User talk:SamHB/Archive 1
You are disrupting this project. Consider yourself on probation
- What does this mean? SamHB 23:22, 26 August 2008 (EDT)
- Your edit comment for my user page said "help as asked, or leave" What did you ask? When did you ask it? Where did you ask it? If you had asked me to do something, I would have done it. I'm on your side. SamHB 23:22, 26 August 2008 (EDT)
Open Letter to Ed Poor
Dear Sam - I understands your frustration. This project should give an opportunity to present sound mathematics on high-school level to an interested public. Ideally, the articles start on a fairly basic level, but present some insights for the advanced - or just curious - pupils.
OTOH, when a pupil comes across false information on the maths' sites, he has reason to doubt the hole project: most people understand maths to be about "being right" or "being wrong" - while most other areas here at CP are not so clear-cut.
So, sound contributions especially on maths should be encouraged - contrary to our experiences.
At the moment, I'm waiting for a reaction of Ed Poor, too. --DiEbDirkE 09:22, 27 August 2008 (EDT)
Response to your second Open Letter
SamHB, your letter may be addressed to Ed Poor, but its contents criticize me as well. I have read the entire letter and despite the "unpleasant things" you had to say about me, I am going to leave the personal remarks in your letter and address them instead. A one-month block is showing quite a bit of restraint on my part, because I found the tone of your remarks towards me more than "unpleasant".
As far as I can see, your gripes against me are contained in
- Boolean value - accusation of parody
- Center - poorly written
- Line segment - you take Ed's side in what you call "a serious misunderstanding"
- My planned agenda
I'll handle these in order by length of response:
- Planned agenda. Don't know what the problem with this list is, but I've now clarified where I compiled it from.
- Line segment. I don't believe there is a misunderstanding on my part and you can view my elaborated argument at the talk page. But thanks for at least sticking up for me that it was not sabotage.
- Center. Your criticism should have been lodged on the appropriate talk page, where I would have seen it and replied a month ago. Better yet, you could have edited the page yourself. I have now explained myself at the talk page.
Boolean value. You replaced this article with a redirect, which I agree with since the material was found redundantly in the larger article Boolean algebra, which I had not been aware of. You also salvaged the non-redundant paragraph about use in programming. In that vein, I followed your actions by replacing the redundant Boolean logic with a redirect, saving the nice pictures.
The acclaim I gave to George Boole may be a bit of a grandiose title, but I feel he deserves more credit than he gets for his fundamental role in the subject. His work forged the way for alternative logics with different truth values (i.e. not just 'certainly true' and 'certainly false' but varying degrees of certainty of truth). This forged the way for concepts like modal logic and intuitionistic logic, and also played an important role in natural language semantics. Basically, he had reignited an interest in the foundations of logic, a subject which had been practically frozen in time since the work of Aristotle (see our own logic article), and laid the way for Bertrand Russell, Godel and others.
The other aspects of the article I don't think are disputable. A Boolean value is one of two things: true or false. Other truth values (e.g. "some", "most", or, in another logic system, "probably") are deviations from these two absolutes. George Boole did generalize the true-false Boolean algebra to more general Boolean algebras (see MathWorld for the general definition). In that respect, the Boolean algebra article describes only the most simple example of such an algebra and though fundamental, it's hardly an interesting example for logicians and hardly what Boole was interested in. The natural analogy is of being an important group, but hardly an interesting one to mathematicians.
So, it seems to me that your "unpleasant things" amounted to a complaint about my writing style, a disagreement with me on a disputed definition, and a deflation of a bit of hero worship. Was that really something to get so worked up about that you took such a rude tone with me? -Foxtrot 04:27, 28 August 2008 (EDT)
Just a few thoughts on functions and groups
As I stated earlier, I like what you are proposing for the math articles.
- Group (mathematics): Perhaps one of the first examples could be a finite symmetry group, like S3 - there is nothing simpler non-abelian.
- IMO, a formulation like The groups below are not necessarily abelian. should be avoided, just point out that the two (and one :-) dimensional case lead to abelian groups, and the others don't.
- function: Please, present some piecewise defined function to smash the idea that functions on R are always expressed as terms
Merry Christmas, BRichtigen 16:57, 25 December 2008 (EST)
- Thanks. I have followed your suggestion for groups. Yes, it's obvious—finite permutations are the simplest and most instructive transformation groups.
- As for functions, that page needs a lot of work to present it correctly. And you are right. The notion of a "formula", such as a polynomial, as being fundamental to the definition of a function is wrong. As is the stuff about "inputs" and "outputs". That page is the only one in the sandbox that retained much of the material in the original mainspace page. And it shows. I need to think about the pedagogical presentation some more.
- And I need to figure out how large a fire to light under the sysops to get them to take mathematics, and mathematical pedagogy for a high-school-level encyclopedia, seriously. I'm already in danger of getting burned by the fires I've been lighting.
