This is a selection from messages that Dr Bill Richter has posted to comp.lang.scheme. ================================================================ 2 July 2004: ....But I think I'm a really really good mathematician, and I think it's quite possible I've noticed something very simple (as opposed to useful!) that you didn't notice. ================================================================ 8 July 2004, quoting Clinger: But Bill had a PhD in mathematics, and he knew that induction had something to do with mathematics, so he thought he knew more about induction than everybody on this newsgroup. I'll answer this charge! It does appear that I know things the group doesn't know about induction & ZFC. I know that 1) Bill-compositionality = Will-compositionality, and 2) F-F & Barendregt rigorously define standard reduction partial functions, which are immediately turned into total/bottom functions, without any need of CPOs or Scott models. You can just say induction + ZFC subset axiom if you like. 3) I know that the Halting problem is about a non-computable function that we can define (as a function!) by ZFC-caliber axioms. I consider these to be shallow accomplishments of mine, and I look forward to everyone else understanding them! But yes, I understand these things because all PhD in pure Math know them (or should). BTW you must know that a Math PhD is no big deal, and my 7 pubs (on mathscinet) looks really bad, but I was an instructor at MIT. Sorry I didn't look you up then. I'd never heard of Scheme! I wish I had! ================================================================ 9 July 2004: I am very happy now, Will. This might sound ridiculous, but to me, the main issue here is that I'd like to think well of the mathematical skills of you Scheme/CS folks. MFe is I think course a reasonable mathematician in his own right, but that's not the point. You're using Math I'd never heard of before, and I think it's really cool, and I'd really like to think you're on top of it!.... ================================================================ 20 July 2004: :D Shriram, compositionality is definitely in my area of competence. Like all the pure mathematicians I know, I'm an expert on mathematical induction, and defining functions by induction. When I tell you what Schmidt's Theorem 3.13 says, you can rely on me. I've been an algebraic topologist for 25 years, and I've published in some pretty good journals, and I've had some pretty good jobs. I have no idea how Will's competence compares with mine. We believe that Will is really good at constructing compositional DS functions. But it doesn't follow that he knows what the definition of compositionality is! He's a DS expert, not a full-time pure mathematician. ================================================================ 20 July 2004, quoting Clinger: BTW, when a mathematician says you are making a mistake in some area of mathematics that lies well outside your own competence but well inside his own, then you ought to pay attention. As I explained to Shriram, induction & functions defined by induction is well within my pure Math expertise. But you're making what I'd call dumb beginner mistakes here. You're much better than I am in DS, and I'm quite grateful for all that you've taught me, but that's not the area we're in right now. We're in my turf right now, pure Math. ================================================================ 21 July 2004: Let me clarify my competence post yesterday. One expects CS folks to be very good at computable functions, and Math folks to be poor at computable functions. One expects similarly Math folks to be very good at ZFC-powered noncomputable functions, but CS folks to exhibit discomfort here. That's the real reason I don't concede that Will's competence here is greater than mine.... But there's no way I think I'm Will's equal about computable functions. You might have noticed that Will ran circles around me earlier in the thread, and I just kept saying, "Cool, great, but let's put this off, OK?" But in the compositionality discussion, I think I can hold my own. It just sounds like the non-computable ZFC-powered Math that I've worked with all my life. Somebody else thinks they're good at it, like Will, great, let's rumble, I won't concede that I'm a novice. ================================================================ 21 July 2004, quoting David Feuer: > A topologist may know something about induction [...] but a computer > scientist is truly an expert [...] David, how could a Math student think this? Where are you studying, what degree are you getting? Don't you use induction ALL THE TIME? And you're not just using full-strength ZFC induction to produce c omputable functions, either. Now the ellided stuff, sure.... Now granted Will knows a lot more about formal languages than I do. And if we had a contest to see who could define the best & most compositional semantic functions, and prove the best theorems about them, Will would win, right? But I don't see how that means Will is an expert on deciding if my semantic functions are compositional. I bet I'm better at point-set Topology than you or Will, but I forget the definition of paracompact! Something like the union of a countable number of compact subsets? So 1st-countable + locally-compact implies paracompact? But metric spaces aren't always locally-compact, e.g. infinite dimensional Hilbert spaces? So I'm light years away from the proofs that you & Will discussed intelligently here. I'd still call myself an expert on point-set Topology, even though I'm way outta practice. If we ever get around to talking about Scott models of LC, I bet I'll teach you something. The point is: expert doesn't mean you know everything! It just means you've won some contests with the other humans who don't know everything either. I'm certainly willing to accept Will as a expert on point-set Topology now, & maybe you. [Editor's note: Bill guessed wrong concerning the definition of paracompact.] ================================================================ 23 July 2004: My most intensive study of Point-Set Topology was actually in High School, where I read most of "Rings of Continuous Functions" in a reading course from a George Mason Math professor, who coincidentally moved into CS, parallel processing maybe. There's a fair amount of Point-Set Topology in my subject, Algebraic Topology, and at some point I began to embrace it, to go out looking for it, instead of running from it. So I think I'm OK at Point-Set Topology. I've been out of work for 9 years.... Notice I didn't graduate from Princeton, but I was there for 4 years, and I proved a really nice result on high-dimensional knots + surgery theory just before going to Northwestern. So I'd call myself an algebraic topologist since 1980, that's really only 24 years.... Most mathematicians would be completely at sea if asked to explain the connection between ZFC and mathematical induction. Maybe Bill could explain, but he has given no evidence of it. Actually, I can't, but I didn't realize it when I posted that. I snuck into the library & looked up Enderton's Set Theory book, and I was rather confused. I think Just & Weese do a better job, but I couldn't find their book. I mean to get back to