User talk:Kiefer.Wolfowitz/Archive 1
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Thanks, Kiefer.Wolfowitz (talk) 00:37, 16 October 2010 (UTC)
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[edit]Peirce & Statistics
[edit]Abduction and model-based inference
[edit]Peirce as a pioneering statistician, e.g. for likelihood
[edit]Borrowed your rocking Peirce paragraph from Founders of statistics, adapted it stylistically and added it to the Peirce article http://wiki.riteme.site/wiki/Charles_Sanders_Peirce#Probability_and_statistics. Thank you, thank you! You needn't consider your work there done, of course. Also made the links to the Peirce bibliography be more direct to their targets there (from the original paragraph at FoS as well), with the magic of span id's that I already put into the bibliography. The Tetrast (talk) 06:25, 27 May 2009 (UTC). Also I made a note in the Peirce article edit line that you originally wrote the paragraph for FoS. The Tetrast (talk) 06:27, 27 May 2009 (UTC).
- Reply.
Thank you for your encouragement, again. About Peirce, I wrote the following for the historical section of likelihood function:
In English, "likelihood" appears in many writings by Charles S. Peirce, where model-based inference (abduction) is distinguished from statistical procedures based on objective randomization.[6]
"probabilities that are strictly objective and at the same time very great, although they can never be absolutely conclusive, ought nevertheless to influence our preference for one hypothesis over another; but slight probabilities, even if objective are not worth consideration; and merely subjective likelihoods should be disregarded altogether. For they are merely expressions of our preconceived notions" (7.227 in his Collected Papers).
"But experience must be our chart in economical navigation; and experience shows that likelihoods are treacherous guides. Nothing has caused so much waste of time and means, in all sorts of researchers, as inquirers' becoming so wedded to certain likelihoods as to forget all the other factors of the economy of research; so that, unless it be very solidly grounded, likelihood is far better disregarded, or nearly so; and even when it seems solidly grounded, it should be proceeded upon with a cautious tread, with an eye to other considerations, and recollection of the disasters caused." (Essential Peirce, volume 2, pages 102--103)
Kiefer.Wolfowitz (talk) 10:43, 27 May 2009 (UTC) Kiefer.Wolfowitz (talk) 17:08, 28 May 2009 (UTC)
Model-based inference and abduction
[edit]My attempt to understand what is "model-based inference" and why you identified it with abduction led me to start reading or re-reading (I'm not sure which) "A Theory of Probable Inference," then I went and checked the Abduction quotes at the Commens Dictionary of Peirce's Terms. I do remember that Peirce revised his view of abduction, and retracted an aspect of it which he had asserted somewhere - and it turns out that the retracted view was in "A Theory of Probable Inference". While retaining the idea of hypothesis-formation and even of some minimal sort of likelihood in the conclusion, in 1902 he dropped the conception of abduction as qualitative induction, induction of characters. In particular, scroll almost half-way down the "Abduction" quotes page and see the quote beginning "… the study of Abduction. Upon this subject, my doctrine has been immensely improved since my essay "A Theory of Probable Inference"" and, a bit further down, the quote beginning "But in my paper on probable inference in the Johns Hopkins "Studies in Logic"". Lucia Santaella gives an account of it Eprint. I don't know whether this affects your identification of abduction with model-based inference. I'm such an idiot at statistics, I don't understand the identification, at least not yet. The Tetrast (talk) 05:21, 29 May 2009 (UTC). Edited, The Tetrast (talk) 05:32, 29 May 2009 (UTC). Actually I'm not a complete idiot at statistics. I wasn't at all fooled by the first problem at Yudkowsky's Bayes Theorem introduction, I'd won an argument about such a problem previously. The Tetrast (talk) 05:53, 29 May 2009 (UTC)
Reply:
Much of model-based inference is abductive. However, some uses of model-based inference can be inductive, e.g. where a well-defined (fitted) model is tested on fresh data using a well-defined procedure. So I wrote poorly if you believed that I identified abductive reasoning with model-based inference. UPDATE: I clarified my contribution to avoid this confusion. Kiefer.Wolfowitz (talk) 17:21, 29 May 2009 (UTC)
That said, I would bet that "most" published accounts of "model-based" inference are (alas) abductive, though, in part because of the anti-Baconian (and anti-Peircean) sophistry of (post-Neyman) Ronald A. Fisher and David R. Cox (two giants of statistics, and the latter being a good man mensch). I fear that most of these models are just being published (as part of pseudo-science) without having influence on experimental inquiry and new observational studies.
