This is a selection from messages that Dr Bill Richter has posted to comp.lang.scheme. ================================================================ 25 June 2004, responding to Shriram Krishnamurthi: Thanks! I'm definitely embarrassed to have made so many dumb mistakes. But it's easy to make dumb mistakes when you're arguing with folks who are also making dumb mistakes. The matter is of course symmetrical... ================================================================ 25 June 2004: It my "math math" guys who fall below my standards. I've been trying to rigorize a part of homotopy theory for almost 4 years now, and the bugs they ignored in constructing the cutting edge field, they now pretend don't exist, the better to destroy the now-passe field. ================================================================ 29 June 2004: Now on to Nielson, who proves a result of my sort! Theorem 4.55: For every statement S of While we have curly-S_{sos}[[ S ]] = curly-S_{ds}[[ S ]] But he wrote (as I quoted earlier) on p 85: The functions curly-S_{ns} and curly-S_{sos} [...] are not denotational definitions because they are not defined compositionally. There's a real communication problem here! I won't say error, because it's an "Applied" book, and the authors are Danish. [Editor's note: Bill is quoting "Semantics with Applications", a textbook by Flemming Nielson and Hanne Riis Nielson. The Nielsons are very careful mathematicians, and wrote exactly what they meant. Here Bill rejects what they wrote for one reason only: what they wrote is contrary to what Bill wants to believe.] ================================================================ 30 June 2004: Joe, it really sounds like you're saying that F-F's treatment of standard reduction is nonsense. You really ought to read it.... ....If you're going to attack folks, even indirectly, it makes sense to read what they wrote! ================================================================ 2 July 2004, responding to Krishnamurthi: You're a young hotshot CS professor, it wouldn't hurt you to learn some Schmidt or Nielson^2, or take up much of your time. Will has no obligation to read my posts: Will (also the DS books) hasn't published false claims opposing me (unlike my homotopy theorists :D). ================================================================ 2 July 2004, addressing Joe Marshall: Could you be saying that you don't know why total-program-E is well-defined as a mathematical function? I wouldn't think less of you if you did! I don't know where this is explained in the CS curriculum. I could give proofs (for tevals_s anyway) with induction & the ZFC comprehension axiom.... ================================================================ 4 July 2004, quoting Clinger: You've been spewing this stuff for two years now, and you still can't see the obvious circularity between your definitions of E and Phi. It's time for pushing and shoving. Push+Shove: you're all wrong. I've got a lot of respect for you, and it's no fun to keep telling this. The problem IMO is that you haven't re-read Schmidt's 3.13. I can't blame you: it took me hours to understand. It's not IMO well-stated, and it's an overly general result for our purposes. But I told you something about it (uniqueness) that you didn't know (you know existence), and you can't really respond to me until you re-read Schmidt's 3.13.... [Editor's note: Schmidt's Theorem 3.13 asserts that functions defined by structural induction over syntax are well-defined.] ================================================================ 6 July 2004: No, the problem is that you aren't showing enough respect for mathematical rigor. I don't care whether you respect me, but I wish you'd show a little respect for mathematics. I think you got it backward, Will. I've shown the math here a ton of respect. But I think you fell into a trap I've fallen in repeatedly: Somebody I don't think is much of a mathematician says something I didn't know, and I jump on it, "That's false, that's nonsense!" Often it happens that they were right. But it's really hard to judge mathematical strength, especially with folks you don't know. ================================================================ 6 July 2004: ....A lot of the problems in this DS discussions is that folks just can't believe how powerful the ZFC axioms are. I wasn't thinking of you at all here, Will. ================================================================ 7 July 2004: So you and others have been wrong for a long time about fundamental induction issues. I don't draw any negative conclusions from that. It's how you deal with these issues that makes an impression on me. There's certainly plenty of Math I don't know myself. I think you (Will) know a lot of Math that I don't know! As long as you & the others fight through the Math, you make a good impression on me. I salute you, Will, for a fighting well in this post. ================================================================ 11 July 2004: Will, I did