User talk:SamHB

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User talk:SamHB/Archive 1

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MVCalc Course Structure

I was thinking of working on lecture 3 tonight and I noticed some oddities in the order of topics. For example, I had planned to cover tangent planes in a lecture or two after the gradient and extrema? I don't know what I was thinking, but I just wanted to say, if you find you would like to refer in a lecture piece to info not yet presented, or if you think one topic naturally flows into another which is for some reason in a different lecture or something, please, feel free to switch up the course order. It may well be necessary, actually! Just remember to change the order both on the pages and on the outline given in lecture 1. JacobB 01:07, 7 January 2010 (EST)

PS: have you considered archiving your talk page? just a suggestion JacobB 01:08, 7 January 2010 (EST)

Earlier you asked about arching your page. I do it just by cutting and pasting everything to User talk:SamHB/Archive 1, and then putting at the top of my talk page For older discussions, see the archives:<1>. JacobB 18:20, 7 January 2010 (EST)

Done. Great minds think alike. I had believed there was some complicated procedure involving renaming files, that one had to do in order to get the history correct. But I looked around at how existing sysops do it, and they don't bother with any of that. Good enough for me. SamHB 19:55, 7 January 2010 (EST)

A rambling philosophical comment: While reading your wave equation stuff, I was appalled at the way you were approaching it, fiddling around (get it?) with the physics, in advance of doing the mathematics. Then I had an epiphany: You and I have very different ways of approaching these problems. We are each very good at what we do. You approach it in terms of "What is the pedagogically right way to present the material in a sequence of lectures, in a fixed order, with quizzes and exercises and such?" I approach it in terms of "What is the pedagogically right way to present the material in terms of separate pages, that the student can follow in whatever order they want, by clicking whatever hyperlinks interest them?" I recently sort of messed up one of your lectures by moving around the concepts of "vector functions" vs. "vector fields". Feel free to move it back. I will put explanation of these concepts in the separate pages, and defer to you on the order in the lectures. Meanwhile, I need to improve the wave equation page, explaining what sorts of mathematical functions satisfy the equation, and then showing how it arises in a large number of physical problems.

About your specific questions about lecture 3, I need to look more closely at your overall order. You seem to have a more "geometric" approach rather than a "pure math" approach. For example, I would be inclined to cover local maxima/minima in arbitrary dimensions early on, just after talking about partial derivatives, so that all that remains in "extrema" problems is the issue of checking the boundaries. What is the correct order of gradients, directional derivatives, and parametric surfaces? Hard to say. I'd have to write up a draft of these topics first. Maybe I'll do that, but not now. I'm too psyched about the wave equation at the moment.

I hope at least some of this makes sense. SamHB 22:59, 7 January 2010 (EST)

I think you're absolutely right about our styles, and I don't want you to defer to me, at all! I think we can create a blend of styles which will yield the best of both worlds. I like what you did with the vector functions/fields, no need to change it back! I'm going to peruse our articles for a bit now, and I'll get back to you in a bit.
BTW, wave equation wasn't done by a long shot. I hadn't talked about boundary conditions, damping effects, etc., let alone solutions. Feel free to add; just know that my version wasn't what I considered a finished product. JacobB 00:19, 8 January 2010 (EST)

Jacob:

As usual, I've put my foot in my mouth. There is nothing wrong with your wave equation section. It just had a style different from mine, that led to the insight of why our styles are different. I didn't even read it all the way through. I just looked at the first few sentences and extrapolated the trajectory from the initial velocity vector. Of course we will check each other's work very carefully when the time is right.

I've gone through the recent email from you and Andy, and noticed that Andy unblocked me largely for the purpose of assisting with the "calc 3" class. Therefore it would be kind of unsociable for me to run off and only write whatever individual pages strike my fancy at any given instant. So here's my first serious comment, based on your outline. But it's on another page. It seems to me that discussing this stuff here, rather than on the actual course talk page seems a little cabal-like and antisocial. So, having gotten personal stuff out of the way, I'm going to continue on the other page.

SamHB 22:11, 8 January 2010 (EST)

image uploaded

the image you emailed me is available here. JacobB 17:59, 9 January 2010 (EST)

course structure and existence proofs

As promised, I'm doing a whole bunch of math material tonight, but I wanted your thoughts on something, and there's also a favor I'd like to ask.

First up, as part of the restructuring we discussed to cover more PDE material, I'm thinking of combining all the integral definitions and calculations into a single lecture, and then the integral changes under coordinate transforms + applications into another lecture. That'll free up one lecture for some more PDE stuff. What do you think of this? I may or may not have done it by the end of tonight, so you can check it out on the lecture 1 page and see what you think.

Second, I'm just going to state the conditions under which the integrals exist, and that they can be evaluated as iterations of single integrals yadda yadda yadda. Would you like to make some existence proofs and link to them from the lectures? JacobB 23:26, 12 January 2010 (EST)

I reorganized the course a little bit, freeing up lectures 7&8. I'm also thinking of deleting lecture 4 and moving a discussion of velocity and acceleration earlier in the course, and skipping completely or downsizing the intended coverage of Frenet frame and curvature.
So, as of right now, that's two lectures freed up, and possibly another, which is tons of space for the extra PDE stuff you wanted to add (which I think is a great idea!). The course structure STILL needs work - any further idea you have would be welcome. JacobB 04:27, 13 January 2010 (EST)

Well, I seem to be falling farther and farther behind your ambitious pace of writing. I really don't have a lot of time to devote to this, so I need to make the most of my time. I haven't even had time to do more than a cursory reading of the CLEP website that you gave.