Peirce criticizes non-Baconian abduction throughout his career, e.g. in his Cambridge Lectures (of 1898?) in the 2nd and 5th, I believe (from memory), e.g. criticizing Carus's discussion of "Bode's law".
I know that Peirce updated his theories and believe you when you correct me that Peirce criticized some of his earlier writings. However, Peirce's two programmatic essays (the ones I cited) were published and read throughout the world during the 1800s and so are very important statistical theories. (The limited audiences of some of his (improved) later statements makes them less useful as references, particularly for assessing Peirce's contributions to statistics.)
(I'm sorry for writing briefly: My earlier answer was erased becuse I mistakenly hit the (Show changes) button!)
Best regards, Kiefer.Wolfowitz (talk) 15:10, 29 May 2009 (UTC)
- This is fascinating stuff. I keep hoping that you'll elaborate on it, the "anti-Baconian (and anti-Peircean)" stuff, etc., so that I can translate it into "Peircean." This stuff makes me want to study statistics (actually it's too late for me), and makes me feel confirmed in my non-Peircean view that statistics is every bit as much that which Peirce called "coenoscopy" as philosophy is (study of positive phenomena in general). By now you've probably realized that you didn't lose your earlier answer when you hit the "Show changes" button, but only when you thought you had thereby lost it and then did other things. Okay, let me try to say something particularly constructive. Your paragraph above - with more specifics spelt out - about pseudo-scientific studies of model-based abductive inference would be of particular interest to Peirceans, many of whom would be quite interested in avoiding pseudo-scientific dead-ends. Can you say a little more? The Tetrast (talk) 04:37, 5 June 2009 (UTC).
- BTW, I just picked up the sequicentennial collection of Peirce (U of Alabama press), which has several articles on Peirce as a statistician. Maybe I could write a non-OR article after all! Cheers, Kiefer.Wolfowitz (talk) 00:37, 23 June 2010 (UTC)
- I happened by here and found your good news on the sesquicentennial articles. It sounds like you're saying that you might write a (non-OR) wiki on Peirce's statistical work & theory. That would be wonderful. I have one recommendation: don't title the wiki in such a way that it ends (I'd use a subjunctive there if English would but let me!) with a closing parenthesis, which I unfortunately did with wikis such as "Categories (Peirce)". The problem is that, when such a URL is pasted into an email or similar thing, the given program usually fails to recognize the closing parenthesis as part of the URL and thus messes the URL up; senders and recipients of the URL (e.g., on a discussion list) often have no idea what's wrong. (I'm mentally preparing to retitle the Peirce wikis where I made that mistake.) Anyway, I'm trying to get back into the swing of these things - despite my recent editing activity, I got a bit rusty during 2010's first half (as I realized when I said some dumb things recently at peirce-l, a list which you might consider joining, by the way, but be careful for your Wiki-anonymity, because I told peirce-l about Kiefer.Wolfowitz's help on Peirce. There was a positive comment on it in another thread but I can't find it right now because I'm not at home). I want to get ready to tackle revising the Peirce section ("History of the concept") in the "Abductive inference" wiki. The Tetrast (talk) 03:13, 27 June 2010 (UTC). Edited The Tetrast (talk) 03:39, 27 June 2010 (UTC)
- BTW, I just picked up the sequicentennial collection of Peirce (U of Alabama press), which has several articles on Peirce as a statistician. Maybe I could write a non-OR article after all! Cheers, Kiefer.Wolfowitz (talk) 00:37, 23 June 2010 (UTC)
- Thanks for your comments. I'll use the sandbox and write a short article and get some comments before creating an article---the recommended approach (and the reverse of my usual practice)! The Peirce-L list sounds interesting. Personally, I'm glad that I learned about the 8th volume from you: Peirce's paper on "evolutionary love" has a nice description of model-based inference, I was surprised to see. Kiefer.Wolfowitz (talk) 13:00, 27 June 2010 (UTC)
- I should also say some of my statements need revision. It seems that Peirce regarded non-randomized model-based inference as deductive (not "abduction", as I wrote), while model-selection is abductive (hypothetical, retroductive). Models reflecting objective randomization enabled properly inductive inference, that is probable inference with well-defined probabilities (attached to methods). Kiefer.Wolfowitz (talk) 14:23, 27 June 2010 (UTC)
- Peirce would, I think, allow any kind of inference within a model, though the selection itself of a model is abductive. The main distinction within a model nevertheless would be deductive-vs.-inductive insofar as, in Peirce's account of scientific method, there's abduction, such that within an abductively selected model (if I get your use of the word "model" correctly), one proceeds to deduce consequences and thence to evaluate inductively through tests. But I think that, for Peirce, insofar as surprises can happen at any point there can be abduction (as well as deduction and induction) within the model. Phrases like "iterated method" and "baby universes" come to mind.
