# Difference between revisions of "User talk:MarkGall"

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:Thanks! I'm not really sure what to do with that one -- the notion and examples are obvious to anyone who knows what a smooth manifold is, but not very useful to anyone else. It's a hard thing to motivate. But hopefully the exotic spheres will be news to some. Jump in if you have any ideas to make it easier to read for people with less background! | :Thanks! I'm not really sure what to do with that one -- the notion and examples are obvious to anyone who knows what a smooth manifold is, but not very useful to anyone else. It's a hard thing to motivate. But hopefully the exotic spheres will be news to some. Jump in if you have any ideas to make it easier to read for people with less background! | ||

+ | |||

+ | If you like the geometric style argument we talked about on [[Talk:Essay:Quantifying Openmindedness]], you should check out "Visual Complex Analysis" by Tristan Needham, a doctoral student of Roger Penrose. It's full of cool geometric arguments for complex analysis and Riemann manifolds that I haven't seen anywhere else. [[User:JacobB|JacobB]] 00:11, 2 October 2009 (EDT) |

## Revision as of 04:11, October 2, 2009

**Useful links**

**Welcome!**

Hello, MarkGall, and * welcome* to Conservapedia!

We're glad you are here to edit. **We ask that you read our Editor's Guide before you edit.**

At the right are some useful links for you. You can include these links on your user page by putting "{{Useful links}}" on the page. Any questions--ask!

Thanks for reading, MarkGall!

**ṬK**_{/Admin}^{/Talk}00:50, 10 June 2009 (EDT)

Hello there, Mark! I am truly glad to see that you are adding new pages for Obama's "Czars." So far, so good for a newcomer to Conservapedia! -RKLuffy88

## Contents

## Czars...

Great work, Mark, but can we please consolidate these into one Obama Czar article? --**ṬK**_{/Admin}^{/Talk} 22:10, 11 June 2009 (EDT)

- As before, I'm happy to merge them -- I only created seperate pages since it was requested on the main page by DeanS to fill in red links he added to Obama Administration. What should the new article be titled, and how would you recommend laying it out? --MarkGall 16:44, 7 July 2009 (EDT)

- One would have to find the articles, as they are not linked from the Obama Administration page. If you can do that, provide the links, I can move them onto the same page, entitled Obama Administration Czars. --
**ṬK**_{/Admin}^{/Talk}21:31, 7 July 2009 (EDT)

- One would have to find the articles, as they are not linked from the Obama Administration page. If you can do that, provide the links, I can move them onto the same page, entitled Obama Administration Czars. --

- Here they are:
- Alan Bersin, Steven Rattner, Gil Kerlikowske, Paul A. Volcker, Carol Browner, Jeffrey Zients, Cameron Davis, Nancy-Ann DeParle, John Brennan, Dennis Blair, Kenneth R. Feinberg, Cass R. Sunstein, Vivek Kundra, Adolfo Carrion, Jr., Gary Samore
- These are all linked at Obama Administration (the sixth section, "czars"), which ought to be updated accordingly. I can go through and clean up the redundant information once your merge is finished. Thanks! --MarkGall 21:46, 7 July 2009 (EDT)

## String Theory

Thanks for adding the attributions to Givental, Lian, Liu, and Yau. Don't ask me why I left out such an important credit.--Lemonpeel 12:36, 16 June 2009 (EDT)

- Lotrsw86? --
**ṬK**_{/Admin}^{/Talk}05:13, 23 June 2009 (EDT)

- Who/what is Lotrsw86? If you suspect me of having another username, I assure you that's not the case. I hope it's clear from my contributions by now that I'm not a vandal. --MarkGall 11:12, 23 June 2009 (EDT)

## Math articles

If you please, try to place an example of a problem within the math articles that are posted. For instance, in your Fundamental group article there could be a problem within each subtopic, broken down in a step-by-step manner to lead the reader in understanding and solving it. Think this is possible? Karajou 01:42, 4 July 2009 (EDT)

- I like your idea about problems in the math articles. The issue here is that it's difficult to come up with problems on the fundamental group that could really be answered at this level. An exposition at this level doesn't give the reader the knowledge to solve any real problems. I don't even prove what the fundamental group of the circle is -- a proof requires much more theory than is in the article, but the intuition is clear. I could ask for intuitive guesses about fundamental groups, but just about every space that a new reader knows about is given as an example already! I will try to think something up, I'm sure it can be done.
- In the article differential geometry which I did a bit of work on a couple weeks ago, I inserted "motivating questions" in a few places, to indicate why someone would care about it. I can certainly do this in the fundamental group article. Actually, I was thinking that on the front page mathematics, it would be neat to put motivating questions under all the headers you created, to give a flavor of these areas of mathematics. What do you think of that idea? --MarkGall 09:33, 4 July 2009 (EDT)