not even know you thought of yourself as a mathematician. I'll think of you as one now! I see that you have 4 papers on MathSciNet, which compares favorably to my 7 :^0 ================================================================ 12 July 2004: > Maybe. I'm frustrated that folks here do not seem to understand > that Boolos-Jeffrey's partial recursive functions are rigorously > constructed without CPOs & minimal fixed points. Why do you think we don't understand that? I certainly think you understand it, Will! Perhaps it would be useful for you to post a lecture explaining something here. One can't expect schemers to have read these tough books.... ================================================================ 12 July 2004: Why would I not think of myself as a mathematician? After all, you still think of yourself as one. You should! I meant: I didn't know that you ever thought of yourself as one. How would I know? Your home page doesn't identify you as a mathematician. I hadn't mathscinetted you. ================================================================ 19 July 2004, addressing Shriram Krishnamurthi: I say that's false, and you shouldn't say it if you're not following the discussion. Go read Schmidt's Thm 3.13, and figure out what you think it means. Don't just trust Will to be getting it right. ================================================================ 22 July 2004: OK, Joe. I think we have to pick up the pace, though. So I really would like you to fish/cut some bait: 1) This thread has mostly been you & I, and if Will hadn't gotten involved, then we might be done by now. But Will did get involved (contributing lots of interesting things), and we're not almost done now, and I'm getting antsy. I want to finish this up. So: 2) If you can't hack this LC_v stuff, just say so.... 3) Similarly, if you can't hack Schmidt's Thm 3.13, just say so, and we'll blow it off.... Back to you! ================================================================ 23 July 2004, addressing Clinger: Of course you know the definition of compositionality (or a definition anyway), and you're an expert user in it. But we can't infer that you know all the possible equivalent definitions of compositionality. We would of course guess that you did, but we wouldn't know that. ================================================================ 24 July 2004: Same thing for the partial recursive function of Boolos-Jeffrey. I think you, Joe, ought to get Will to give you a lecture about this, since you're both at Northeastern, and Will seems to understand this.... 5) Proofs 3 & 4 take place in a context that CS folks may not be familiar with, the ZFC-powered world of pure Math. All DS takes place there, certainly Scott models also require this pure Math world. Will knows quite a lot about this, but his troubles with 4 indicate that he may not be as fluent here as I am. 6) I don't mean that the pure Math folks know what the ZFC axioms are! Just that we pure Math folks are fluent in sets 'n functions stunts which we understand to be derived from the ZFC axioms. Will would be in a much better position than I to give these ZFC-derivations. ================================================================ 26 July 2004, quoting Marshall: > But I'm not convinced that you understand why |--->>_v is a > well-defined partial function. I certainly think I do. You've posted nothing explaining your understanding. I don't expect you to understand this. I'd expect you to write great Scheme code, and to have a much better idea than me about what DS is good for.... > Please talk to Will. For some reason, Will can't understand my > semantic functions & proof of compositionality, but I think he > understands this very very well. Will and I talk quite frequently. I assumed you did, and he seems to think highly of you. I recommend you get a pure Math lecture about this sort of thing from Will. I'm sure Will can explain this, because of his Point-Set Topology skills. ================================================================ 28 July 2004: Joe, since you haven't had the pure Math courses I and the visitor had, still less the ZFC courses we didn't have, I wouldn't think poorly of you for not knowing how to well-define |--->>_v! I instead think well of Will for no doubt being able to justify this. ================================================================ 28 July 2004: Sounds great, Will! I'll definitely think of you as my superior in point-set Topology here now. Thanks. ================================================================ 28 July 2004: ....That doesn't make me a DS expert, by any means! But you guys told me the definition of compositionality, and I proved I could do it, and when you guys barked, that tells me that you have some problems with the definition of compositionality. Now you, Matthias, may have overcome these problems, but nobody else seems to have, yet. ================================================================ 31 July 2004, addressing Will Clinger: Before last night, I thought you were doing what my pure Math guys do: more or less intentionally making mathematical errors for political purposes.... But now I think you genuinely believe what you say. I don't think you're merely keeping yourself ignorant of your obvious errors.... ================================================================ 3 August 2004: But Keith, you have no chance of understanding my arguments unless you understand 2 prerequisites: 1) Why F-F's standard reduction function eval_v^s is a well-defined partial math-function. 