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From: Bill Rowe on 14 Jan 2010 05:49 On 1/13/10 at 5:56 AM, fateman(a)cs.berkeley.edu (Richard Fateman) wrote: >Bill Rowe wrote: >>On 1/11/10 at 5:27 AM, fateman(a)cs.berkeley.edu (Richard Fateman) >>wrote: >>>When one first reports a behavior that one believes is a bug, the >>>natural hope is that it will be fixed. >>Which is very reasonably when what is reported as a bug is indeed a >>bug. But it is not reasonable to expect something reported as a bug >>to be changed when it is not a bug. >It seems to be inevitable that people will, with such a complex >system as Mathematica, have differences of opinion as to whether >some behavior constitutes a bug or not. When WRI declares "this is >a feature not a bug", that does not necessarily change peoples' >opinions. In fact, WRI has, from time to time, changed its opinion >on what is a feature or a bug. Certainly it is true a declaration from WRI might have little or no effect on someone's opinion. And it is certainly true there will be those who have different opinions as to what a bug is. But in the final analysis, it only matters what WRI defines as a bug in Mathematica. I don't expect WRI to change Mathematica to fix a "bug" if the behavior being changed is not a bug from their perspective. And in this thread, it seems very clear the behavior of ReplaceAll with respect to complex values is not a bug. >>Nor is it reasonable to expect WRI to intuit your meaning of bug >>when it differs from the standard accepted difference. That is, the >>behavior being discussed is simply not a bug. It is exactly the >>behavior the documentation indicates should occur. >Especially when the documentation is vague or lacking on what should >occur, the difference between a feature and a bug is elusive. No disagreement here. >>You appear to be suggesting Mathematica should be written to enable >>someone to do mathematics without understanding much in the way in >>which Mathematica works. >Yes. One of the goals of the people who have been developing >software for "symbolic mathematical computation" starting in the >1960s, was that, to the largest extent possible, the newly >discovered and implemented algorithmic underpinnings of constructive >mathematics should be merged with the natural notations and usage of >practicing mathematicians, scientists, engineers, etc, so these >computer systems could be used most widely and most effectively. >>While I can there are those who want something to just work without >>additional effort on their part, >Yes. >>I don't see this as happening with anything as powerful and complex as >>Mathematica. >It is a particular conceit of Stephen Wolfram that he has invented a >new and improved notation and method for designating computation, >and that if only everyone learned it, mathematics and perhaps all of >science would be so much better for it. And I see it echoed here -- I've no specific knowledge of Steven Wolfram's views regarding what you write above, but this totally misses my point. I make no claim as to whether notation used in Mathematica is superior or inferior to notation used in mathematics or that anyone will be bettered by learning Mathematica notation. But to use Mathematica efficiently and effectively, it is essential to learn the notation used in Mathematica. Failure to do so severely limits what you can do with Mathematica. The point is effective use of any software tool requires understanding that tool. This point has absolutely nothing to say about whether the tool that is Mathematica is better or not for some particular use. Nor does it say someone who has learned to use Mathematica is in anyway "better" than someone who has not. >why don't we have all high school students learn Mathematica? >(Uh, answer: maybe Mathematica is (a) unnecessary, Clearly true to a large extent since mathematics has been done long before any version of Mathematica existed. >(b) unnecessarily complex, Given the complexity of mathematics and what Mathematica is designed to do, I don't see Mathematica as "unnecessarily complex. >(c) not as powerful as you think, Since I've yet to fully master all of the capability in Mathematica (and probably never will), it seems clear Mathematica isn't significantly less powerful than I think. >(d) the complexity is not required to provide the power, Possibly true, but I very much doubt that it is true. >(e) Have you really examined all the history of introducing computing >to lower grades in school? No, I have not. But my knowledge of the history of introducing computing in to lower school grades is not germane to this thread. In fact, the whole question of why Mathematica is not widely used in high school really has little to do with this thread. Given funding made available to high schools, the cost of a Mathematica license almost certainly puts Mathematica out of reach regardless of complexity and capability. >(f) Even if we agree that "algorithms and/or computing" is a good thing >to know, is Mathematica the tool?) There may be better tools than Mathematica. But that is beside the point. Making efficient/effective use of Mathematica entails more than just a passing knowledge of algorithms and computing. A lack of knowledge in these areas will severely limit what can be done with Mathematica. >>Someone who "merely knows" mathematics and has no interest in >>FullForm, Reduce, Eliminate, ReplacementRule etc would be well >>advised to do mathematics by hand and not use Mathematica at all. >You know, there are a few alternatives other than doing mathematics >"by hand" va. Mathematica that do not require knowledge of these >items, and I hope you and other readers of this note consider that >your comment it is an example of your "drinking the {wolfram} kool >aid". >Is the choice "learn internals of Mathematica" or "don't use >computers"? No. The advise is if you want to master the use of Mathematica as a problem solving tool, you need to learn something about the design of Mathematica. If you are unwilling to do that, you would be well advised to use a different tool. This in no way says Mathematica is essential to solving a particular problem. I do not have the view it is the "Mathematica way" or the highway. I do have the view effective problems solving using Mathematica requires more than just a knowledge of mathematics. Note, the point I am expressing here is applicable to any CAS not just Mathematica. >>It simply is not reasonable to expect good results from a tool if >>you are unwilling to learn how to use the tool. >One of the attributes of computer software is that it is almost >infinitely malleable. When a particular design of a software tool >turns out to be ill-suited to a particular task, it is worth >considering whether a better alternative or additional tool can be >designed. Even if you have learned to use the existing tool, that >does not mean you are constrained to use it to the exclusion of >others, nor that you are forbidden from designing another, or >suggesting that other people help design other tools. I've no disagreement with the above. But none of what you say here changes the need to learn how to use a tool in order to make effective use of that tool to obtain good results.