Anyway, if you write a sandbox version of an article on Peirce's statistical work, I'd like to send it out to peirce-l for comment. Mostly, folks will just be happy that you're doing it, but some valuable critical comment may also occur, there are some serious experts on that list. Now if I can just awake from this curious half-slumber that I've seemed to be in lately - The Tetrast (talk) 04:35, 30 June 2010 (UTC)
P.S. The 8th volume of Writings? Yes, that would contain the Monist Metaphysical Series (with "Evolutionary Love"). That's also in EP. Take a look at Charles Sanders Peirce bibliography#Articles_by_Peirce,_published_in_his_lifetime, there's a lot there, all of it linked to the texts online. Various series of articles are now sub-bulleted accordingly I myself have to look at "Evolutionary Love" again, then I'll finally get the phrase "model-based inference." The Tetrast (talk) 03:30, 3 July 2010 (UTC).
- Peirce would, I think, allow any kind of inference within a model, though the selection itself of a model is abductive. The main distinction within a model nevertheless would be deductive-vs.-inductive insofar as, in Peirce's account of scientific method, there's abduction, such that within an abductively selected model (if I get your use of the word "model" correctly), one proceeds to deduce consequences and thence to evaluate inductively through tests. But I think that, for Peirce, insofar as surprises can happen at any point there can be abduction (as well as deduction and induction) within the model. Phrases like "iterated method" and "baby universes" come to mind.
- I should also say some of my statements need revision. It seems that Peirce regarded non-randomized model-based inference as deductive (not "abduction", as I wrote), while model-selection is abductive (hypothetical, retroductive). Models reflecting objective randomization enabled properly inductive inference, that is probable inference with well-defined probabilities (attached to methods). Kiefer.Wolfowitz (talk) 14:23, 27 June 2010 (UTC)
~
- I'm sorry for my delay in responding, which is a token of respect rather than disinterest. It takes a lot of thought to respond at the level that your comments merit, and I'm rather tired (when editing) lately. Best regards, Kiefer.Wolfowitz (talk) 15:05, 6 July 2010 (UTC)
Fisher information
[edit]- Hi, I finally got a chance to read in detail through your very knowledgeable contributions to Fisher information. I learned a lot about this subject. I shortened some of your ref tags slightly -- I think ref tags should be used only for directly corroborating an assertion in the article. I hope you find my changes acceptable. I wonder if you would be willing to write a short "History" section for this article? It could appear before the Properties section, for example. This would allow you to write the story of the development of this term in more detail and I think it would be a valuable contribution to Wikipedia. As an example, you can look at Matrix (mathematics)#History. Cheers, --Zvika (talk) 07:20, 1 June 2009 (UTC)
Thanks again for your kindness. However, this time, your suggested project far exceeds my competence and time, I must admit. However, I am certain that the readers should go directly to Savage or to Stephen Stigler, who have greater knowledge and style! (I am limiting myself to some slight revisions of a few articles now: My contributions in the last week should be sufficient pro bono professional service through the summer!) Best regards,Kiefer.Wolfowitz (talk) 19:17, 1 June 2009 (UTC)Kiefer.Wolfowitz (talk) 17:25, 3 June 2009 (UTC)
- That's completely understandable. You have done an amazing amount of work for someone who's only been here for a few weeks. Best, --Zvika (talk) 19:28, 1 June 2009 (UTC)
Archiving "Statistics" discussion
[edit]Hi saw you remove some sections from Talk:Statistics. Its general practice to leave old material in the talk page or possibly archive it Talk:Statistics/Archive 1. --Salix (talk): 17:53, 7 June 2009 (UTC)
- Sorry, I was unfamiliar with this policy. Could somebody less likely to damage ongoing discussions restore the old stuff, please?Kiefer.Wolfowitz (talk) 18:09, 7 June 2009 (UTC)Kiefer.Wolfowitz (talk) 16:16, 9 June 2009 (UTC)
Please do not delete comments made by other editors on talk pages as you did here, here, and here. BTW - the talk page for statistics is automatically archived - there is no need for any manual archiving. Thanks —G716 <T·C> 20:55, 7 June 2009 (UTC)
- Please read my previous acknowledgment (which appeared 2+ hours before your comment). Thanks for your suggestion, though. Best regards,Kiefer.Wolfowitz (talk) 16:37, 8 June 2009 (UTC)
Contributions to polynomial regression
[edit]Thank you for your contributions to polynomial regression, very nice work. Skbkekas (talk) 16:46, 21 June 2009 (UTC)
- You are welcome! I tried to make only consensual edits. I looked again at the article, following your encouraging words, and tried a few more edits, which I hope you can examine (and save me from errors!). Thanks! Kiefer.Wolfowitz (talk) 17:02, 21 June 2009 (UTC)
Please see Bayes linear statistics
[edit]Given your contribution to the article on Bayesian probability, could I encourage you to look at Bayes linear statistics as it seems to require attention from someone with deep knowledge of what is going on (and its relation to other topics). If you look at the history/talk, you will see that it has had a messy start. And if you have not found it yet, you might want to join in at WP:WPSTAT ... the talk page there can be a good place for things like trawling for comments on your recent major template edits. Melcombe (talk)
- Dear Melcombe,
- Experimental design : I have asked personally some of the contributors on the experimental-design articles and also I have asked for feedback on the discussion page where the Template:Experimental design prototype appeared. Following your suggestion, I should add a new section at the WP:WPSTAT talk page and ask for feedback. (Maybe this week??)