My particular areas of interest are integration in its various forms, and curvilinear coordinate systems. That means, for example, the various forms of Stokes' theorem, and line integrals / surface integrals, etc. All this stuff is hard to cover properly; my bookshelves are filled (exaggeration) with books that do it badly, and don't really explain what a "differential form" is, or what it means to integrate it. Doing this really right (e.g. Spivack Calculus on Manifolds) requires some mathematical machinery (exterior forms, or, if you like, alternating covariant tensor fields) that goes well beyond what is appropriate here. But I'd like to give it an intuitive but not mathematically rigorous treatment.

The starting point should be the change of variable theorem. Students already know the basics of that from Calc 1 and Calc 2, of course. But we can take it to the next step, showing how it ties together the material on parametric curves/surfaces, and integrals over same. How? You change to the coordinate system of the parameter(s), so that the integral becomes a standard (Cartesian) Riemann integral. Of course we know that, but we need to make it central to the presentation.

About theorems and "rigor": Of course I like my math rigorous, but there's one area of math (well, maybe more than one, but humor me) where the "Oh, I see how that's true" insight is very useful in advance of all the rigorous "Let S be an open subset of a smooth submanifold of ..." theorems. And that area just happens to be the area we are in. So, for example, the geometric insight of the 2-dimensional Stokes' theorem is useful, and the rigorous proof is just unnecessary tedium. (They'll see it again if they major in math.)

So I'd like to see:

  • Review of integration, change-of-variable theorem.
  • Integration over 2-dimensional regions to find, for example, areas. Of course, plain 1-dimensional integration can find the area of a region bounded by a function, the x-axis, and 2 vertical lines, but we want to break out of that.
    • Use of the change-of-variable theorem to deal with such integrals.
  • Path integration, with the change-of-variable theorem changing to a coordinate system for which this is natural, and the connection with parametric curves and surfaces. (A parametric curve of surface is just a coordinate change that makes the curve or surface trivial.)
  • Continue to higher dimensions.
  • Easy proof of Stokes' theorem (well, not easy, and maybe not a rigorous proof) by choosing a coordinate system that "flattens whatever the curvy surface was.
  • Similarly for divergence and Green's theorem; show that Green's theorem is just a trivial case of Stokes' theorem, and the change of coordinate system converts the latter into the former.

I find that the pages on this stuff (not your lectures, the article pages) are scattered all over the place, with Iterated integral, and Double integral, and Line integral and Surface integral and Vector integration. They would benefit from being consolidated into a smaller number of more comprehensive pages.

Other subjects I'm interested in are Laplace's equation, the physical significance, and simple applications of separation of variables (Fourier series over a circular membrane) to solve it. This is probably way too ambitious. Please stop me from doing it.  :-)


About your question about proofs, what do you have in mind for existence proofs? Do mean prove Fubini's theorem? And the conditions under which a multiple integral, in which the individual slices all converge, doesn't converge? That theorem, if I recall correctly, is very hairy. And those conditions are mostly of interest to upperclass topology and analysis majors. Do I misremember? If you say that I do, and you really want those proofs, I will read up on them. On the other hand, a sort of intuitive "hand-wavey" not-really rigorous presentation is something I'm all in favor of.

SamHB 20:57, 13 January 2010 (EST)

I'd like a proof of some basic conditions under which a Riemann integral is defined. We don't need to cover all cases in which it is defined, and we don't need to explore more advanced forms of integration, but right now we have nothing.
While I'm all in favor of a brief discussion of Laplace's equation, using Fourier series at this level is probably too advanced.
Working on the various special cases of Stokes theorem is great, and I encourage you to. We have some unassigned lectures, so feel free to explore those areas in those open lectures. JacobB 17:05, 14 January 2010 (EST)
OK, that's much easier than Fubini's theorem. I believe the official statement is that is is defined if the set of discontinuities has measure zero and the integral is finite. Or we could dispense with the finiteness and say "Yeah, it's defined, but it's defined to be infinite." That's better than saying "I have no idea." In Lebesgue integration theory, I believe that it is considered to be nonintegrable if the integral is infinite; I've never liked that. But never mind. I'll look up stuff and try (for once) not to re-invent the wheel this time. Anyway, more to the point, for our purposes we can use a weaker condition: the set of discontinuities is finite. Getting the students involved in Lebesgue measure is probably not what we want to do. And, of course, we are doing the Riemann integral, not the Lebesgue integral. This stuff (showing that the limit exists) will belong on the Riemann integral page. It will be necessary to get that unlocked. SamHB 23:04, 14 January 2010 (EST)

We also need some material on coordinate transforms, which isn't accounted for at all in the current course structure. Care to help me with that? Also, Riemann Integral has been unlocked by TK. JacobB 20:52, 16 January 2010 (EST)

riemann sums.gif

Gifs often don't work very well when we try to resize them, I'm not sure why. I've uploaded a jpg version of the file here. JacobB 10:46, 19 January 2010 (EST)

More about course structure

A few thoughts -- I don't think we should try to do exterior derivatives; that's just too advanced. That is, I can't picture having one course go all the way from talking about polar coordinates up to doing exterior derivatives. Of course, we need it for the general Stokes' theorem, so we may need to do some hand-waving. I'll look at the Stokes' article.

