference. --Vaughan Pratt (talk) 17:53, 13 July 2010 (UTC)

## Mesopause edit comment

My edits were as follows:

• Edit 1: Moved "Not to be confused with" into a template (it was already there - added by User:99.164.137.251 [2]. I also moved references into proper inline templates.
• Edit 2 & 3: Revert destruction of proper inline references by unregistered user. (taking it back to previous state, which happened to include the "Not to be confused with" bit)

In other words - I did not add that bit in the first place, and each time it was returned to the article, it was because someone had vandalised the page by destroying the references. I really couldn't care less whether that bit was in the article or not. WP:AGF

--Ozhiker (talk) 23:13, 12 July 2010 (UTC)

Oh, my apologies. Thanks for filling me in on what happened. I made the mistake of looking for earlier occurrences at the top of the article, but they were at the bottom and so I missed them. I naively interpreted the three reintroductions of it in red as intentional on your part.
Looking more closely it looks like the history of that bit seems to go back even further, to User:64.216.160.226 [3] on 24 March 2009. User:Conquour1 took it out on May 1, User:99.164.137.251 put it back on May 3 as you noted. Seeing it materialize at top in your 16 June edit, I failed to see it way down at the bottom and so took it to be original with you. I also failed to see it rematerialize at the bottom of the revert of 30 June because it wasn't in red (in retrospect I should have checked all the +'s). So when your revert of the unexplained revert put it back I failed to see the big picture. This revert-unrevert then happened again, and I was still none the wiser. Very sorry about that! Had I picked up on the bigger picture I'd have pinged you at your talk page first.
So actually User:Conquour1 may have been the only one to object to that item, when I'd been thinking two people had objected That's not enough for me to care either way then, so I've undone my edit. But I guess my unkind comment remains in the history forever, yes? Hopefully the follow-up comment exonerates you. --Vaughan Pratt (talk) 00:09, 13 July 2010 (UTC)

## Standard Dry Air

Someone offered you up as someone to poke for your thoughts on the above article. It looks like it could use some TLC. –xenotalk 18:29, 9 August 2010 (UTC)

Thanks, xeno. I don't see anything in this that isn't already in Atmosphere of Earth, but if there is it should be merged in. Seems to me the right thing would be to reduce this page to simply a redirect to (the relevant section of) that article. I'll leave a suggestion to that effect on its talk page and leave it to others to implement if that meets with consensus. --Vaughan Pratt (talk) 19:07, 9 August 2010 (UTC)
I wouldn't hold your breath (no pun intended!); the article doesn't seem to be well-watched. –xenotalk 19:12, 9 August 2010 (UTC)
I'll put it on my watchlist, and try to remember to do the merge in a week. If you notice that I've forgotten either bug me or do the merge yourself. Unless you see something not already in the redirect destination, simply replace the whole body by #REDIRECT Atmosphere of Earth#Composition. --Vaughan Pratt (talk) 19:17, 9 August 2010 (UTC)

## Further doings at Talk:Proof (truth)

I thought you might be interested to know that a substantial initial segment of that page has now been archived, by the user who was talking about "argument from authority" back in the early days (User:Dodger67, who signs his name 'Roger'). I was rather annoyed by this, but if it doesn't bother you I suppose I'll let it go. Maybe you'll want to copy some of the material back to the main talk page, at least. False vacuum (talk) 21:18, 16 September 2010 (UTC)

Thanks for letting me know. However archiving that material is fine by me. The only thing I would like for the article at this point is to become the primary topic of "proof," just as "straw", "drill", and "count" have primary topics. "Proof" as an obsolete term for alcohol by volume hardly counts as equal to demonstration of truth, while galley proof, proofreading, and the baking concept seem even more marginal than the synonyms for straw, drill, and count, and hence belong on a dab page accessed via a hatnote from the main article. I honestly don't understand why people are dragging their heels on this, it makes no sense. --Vaughan Pratt (talk) 22:59, 16 September 2010 (UTC)
I agree with you, of course, but there still seems to be some dispute about the generality of the definition in the article, which I am trying to resolve. Perhaps it won't be too much longer. False vacuum (talk) 07:19, 19 September 2010 (UTC)
Then again, perhaps it will be much longer... --Vaughan Pratt (talk) 05:00, 27 March 2011 (UTC)

## Boolean algebra

A discussion of the situation at Talk:Boolean algebra has been revived. 01:16, 9 March 2011 (UTC)

## Stone representation

Hi Vaughan,

So I was thinking about the Stone representation a little more, specifically about P(omega)/Fin and more generally P(omega)/I for I an ideal, and I admit it's kind of slick. I don't see how it saves you from working with representatives, ultimately, but it is a nice formulation.

I can't quite work out some aspects of it, though. For example, take the fact that P(omega)/Fin has no nontrivial countable sups (at least of pairwise incompatible elements; I think in general). Does that work out in the Stone space, something like the candidate for a sup would be the union of the corresponding clopens, but that turns out to be derived from a principal ultrafilter? I can't see why that should be so and doubt that it is so. Does the representation respect only finitary operations?

Also, what about, say, P(omega)/I for some other ideal I? I wanted to say, OK, that's the set of all sets of the form {U | X\in U and U does not contain any element of I}, for X not in I. But that doesn't appear to be clopen. I see how it's closed, because its complement is the union of {U | X^c \in U} and { U | Y^c \in U} for Y in I, but not how it's open.