- The article Bayes linear statistics, seems to be closely associated with the work of Michael Goldstein, including his book of the same name (with David Woolf). In an ideal world, an article on Goldstein's Bayes linear statistics would be a subsection of a larger article, e.g. "Linear model (Bayesian)", which doesn't exist. I don't feel especially qualified to edit that article, at the moment, though.
- Thank you for your recognition of the work on Bayesian probability. Thank you for the invitations at to join WP:WPSTAT. I shall check that I have joined. Best regards, Kiefer.Wolfowitz (talk) 12:10, 25 June 2009 (UTC)
Nielsen Theory
[edit]Hi Kiefer- thanks for the reference added to Nielsen theory. Is that book really about Nielsen theory as described in the article (i.e. topological fixed point theory)? I haven't read it (I thought I'd read all 3 books on Nielsen theory) but it sounds like it's about some other aspects of Nielsen's work. Staecker (talk) 13:02, 29 June 2009 (UTC)
- Well, the book's about some aspects of Nielsen theory, and should be of interest to your article's readers. Its exact relation to the "actually existing" article, I leave to you to judge. (I added Nielsen's book after improving the Werner Fenchel article. I believe that Nielsen's papers have been republished in a volume by Birkhauser, but this is my memory of a book I saw 10 years ago.) Feel free to remove or comment-out the entry, if that's your judgment.
- Kiefer.Wolfowitz (talk) 13:17, 29 June 2009 (UTC)
'Minor edit' tag
[edit]Hi, I noticed you tagged this edit as a minor edit - I agree with removing the material, but the 'minor edit' tag should generally be reserved for things like spelling/grammar fixes or reversion of clear vandalism. --GenericBob (talk) 01:22, 12 July 2009 (UTC)
- Sorry for the mistake. I started to correct a minor error, then I decided to kill the whole section, without undoing the "minor" tag. Thanks for calling that mis-labelling to my attention. Best regards, Kiefer.Wolfowitz (talk) 14:06, 12 July 2009 (UTC)
- Ah, no problem then :-) --GenericBob (talk) 11:38, 13 July 2009 (UTC)
Matroids
[edit]Hi. I noticed you took out "first and only" about Welsh's book, not a bad thing to do, but I wondered which other comprehensive books you know on matroid theory? Are you thinking of White's series? I'm not sure I'd include it because it covers a lot but it's a bit too loosely organized, like a collection of disparate essays on many aspects of matroids. There were none before Welsh, that I know of. I am putting back "first" for now (and I agree on leaving out "only"), but please do satisfy my curiosity and tell me what you think. Thank you. Zaslav (talk) 21:41, 13 September 2009 (UTC)
- I'm an amateur and thought that Welsh's book is an excellent book, but doesn't tower above the rest of the literature (at least not today), because of the 3+ White volumes and Oxley. Perhaps my editing was unjustified regarding "and only", because the other single-volumes are less comprehensive.
- Oxley's book is less comprehensive than Welsh's. There have been various books on matroids, with more emphasis on applications or use by engineers, like the Hungarian Resci (sic?) or Murota, which are substantial. Truemper's book on matroid decomposition and Schrijver's volumes on Combinatorial Optimization have a wide scope.