Should we be keeping any of the exercises/problems secret for use in a final exam? I thought of a very doable but interesting (read: diabolical if you haven't followed the lecture!) problem for integration of parametric surfaces.

I've moved the stuff earlier. Lecture 2 is now bloated, while some others are emaciated.

SamHB 22:22, 22 January 2010 (EST)

my recent edits

See your email - my removal of this content was not a commentary on the quality of your contributions at all, but just trying to keep Conservapedia on-mission. JacobB 21:45, 24 January 2010 (EST)

great work!

nice stuff on coordinate changes JacobB 23:36, 3 February 2010 (EST)

Wow!

Wow, terrific effort!--Andy Schlafly 23:19, 7 February 2010 (EST)

some help?

I'm trying to formulate a parametrization of one side of a hyperbola \vec{r}(t) so that \vec{r} \ '' = a\vec{r}\left| \vec{r}  \ \right|^{-3} for a constant a \ . I've been doing all kinds of research on hyperbolic trajectories, but can't find what I'm looking for. JacobB 03:31, 10 February 2010 (EST)


You haven't been shooting alpha particles at gold foil lately, have you?  :-)

It looks as though you want the actual trajectory, parameterized by time, of a particle in an inverse square repulsive field. That is, x(t) and y(t) in closed form. You may be out of luck on that, though I can't say for sure.

This is, of course the famous Kepler problem, which has the famous and elegant conic section solution for r in terms of theta. Let μ be the attractive/repulsive acceleration, so that

\mu = GM\, in the gravitational case, or \mu = \frac{Q_1Q_2}{4\pi\epsilon_0} in the electrostatic case. And L is the angular momentum divided by the mass. (μ is part of the problem statement; L and e are constants of the integration.)

For the attractive case,

r = \frac{L^2}{\mu(1 + e \cos \theta)}
\frac{d \theta}{d t} = \frac{L}{r^2}
\frac{d r}{d t} = \frac{\mu e \sin \theta}{L}

which is the neat and elegant conic that we know and love. But it doesn't track the actual passage of time.

For the repulsive case, I'm still going to have μ > 0, so the solution is

r = \frac{L^2}{\mu(-1 - e \cos \theta)}
\frac{d \theta}{d t} = \frac{L}{r^2}
\frac{d r}{d t} = \frac{- \mu e \sin \theta}{L}

How to get the time dependence? Warning: I haven't checked this stuff personally yet.

According to wikipedia, we can set

a = \frac{L^2}{\mu(e^2-1)}
b = \frac{L^2}{\mu\sqrt{e^2-1}}

Now introduce a new parameter E (why the heck did they call it that?) in place of t, and we can get x and y in closed form:

x = a(e - \cosh E)\,
y = b \sinh E\,
\frac{d x}{d t} = - a \sinh E \frac{d E}{d t}
\frac{d y}{d t} = b \cosh E \frac{d E}{d t}
t = a \sqrt{\frac{a}{\mu}} (e \sinh E - E)

The first two of those equations get x and y in closed form as functions of E, so we need E as a function of t. The last equation gives t as a function of E. But I don't think that can be inverted in closed form!

SamHB 21:16, 10 February 2010 (EST)

glad to see you're on

can you see Calc3.10? i think i wrote this WAY too advanced, but i also feel like fourier analysis is really the only way to understand what's happening there. any thoughts? JacobB 23:15, 17 February 2010 (EST)

Yeah. I saw what you wrote a couple of days ago (how's that for a dangling participle?  :-) Too advanced. I'm not familiar with this particular technique, and will have to brush up on it. But: Delta? Is that the Dirac delta function? Or some representation of a kernel? They won't follow it. And the subscript *. Fourier transform? I'm not familiar with that notation.
The way I would present it, and Laplace's equation too, is to show some simple examples of solutions. You and I know that as the first few eigenfunctions. The student can't learn how to solve PDE's until they have seen some examples of solutions. PDE's are way too hard otherwise. (It's like teaching integral calculus. We start by showing some lucky guesses -- "Hey, the sine function has the derivative that we want, let's talk about it for a bit." -- and then we get down to techniques for solving them for real.
This gets into the method of separation of variables. It's simplest form is with Laplace's equation on a disk. (I know much more about Laplace than the heat equation, so maybe what I'm saying doesn't apply to the heat equation.) We work out the standard solutions by guessing. They are of the form r^k cos (2\pi\k (\theta +M)) or something like that. We show that those work. And that any linear combination works. We're almost there! If the problem is to find the equilibrium temperature everywhere, given the temperature at the periphery, we just have to figure out how to represent that as sines and cosines. I'll be darned! Fourier series will do it!
Then we show how separation of variables works in general -- "We look for solutions of the form X(x) Y(y), such that they are each subject to their own differential equation.
But it's probably still too complicated.
SamHB 00:10, 18 February 2010 (EST)