By the way, I am giving a talk at the UNLV sectional AMS meeting (special section on set theory) on my paper with Gao on the complexity of the isomorphism relation on quotient B.a.'s, focusing on certain invariants derived from ideals and definable in terms of their quotient B.a.'s. Don't know if you're coming. I'll be thinking about whether there's any interesting connection with the Stone spaces. --Trovatore (talk) 21:38, 22 March 2011 (UTC)

Not sure where to start since Stone duality is a big subject (see Johnstone's book) and I don't know which bits you're missing that are preventing you from answering all this on your own.
I assume you're aware that quotienting by a lattice ideal only makes sense for Boolean lattices, not general lattices, and that the reason it works in that special case is because a Boolean lattice ideal happens to also be a Boolean ring ideal, which one can quotient by (as an extension of how one quotients a group by a normal subgroup; in this case the group is defined by XOR, abelian whence "normal" is redundant, and the extension from normal subgroups to ideals is with multiplication aka conjunction).
Duality is most easily discussed abstractly in terms of morphisms, which makes it nothing more than the extension to categories of the Duality Principle for posets. I can explain Stone duality without functors, natural transformations, limits, adjunctions, or monads, just morphisms composed associatively and the duality principle for categories. If that's ok with you I'll describe how all that works from my point of view (which is the only way I've been able to understand all this stuff). I doubt you'll find exactly my point of view of Stone duality anywhere, but it's equivalent to other accounts and hopefully you'll find it simpler provided you're ok with abstract morphisms as a concept in its own right. --Vaughan Pratt (talk) 00:36, 24 March 2011 (UTC)

## Coalgebra

I don't understand this edit. Do you think that an article about the things that are dual to unital associative algebras is helpful to readers who want to know what a universal coalgebra is? I think we don't usually link to examples in such a misleading way, and given the name confusion it seems even more important not to do it. Besides, we should really have an article on universal coalgebras. Hans Adler 12:53, 24 March 2011 (UTC)

I agree with Hans. Also read my comment on the talk page which Hans' edit was a reaction to. Either somebody knowledgeable about universal coalgebra should create a page (or a section at Universal algebra), or maybe the sentence should be removed altogether if this interests nobody, or in the meantime the link should remain red. But it should not point to coalgebra, which seems only to create confusion. Marc van Leeuwen (talk) 17:28, 24 March 2011 (UTC)
Everyone's right in their own way on this one. I'll reply at Talk:Coalgebra Talk:Variety (universal algebra). --Vaughan Pratt (talk) 20:34, 24 March 2011 (UTC)

## Equational logic

Since you seem to have good enough knowledge of that, you should probably write the article. A redirect (to variety) is not satisfactory, and the non-mathematicians discussing Boolean <whatnot> with you will most likely have no clue (or you have to repeat the basics of that on talk pages over and over). That article would also be useful for a more CS-ish reason, because writing a serious (non-redirect) article about term rewriting is frankly impossible without that prerequisite. Tijfo098 (talk) 21:48, 24 March 2011 (UTC)

Richard Muller's just-announced Earth Project expects to persuade global warming deniers of its reality by improving the extant data and its error bars. I think it's reasonable to hope that the improvements that project can make will be of benefit to climate science, but it's ridiculous to imagine anyone's going to switch sides on that account. Better inference from the extant data might help, but as it stands now the data is already a perfectly fine basis for a rigorous demonstration of the reality of global warming. Climate scientists have the science essentially right, if not completely settled, but they've done a miserable job to date of conveying the logical basis for global warming to the public, with holes in their reasoning one can drive a truck through. That's what needs fixing, not the data.
Same with Wikipedia: an article on equational logic would be of benefit to Wikipedia (I've been teaching it at Stanford since 1981, and it's high on my priority list of articles to write for Wikipedia), but no one is going to switch sides on the question of whether to move Introduction to Boolean algebra to Boolean algebra because of an article on equational logic. They will only switch sides if you can persuade them to examine their own reasoning when it's challenged, and either to defend their reasoning or agree that it's flawed. As long as they do neither the contemplated move will remain unresolved. Likewise those on either side of the global warming debate aren't going to switch sides if they aren't willing to respond to criticisms of their own reasoning and admit to any flaws that may be brought to light. More information won't change that, in fact it will just further cloud the reasoning.
Meanwhile I'm too burned out by general opposition on Wikipedia to my contributions, e.g. my article Proof (truth) that I attempted unsuccessfully to write last year as a replacement for the inappropriate dab page Proof, to plan on writing any more Wikipedia articles. It's way too time consuming. When Wikipedia comes up with a way of preventing narrow-minded opposition from radically wasting the time of subject matter experts I'll reconsider. --Vaughan Pratt (talk) 00:34, 25 March 2011 (UTC)
I can only quote your own words back "Ah, good point about alcoholic proof, I was losing my perspective about the relative importance of subjects. I'm off to the fridge for a beer." It's easy to lose perspective here and think that weighted automata or Ockham algebras matter much here. Tijfo098 (talk) 05:56, 25 March 2011 (UTC)
Thanks Tijfo098, I really appreciate that there are a few like-minded people out there. Obviously the mistake I'm making is to engage in arguments that anyone with more sense than me wouldn't touch with a ten-foot pole. I just wish CMBJ could spare a few minutes from his urgent project. (Wait, did you just knock the magna opera of Manfred Droste and Blyth and Varlet? ;) They're my friends, are you challenging me to produce those articles too?)--Vaughan Pratt (talk) 06:37, 25 March 2011 (UTC)
(By way of clarification, my position on the beer in the fridge is that when someone says to me "show me the proof" and I say "that's easy, it's 80 proof", or "sure, here's the galley proof of my latest article", they're going to wonder if I've lost my marbles. It should be even more obvious what the primary topic of "Proof" is than of Drill or Count or Straw or Law. My take on those claiming otherwise is that there can be no explanation for their weird position other than that they're detached from reality. As can happen when one spends all one's waking hours on Wikipedia instead of in the real world. As always I'd be delighted to be proved wrong.) --Vaughan Pratt (talk)

"are you challenging me to produce those articles too?" Ha, ha. No, I (temporarily) have both books so, I'm not asking for any favors (for myself) in that respect. If you want to hear wikiwar stories: the gap in coverage about weighted automata occurred to me because there's a chapter in Droste solving the Monty Hall problem by modelling it as a Markov decision process, and then using dynamic programming (aka "iterated value" method in decision theory jargon). It was interesting for me to discover a general algebraic framework (automata over semirings) for those ancient tools (MDPs). The gap in coverage of Ockham algebras surfaced when I looked at Kleene algebra, and noticed that some were incredulous on talk that there may be two algebras named after Kleene, so I added Blyth & V as the definitive ref...