From: AES on 15 Jan 2010 03:19 In article <hhhmhl$o48$1(a)smc.vnet.net>, Valeri Astanoff <astanoff(a)gmail.com> wrote: > > Imho, when applying a rule lhs -> rhs > it's a risky practice to use the same symbol > in 'lhs' and 'rhs', because, very often, there is > no easy way to check what has been done. > > Anyway, for occasional users, you're right : it's crazy! > Thank you -- that's really my primary point. And I'd add: it's damaging (to users, and to Mathematica). As for writing rules, I'd not even try writing something compound, like a + b or especially something like 1 + I, on the lhs, because I'd have no intuition as to how this would work (how spaces would be handled, etc.) But a single character on the lhs? It works correctly AFAIK for every other single-character in the alphabet. Why shouldn't one expect it to work for I?
From: AES on 15 Jan 2010 03:20 In article <hhhmn8$o9t$1(a)smc.vnet.net>, Leonid Shifrin <lshifr(a)gmail.com> wrote: > . . . so to use it correctly one should have a pretty good idea of the > internal representation of participating expressions in Mathematica, as well > as on possible evaluations that may take place. This is certainly not > intuitive . . . In other words, the vast majority of college students, working engineers and scientists, and generally anyone with less than an MS degree in Math, should stay miles away from Mathematica. At least that's what these words imply to me . . .
From: AES on 15 Jan 2010 03:20 In article <hhhmn8$o9t$1(a)smc.vnet.net>, Leonid Shifrin <lshifr(a)gmail.com> wrote: > It would perhaps be nice if such > cases were more systematically documented, but they have nothing to do with > bugs, as Daniel Lichtblau and many others already explained. > > Hope this helps. > > Regards, > Leonid Thanks for shared reaction on documentation (though I don't think that problem will be solved soon). I'm not sure I ever called this a bug -- but in any case "product defect" is a characterization I'll stick with.
From: AES on 15 Jan 2010 03:20
In article <hhpl28$9lf$1(a)smc.vnet.net>, Leonid Shifrin <lshifr(a)gmail.com> wrote: > > I stick to my view of replacement rules as being aimed primarily at advanced > users, or at least as a tool that should be used with much care. But on the other hand, innumerable software apps of all varieties and at all levels down to the most elementary (e.g., nearly all word processors, text editors, graphics programs, spreadsheet programs, email programs, and so on) include "Find and Replace" capabilities. These capabilities frequently have varied options: "Find Next" "Replace and Find" "As Word" "Start at Top" "Replace All" "In Selection Only" and so on. Many have optional GREP abilities. So: 1) Most any computer user at even a very elementary level knows about these tools, rather expects to have them available, and expects them to function as they in fact do function. 2) In particular, they operate (visibly!) on what you see -- not some arcane internal representation. 3) So, if such a novice user goes to Mathematica, it's only to be expected that this user will thnik that Mathematica's ReplaceAll should function in a similar fashion (and, helpfully, Mathematic's /. operator most of the time does function in that way) (sarcasm mode in that parens). 4) So why can't Mathematica also have a TextReplace[ ] function, or something similar, that would function in that way _on what the user sees or has typed (or copied and pasted) into a selected cell_. Given such a function my input would be Find " I " and replace it with " (-I) ". |