![]() A daily dose of philosophical food for your noodle! |
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| Thursday, July 3, 2008 at 9:01:09 mst
Comment ID: #1 Name: Mike Hardy E-mail: hardy(at)math.umn.edu Since a more traditional way of using hyphens is one of my religious passions, Diana, can I possibly talk you into writing "range-of-the-moment thinking"? | ||
| Thursday, July 3, 2008 at 9:20:07 mst
Comment ID: #2 Name: Diana Hsieh E-mail: diana(at)dianahsieh.com URL: http://www.dianahsieh.com/blog Mike -- I do normally use hyphens for phrases like "range-of-the-moment." (In all likelihood, I probably don't always use them correctly; I should look up the relevant rule. However, I'm in favor of the proper usage in principle.) | ||
| Thursday, July 3, 2008 at 21:43:59 mst
Comment ID: #3 Name: William H. Stoddard E-mail: whswhs(at)mindspring.com URL: http://whswhs.livejournal.com/ I can comment on this issue of hyphenation, as a professional copy editor who has to deal with it regularly in scientific and scholarly material. | ||
| Friday, July 4, 2008 at 22:37:13 mst
Comment ID: #4 Name: Andrew Baker E-mail: smoke_owner(at)mac.com Would some one not revealing that he is seriously ill be lying to protect privacy? I can think of one real example of that happening, Freddie Mercury didn't publicly reveal he had AIDS until the day before he died. A surface examination such an occurrence seems to be moral. | ||
| Saturday, July 5, 2008 at 16:05:35 mst
Comment ID: #5 Name: Mike Hardy E-mail: hardy(at)math.umn.edu I am curious about Pat Corvini's work but afraid I may be bitterly disappointed if I shell out $75 (or whatever it was) for each lecture and find her work to consist of brilliantly done expository accounts of what everyone (except non-mathematicians) already knows. Circumstantial evidence makes me suspect that would happen: I google her name and find comments praising her, of which this was typical: someone said he was quite impressed with her idea for a way of looking at negative numbers, including her idea of using debits and credits to represent respectively negative and positive numbers. The guy actually used the possessive pronoun: "her" idea. As if it were a novel thing rather than what everyone has always known. One person whose comment I found on the internet said she did a superb job of explaining "epsilons and deltas", that 19th century idea that is sometimes presented in freshman calculus courses, and that many in the audience thought it was a new idea that she'd come up with. (19th century is very modern for a topic presented in a first-year calculus course; most of what's done in first-year calculus is 17th-century stuff.) | ||
| Monday, July 7, 2008 at 9:49:43 mst
Comment ID: #6 Name: Dana H. Pat Corvini in no way claims that the idea of positive numbers as credits and negative numbers as debits is her own! That would be preposterous. I took her course this year, and she uses this simply as one illustration to contrast integers to natural numbers and explain what gives rise to the need for them. Remember that she's lecturing to a general audience, not a bunch of mathematicians, so she needs to concretize what she's talking about. | ||
| Tuesday, July 8, 2008 at 13:27:45 mst
Comment ID: #7 Name: Gilliatt Dr. Corvini does not describe integers as "debits and credits". That is merely one application of integers to which she refers as an example. She introduces integers in the context of counting entities when there are "opposing" or "canceling" effects or objects involved: credits/debits, liabilities/assets, forward/backward, plus/minus electric charge, etc. This is not necessarily new, either, but as Dana H. commented, what is new is the focus on the "what" (the referents of the concept). Corvini is able to use the Objectivist theory of concepts to provide numbers with this content for the first time. In her analysis of the postulational method, this content is vital. For example, mathematicians use the postulational method to "construct" the integers from the counting numbers, but Corvini points out that counting numbers and integers do not refer to or measure the same kind of thing, and that this postulational method is unnecessary and invalid. (It's valid to say, "There are 29 people in the room right now [counting numbers]," but it is invalid to say, "There are +29 people in the room right now [integers]," because the counting of the number of people present is not the kind of counting that admits of opposing or canceling effects.) | ||
| Tuesday, July 8, 2008 at 13:33:31 mst
Comment ID: #8 Name: Gilliatt And I should point out that in her 2005 course, "Achilles, the Tortoise, and the Objectivity of Mathematics", she likewise doesn't just explain "epsilons and deltas" for the non-mathematician. I don't recall that she ever even used that terminology. Again, what she was doing was providing content and resolving conceptual errors in the treatment of the concept of infinity. "Epsilons and deltas" aren't new, but her grounding of the concepts involved is. | ||
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