By the way, I've read Boolean algebras canonically defined, and I like the encyclopedic approach to providing multiple definitions from different perspectives. Perhaps one thing that could be added is the original motivation for developing Boolean algebra, which was to find axioms for (what is now called) relation algebra—a Boolean algebra is an algebra of unary relations. I've learned that from [4]. Of course, unlike the unary case, a binary relation algebra may not be representable. Add to that the fact that binary relation algebra turned out to be only a fragment of FOL, and it explains their obscurity today. Tijfo098 (talk) 08:07, 25 March 2011 (UTC)

God, sanity in Wikipedia. I saw a rainbow this afternoon, it lasted slightly longer. --Vaughan Pratt (talk) 08:18, 25 March 2011 (UTC)

## A constructive approach to Birkhoff's theorem

Hi, Vaughan. In your spare time, you might be interested in this constructive approach to Birkhoff's theorem. I would be curious to know your opinion about it. Anyway, thanks for all the discussions we shared. Even if we might not have fully agreed, I learnt a lot. --Hugo Herbelin (talk) 22:39, 24 March 2011 (UTC)

Hi Hugo. I very much appreciated your willingness to engage constructively on what has been for me a most unconstructive debate of long standing (since 2008). And thanks for the pointer, which I'll look at now. At first glance I'm not even sure what the problem is, at least in the case of a finitary signature (as a finite or countably infinite list of natural numbers), since the free term or anarchic algebra on countably many generators is countable and the congruences on it therefore form at most a continuum-sized set. I prove the theorem in six lines in my class notes, see page 33 of http://boole.stanford.edu/cs353/handouts/book2.pdf , and there's nothing nonconstructive there, using no objects larger than countable sets. Maybe there's a bug in my proof, I'll look for one. --Vaughan Pratt (talk) 01:04, 25 March 2011 (UTC)
(Back from dinner.) Ok, I looked for problems in my exposition of Birkhoff's proof. (I miscounted btw, it's ten lines rather than six since the four lines of Lemma 8 should be counted.)
I see only one occasion for concern. Lemma 8 chooses a homomorphism he from T for each falsifiable equation e. On the face of it that's a use of Choice, since C will in general have more than one counterexample to e.
Now if the falsifiable equations could be well-ordered, as they certainly can be when the set X of variables can be well-ordered, e.g. when X is finite, this would not be a problem since we could work systematically through them and for each falsifiable e observe that there exists a counterexample to e and use it.
But in the proof of Theorem 9 we need to form T(A)/ΘA(C), and the set A of elements is just some set, suggesting that maybe we're stuck with appealing to Choice after all. (Which is what my proof does in effect, but the course, CS353 Algebraic Logic, assumed ZFC rather than ZF throughout so that it would not be slowed down by the distraction of what could happen without Choice.)
In this case the dependence on Choice can be seen to be inessential because each term in T(A) depends only on the finite set of elements of A formed in its construction. Hence T(A)/ΘA(C) can be obtained as the direct or inductive limit of T(A)/ΘB(C) over all finite subsets B of A, as pointed out by Carlström.
T(A)/ΘB(C) doesn't require Choice because B is finite whence ΘB(C) is countable which makes it well-ordered. And since all this stuff is representable set-theoretically, and the category Set is cocomplete, I don't see where Choice is needed in the construction of these inductive limits. I therefore don't see eliminating Choice as the big deal here that it is in some situations where it turns out it can be eliminated with a lot of work. If there's some need to change the conditions under which Birkhoff's theorem holds without Choice, or to devote 11 pages to the matter in case there is such a need, you have my full attention, but for now I'm not buying it. --Vaughan Pratt (talk) 06:21, 25 March 2011 (UTC)
Hi Vaughan, (late reply sorry). I also think that Choice is not needed in this proof. Actually, by "constructive proof", it is meant here a proof that does not use impredicativity. Indeed, we have to notice that Carlström is a former student of Per Martin-Löf whose constructivism rejects impredicativity. Otherwise said, I think that the point of Carlström's proof is not to give a different proof of Birkhoff's theorem but rather to reformulate the theorem so that impredicativity is not used. In the proof of Birkhoff (as given in your notes), impredicativity occurs in the definition of ΘX(C) (a set of equations defined by quantification over the set of algebras, the set of equations being itself equippable as an algebra of the initial set). The new formulation presupposes instead the existence of a generic, i.e. morally of ΘX(C), thus shortcutting the construction of ΘX(C) that is problematic for this kind of predicative constructivism.
Somehow, even if the modified statement is arguably as useful in practice than the standard statement, it fails in my opinion to bring out the constructive content of the proof, where by constructive I mean here what equational theory the proof actually constructs. In the modified proof, nothing is constructed since the equational theory that makes the theorem work is already given in the hypotheses (as being the equational theory of a generic). In the original proof, the equational theory is the result of some construction, accordingly an impredicative one to the eyes of predicative constructivism, but not as so trivial as in the modified version. There is a parallel to do here with Tarski-Knaster fixpoint theorem whose general proof exhibits an impredicative construction and whose proof would just be void if the existence of the fixpoint were a presupposition of the statement. --Hugo Herbelin (talk) 08:35, 1 April 2011 (UTC)
Here are two naive notions of impredicativity:
1. Quantification over a class, for example the class of all Boolean algebras, or all ordinals.
2. Existential quantification over a class.
I'm comfortable with the latter, because the existence of a class such as Boolean algebras raises the question of whether some partial ordering of some royal family on some planet in the Andromeda galaxy could be admitted to membership in that class.
However I'm not comfortable extending impredicativity to universal quantification over classes. Universal quantification means you are given some class C and are supposed to do something with it, such as making some claim about it. In this case the class is given, whence membership is not in question: the members of C are whatever they are because C has been handed to you. That's perfectly predicative.