Agreed. We may need to consider not including this material in the course at all. On a seperate note, I was hoping you might be able to add some exercises for your Jacobian stuff in Lec. 2? JacobB 22:09, 25 February 2010 (EST)

Yes. I'm working on putting together the presentation of vectors in curvilinear coordinates. In case you hadn't noticed, I'm using a somewhat nontraditional definition of basis vectors -- they aren't normalized. The formulas for dot, cross, div, and curl are more natural, and they can handle any coordinate system, not just orthogonal ones. Still needs more work. A lot more. And I can't put in as much time on this as I would like. I will work out exercises for them.
By the way, I thought of a really cool problem. "You are designing a universe. You want Maxwell's equations to be true, because they are so elegant. You want the electric field around a point charge to be a radial vector, proportional to the radius raised to some power. What does that power have to be, so that the divergence will be zero?" The answer is, of course, -2. And, when things are expressed in spherical coordinates and the correct divergence formula is used, it is very easy.
SamHB 23:53, 25 February 2010 (EST)

3.3

Can you take your line/surface integral stuff from lec 3.3 and merge it with the material on these topics presented in 3.5? JacobB 17:00, 27 February 2010 (EST)

OK. But not right now. I finally put together the divergence/curl stuff, so a huge delivery is about to happen. It may be that, in addition to your request, the div/curl stuff will need to move to a later section. SamHB 23:07, 27 February 2010 (EST)

Done. It's all in a pretty messed-up state, but at least it's in one place. And the right place--lecture 5. There's nothing about integration in earlier lectures. Well, a little bit--the arc length discussion requires an integral, but it's a completely vanilla integral. Lecture 5 is where the fancy-shmancy integrals on manifolds occur.

In fact, a thing to think about is the relationship between the lecture 4 material--tangents, binormals, torsion, etc. (that is, the stuff that you are interested in :-) and the generalized coordinate/manifold stuff (the stuff I'm interested in :-). They are both part of multivariable calculus, but sort of at opposite poles of the subject. Maybe we could think about switching lecture 3 and lecture 4. Not saying we should; I haven't thought about in any detail. But it's a possibility.

Forget that. I've looked again. The lectures are in the right order. SamHB 22:54, 1 March 2010 (EST)

Hope this makes at least some sense.

SamHB 22:51, 1 March 2010 (EST)

New Musical Examples up at Mannheim

Enjoy! JDWpianist 15:02, 5 March 2010 (EST)

My MV Material - heads up

To JacobB or anyone else who works on the MV course. (Or anyone interested in the topic.)

The material that I wrote, mostly in lecture 3.2, used a somewhat radical approach to vector components. I used somewhat unorthodox definitions of generalized coordinate systems -- "natural" coordinates rather than "orthonormal coordinates + Lamé coefficients". The latter are more common, but natural coordinates are, in my opinion, actually simpler and, well, more natural. Here is the difference: What I call "natural" coordinates allows for arbitrary coordinate systems; not just the orthogonal ones that are in common use. All the common coordinate systems (polar or confocal in 2D, cylindrical, spherical, etc. in 3D) are orthogonal, in the sense that the coordinate lines, curved though they may be, are always orthogonal to each other at any point. I used "natural" coordinates, such as are used in tensor calculus, that don't require orthogonality. It's true that I made heavy use of the common simplification for common coordinate systems, but I used a very general treatment in the early stages.

The most important difference is that, in the "natural" formulation, basis vectors are not unit vectors. That is, I used a different formulation of what the components of a vector mean. The components of any given vector, in common orthonormalized coordinates, is bigger than the natural components of the same vector, by a factor of Hi, the ith Lamé coefficient.

In an orthonomalized system, the metric tensor is diagonal. For example, in spherical coordinates, the metric is

[g] = \begin{bmatrix} 1 & 0 & 0 \\ 0 & r^2 & 0 \\ 0 & 0 & r^2 \sin^2 \theta \end{bmatrix}

The Lamé coefficients are the square roots of those diagonal entries. (The metric is positive-definite, no?) So we have

h_1 = 1\ \ \ h_2 = r\ \ \ h_3 = r \sin\theta

In an orthonomalized system, those are the only things you need to know, but the formulas are very hard to explain and motivate. In my treatment of, for example, the cross product, you can see them lurking in disguise, in the form of the various square roots of gii.

Important point: The basis vectors (that is, vectors with components like (0, 1, 0)) are not unit vectors in the sense of having a real, physical length of 1. In an orthonomalized system, their physical length is 1—the formula for the length of a vector is always the square root of the sum of the squares of the components, although the meaning of those components is actually very complicated. In a "natural" system, the inner product is given by \sqrt{\sum g_{ij} V_i V_j}. Which of course simplifies somewhat when the system is in fact orthogonal and the metric is diagonal.

My guess is that you aren't really inclined to do things with "natural" coordinates in the MV lectures. (In fact, it's possible that you are banging your head against your desk right now as you read this :-) So you will probably want to rewrite some of my material. The part about thinking of a coordinate system in terms of its J matrix to any Cartesian system, and then using JtJ as the metric matrix is still probably useful. (I intended to have the proof that g is independent of which Cartesian system you use (though J itself is not) be an exercise. It involves showing that the transformation between any two Cartesian systems is an orthogonal matrix, and, when you insert such a matrix into the JtJ computation, the transpose turns into an inverse and they cancel.)