- I added two problems/solutions to fundamental group. What do you think? One is for conceptual understanding, while one tests ability to manipulate the definitions. I'll try to add more. What do you think? --MarkGall 21:51, 7 July 2009 (EDT)

## big bang

You undid my edit; why? The list of astronomers I posted contained many people who are far more knowledgeable than either Arp or Burbidge, as evidenced by their continued research in the field of cosmology. While Arp and Geoff might be fine astronomers, they certainly do not understand the preponderance of data that contradicts their pet theories; if their's are notable names to be attached to an article in opposition to the Big Band Theory, why should the names of proponents not be included?

- You added a useless list of mostly obscure scientists. It did nothing to improve the exposition of the article and created the appearance that the theory is more widely supported among scientists than it actually is. --MarkGall 16:53, 2 September 2009 (EDT)

## Edit summaries

Hi, Mark. Could you be more specific than *reinserted some correct info* when you edit difficult or advanced articles like Infinity? Our readers and contributors need to know WHAT is being inserted and WHY. --Ed Poor ^{Talk} 10:36, 18 September 2009 (EDT)

- My apologies. I was reinserting some correct information which I had inadvertently removed when taking out some apparent vandalism, and didn't think to state what it actually was. That material's been there for some time so I hope it won't be controversial, but I'll try to pay more attention in the future. --MarkGall 11:28, 18 September 2009 (EDT)

## Possibility

Mark, it just dawned on me that you might enjoy teaching a math course here to high school homeschoolers. Just a thought for you to consider ...--Andy Schlafly 10:42, 19 September 2009 (EDT)

- Mr. Schlafly, I would certainly love to do that at some point. Unfortunately, for now I don't have time to put in the effort it would require to do it well -- I'm busy enough teaching undergrads (who I suspect are much less motivated than the homeschoolers here!) and keeping up with my own work. I'd consider it at some point in the future, perhaps next year so I can develop materials over the summer. I saw that you once tried to start up a math course here -- if enough interest materializes again, I'd be happy to be an assistant teacher and help out as much as I'm able! --MarkGall 10:49, 19 September 2009 (EDT)

- Mark, that's fine and I appreciate your work ethic! Maybe I'll get a math course started sometime early next year, and with your help it can grow.

- The advantage of teaching with the wiki software is that a course can improve dramatically each time it is taught. I'm seeing that with the Economics course now. Thanks again for your insights and effort.--Andy Schlafly 12:35, 19 September 2009 (EDT)

## Templates etc.

(Sorry about ping-ponging this thread all over my page, Andy's page, and your page, but it will be finished very soon.)

Thanks for weighing in on this. I've made the "H" change, calculus; I don't think there's any issue about that one.

On the "A" change (topology/Riemann), I've been going back and forth in my mind about how to do this. I don't think that it being an open question or not is really important. These things are really just decorations. Though I think the best description should be along the lines of "You should know what the equation to the left is talking about before reading this article." (Sort of like the "You must be this tall to go on this ride" signs at amusement parks :-) Or maybe it should be stronger, as in "You should know what this is talking about *and be able to solve it*." Which of course means Riemann is not suitable. And I think the higher homotopy groups would cut me out. :-( My topology study ended at about the point of the higher homotopy groups. :-( In any case, by the "and be able to solve it" criterion, which works for the other 3 templates, pi-1 of S-1 is about right.

In any case, let me know if this is OK, or if you want pi-m of S-n, and we can let Andy re-protect them. Unprotecting the two lower ones ("E" and "M") was not necessary; it was never my intention to modify those, but I was in too big a hurry last night, at 12 minutes past midnight, to deal with such subtleties. PatrickD 09:51, 22 September 2009 (EDT)

- Sure, sounds good to me. \pi_1(S^1) is about the right level. Thanks for fixing this! --MarkGall 14:19, 22 September 2009 (EDT)

## Incompleteness Theorem

Mark:

I'm planning to work on the issues of logic, completeness, undecidability, and the Gödel incompleteness theorem next. Basically, everywhere I look, I see things to do, and I happened to look at the Undecidable page and the Axiom page. The latter is fairly straightforward -- the characterization of the axioms of geometry being "challenged" by Non-Euclidean geometry needs to be clarified.

But the "undecidable" stuff needs a lot more care. I'm pretty sure I understand the issues, but I'm not 100% sure, so I want to run it by you. It seems to me that essentially all of the material about "Famous undecidable statements" is wrong. These may be statements that are at the edge of what ZF and ZFC mean, but they don't relate to the Gödel incompleteness theorem. And "undecidablility" is about the Gödel incompleteness theorem, *not* about the axioms of ZF.