If it wasn't, the theorem itself would be intrinsically impredicative. In that case Carlström would be claiming to have a predicative proof of an impredicative theorem. Given that a proof necessarily incorporates the theorem it purports to prove, I don't see how such a thing could be possible. But then I suppose that's the point of his restatement of Birkhoff's theorem.
But even if some community took the (unreasonable to me) stand that quantification of any kind over a class was impredicative, and that mathematics should be predicative, one could make Birkhoff's HSP theorem predicative in that sense simply by choosing one's favorite regular cardinal κ and insisting that algebras consist of ordinals below κ. Some people actually do this, sometimes for relatively legitimate reasons (e.g. when defining a particular class such as the ordinals), sometimes out of a misplaced sense of what should count as predicativity, e.g. considering universal quantification over a class to be impredicative. This is a generic approach to foundations of algebra aimed at making it predicative in this much stronger sense that can be applied to all theorems about algebra, not just Birkhoff's.
Anyone who takes 11 pages to deal with an issue that could have been disposed of in 11 lines is likely to have created enough room for several fallacious arguments, especially with matters like impredicativity, about which competent logicians have written at lengths commensurate (one assumes) with the difficulty of the concept.
The bottom line for me is that C in Birkhoff's theorem is a given (hence predicative) class of algebras which by definition of "theory" contains the counterexamples to precisely the non-laws of C, meaning those equations of the given language that do not hold universally of C. ΘX(C) where X is the set of elements of a given member of a given class C seems to me a perfectly predicative notion. If X is uncountable then choice (as distinct from impredicativity) arises as a concern. However this is easily dealt via the observation that ΘX(C) is the union of ΘY(C) over all finite subsets Y of the set X, and then forming the appropriate small colimit in Set (small because X is small and so is the set of all finite subsets of X). Anything more than that in this approach to eliminating AC from the proof is symptomatic of confused thinking.
I would be very interested to know both Martin-Löf's and Carlström's views on the above line of thinking, and to determine on which points each of us differ. --Vaughan Pratt (talk) 15:56, 1 April 2011 (UTC)
I'll assume that when you're talking about class, you're talking about class in the set-theoretic sense. Then, impredicativity is not quantifying over classes but simply quantifying over predicates. As far as I understood set theory, set theory is impredicative by the simple fact that, via the comprehension axiom, quantification over sets potentially contains a quantification over a predicate. The line of work Carlström is doing is actually not formalized in set theory but in (predicative) type theory (typically Intuitionistic type theory).
AC has nothing to do directly with Birkhoff, as far as I can judge (but see below).
The impredicativity is only in the construction of the set ΘX(C) as an intersection of the identities of the algebras in the class C, i.e. in the construction of a set by universal quantification over sets. This is something that is probably inoffensive for most of logicians (but, for some reasons, this community cares about it).
Then, if the class had been instead a set well-ordered by some ordinal (and I agree that AC might come into play here), impredicativity could indeed have been avoided by constructing the intersection by well-founded induction (again: as far as my understanding of set theory is correct). --Hugo Herbelin (talk) 19:45, 1 April 2011 (UTC)
Impredicativity has been used with various meanings. The naive meaning I wrote about, based on the distinction between sets and classes, is the one apparently assumed by Carlstrom in his first paragraph, where he says "The crucial product is taken over all quotients of a term algebra that are members of the class considered. From the predicative point of view this is not a set." If you have a different meaning in mind based on the notion of predicate then I'm not clear as to how it bears on the concern raised by Carlstrom, who never once uses the term "predicate" in his paper. --Vaughan Pratt (talk) 23:26, 1 April 2011 (UTC)
Hi Vaughan, I looked more precisely at your proof and I now understand your comments above "back from dinner" about the use of choice in Lemma 8 (I thought at first that your Lemma 8 was just the same as Carlström's Lemma 1 and did not enter into the details of it - I'm embarrassed).
I also looked at the proof given in Burris and Sankappanavar's textbook which is again different and I'm starting getting a flavor of what the "crucial product" problem is. I didn't understand how Burris and Sankappanavar avoid the apparent taking of the product over a class, but Carlström says that this can be avoided by using "the power set axiom and the full separation axiom (with quantification over all sets)". Assuming this, then, it is in the "quantification over all sets" that impredicativity lies (more precisely, to emphasize the connection with predicates defined by quantification over predicates, when you define a set by quantification over a set, as in {x∈A | ∃y P(x,y)}, then the quantification over y in the predicate λx.∃yP(x,y) includes a quantification over predicates that include the one being defined since among the different ways of defining a set, there is the comprehension axiom whose role is exactly to turn a predicate into a set).
Back to choice, there is no need for choice in Carlström's Lemma 1 because T(x1...xn)/ΘX(C) is embedded in GnGnn (for some generic Gn of the n-variables equations) and both the domain and codomain are made of basic set constructions. Then, couldn't we use the same idea as Carlström but directly reasoning over A instead of over its finitely-generated subsets. I mean, embedding your T(A)/ΘA(C) into GGA by defining h(t) = <σ(t)>σ∈A→G, where G is some generic (and σ(t) replaces the variables of t in A by their value in G). Then, we would get the best of the two proofs, i.e. a proof that uses neither choice nor closure over inductive limits, and whose only use of impredicativity would be to prove the existence of a generic. Does it make sense?
By the way, ΘX(C) and ΘA(C) are about laws, aren't they, so the variables of the equations in there are universally quantified, hence bound, hence with irrelevant names (alpha-conversion). So, the indices X and A could in principle be removed in the notation (what explains that the sets are actually equal). --Hugo Herbelin (talk) 00:03, 4 April 2011 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── (I seem to be drowning in things to respond to lately, with a steadily increasing lag time.)