But my definitions of the dot product and cross product involve the metric, whereas, in the traditional formulation, the formulas are the same as in Cartesian coordinates. Because all the vectors are calibrated with respect to a locally orthonormal system, and that's all that matters for dot and cross products.

Curl and divergence are another matter. The formulas for these are way hairy no matter how you do it. (Though, if you use the "natural" formulation and do tensor operations, they are trivial cases of the covariant gradient. But you probably don't want to do that.) I have the polished formulas written down on paper somewhere; never got around to typing them in. Let me know if you want them. Otherwise, use the traditional formulas, from whatever textbook you like.

Good luck!


Incidentally, the page math.arizona.edu/~vpiercey/Lame.pdf, which I wasn't aware of when I started with MV Calc, has an excellent treatment of how the Lamé coefficients are used in practice. It's interesting reading, and might have useful pedagogical ideas.

SamHB 22:20, 30 June 2010 (EDT)

Great. Let's teach beginning differential geometry to engineering students. Oh, is that a sig sauer over there? Hand it to me? Great, thanks. *blows brains out*. In all seriousness, thanks for your contributions, but let's keep the most advanced material for the most advanced courses, alright? This is multivariable calculus, not rocket sci... errr, you get the idea.
On another note, I have been away for a long time (a month? Has it been that long? ugh...) so our Calc I and II courses aren't built up at all. Feel free to help out there. JacobBShout out! 21:04, 21 July 2010 (EDT)

College Math

As I've always said, our purpose should be to introduce math to our core readership - not to display one's erudition or to publish the most obscure, jargon-ridden and unreadable articles possible.

I haven't seen any evidence that the undergrad and post-grad math hackers have the slightest inclination to make mathematics accessible to our readers. If this changes, I'm happy to help them, but refusal to write articles on high school algebra with variables like x isn't very convincing. --Ed Poor Talk 16:32, 26 September 2010 (EDT)

Good to see you again!

Good to see you again! More math learning is always welcome ....-- Schlafly 00:18, 13 November 2010 (EST)

It starts with the compass and straightedge article. I'm serious. Can you just restore it, please? If there's some deeper reason why you don't want to, could you email me? Please? SamHB 00:35, 13 November 2010 (EST)
I didn't delete it. Aren't there other entries you could improve as the person who did delete it can reconsider?--Andy Schlafly 00:49, 13 November 2010 (EST)
We should take this off line. I will send mail to you and Ed. But there is one thing that needs to be said at the outset. You may wonder why I am being so single-mindedly obsessive about "Compass and Straightedge", to the exclusion of all else. It's this: That article was contributed to by many people, in the true spirit of a wiki and of the "best of the public". Aside from the parody sentence, it was a decent article, and was about a topic that (IMHO) is important as supplemental material for math students at the high-school and junior-high level. It is something that is often not covered in regular curricula because it's off the beaten track. It's a prime example of good "enrichment" material. And it's interesting. The article was deleted because of one act of vandalism. You ask "Aren't there other entries you could improve ..."? Yes, but why should I put effort into things if they are in danger of being destroyed due to the actions of one jerk? I am one of Conservapedia's most prolific math/science/engineering/technology contributors. That deletion calls into question any contributions I might make.
[Note for anyone mystified by the order in which things happened: The preceding was intended to be posted before the email, and hence before the restoration actually occurred. It got sent along with the email. The restoration then occurred. Thanks! But I still think the explanation is important.]

SamHB 15:50, 13 November 2010 (EST)

Stay off the grass signs

Ed's talk page isn't locked...even though it says so. New users and those not registered cannot edit it....but it will allow you to save to it, regardless of what it says. At least that is what I have been told, I've never created another user account! --ṬK/Admin/Talk 22:01, 28 November 2010 (EST)

Right you are. I didn't even notice the open edit box just below the sign. I guess I confused the green color of the sign with the grass itself  :-) SamHB 22:21, 28 November 2010 (EST)

More thoughts on math

In a recent note to Ed Poor, I picked out 4 articles that I thought would be useful to write (or improve), and timely, based on various earlier discussions.

  • Compass and straightedge—Well, I've rewritten most of that, along the lines that I had told Ed I would do. But it still needs a decision about how much to say about the connection with Mr. Galois.
  • Elementary Algebra—This was the subject of the mail alluded to above [on Ed's talk page]. What do you [Ed] think of the changes that I made? Is the next step to talk about quadratic equations? Or perhaps polynomial factoring? Or something else? Would you like me to do it, or do you want to work on this yourself?
  • Peano axioms—There is at present no article on this subject. I think it would be very interesting and fascinating for our readers. And it can be done in an accessible way. It's really not esoteric. Anyone old enough to appreciate what "theorems" are, and that you "prove" them (as opposed to taking your teacher's word for them), can appreciate this. People probably cross this threshold around 9th grade or so, usually in the context of elementary plane geometry. (I can't believe that you never took plane geometry! But I'm sure you developed an appreciation of proofs in whatever classes you were taking at the time.) Now most people have been doing ordinary arithmetic for a long time before learning about theorems, and they think they know that addition is commutative. So you go to these people and ask "So how do you know that addition is commutative? Can you give me a proof? Aha! That is what the Peano axioms are about.
  • Center—This has been a disaster for a long time. I really don't know how to write the "headline" sentence for this; that is, what's the first thing you say about what the "center" of a geometrical shape is? Do you have any ideas? I'd really like to see your take on this article; I really don't know how to begin.