this.... Did it sound like I was saying I was an expert in ZFC? That's certainly not true. I'm not a set-theorist, or a logician. I've read a fair amount in the last 9 years, but prior to that, I didn't know zip. I even flunked 2 Math logic courses when I was an undergraduate. I mean I'm an expert *user* of ZFC, like all the pure mathematicians I know. I don't mean that we pure mathematicians generally even know what the ZFC axioms are! We're like plumbers: we use it, it works. ================================================================ 23 July 2004 quoting David Feuer: > So you've never heard of Moore-Smith convergence? I sure haven't, David! Hey did you ever read Jack Kerouac's book "Dharma Bums"? It's pretty silly, but there's a great line by one the characters, Japhee Rider (actually the poet Gary Snyder), "Comparisons are odious!" See, mathematicians are really pumped up about who's great, and who's better than who, but practically everyone who's ever published a paper knows something that nobody else knew. So the comparisons are all, "My theorem X is better than your theorem Y," which is rather vague and imprecise, wouldn't you think? I don't believe I've done a lot of chest-thumping about my credentials. Certainly I don't expect anyone to be impressed my Math credentials, such as they are. From time to time I respond to attacks on me, why don't I show more respect for other peoples credentials, where do you get off posting without spending years reading DS books & papers. Why don't we just do the Math? And why don't you, David, drum up something intelligent sounding to say about Schmidt or compositionality or LC_v or the Scott topology or something? [Editor's note: When David Feuer answered "Because I don't know anything about them," Joe Marshall admonished: "Don't let something as trivial as *that* stop you!"] ================================================================ 25 July 2004, addressing Joe Marshall: BTW IMO you & I make a good team. I've got the Math watts... ================================================================ 29 July 2004, addressing Clinger: But I'll tell you what I think of you: I'm now convinced you're a reasonable mathematician, after you explained your point-set Topology prowess. (BTW I was the top student in a Princeton point-set Topology course (producing 2 tenured Math profs & a famous mathematical biologist, all 2 years ahead of me), but it was just one semester, taught by an algebraic topologist). I used to think that MFe was a lot better than you in pure Math, but I wouldn't say that any more. ================================================================ 4 August 2004: ....DS is done in the framework of pure Math, of which I am an expert user, but there are fundamental ZFC issues that I don't understand very well (like all the pure mathematicians I know).... ================================================================ 11 August 2004: Anyway, I didn't post here asking for help, although I have received quite a lot...I came here to teach, and to fix the crazy feud we had 2 years ago. I still think a fix is possible, although the thread has gone on long enough to reconcile me to the prospect that I typed a 1/2 Meg for my own mathematical enjoyment. But if we are done with the discussion, let me make a social point: A big problem with the thread 2 years ago was my arrogant attitude, and it was partly intentional. It looked to me then that my chances of being hired in the CS/Programming world was poor, and my Math chances were good. And I was kinda looking for my walking papers. I figured I'd do better at Math if I worked on it exclusively. So I was pretty happy with the outcome, getting kicked of c.l.s. and into Math. But 2 years later, my Math chances don't look so good. I'm not quite ready to give up, but my guys have prevented me from submitting even a single paper. Makes me think I'm not going to be able to parlay my bug-fixes into a Math job. So I've been much less arrogant this time. ================================================================ 12 August 2004: I think it's analogous to my skills in Logic/Set-Theory/Boolos-Jeffrey: I'm on the extreme high end of the pure-Math-world spectrum for working pure mathematician. But as you & others have noted, it's nothing to write home about. ================================================================ 17 August 2004, quoting David Rush: I'm pointing out that at this point in the discussion there are a very few possibilities: 1 - You are right, and the CS community is wrong 2 - The CS community is right, and you are wrong 3 - The CS community and yourself are interested in fundamentally different things I'm right, there's no doubt about it. I am really good at the pure Math sets 'n functions drill, and that's all that's going on here. Now when we get to computability, I'll flounder! But I don't think it's 1. We haven't seen the CS community vote here. We've only seen 3 CS hotshots vote, Will, MB & Shriram. I bet what I think is really well understood, in particular, by Schmidt and MFe, from whose paper I got my def of compositionality. [Editor's note: Bill does not know David Schmidt or Matthias Felleisen. We do. Felleisen was Shriram's PhD thesis advisor. Felleisen's office is across the hall from mine, and we are co-directors of the Common Larceny project.] ================================================================ 25 August 2004: This is false, and it's essentially the third time in a row that Will has made the same mistake, so I will not look at Will's RichterFAQ again. I'll refute once again, but first let me express my gratitude to Will for my extended cls tutorial. I've learned a lot from Will, not about compositionality, but about my failures to understand the ZFC formalization of pure Math. I mean to rectify the axiomatic ZFC ignorance that Will's posts unearthed. There's another way in which my correspondence with Will here was positive: It's almost as if Will was considering me as a thesis student. Will's from the old school, the school of hard knocks, and that's the school I'm used to as well, where an advisor grills a new student mercilessly. So if there are any kids reading on cls thinking about attending Northeastern and working with Will, I recommend this highly. A good question for such kids to ask is, "If Will could teach so much to a top-notch pure mathematician like Richter, I wonder how much he teach me?" ================================================================ 30 August 2004: I know I'm right about compositionality, but I don't want to appeal to authority, partly because my authority isn't recognized, but also because it's so elitist and demoralizing. ================================================================ 3 September 2004, quoting Anton van Straaten: As for ungraciousness, to understand that, I suggest you engage Bill in a technical discussion (off-group!) Bill possesses some unique skills when it comes to teaching his correspondents that they're not saints. I think folks would find me a lot of fun to talk to, either on- or off-group, if they didn't start with the assumption that they already understood the pure Math as well as I did, if not a whole lot better. ================================================================