B&S avoid taking a product over classes because they compute such products one algebra A at a time (see II-§8 Exercise 11 on p.60). This allows them to take a product over a subset of Con A indexed by a set I, where Con A is the lattice of congruences on A. When A has finite cardinality n, Con A has cardinality at most the n-th Bell number, while for infinite A, Con A has cardinality at most that of the power set of A. B&S don't in general need the whole of Con A in the proof of Birkhoff's theorem. However in Corollary 10.11 they take |X| ≥ |A| where A could be arbitrarily large, and then prove Theorem 10.12 by directly appealing to §8 Exercise 11 which means they're taking a product over an arbitrarily large I (since I has to cater for all possible finite subsets of A, of which there will be arbitrarily many if A is arbitrarily large), but still set-sized.

The proof in my notes has the same arbitrarily large index sets (but they are sets, not classes). The way round this that I mentioned above is to form arbitrarily large free algebras as colimits of finitely generated free algebras. But that assumes a class that is closed not just under HSP but also colimits, otherwise how to build arbitrarily large free algebras?

So it looks like we need to restate Birkhoff's theorem by adding closure under colimits. With this in mind I re-read Carlstrom's article.

Carlstrom's first restatement of Birkhoff's HSP theorem is as follows.

Theorem 4. If C is a class of algebras that

1. is closed under homomorphic images,
2. contains precisely those algebras whose ﬁnitely-generated subalgebras are in C,
3. contains every power of a generic algebra G,

then C is axiomatized by Ids G.

He says he likes this version because 1-3 are easier to check, they are what he uses in the proof, and they follow easily from the conditions of his second restatement of Birkhoff's HSP theorem, namely the following.

Theorem 6. If a class C contains a generic family {Gi} and is closed under

(÷) homomorphic images,
(−) subalgebras,
(+) inductive limits,
(×) products,

then it is axiomatized by Ids(ΠGi).

First, his indexing of the four conditions with the four rational operations is kind of cute. Second, I would weaken the last condition to require only countable products, since every free algebra is a colimit of finitely generated free algebras and these embed in countable products of counterexamples to nonequations. Third, why is any generic family needed? Fourth, I will have to mull over his discussion in the 4th paragraph of the 4th section before I can have a sensible 4th. Fifth, that Thierry Coquand and Thomas Streicher have provided feedback is a good sign. At some indefinite point in the future I'll be able to say more. --Vaughan Pratt (talk) 08:20, 7 April 2011 (UTC)

## Shellsort

Dear professor Pratt,
I have found your edits in Shellsort. I appreciate that you found it worthwhile to read my paper. Regrettably, its last graph is unfair to Tokuda's sequence. A corrected version can be found in my short survey [5] (in Polish). As can be seen, such optimized sequences give negligible profits but the question why their elements have these very values remains interesting. Maybe some day I will return to the topic, this time using a multi-armed bandit strategy to search the increment space. Best regards, MCiura (talk) 19:33, 28 March 2011 (UTC)

Meanwhile someone has added "according to research by MCiura" which weakens the statement a bit. Feel free to dive in and fine tune the claims there even further. I agree that the empirically found numbers are "interesting," one might say "chaotic" in a suitable technical sense. --Vaughan Pratt (talk) 20:10, 28 March 2011 (UTC)

## Be more kind to Hugo

He does get the math wrong at times, no doubt. He reverted me once because of that and CBM had to revert him. But referring to his edits as gibberish is perhaps too rude. I would not have referred to something a student has written that way in real life, and probably neither would you. Respectfully, Tijfo098 (talk) 06:56, 2 April 2011 (UTC)

People should not be editing Wikipedia the way a student submits a homework. If a student gets a homework wrong one helps him or her to get it right, without being judgmental no matter how confused the student is. One certainly doesn't tell the student to stop on that account. But if someone writes utter nonsense in a Wikipedia article then they should be told to stop because they should not be editing blindly in an area they obviously don't understand. If they suspect a mistake in the article they should first raise their suspicion on the talk page to establish whether it really is a mistake. The talk page is more like the classroom setting you have in mind, where people should be helping each other. Wikipedia talk pages can be a great educational experience.
What is rude is being dismissive on the talk page. It is also rude to simply click on the undo button to revert all the thought and typing that goes into an edit, but occasionally it has to be done because the article is not a substitute for the talk page. I don't see the point of pretending it's not rude by tiptoeing around it in the comment: best that the word reflect the deed. BOLD editors should not mind BOLD comments on their mistakes.
I realize other people may have other philosophies on this, and that theirs might be better, but I would need to understand why before switching. --Vaughan Pratt (talk) 13:42, 2 April 2011 (UTC)

## 3RR

FYI, with reference to your summary for this edit, the rule is that WP:3RR kicks in for more than three reverts within a 24-hour period.  --Lambiam 11:47, 6 April 2011 (UTC)

Good point, I must have been thinking of baseball's three-strikes rule, or else I was subconsciously counting the WP:OWN and WP:POVFORK violations that Hans Adler pointed out. In StuRat's case they ought to have a WP:DEAF guideline for those who can't hear complaints about quality of content. --Vaughan Pratt (talk) 16:46, 7 April 2011 (UTC)
We have WP:IDIDNTHEARTHAT.  --Lambiam 17:26, 7 April 2011 (UTC)

## Scrap the article Principle of bivalence

Have you been following any of the back-and-forth there? I've come to your side. Maybe for different reasons (mine being based on the history). I can see no justification for the creation of a whole new phraseology that seems, until I'm persuaded otherwise, to be just a case of Bullshit in the philosophic sense. I'm going to try to recruit Lambian, if I can, too. Bill Wvbailey (talk) 17:11, 13 April 2011 (UTC)

## Personal attacks

Please do not make personal attacks as you have done so at Talk:Planck's law. Wikipedia is a collaboration, sometimes we don't all agree on how best to improve articles. However, there is no excuse for making personal attacks. Please read WP:NPA and WP:AGF. Further attacks or suggestions on how to circumvent the WP:3RR at the Planck's law may lead to you being reported and possibly blocked from editing by an administrator. Thanks Polyamorph (talk) 06:32, 17 October 2011 (UTC)