I would really like to hear what people think about doing the Peano axioms. They are awesome. And I believe they are neglected in "traditional" ("brick and mortar") math education.

Ed made a suggestion of doing propositional calculus. I don't agree. Plain logic (if x implies y then not y implies not x) is of course very important, and is always covered. Or should be covered. But the actual topic of propositional calculus goes beyond that in ways that will not be useful to teenagers, and will, frankly, bore them. I did not appreciate what this material really meant until I was a college upperclassman. Of course, I didn't like the game of "Wff'n proof" either. Anyone who liked that game as a child (Hi, Ed!) very well might find it invigorating to write an article on propositional calculus. But leave me out of it.

SamHB 00:23, 6 December 2010 (EST)

I don't understand your objections to making math and logic accessible to underclassmen, high school students, and the layman in general. In particular, your statement that propositional calculus goes way beyond teenagers and will bore them does not explain why you refuse to help describe the parts that they can understand and enjoy. --Ed Poor Talk 10:42, 12 April 2011 (EDT)
As I believe I have emphasized to you again and again and again, I do want to make math and science articles accessible. I believe that everything I have written (well, not MVCalc; that was JacobB and me going overboard) is accessible. If you find exceptions to this, please let me know, accept my apologies, and let me fix it.
Please don't take my reluctance to write on a given topic as "refuse to help describe ..." The are many articles I haven't contributed to. Click "random page" to see them. My inaction on propositional calculus is that it is not particularly interesting to me personally. I'm much more interested in the areas of math that would be considered "pre-calculus". Now I know that you are interested in logic. (Was I right about "Wff-N-Proof"? Dark blue vinyl case, pink foam rubber, wooden cubes with logic symbols on them? It's been a long time. I no longer have my set. I think it went the way of so many of my childhood things.)
I admit that my statement that prop calc will "bore" teenagers may have been a bit of projection on my part. You're most welcome to disagree. So, by all means, write about it!!!!! Don't read too much into my reluctance. If you write well, you may even convert me to liking logic. Maybe I'll even buy a copy of Wff-N-Proof on Ebay. Who knows? Go for it!
SamHB 23:43, 14 April 2011 (EDT)
I think my dad's WFF n' Proof set had blue or bluish-gray foam rubber, but yes, that was my introduction to PC. I still use the "Polish notation" when doing proofs, as I prefer it to infix notation. C-w-Klb (where w = write well, l = like logic, b = buy a copy ;-) --Ed Poor Talk 00:02, 15 April 2011 (EDT)

Goodness gracious, has it really been 2 years? How did I ever forget you as a potential collaborator? --Ed Poor Talk 22:13, 1 June 2013 (EDT)

Both sides of the Ada Lovelace story

  • I'm just going to overwrite you for now, see talk. Sorry.

No problem, good faith, and all that. --Ed Poor Talk 00:40, 15 April 2011 (EDT)

Federal Debt Limit

User:RobSmith suggested I get approval from other committee members on featuring this on Friday. Thanks.--JamesWilson 23:40, 27 July 2011 (EDT)

I'm sorry; I didn't get to it on time. I see it's featured anyway.
In any case, I stay away from politically sensitive articles. (Maybe I shouldn't be on the committee.) I have a number of issues with the article—it seems to be just a "hatchet job", as political issues tend to be. To pick just one example of many questionable statements:
In fact, it is almost unheard of for a credit card company to give a credit line increase to someone who's maxed out on his credit card.
This is true, but it is in the context of saying why the debt limit should not be increased. Now maybe it shouldn't be increased in this case, but that isn't a convincing argument. The debt limit has been increased many many times in our history. If the comparison were apt, that would be equivalent to a credit card company increasing the limit, many times, on a maxed-out account. Which no credit card company would do. But the fact that the debt limit has been increased many time shows that the comparison can't be a good one. The federal debt is not a credit card account. SamHB 12:47, 30 July 2011 (EDT)
You may remove yourself from the committee if you wish. As for your edit to the Elvis article, I added a cite for the nervousness. Thanks.--JamesWilson 21:40, 30 July 2011 (EDT)
OK, that really surprised me. I had assumed that Elvis's gyration came about "naturally", that is, he just "felt" the music. The article you cited was certainly eye-opening. It seems that his musical career had a rather difficult start, complete with ridicule from other people. I'm glad he overcame it. SamHB 12:46, 31 July 2011 (EDT)

Why is it

that you are leaving?--SeanS 23:27, 18 August 2011 (EDT)

Sorry!