- SamHB 14:08, 27 December 2008 (EST)
Math articles, 1
The following was placed on Ed Poor's talk page a few days ago. In the interest of not having my musings on the subject scattered too widely, here is a copy. SamHB 15:07, 30 December 2008 (EST)
- I have a whole lot that I would like to discuss with you about math articles. I've been reluctant to do it because I'm keenly aware that (1) the 90/10 rule makes editing talk pages extremely "expensive", and (2) the last person to suggest making a discussion page for this topic got banhammered and reverted. So I apologize in advance for the length of this; there's a lot of material to cover.
- Expanding on your comments at Talk:Axiom_of_Choice#Note_to_Ed_Poor_about_Pedagogy, we need to be flexible about the "one size fits all" principle.
- There are topics which really require multiple articles to deal with the different levels—a single article would be too long and intricate to do the job.
- There are topics that, IMHO, are best handled by a single article, divided into clearly-marked sections at different levels of expertise.
- There are topics that really have only one level of expertise that we should handle, and that therefore should have just one homogeneous page. Derivative is an example. If you're not ready to read about calculus, there's nothing we can put in a page that will help you.
- You mention the various "introductory" articles at WP. This is a consequence of category 1. I submit that we have far less need of category 1 than WP does. In fact, I can't think of any such mathematical topics off the top of my head, though I'm sure there are some. WP has an article "Introduction to general relativity", and the real article. But the latter is for the world-class experts that use WP. We have no need for that. We at CP are not catering to people who need to know about Calabi-Yau manifolds or frame-dragging.
- Category 2 is what I would like to argue for. I believe that a lot of the inappropriate targeting that you and I both have found objectionable in existing articles is due to failure to segregate the material properly. There are topics for which this is the right treatment. They can be handled by using multiple instances of the templates within one page. Separating into multiple pages makes the individual pages too short and unconnected. My page on User:SamHB/Continuity is an example that I have put together to illustrate this. It can be understood at 3 levels: smooth graph, limit, and topological open sets. The page User:SamHB/Dense subset is another example in which I think the approach is reasonable. I'm not suggesting widespread use of this technique—I only used it twice in 14 articles.
- Of course, most articles are in category 3. They should still use the templates. Some of these articles are at high levels with no corresponding article at a lower level. For example, if you are not ready for the abstract mathematical reaoning of User:SamHB/Group (mathematics), there's just no article about it that will be appropriate for you.
- I would really appreciate it if you would look at the articles I have written (yes, it's a lot of material, and you are very busy) and comment on it. I look forward to collaborating with you and the other contributors on making a high-quality mathematics presentation.
- You mentioned the belief that we need about 3 to 5 levels of expertise. We're generally in agreement. I think the 4 templates that we have now (Math-e, Math-m, Math-h, and Math-a) seem to work well.
- You also mentioned the possibility ("I'll probably move this thread to the appropriate page") of making a discussion page for these issues. I will watch for such an activity, and probably participate.
The following had been on the axiom of choice talk page. I have replaced other people's signatures with statements that the signatures existed. (I consider it unethical to cut and paste another person's signature.)
- A couple of things before we begin:
- I come in peace. We have had bitter arguments in the past. I come in peace.
- The bulk of this message was written before the recent flap about deleting the axiom of choice article, though it does relate to that article. It was written just after your "grad students, stop showing off" comment. You need to understand this context. But it has suddenly become extremely timely. Please be patient.
- The article someone wrote giving the pronunciations of the numbers from 1 to 10 was (sorry about personal remarks!) utter garbage. That's not the way to go. I hope to explain. But I think things that you have written may have contributed to people thinking that's what you wanted. I hope to convince you that it isn't what you should want.
- I'm sure you are aware that the people to whom you issued the "three weeks" ultimatum are dead and gone.
- There's a whole lot that I'd like to say on the subject of math pedagogy. (And that awful game of "wff 'n proof" :-)
- For background, you might want to look at some things I wrote a few days ago Talk:Boolean_algebra (you might not have seen it yet) and my draft of an article about paradoxes including some material incidentally relating to AC, in my sandbox User:SamHB/Mathematical_paradoxes.
- I see that you are complaining about "grad students showing off" when they should be working on more fundamental issues of logic and proof theory. While I don't agree that they were showing off (they were simply trying to fix a disaster), I do agree that the page is a disaster. Among other things, it and its talk page have been block magnets from day one.
- But we do need a page on that topic. You might want to look at my paradoxes draft to get an idea of the level that I consider appropriate. Note: It was not intended as a draft of AC. It just happens to talk about AC in another context.
- Now, about proof theory. I already expressed in Talk:Boolean_algebra the view that mathematical logic should be considered a topic that is simply out of reach for CP. But, from what you have written above, you are interested in proof theory on a much more basic level. What you have written at Talk:Addition also shows that you want CP's math and science articles to reach all the way down to the fundamentals.