Sorry, what exactly was my "personal attack?" I've been editing this article for some years with no problems, suddenly out of the blue someone starts reverting all my edits and I complain. How does that constitute a "personal attack?" --Vaughan Pratt (talk) 06:35, 17 October 2011 (UTC)
Directly from WP:NPA "Comment on content, not on the contributor". Polyamorph (talk) 06:41, 17 October 2011 (UTC)
(a) I take it you've lodged your complaint with Headbomb about his comment on me as a patronizing a-hole. Or is there some asymmetry here that you haven't filled me in on yet?
(b) As a numerical percentage (99%? 50%? 1%?), what fraction of what I wrote was about the content, vs. about the contributor? Your vagueness here isn't exactly helping me reform my wicked ways.
My apologies if my answers seem a little testy but you must admit you're coming on awfully strong here under the circumstances. --Vaughan Pratt (talk) 07:14, 17 October 2011 (UTC)

## October 2011

This is your only warning; if you make personal attacks on other people again, as you did at Talk:Planck's law, you may be blocked from editing without further notice. Comment on content, not on other contributors or people. Polyamorph (talk) 07:56, 17 October 2011 (UTC)

What are you talking about? You haven't ever lifted a finger to help the Planck's law article, whereas I've been working on it for over three years. If anyone's making personal attacks it's you and Headbomb attacking me for working on this article, calling me a "patronizing asshole," etc. You think that's not a "personal attack"?

Nor have you responded to my questions to you regarding what you're complaining about. Instead you threaten me with excommunication while saying nothing about the charges. You're straight out of a Franz Kafka novel.

This is insane. What's gotten into the two of you? --Vaughan Pratt (talk) 08:31, 17 October 2011 (UTC)

Headbomb's comment is a personal attack, yes. However, it was in retaliation to your own attacks on him (e.g. saying he knows nothing about physics, among others). That doesn't make it excusable though. Nevertheless, to continue arguing the way you are is not constructive. Please stop and comment on the content itself and try to work together constructively. Thanks Polyamorph (talk) 08:35, 17 October 2011 (UTC)

I'd love it if Headbomb would engage in constructive conversation, which so far he has shown no willingness whatsoever to do. I'm ready if he is, but I don't sense much willingness on his part. The big problem I see is that he never listens to anyone, he acts like he's deaf (and angry, but the deafness is the big problem). The only reason you're picking on me is that people like Chjoaygame and Q Science and PAR andothers aren't being as outspoken about his deafness as I am. What do you suggest? --Vaughan Pratt (talk) 08:41, 17 October 2011 (UTC)

But I do appreciate your point about assessing his physics ability, which I'll stop doing. --Vaughan Pratt (talk) 08:43, 17 October 2011 (UTC)

Incidentally the beginning of the problem was Headbomb's aggressive editing-and-reverting right from the beginning. People were far more polite about it initially than he deserved, but it quickly got old. --Vaughan Pratt (talk) 08:45, 17 October 2011 (UTC)

I suggest you try to be the better person. By all means start a discussion on the science itself and the problems that you have with the derivations. But don't make it personal. If you see an argument coming, take a deep breath, relax, and comment only on the content, not on the problem you have with the particular editor. If you really have a problem with another user's behaviour you can go to WP:ANI and report it. However, if there is evidence that both parties are at fault it won't necessarily turn out in your favour. An article talk page is for discussing the content of the article only and (in general) not another user's behaviour. I understand how you feel, that you have been attacked yourself and your edits have been reverted, it's natural to feel strongly about major changes. But rise above it. Cheers Polyamorph (talk) 08:49, 17 October 2011 (UTC)
Fair enough. Having been obliged by MIT and Stanford to convert students' struggles with their work into grades for forty years, it will be a bit of a struggle for me to break that habit. If I'd been teaching at a university that didn't ask for grades I would not be finding it so difficult. Not sure how common that problem is. --Vaughan Pratt (talk) 08:58, 17 October 2011 (UTC)
WP:CIVIL outlines how wikipedians are expect to interact with one another. Unfortuntely, it's quite common for discussions to get out of hand and personal on wikipedia. We all make these mistakes from time to time but if we all remember to be nice to one another things usually work out amicably. This applies to both parties, if someone is being incivil to you, then don't respond with incivilty back. If things do get out of hand administrator action can be taken. But no one wants that. We just want everyone to get on with each other. :) Cheers Polyamorph (talk) 09:32, 17 October 2011 (UTC)
So noted. --Vaughan Pratt (talk) 09:43, 17 October 2011 (UTC)

## Convex optimization

There is an intense discussion regarding the recent edits to the convex optimization article. You are welcome to share your views as well. Isheden (talk) 10:49, 27 October 2011 (UTC)

Done. Hope I didn't subtract from the clarity. --Vaughan Pratt (talk) 07:46, 2 November 2011 (UTC)

## request for citation

Hi,

I have been trying to get the Planck's constant article straightened out at the point where you added this comment:

It would be mathematically correct to say that as Planck's constant tends to zero (assuming the Boltzmann constant is held fixed) Planck's law tends to the classical Rayleigh-Jeans law. Whether it's worth saying in this article is a separate question, which I for one would not answer strongly in the negative.

I think that rather than implying that E=0 in classical physics, it would be better to explain it as you suggested. I changed the article accordingly, and received a request to document my claim. (See the tail end of the discussion page.) Could you possibly provide me with a citation that I could copy over to the article?