Hey Sam - I appreciate your note on my talk page! I reverted you on the main page talk and immediately came here to discuss it, but then I was locked out of the site somehow! So sorry this is two days late; I reverted you on main page talk because that's really not the place to go for article problems or requests to sysops, but as to you're issue - you're an editor of this site! You're totally free to revert someone - and if they edit war with you you can always go to an administrator or someone with blocking rights - like me! - to get some help. I'll take a look at the page you were talking about and we'll see what we can do.--IDuan 16:19, 20 December 2013 (EST)

No problem. I was disappointed by your action and then failure to post the promised talk item, but you have my sympathy over the network problem. It's happened to me a number of times.
I wasn't happy about your reverting my stuff in main talk, because I believe you aren't supposed to delete talk-page material unless it is libelous or seriously bad. But the rules may be different for main page talk.
In any case, I've reviewed AK's comments, and I'm not nearly so upset with what he's doing than I was. I no longer think it is, by its nature, a "crackpot" page needing to be put into essay space. It's just that he read George Simon's books (I haven't read them, but the Amazon reviews are quite good) and took Simon's definition of "disturbed character" too literally and too generally. People invent terms all the time when they are writing self-help books. The problem isn't that it needs to go into essay space, it's that the article needs to be renamed. It should be titled "George Simon", and should be about his writings in those two books. There's a lot of good material that AK put in there. But it isn't about "disturbed personalities" in general, that's just a term that Mr. Simon uses in his books.
Anyway, I need to do a lot more thinking about this, and post a long message on the D-P talk page, rather than your talk page. But no time for that just now. I'll be back, and, hopefully, make peace with AK.
But the spontaneous generation/Pasteur/Clenceau/Lamarck/Darwin stuff has to go, unless Simon's book actually discusses those topics. If AK feels strongly about those topics, there are plenty of other pages for that, not a page about a "pop-psych" self-help book. And, of course, I take back all my stuff about listing mass murderers. If these are self-help books about toxic personality types that one runs into in one's everyday life, I doubt Mr. Simon wrote about etiquette when dealing with mass murderers at social gatherings.  :-)
Thanks for your help in all this. SamHB 23:51, 20 December 2013 (EST)
No problem! I'm confident you and him can find a compromise. As to talk page edits - user talk pages are generally your own - you sort of have control over what is put here; other talk pages should stay on the subject of the main page - or specifically on the subject of the article. We don't especially like if, say, everyone starts a huge random debate on Barack Obama on the Barack Obama talk page - that's for debate pages - we want the talk pages to be used to discuss how to improve the article. Main page talk can be more iffy - because often it's used as reactions to MPR - but still a comment as random as "move this random page" can be reverted - because that has nothing to do with the main page.
You're a great editor - I hope all this isn't frustrating you too much.--IDuan 23:58, 20 December 2013 (EST)

Daily Beast evolution article

The following material was lost in a database glitch early on 25 January 2014. I was not able to recover the last few sentences, but it's mostly here. I doubt that anyone wants to continue the discussion; it had pretty much run its course. But if you do want to continue, feel free. After all, this is a talk page. SamHB 01:24, 26 January 2014 (EST)


It would take very selective skimming indeed of the Daily Beast article to come to the conclusion that the article is about "evolution having a bad year". The point of the article is very clearly that deniers of evolution continue to become more and more extreme, fringe and marginalized, and that "Truth, alas, seems to resemble a commodity...to be purchased by the highest bidder or the most powerful political leader". CescF 14:28, 22 January 2014 (EST)

CescF, which Daily Beast article are you referring to? Could you please give us the title of the article? Conservative 19:59, 23 January 2014 (EST)

It was a Mainpageright item,, added by you, at 08:24, 5 January 2014, here. It said:

  • The pro-evolution news website The Daily Beast declares "2013 Was a Terrible Year for Evolution". Meanwhile, global evangelicalism is growing![1]

The cited blogspot item said:

On January 2, 2013, a leading news website The Daily Beast, which is a liberal leaning pro-evolution website, declared that:

2013 Was a Terrible Year for Evolution
Never mind the increasing evidence .....

The cited dailybeast article said, in part:

  • "The trajectory [of general public acceptance of evolution] is not encouraging, especially as it runs in parallel with a steady increase in the evidence for evolution—evidence now piled so high that not even one evolutionary biologist at any of America's research universities rejects the theory. Evolution is as widely accepted in biology departments as gravity is in physics departments."
  • "We were hopeful that these evangelical students would become leaders of their faith communities and gradually persuade their fellow evangelicals that evolution was not a lie from hell—which was what many of them had been taught in Sunday school. But instead scientifically informed young evangelicals became so alienated from their home churches that they walked away, taking their enlightenment with them."
  • "An alarming study by the Barna group looked at the mass exodus of 20-somethings from evangelicalism and discovered that one of the major sources of discontent was the perception that 'Christianity was antagonistic to science.'"

That is, the behavior of intellectually backward evangelicals has caused many evangelicals to leave their church. They are not "questioning evolution" so much as "questioning their religion". This can't be what the evolution-deniers want. Since the writer is himself an instructor at an evangelical college, he found that trend disturbing.

  • "Many of my most talented former students no longer attend any church, and some have completely abandoned their faith traditions."

