User talk:Vaughan Pratt

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[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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. --KSmrq^T 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. --KSmrq^T 05:45, 9 August 2006 (UTC)

[edit] hyphen, minus, en dash, em dash

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

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

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

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

[edit] 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)

[edit] Discussion about renaming "Boolean algebra"

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

[edit] 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)

[edit] 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)

[edit] Invite

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

Gregbard 02:55, 25 July 2007 (UTC)

[edit] 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)

[edit] 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)

[edit] Deletion of the Erdos Number categories

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

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

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

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

[edit] 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)

[edit] 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)

[edit] Sandbox

/Sandbox

[edit] Boolean algebra task force

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

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

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

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

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

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

[edit] "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)

[edit] Image copyright problem with Image:Bands.svg

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

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

[edit] Image copyright problem with Image:BarsParams.svg

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[edit] 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 (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)