Thanks. P0M (talk) 16:53, 29 October 2011 (UTC)

To begin with, it is fallacious to argue that E tends to 0 as h tends to 0 because the denominator is also tending to 0, more precisely to hν/kT. The two h's cancel. So there had better not be a source for the E=0 statement!
The denominator in the Wien approximation?P0M (talk) 20:13, 29 October 2011 (UTC)
No, in Planck's law. --Vaughan Pratt (talk) 03:25, 30 October 2011 (UTC)
As to whether there is a source for the h's cancelling, there must surely be, but it's an algebraic triviality. If Wikipedia needs sources for every algebraic triviality it will seriously impede its progress. It should suffice to get a consensus of competent editors to agree that the two h's obviously cancel.
Incidentally this assumes that, if T is allowed to change, h/T also tends to zero as h tends to zero. Letting h decrease moves the Wien peak to a higher frequency in proportion to 1/h, i.e. the ultraviolet catastrophe is merely approached until h actually becomes 0. --Vaughan Pratt (talk) 18:00, 29 October 2011 (UTC)
Actually Planck's original paper in December 1900 would be a fine source, because Planck pointed out that, by subtracting 1 from the denominator of the Wien approximation, the resulting formula tended to the Rayleigh-Jeans law as hν/kT tended to 0. This can happen either by decreasing h and/or ν, or by increasing k and/or T, or both. However it happens, the two h's cancel; this is true even if it is h that decreases to 0. --Vaughan Pratt (talk) 18:18, 29 October 2011 (UTC)
I've downloaded "On the Theory of the Energy Distribution Law of the Normal

Spectrum," from December 1910, but I don't find the material you referred to. I will look at other of his papers.P0M (talk) 22:56, 29 October 2011 (UTC)

I think that I must not have expressed myself clearly. The problem that I have with the original formulation:

This is the origin of the often-quoted summary that "the Planck constant is zero in classical physics" or that "classical physics is quantum mechanics at the limit that the Planck constant tends to zero". The Planck constant, of course, is never zero, but it is so small compared to most human experience that its existence had been ignored prior to Planck's work.

is that an article for the average well-informed reader should consist of statements that are not only defensible but that also do not confuse readers, e.g., a high school student with an inquiring mind, by laying traps.

The article has just presented the equation:

$E = h\nu.\,$

and following that it says, to the reader who does not otherwise know what is going on, that in classical physics h = 0. What can the student make of:

E = 0 ν

other than

$E = 0$

I was about to write that I have no idea of what the inquiring high school student would make of that equation, or of the supposedly frequently uttered "the Planck constant is zero in classical physics," but in fact I do because prior to becoming a freshman physics major at Stanford in 1958 I was that kind of student. I spent several years eliminating from my internal picture of the universe some misconceptions gained from "a boy's book of electricity"-type books. (I knew that Gamow's work was good, but I didn't always recognize when somebody else's stuff was bad.) I would have tried to figure out how and in what context classical physics could come up with such a strange-seeming conclusion.

I agree that there should not be a source for the "E = 0" statement, and in fact it is the implication of that statement that I want to avoid.

I just realized that you had added a second response immediately before I started to edit so I will now look for Planck's 1900 statement. Actually, to me the Rayleigh–Jeans law section on the "Comparison to Planck's law" seems quite clear.

The problem with writing or editing for Wikipedia is (for me at least) the demand for citations for things with which I am often an eye witness. I do a great deal of work on spiders and, for instance, may have a Black Widow in a fruit jar on my desk where I can easily measure the length of her fangs, but I have to find some printed source for the information. Maybe the Plank document will give me the citation that I need.

Thank you very much for your help. By the way, did you ever have contact with Prof. Restrepo of the Stanford Math. Dept.? He was the best math teacher I have ever had. Unfortunately Stanford apparently did not keep him and he went back to South America. If only he had written a calculus textbook!P0M (talk) 19:03, 29 October 2011 (UTC)

Sorry about that, the hazards of RWM (responding while multitasking---I only just now have been able to sit down and do justice to my reply). I mistakenly assumed E must refer to black body radiation. Since the point of E = hν is to partition energy into a sum of discrete quanta, inferring E = 0 from h = 0 would mean that total energy is partitioned as 0 + 0 + 0 + … which is counterintuitive given that total radiation energy is normally nonzero. E = 0 is a strange thing to infer from h = 0 in any context.
I had mistakenly assumed that Planck's first paper on his law would contain the details of his talk on it a few weeks earlier, but apparently he'd already moved on beyond that to give a statistical mechanics treatment without mentioning Rayleigh-Jeans, which he must have covered in his talk. This 1917 paper by Einstein makes the connection in the first page, so that might do as a source.
I knew Tomas Uribe Restrepo at Stanford, if that's who you mean. But Restrepo is a pretty common surname in Latin America. --Vaughan Pratt (talk) 03:25, 30 October 2011 (UTC)
My calculus teacher got his Ph.D. in the very early 60s, and then must have gone somewhere else. I doubt that the person you knew at Stanford could be the same person -- unless he had so many math students in his classes that he created a vacuum in any competing sections. Unfortunately students of my generation never called professors by their first names.
I have followed the math through several related articles, and I think I have identified the equations that you must have had in mind. Everything seems to check out, but I need to start all over with calculus and higher math before I would really trust myself. I have reverted my own changes and will see whether the others currently editing the article will fix it.
Thanks again for your help.P0M (talk) 05:33, 30 October 2011 (UTC)
On this question of whether you trust yourself, you should also be asking whether you trust the other editors more than yourself. I haven't been following the Planck's constant article, but what you say about it makes sense to me. --Vaughan Pratt (talk) 05:42, 30 October 2011 (UTC)

## Shellsort

Dear Vaughan Pratt, Marcin Ciura has recently rewritten the article on Shellsort. It is currently nominated to be promoted to a "good article". As you are the author of one of the sources references in the article I wondered if you would be interested in reviewing the article. Is so, you can start a review here. Regards, —Ruud 20:00, 7 November 2011 (UTC)

## You are invited to join Stanford's Wikiproject!

 As a current or past contributor to a related article, I thought I'd let you know about WikiProject Stanford University, a collaborative effort to improve Wikipedia's coverage of Stanford University. If you would like to participate, you can visit the project page, where you can join the project and see a list of open tasks and related articles. Thanks!

ralphamale (talk) 21:28, 24 January 2012 (UTC)

Thanks but I'm trying to focus my Wikipedia edit time on my areas of expertise. There is no shortage of people with more Stanford expertise than me. --Vaughan Pratt (talk) 00:46, 25 January 2012 (UTC)

## Boolean algebra

Hello, Vaughan, good to 'see' you here. I have recently been reading up on Boolean algebra, and of course dropped by Wikipedia to see what I could learn here. I was surprised to find Boolean algebra defined as "In mathematics and mathematical logic,...the subarea of algebra in which the values of the variables are the truth values true and false...", that is, the two-element Boolean algebra. I don't believe that's the usual mathematical definition, though it does seem to be the usual definition in logic design and computer science. And the lead doesn't discuss connections to lattices, order theory, etc.