- Before Welsh, Tutte's lecture notes on matroids were published in a book, also, but they are very selective and more demanding.
- Regarding the article, it would be nice to say more about Jack Edmonds's prophetic emphasis on greedy algorithms and polynomial-time complexity, or reference Lawler's book (which has been reprinted by Dover, and so may be useful to the public). I'm sorry for answering briefly, but this week is very demanding in the real world .... Sincerely, Kiefer.Wolfowitz (talk) 19:51, 14 September 2009 (UTC)
Peirce's criterion
[edit]Hi, Kiefer, hope all goes well with you. seberle asked a question on the Peirce talk page here Talk:Charles Sanders Peirce#Peirce's criterion about the CSP "Probability and statistics" section remark about Peirce's improvement of the treatment of outliers and its embedded link to the article on Benjamin Peirce's development of Peirce's Criterion. I wasn't able to answer the question by searching the 'Net, so I told him to ask you but he didn't. Can you help out? The Tetrast (talk) 00:27, 4 October 2009 (UTC).
- Thank you for taking care of it, Kiefer! The Tetrast (talk) 23:07, 6 October 2009 (UTC)
- Hi, Tetrast! Many months late, I added some references on Charles Sanders Peirce and Benjamin Peirce to the articles on Peirce's criterion, Benjamin Peirce, United States Coast Survey, and outliers. (I didn't find the articles listed in the articles published during Peirce's lifetime.) My formatting remains fallible, and if you fix my goofs in one article, I will update the others accordingly. Best regards, Kiefer.Wolfowitz (talk) 19:29, 15 February 2010 (UTC)
- Hi, Kiefer, I guess it's time I got back to editing! I'm on it. Also I notice your numerous good edits at the main Peirce article. You made a good point about Putnam. Re math's nature, C.S. was sure that he was in full agreement with B. about about it but I agree that it is a bit hard to see in some regards (in particular about math's focus on the purely hypothetical) from what B. himself wrote. I have to look into that again. Best, The Tetrast (talk) 19:59, 17 February 2010 (UTC).
- P.S. I added "On the Theory of Errors of Observation" to the CSP bibliography. The Tetrast (talk) 20:15, 17 February 2010 (UTC).
- Hi, Tetrast! Many months late, I added some references on Charles Sanders Peirce and Benjamin Peirce to the articles on Peirce's criterion, Benjamin Peirce, United States Coast Survey, and outliers. (I didn't find the articles listed in the articles published during Peirce's lifetime.) My formatting remains fallible, and if you fix my goofs in one article, I will update the others accordingly. Best regards, Kiefer.Wolfowitz (talk) 19:29, 15 February 2010 (UTC)
Re: Treatment and therapy
[edit]Actually I think I'll just undo all of the changes I made and then we can go from there. I find that easier than going through my edits and seeing which ones should go to which places. Especially since I'm not sure I grasp where the edits should go. :) I'll do that in a few minutes. --User:Woohookitty Disamming fool! 09:21, 23 December 2009 (UTC)
- OK. I think I got all of them reverted. The vast majority anyway. --User:Woohookitty Disamming fool! 09:34, 23 December 2009 (UTC)
- Thank you! :) If you need any help, let me know. I'll leave treatment alone for now. --User:Woohookitty Disamming fool! 09:55, 23 December 2009 (UTC)
2 categories removed
[edit]I removed 2 categories on your user page that (a) don't exist on as categories as far as I can tell, and in any case (b) Kiefer.Wolfowitz is the only person listed in that category. Perhaps those two categories can be created as subcategories on existing categories.141.217.105.21 (talk) 18:25, 13 January 2010 (UTC)
- Please cite whatever Wikipedia guideline these categories violate, here: When informed, I would be happy to take corrective action on the categories or delete them myself (certainly within a week). Thanks. Kiefer.Wolfowitz (talk) 00:27, 14 January 2010 (UTC)
- FYI, I linked super-categories and so these categories are populated---sometimes by volunteers! ;) Kiefer.Wolfowitz (talk) 00:37, 17 January 2010 (UTC)
Your handle?
[edit]Hi Keifer, I couldn't help but notice your handle (Keifer.Wolfowitz), and wonder about its origins. I was a student at Cornell University in the 1960s, and learned statistics from Jack Keifer. I wanted to take Jacob Wolfowitz' course in information theory too, but I kept having schedule conflicts and had to fall back on reading his book and talking to him in the hallways. Later, as a postdoc at the University of South Florida, I discovered that he (Wolfowitz) had moved there too, and we had several more fascinating discussions. Those two (Kiefer and Wolfowitz), along with Harry Kesten, Kiyoshi Itō, and Paul Olum, had a profound impact on my career. (That's a lot of name-dropping, but in those days they were just little-known mathematicians.) Were you there at Cornell too? Turbulent times! —Aetheling (talk) 06:27, 18 January 2010 (UTC).