My understanding is that the Gödel incompleteness theorem says, roughly

- Any logical system rich enough to express integer arithmetic is "incomplete" in the sense that it is not true that, for every well-formed formula F, either F or not F is a theorem (has a proof in that logic).

The logical systems being analyzed by Gödel are simple logics about integers, with nowhere near the sophistication of ZF or ZFC. The non-provability of AC in plain ZF is not really what the Gödel incompleteness theorem is about. You simply add AC, get ZFC, note that the result is still consistent (that is, you now have a trivial proof of AC because it is an axiom, but you do not have a proof of not-AC) and move on.

Hence, it seems to me that all the things in the article related to AC (Banach-Tarski, Continuum hypothesis, large cardinals, non-measurable sets) belong in a different article, since they distract from Gödel's contribution. Only the halting problem (a result from the closely related field of theoretical computer science) is directly relevant to Gödel. And that's what "decidability" should be about.

Of course, fact that neither AC nor not-AC has a proof in ZF is an example of incompletness, but it's not what Gödel was talking about. That is, plain ZF is incomplete, but incomplete logics are a dime a dozen. Gödel showed that *no* logic rich enough for integers could be complete.

Does this make sense?

PatrickD 23:07, 23 September 2009 (EDT)

- Hi Patrick,

- Logic's not my forte (you may have noticed I haven't really touched those articles), but I believe everything you say is correct. I am certain that the only thing on the list of "undecidable problems" which is actually undecidable is the halting problem. "Undecidable" is certainly not the same thing as "not provable within ZF", and choice is independent of ZF, not undecidable. Your statement of incompleteness is also good, and I think understandable.

- If you haven't seen it, there's a nice little book called "Godel's Proof" by Nagel that sketches the proof (in 100+ pages) in a fairly nontechnical way. I couldn't give a formal statement of the theorem, but your summary is more or less the same as the one there. I'm looking forward to seeing the article!

## Dirichlet's theorem

Thanks for explaining the requirement!--Andy Schlafly 00:38, 1 October 2009 (EDT)

- No problem... thanks for catching the error in the statement! Can't believe I missed that one. --MarkGall 00:48, 1 October 2009 (EDT)

## Functors

Sorry to mess up your elegant article on mathematical functors with low-class computer stuff, but there are probably more people familiar with the latter usage. :-(

Was the material on contravariant functors OK? I remember learning about this back in college. The cohomology functor is contravariant, right?

PatrickD 15:31, 1 October 2009 (EDT)

- My article's not elegant at all! It's just a cleanup until the CP treatment of category theory gets redone (if ever; I don't think it's a high priority). Thanks for adding the CS definition -- I'd heard the term, but never knew what it was before! I think the ideal situation would be a single page about basic notions in category theory -- definition of category, examples, definition of functor, examples, definition of natural transformation, examples, .... It doesn't make sense to me for functor to have its own page. I'd put things like "pushout square" and "adjoint functor" on their own pages, if they were ever written, but I'm not sure they belong here.

- You're right on about contravariant functors. I probably should've mentioned it. Sometimes these days when people write "functor" they just mean covariant functor, and a controvariant functor from A is just regarded as a covariant functor from A^op (A with all arrows reversed). It's definitely more illuminating this way, and cohomology is indeed an example.

- The other example I'm thinking about adding is Hom(-,V) and Hom(V,-), both functors from Vect_k to Vect_k. Given a fixed vector space V, Hom(-,V) is the functor that sends an object W in Vect_k to the set of linear maps from W to V, which is itself a vector space. The first of these is contravariant and the second is covariant (or the other way, I always get it wrong), and it's easy to write down why. It's a nice pair of examples in an easy-to-understand category. --MarkGall 17:00, 1 October 2009 (EDT)

## Awesome work!

Great job on some of these math articles, especially all that content to diffeomorphism! JacobB 17:57, 1 October 2009 (EDT)

- Thanks! I'm not really sure what to do with that one -- the notion and examples are obvious to anyone who knows what a smooth manifold is, but not very useful to anyone else. It's a hard thing to motivate. But hopefully the exotic spheres will be news to some. Jump in if you have any ideas to make it easier to read for people with less background!

If you like the geometric style argument we talked about on Talk:Essay:Quantifying Openmindedness, you should check out "Visual Complex Analysis" by Tristan Needham, a doctoral student of Roger Penrose. It's full of cool geometric arguments for complex analysis and Riemann manifolds that I haven't seen anywhere else. JacobB 00:11, 2 October 2009 (EDT)