2) The proof (& harder, the statement) of Schmidt's Thm 3.13. Will & MFe (who posted only once, at the very beginning) may be the only other folks here besides who understand both of these. Anyone else who wants to evaluate my arguments would have to learn these things, and everybody's busy. I draw 2 conclusions: 3) If you don't understand 1 & 2 above, you're going by gossip if you say I'm making errors. Will understands 1 & 2, but I don't prefer his proof of 1, and we haven't been able to communicate yet about 2. 4) I don't want to attack Will, because he's got by far the best position to understand me! I'm not even sure if Will has made any actual errors himself. He strikes me as dense for not understanding my clear proofs, but that's not an error, that's a communication problem, and my proofs would only be clear to Will anyway. ================================================================ 6 August 2004: Great, and that's my QED. That's why engineers can't build the partial function |--->>_v, even though it's called computable. What engineers can build, with silicon (did you really build a computer? Wow! Probably a lotta folks here have.) is the algorithm |--->>_v. But you can't build with silicon it's actual domain of definition, NotHalt. > We need more interaction between pure Math and CS, at least on DS > points. It was clear to me that folks here don't understand > simple points about sets & functions that are drilled into pure > Math folks. This is not clear to me at all. CS people tend to think very hard about sets and functions. It is not that they don't understand the simple points, it that they doubt they are as simple as they appear. OK, fine. They're only simple points to me & all the pure mathematicians I know because we've worked hard developing a skill. I'm happy to teach this here, but I can't teach anyone anything if they falsely think they already know it. I don't think math is that different from programming. It takes work hard, real attention to detail, you have look for bugs yourself, and seek out bug reports from others.... and it takes imagination & creativity to be good at it. ================================================================ 8 August 2004: I didn't know Will or MB had Math PhDs. That's cool. Do you know what their areas were, what their thesis were about? I was a postdoc at MIT, so I know that the MIT Math Dept has 2 subdepts, Applied Math and Pure Math. I wouldn't expect someone who got a degree in Applied Math, or Statistics to be fluent in the lingo of modern pure Math. The fact that no one here has understood me yet shows, as I said, either disinterest (I'm guessing Shriram and MB), or a lack of fluency in pure Math (I'm guessing you and Will). I've even got a theory about Will's problem: Will surpassed me in 2 Math areas at 2 different times: point-set Topology as an undergraduate, and Math Logic (at some point in his later, real, career). But I'm thinking that Will hasn't put his 2 accomplishments together. I'm thinking that Will hasn't understood that the Math Logic he knows backward & forward can be used to foundationalize the point-set Topology he did in his youth (by syntactic ZFC proofs), but that in fact, point-set Topology and DS use a much more naive, user-friendly and less rigorous approach: more or less the Naive Set Theory that Halmos describes. I don't think of Math-Logic/Set-Theory as even belonging to pure Math! That sounds crazy, and it shouldn't be true, but in practice I think it is. No pure mathematicians I know are logicians or set theorists. They just use sets in a plumber-fashion, but they can really whizz the pipes around. MIT has an excellent Math-Logic Math faculty, perhaps that's Will's area. I'll go out on a limb, Joe, and guess that your problem is that you don't take me seriously, on the grounds that MB, Will & Shriram know this pure Math sets 'n functions drill as well as I do, if not better. You can take my word for it: I'm better at the drill :) [Editor's note: I am a graduate of the pure math program at MIT.] ================================================================ 10 August 2004: Thanks, Jim! I saw that, but I didn't hit it, and it didn't occur to me it was Will's thesis. But sure enough, it's Will's 1981 MIT thesis, in the dept of Math and CS, submitted to the Math dept. That sounds a little odd. And his thesis advisor was Carl Hewitt, from the Electrical Engineering and CS dept [Editor's note: There is no "dept of Math and CS" at MIT. Bill misquoted the phrase that identified the interdisciplinary scope of my thesis research.] It's 175 pages, so it would take me a while to read. I bet it's really good stuff, and I'd get a lot out of it. But this bio info I posted here definitely reinforces my belief that my fluency in the lingo of pure Math sets 'n functions is a lot higher than Will's. ================================================================ 12 August 2004, addressing Clinger: If you can't understand this, there's no point in me talking to you about this anymore, because it means your understanding of the pure Math world of sets 'n functions is inadequate for the discussion. BTW I found your PhD discussion to be very relaxing. It seems clear to me now that you really have a CS PhD, but you're on the extreme high end of the pure-Math-world spectrum for CS PhD. I could of course be wrong, and I haven't yet read your thesis (which Shriram speaks highly of). But MIT is a pretty special place, in terms of collaboration between the Math dept & the Eng/CS depts. So it's not surprising that you've failed to understand my pure Math lingo.... Your behavior would be substandard for a real pure mathematician. E.g. it took you 21 days to respond to my objection to your your claim that "it is really the definition that is compositional, not the semantic functions that the definition defines," and you still haven't actually posted a definition of c.l.s.-compositionality. So it's relaxing to realize that I was holding you to overly high standards. And also relaxing, I shouldn't get upset if a CS person falsely accusing me of Math errors on his home page. A few days ago, when I thought you had a real pure Math PhD, I was sweating, I thought, "What if my guys see this? I'm behind the 8-ball enough as it is!" :) [Editor's note: As can be seen from the excerpts in category 4, Bill objected to my definition of compositionality on 23 June by writing: "I'm sure this is false". On 26 June, Bill admitted that a standard textbook "defines compositionality exactly as" I had.] ================================================================ 15 August 2004, responding to Marshall: I'll try to look at Mike Sipser's book. Thanks. I didn't realize that Sipser was on Will's thesis committee. But again, I don't think of Sipser as a pure mathematician, but as a logician, maybe a set-theorist, a recursive function theorist. All 3 good subjects, which I'm weak in, but that's not the issue with compositionality. It's the hurly-burly of pure Math sets 'n functions. [Editor's note: In August 2004, Sipser was chair of the math department at MIT.] ================================================================ 25 August 2004, quoting Marshall quoting Richter: > Thanks for all the references & citations, but it wasn't relevant > to my question. That's interesting you've done all this > reading... I suspect you think I'm an undergrad or grad student. I asked you before to tell me what your Math training was. I looked you up on the Northeastern CS home page & couldn't find you. I'm like that here at NWU. But I figure you're about my age, not new at this, maybe a research assistant of Will's. I never thought you were a undergrad or grad student. For one thing, you're too calm! I'm a lot calmer than I was 10 or 20 years ago :) After you've had enough hard knocks in the real world, usenet insults don't do the trick anymore :) [Editor's note: Evidently not. By the way, Marshall's references and citations were directly relevant to Bill's question.] I should say, maybe, that you've made a bad impression on me mathematically. I've corrected you many times (once maybe in error on engineers building partial functions) and I don't remember you once posting, "Thanks for straightening me out." You just let things drop. But it could easily be your age & experience: you know a lot, but it's hard at this point to learn new tricks maybe, especially from strangers on the net who are squabbling with your team. Anyway, you've made a good impression on me with your calmness. [Editor's note: Unlike Bill's many errors of logic or mathematics or computer science (see category 4), most of Marshall's errors were caused by taking Bill seriously. Most of Bill's "corrections" took Joe to task for thinking Bill actually believed some absurd thing that Bill had written.] ================================================================ 1 September 2004, quoting Aatu Koskensilta: Don't you think it might be conceived as a little arrogant to presume that computer scientists are unable to follow ordinary mathematical arguments You can call it arrogant, but I say it's true: CS folks here have failed to follow what I think of as ordinary mathematical arguments. But I've been in the pure Math biz for 25+ years, so maybe I'm out of touch with what's an ordinary argument in the pure Math field, and what's a really hard convoluted pure Math argument. ================================================================