- I'd like to argue that reaching too high and reaching too low are both pitfalls to be avoided. I've already discussed the issue of reaching too high, and that we have to be careful that, wherever we do reach, the path is solidly filled in. But, when we reach too low, we turn CP into a "textbook of common-sense notions". We are an encyclopedia. Something you look things up in when you already have basic knowledge of the subject, either to go on to the next step or to fill in gaps. We are not an introductory textbook. People do write such books (remember Dick and Jane?) and they are used in primary school. But I doubt that we have the expertise or time to write such things. (I speak only for myself. If you can do it, by all means do so, but I question the wisdom of following this path.)
- Take the case of proof theory, which you raised both here and on the Boolean algebra talk page. The real "professional grade" topic is too high. (Except maybe for people who liked WFF_'N_PROOF :-) But you raised the question "how to prove a theorem of geometry". I submit that that's too low. The question in a student's mind that you would be trying to address would be something like "What does it mean for a proof of Pythagoras' theorem to be correct?" What does the proof mean? What does the statement mean? I submit that these are common-sense notions. 7th graders (or whatever) just need to be shown the statement and the proof, and they'll figure it out. Of course, they need common sense knowledge of how to interpret the sentences, but that isn't something we can teach them. As they go on in their mathematics education, they will become more adept at these issues. And, in graduate school, they may learn about formal proof theory. By the way, the existing Pythagorean_Theorem article is excellent. Among the best math pages we have. It needs no additional supporting articles from below.
- SamHB 11:27, 5 December 2008 (EST)
- SamHB, what a surprise. Another "Open Letter to Ed Poor", albeit with a slightly different title. And as usual, it mixes in legitimate concerns with swipes at editors. I agree with you that it's important that the math articles don't get watered down to too low of a level. I'll totally give you that. But, I won't give you the swipe from aside about the Axiom of Choice article. It is not a poor article, in fact it's had numerous contributions to get it to its informative state, including several from Andy himself. We are one of the few places where students can learn about the implications of the Axiom of Choice before being compelled to use it in all their proofs. People who have tried to change that in the past, and we have kept steadfast to our position. If it's a block magnet, it's only because people like you don't agree with the article's position and want to change it to your own. [By Foxtrot, 14:29, 5 Dec 2008]
- Sam's open letter would be more interesting if I knew who he was. But I disagree with his high/low caution. We don't need a "one size fits all" approach to any topic. Anything that's hard to grasp, like genetics or molecular biology, will need an introductory article. Wikipedia has more than one article whose title is like, "Introduction to X".  Some topics can be covered in a single middle-level article. Usually, we have a simply intro - which tells the reader what we're going to tell him; then the we tell him (in the body). But a complex subject may require multiple articles. Wikipedia has over 100 articles trying to explain evolution. Which by the way shows it's not a simple topic. So we shouldn't dismiss the controversy over it by saying, "Well, the experts say it has been proven." We can prove that Galileo was right (and Aristotle was wrong) with a single, 10-second demonstration. So don't tell me science has to be complicated.
- Math is complex enough that it requires division into multiple levels. We need at least three, and I wouldn't be dismayed to end up with 4 or 5. Arithmetic starts with counting (and the definition of whole numbers vs. counting numbers (see Integer). Then we get addition and subtraction, which in turn provide the basis for multiplication and division. Next, we teach fractions and decimals. While we're doing this, we try to bring out rules such as the commutative and distributive laws, but kids aren't really tested on this.
- The next jump is to using variables ("unknowns"). Actually, we start by using blank spaces marked with underscores: 2 = 7 - ________ and then progress to clever shapes like a box! Somewhere between 6th grade and 9th grade we *gasp* take the astonishing step of using a letter like x for the unknown. It seems kids have to be somewhere around 12 years old to be able to do abstract reasoning like that (see Piaget). From there we make rapid progress through algebra (or "school algebra" if you like showing off), plane geometry, trigonometry and what high schools like to call "advanced mathematics" - meaning analytic geometry, differential calculus and integral calculus.
- Math majors at college and in grad school get to study on the next couple levels.
- Now what I am proposing - and I'll probably move this thread to the appropriate page - is that we focus on the first 2 or 3 levels before spending too much time on the upper couple of levels. [By Ed Poor, 18:32, 6 Dec 2008]
Math articles, 2
Yes, there is a lot to do. As the articles are lacking in visual aids, is there someone I can send images to in order to get them uploaded? Thanks. WilliamBeason 14:20, 30 December 2008 (EST)
- Well, you can post them at the Conservapedia: Image upload requests page, or just put them on my, or any other user with upload rights', page. Hope this helps! JY23 14:22, 30 December 2008 (EST)
- Thank you. WilliamBeason 14:53, 30 December 2008 (EST)
Is this template for calculus articles good? template:calculus If any changes need to be made, let me know. After that I'll send it to be approved. Later on, sections under "Derivatives" can be added. (currently, derivatives is the only article concerning derivatives ... I'll have to fix that soon) WilliamBeason 18:09, 30 December 2008 (EST)