- Hello Aetheling!
- I have visited to the happy shores of Lake Cayuga only a couple times in my life. I was very happy that Ithaca's voters had in the early 1990s elected a Cornell Professor (of Electrical Engineering) to be the Ithaca mayor! More often, however, I have been to Cornell University in spirit --- whether following a recipe from the Moosewood Restaurant or reading something from one of the many great Departments of Mathematical Sciences at Cornell.
- My first editing was on the Optimal design of statistical experiments, so I chose Kiefer.Wolfowitz to honor their important optimality conditions (equivalence theorem) --- and to give the Wolfowitz name better press after the shennanigans of son Paul!
- (I didn't recognize Paul Olum, but am happy to learn about a geometer and student of Whitney, especially when Olum seems to have been such a mensch! BTW, did Kesten inspire the hero of Resnick's Adventures in Stochastic Processes (the protagonist who had trouble with College Republicans!)?Kiefer.Wolfowitz (talk) 20:40, 18 January 2010 (UTC))
- Best regards, Kiefer.Wolfowitz (talk) 17:39, 18 January 2010 (UTC)
- To the best of my (sadly incomplete) knowledge, Harry Kesten was not political and would never have tangled with "College Republicans". Anyway, a belated and warm welcome to you -- we sure can use the help with Wikipedia. —Aetheling (talk) 03:33, 20 January 2010 (UTC).
- Well, we may just suppose that Resnick was being silly! Kiefer.Wolfowitz (talk) 16:23, 20 January 2010 (UTC)
Heuristics
[edit]You commented out something at geometry of numbers, which was in the nature of an aside. I seem to have this discussion about heuristic remarks quite often. I was actually asked recently about a related remark at Generalized continued fraction#higher dimensions, by someone who wanted to know more (and was helped, it seems).
To try to put this all in context, we write for the "general reader", whoever that is. On the other hand no degree of special knowledge is forbidden here: editors are asked to put everything in context, though. I would argue that heuristic remarks do "put things in context", and there is a tag on that geometry of numbers page asking for some work on the article for accessibility. On the other hand the general tightening up against "original research" means it is harder to source precisely such remarks, often "folklore" and very useful, but not always written down because the professionals don't see the need. Which is a shame: that whole culture of only making public the formal side of mathematics does the subject no favours.
If you had added a request to source the remark, this is part of the game of reducing such heuristic remarks to only those that have already been recorded (a loss, I think, but where policy leads). Just commenting it out on the grounds of sophistication assumes an audience, and I don't see it. Remarks motivating a field of mathematics are a plus, and if we go back to Minkowski and what he was trying to do in founding this field, I think amplification would probably help all round. (I believe he failed in trying to do all of what he had set himself, but that is of its own interest.) Charles Matthews (talk) 12:29, 25 January 2010 (UTC)
- Hi Charles. Thanks for your understanding words and nice tone! What you wrote was undocumented and hard to understand (for me). Maybe such asides are more appropriate for a personal page (accessible from your user page), until they are developed a bit more? Maybe you could look at Minkwoski or the fellow from Cincinatti's book and see what Minkowski had to say about motivation? Or Gruber etc.? (There's at least one book on higher-dimensional continued fractions, btw.) Kiefer.Wolfowitz (talk) 22:04, 26 January 2010 (UTC)
- I did an extensive re-write. I provided sources for the statements, and raided some material from related articles to flesh out the article. I killed your small paragraph on algebra, which had no references. Of course, you should consider reviving it, but I would ask that you try to find some references and provide more context for the reader. Kiefer.Wolfowitz (talk) 17:24, 27 January 2010 (UTC)
- Thanks for working on the article. Despite being a student of Cassels, I'm no expert. Charles Matthews (talk) 19:04, 27 January 2010 (UTC)
- If you are a student of the abbreviator of the Tate-Schaferevich group in the context of that which is difficult to eliminate (and W.C.), then you are a better mathematician than me. Being ignorant helps me write on WP. Thanks for your understanding. I like Cassels's lectures on economics, which are often very funny! Best regards, Kiefer.Wolfowitz (talk) 19:07, 27 January 2010 (UTC)