I hope this helps. SamHB 00:20, 24 January 2014 (EST)

SamHB, this helps show that liberals have a penchant of engaging in liberal wordiness. Which Daily Beast article in question is this? What is the title of the article? Until Darwinists are willing to face reality and give the name of the article, I am afraid it will be quite apparent that they are generally a proud lot who like to stay inside in their self-made Darwinism cocoons.
Second, global evangelicalism is exploding in adherents while global atheism and agnosticism have had a longstanding trend of decline since 2000 A.D.[2] In an age of globalization (immigration, travel, etc), this does not portend well for Darwinism, since its most vocal adherents since World War II, have historically been atheists/agnostics. See: Evolution and Global Christianity and Global atheism. Conservative 09:12, 24 January 2014 (EST)
By the way SamHB, what religion/worldview do you hold to? Are you an atheist? Do you subscribe to liberal Christianity which has had a long period of contraction in adherents and whose adherents are more likely to engage in marital infidelity? See: Liberal Christianity and marital infidelity. Conservative 09:22, 24 January 2014 (EST)
Oh for Heaven's sake, Conservative, since you want to be a pedant, it's the article referenced by you on your blog. You knew this, of course. Now, we await your response, which will be "What evidence do you have that the article linked to is written by me?" CescF 19:09, 24 January 2014 (EST)
Some of you are missing the point. User:Conservative was merely dictating that you cite the title of the article, "2013 Was a Terrible Year for Evolution," in your questioning that the article claims that 2013 was a terrible year for evolution. As you recognize the title was ironic, it might not have occurred to you that doing that would end this debate with a win for Conservative. MelH 19:18, 24 January 2014 (EST)

From a scientific perspective, the 3 weakest links of Darwinism are: the origin of life, the fossil record - especially the Cambrian Explosion and dearth of credible transitional fossils, and the information/complexity issue. And Meyer's had brisk sales of his book on the Cambrian Explosion and the Darwinists had no credible rebuttal of his book and his book did appear to change some notable scientists minds to some degree. Furthermore, the evolutionist Nick Matzke thoroughly embarrassed himself by quickly giving a review of Meyer's book when it was obvious that he didn't read it and wrote his review ahead of time before reading the book. Matzke showed himself to be a clown and not an intellectual.

Plus, global evangelicalism/creationism saw significant growth in 2013.

It was a terrible year for Darwinism. There is no point in denying this fact.

In addition, besides mentioning the brisk sales of Meyer's book, the author of the Daily Beast article mentions a significant recent Gallup poll relating to the USA which was unfavorable to Darwinism. The title of the article was not ironic. Conservative 22:23, 24 January 2014 (EST)

Well, it was not my intention to help show that liberals have a penchant for engaging in liberalwordiness, and in fact I don't see how one could draw any conclusion about liberals from what I wrote. In any case, I was only giving a few short excerpts from a much longer web page that Conservative, directly or indirectly, linked to. Also, she is, for example, essentially the only contributor, through over 4000 edits, to the Atheism article, which for a while was over 200 kilobytes.
As far as the question of what article it was, I thought I made that clear, in excrucuating detail, with the web links that I gave. To repeat, the article is here. In plain text, that URL is http://www.thedailybeast.com/articles/2014/01/02/2013-was-a-terrible-year-for-evolution.html, but you should be able to get to it by clicking on the link. If you look at it, you will see the title. It is "2013 Was a Terrible Year for Evolution". I don't know whether Darwinists in general are unwilling to give the title of the article, but I have no problem doing so.
Second, you might be interested in this article. Its title, by the way, is "'Red' States Have Higher Divorce Rates Than 'Blue' States, And Here's Why".
As far as the personal questions, I didn't say what my religion/worldview is, nor did I say whether I am an atheist. Those considerations are not germane to the topic. As far as the question "Do you subscribe to liberal Christianity which has had a long period of contraction in adherents and whose adherents are more likely to engage in marital infidelity?", the absence of a comma after "Christianity" shows that you were were using a "restrictive" subordinate clause. That is, you were effectively asking whether I belong to any subgroup of liberal Christianity that is experiencing a high rate of marital infidelity. I can assure you that I do not belong to any such subgroup. See the "red state / blue state" article cited above for why this is not surprising.
I hope this helps clear up the question of what the title of the article whose title is "2013 Was a Terrible Year for Evolution" is. SamHB 23:34, 24 January 2014 (EST)

A few more sentences, by User Conservative, were lost at this point. I recall that one of them was her assertion that I am not a Christian. If I were more thin-skinned, I would accuse her of libel. However, being a Christian, I won't. I would simply advise Cons to judge not, lest she be judged. And to try to be more compassionate and gentle with people. SamHB 23:55, 27 January 2014 (EST)

Thanks for un-memory-holing the thread, SamHB. As former Supreme Court justice Potter Stewart said, "Censorship reflects a society's lack of confidence in itself". CescF 01:28, 28 January 2014 (EST)
Was all that stuff oversighted? They used to do that to me on Wikipedia. PeterKa 22:11, 28 January 2014 (EST)

Spammer

I don't have blocking powers. VargasMilan 00:21, 28 September 2014 (EDT)

Ummmm, I believe you do. SamHB 01:32, 28 September 2014 (EDT)
Vargas, I should have congratulated you when I promoted your account to blocking rights. Thanks for your contributions to the site.--Andy Schlafly 00:37, 29 September 2014 (EDT)
You're welcome, Andy. Thank you for the privilege of editing here. And thank you for the kind words as well, Sam. VargasMilan 01:05, 29 September 2014 (EDT)
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