I was about to dive in and start editing, until I noticed that this topic has (unsurprisingly) been discussed before, and that you were involved in it. So I though the better part of prudence would be to discuss with you first.

I'd have thought that there should be a Boolean algebra (logic design) and a Boolean algebra (mathematics) with a master article Boolean algebra covering the general topic. Instead, the mathematical theory of Boolean algebra is treated as some sort of strange play on words: the 'subject' vs. the 'object'; the singular vs. the plural. This surely clarifies nothing for either the beginner or the sophisticate. Then, off to the side, there's Two-element Boolean algebra, a redundant and not very well-done article.

I have been using as my guide to the field Frank Markham Brown's Boolean Reasoning (Google Books, Amazon), which seems to be a good survey of the literature not restricted to switching theory (review), with some historical depth. For example, he mentions that the "Shannon expansion" was introduced by Boole himself; and gives credit to Blake (1937) for the complete sum form, usually credited to Quine I think.

Of course, if you have better reading suggestions, please let me know.

PS I still remember when you lent me your BMW 2000 for some errand I had to run. I recently got myself a BMW (a 2001 convertible) -- fun car. --Macrakis (talk) 17:07, 4 August 2013 (UTC)

Hi Stavros, long time no see. Take a look at the lead I wrote here from March 2011 (scroll down to "Revision as of") and let me know what you think of it compared to the present version, which has changed a lot. What hasn't changed significantly is the body, which except for the history section is pretty much as I wrote it in February-March 2008, accessible now (as a side effect of a move) only from this edit history. Prior to 2008 I had written two Wikepedia articles on the subject neither of which I felt met the need of a "master article" as you put it, so the present article was my third attempt.
Regarding your "strange play on words," take a look at the lead of the article Algebra, which says For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers. * As a single word without article, "algebra" names a broad part of mathematics. * As a single word with article or in plural, "algebra" denote a specific mathematical structure. That is, one can study algebra, or one can have an algebra. It then goes on to say * With a qualifier, there is the same distinction and gives "linear algebra" as an example of the first kind and "Lie algebra" as one of the second kind. In the case at hand, "Boolean algebra" is a nice example of both kinds: one can study Boolean algebra, and there are four Boolean algebras of cardinality at most eight. Which of these two uses of "Boolean algebra" is the one that sounds strange to you?
Brown titles his book "Boolean reasoning: the logic of Boolean equations." If that's what it's about then that's where one would expect him to begin, namely with elementary Boolean algebra in the sense of Elementary algebra as taught in high schoool. Instead he first takes the reader through an exposition of mathematical structures in general (Chapter 2) and then defines the notion of a Boolean algebra (Chapter 3). From a pedagogical standpoint this is completely backwards as it imposes a significant and unnecessary cognitive load on those interested in the subject matter of the title, which can be treated in great depth without ever bringing in the notion of a Boolean algebra per se. In particular Chapters 4-10 contain nothing that needs to make use of any Boolean algebra other than the two-element one. All you need are the operations and their associated equational logic. As far as Chapters 4-10 go, Chapter 2 is a complete waste of the reader's time.
Wikipedia does treat Boolean algebras, namely in the article Boolean algebra (structure). Sections 1-5 of the article Boolean algebra could well be described as "Boolean reasoning: the logic of Boolean equations," which is Brown's title. Section 6 has something to say about Boolean algebras per se but with a hatnote linking to Boolean algebra (structure) as the main article.
Regarding the "usual mathematical definition" of a Boolean algebra. in his book Lectures on Boolean algebras mathematician Paul Halmos defines a Boolean algebra to be a ring satisfying x2 = x. Logicians sometimes define it as a complemented distributive lattice, either explicitly or implicitly by listing the equations saying as much (essentially the equations Brown gives), though there are other equations to the same effect. Which definition would you say was more "mathematical," the one given by mathematicians or by logicians?
Yet another definition of a Boolean algebra is as any algebraic structure satisfying the same equations as the two-element Boolean algebra. The same approach can be taken with commutative rings: a commutative ring can be defined as any algebraic structure satisfying the equations satisfied by the ring of integers. Such definitions are just as rigorous as giving an explicit list of axioms, and are arguably better motivated and easier to grasp for a novice.
For Boolean algebra the approach of starting from 0 and 1 as the motivating (and also prototypical) values was adopted in the hope that it would put the least cognitive load on those wanting an introduction to Boolean algebra in general. In that respect Brown's Chapters 2 and 3 are a major conceptual hurdle to the basic ideas of Boolean reasoning. In fact there are many people who apply Boolean algebra to their work who aren't even aware that there is such a thing as a Boolean algebra---the author of an early Wikipedia article on Boolean algebra, StuRat, claimed that "a Boolean algebra" made no more sense than "a bread."
Regarding the article Two-element Boolean algebra, I'm not sure who the intended audience is. Presumably it's intended to serve needs not met by Boolean algebra, but if so it would be nice to know what those needs are.
Incidentally the BMW was a 1600, vintage 1968. Massachusetts wasn't kind to it, by 1975 the floor was pretty badly rusted through. I'd completely forgotten lending it to you. :) --Vaughan Pratt (talk) 00:17, 5 August 2013 (UTC)

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