User talk:Linas/Archive5

Scientific Community Methaphor

I would like you to consider voting on Wikipedia:Articles for deletion/Scientific Community Metaphor. Cheers --R.Koot 11:03, 17 November 2005 (UTC)[reply]

Hamiltonian Mechanics

You've not replied to my point on the classicial e/m Hamiltonian (see talk page) - I think it's an important example, used at undergrad level, so should be in. I may reinstate. Linuxlad 09:04, 18 November 2005 (UTC)[reply]

OK, answered on the Talk:Hamiltonian mechanics; sorry hadn't seen that comment earlier. linas 22:40, 18 November 2005 (UTC)[reply]

Prime number theorem

Jitse, can you add a few sentences about n^2+n to prime number theorem? I just skimmed that and saw nothing. Acutally, I'm surprised, since I would have thought the exponential integral bound would have been not square-rooty like that ... but whatever. linas 14:45, 10 November 2005 (UTC)[reply]

I'm not so fond on working on articles so far outside my research areas, but I thought, why not write this up as I have already done most of the research for the AfD discussion. So, I had a look at prime number theorem and I gathered that I should first improved the article a bit here and there. Then I added a section on prime gaps. And of course, then I discovered that another article, namely Cramér's conjecture, already had about half of what I wrote down. Ah well, such is life.

The prime number theorem only gives the average length of the gap between two consecutive primes, but the individual gaps may be much larger. Nevertheless, there is an enormous difference between what is proven (even assuming that the Riemann hypothesis is true) and what is conjectured (which is supported by numerical evidence). Mind the gap. -- Jitse Niesen (talk) 23:08, 18 November 2005 (UTC)[reply]

Thank you! Your comments on the AfD looked so confident that I figured you could slap in a few sentences. My predilictions for authoring run in the opposite direction: there are many topics that I could write about in my sleep; and although articles on such topics can write themselves quickly and pleasantly, they will not wake me from my mental slumber. So instead, I try to mostly write about things that I've only recently studied and am trying to master. Such authoring is hard and painful and a bit error-prone, (and worse, make me look foolish in front of those who know better), but it helps me (re-)learn the subject. So there, the secret is out :). linas 23:55, 18 November 2005 (UTC)[reply]

Organization of Category:Physics

Hi Linas, so wrotes wrong with the organization of the physics category now? I'm interested in helping. Karol 17:55, 20 November 2005 (UTC)[reply]

I answered on Wikipedia talk: WikiProject Physics linas 18:28, 20 November 2005 (UTC)[reply]

insanely fractal

Hi, Linas. I'm not sure it was your quote, but as far as I can tell, in discussion on Bell's Inequality you mentioned that

one problem that was solved recently is that of the wave functions of an ideal gas in a box. The wave functions are insanely fractal, and permeate the entire box (even if you've confined all the atoms to on side; the wave functions interfere destructively on the empty side).

Where can I read more about this? Thanks in advance. Dmanin 07:56, 21 November 2005 (UTC)[reply]

I don't know. I first saw/heard about this in a talk by a professor from U California Santa Barbara, don't remember his name; wish I did, because I've wanted to write him :-(. However, I beleive that the general means of solution are similar to finding the wave functions for the Bunimovich stadium and other systems in quantum chaos. What was new in the talk was the realization that the quantum chaos results gave insight into some classical results from stat mech. Does that help? If not, let me know; there's a pile of papers here I've been meaning to dig through. linas 14:20, 21 November 2005 (UTC)[reply]

What a pity. Well, I'm afraid I'd only be able to glean som general feeling from that anyway, my qualification is far from sufficient for a meaningful discussion even. I thought that studying quantum systems that are classically chaotic might shed light on how they become classical, and your comments in Current Working Hypothesis are very interesting to me in view of that. And on nonconservation of measure, indeed. Chaos explains how you can't idealize environment away, right? That is, how you can't take a limit of completely isolated system. That solves paradoxes of Poincare recurrence theorem in thermodynamics (as far as I understand), and also, it turns out, has a bearing on the transition from quantum to classical. How appropriate! Dmanin 07:12, 22 November 2005 (UTC)[reply]

(And, yes, irreversibility is the word in both cases! Dmanin 07:37, 22 November 2005 (UTC))[reply]

I don't know of any simple, generally readable treatment of quantum chaos. There is a strong program called geometric quantization that tries to understand quantization but it is very absstract. I'm not sure what you mean by saying: "can't take a limit of completely isolated system". Almost all traditional classically chaotic systems are "isolated" and do not require an environment for exhibiting chaos: everything from the logistic map, Duffing map, van der Pol oscillator. I'm not sure that Poincare recurrance is paradoxical: it is a statement about the finite volume of phase space, and that only so much can be fit in a finite compact space. The Baker's map shows a dramatic form of recurrance.

As to irreversibility, there are now many theories, but these are not quite entirely satisfying. At least some (many?), but not all, of those irreversibility theories do require contact with the outside world. linas 14:52, 22 November 2005 (UTC)[reply]

Sorry, I was too cryptic. Here's what I meant: Poincaré theorem is not paradoxical in itself, of course, but it contradicts thermodynamical irreversibility. (Yes, I know of Smoluchovsky's explanation, but that's a separate story.) Now, Poincare theorem hinges on the fact that phase trajectories don't intersect. But this premise breaks if there is environment-induced noise in the system. Roughly speaking, environment influence introduces a timescale for the duration of the period for which the system can be considered isolated. If the system is chaotic, this isolation timescale grows only logarithmically with decreasing noise level. Hence, Poincaré recurrence timescale has to be compared with this isolation timescale (and not with such an extrinsic timescale as human lifespan). The limit of large system (recurrence timescale $\rightarrow \infty$ ) which is perfectly isolated (isolation timescale $\rightarrow \infty$ ) is therefore ill-defined, and since isolation timescale grows "very slowly", while recurrence timescale grows "very quickly", physically speaking, we can't have large isolated systems.

If Poincare theorem proof fails, it doesn't mean in itself that irreversibility is proven, but at least there's nothing that would principally prohibit it.

There's more, but I have littered your space sufficiently already...

- Dmanin 03:23, 26 November 2005 (UTC)[reply]

Ah, well, don't worry about "littering". I didn't know that, and that was quite interesting, actually. As it seems you know this subject, perhaps you may want to expand the article on Poicare recurrence to say what you just said above? linas 05:13, 26 November 2005 (UTC)[reply]

Thanks a lot, but I don't exactly know what I said above. That is qualitative reasoning, and I don't have any hard math to back it up. It's very unlikely that I'm the first one to think of it, so either I'm mistaken, or this is written somewhere, and I'd like to know where. But you're right, it might make sense to raise the point where it belongs, although Poincaré recurrence theorem needs first to be expanded from the stub it is now to a real article. Dmanin 06:28, 26 November 2005 (UTC)[reply]

I'm guessing that some of what you want might be in Irreversibility and Causality, Semigroups and Rigged Hilbert Spaces, (1996) Arno Bohm, Heinz-Dietrich Doebner, Piotr Kielanowski, eds., Springer-Verlag, ISBN 3-540-64305-2. Much of the work on fractals and the relationship to operator algebras are explored by David Ruelle and those influenced by his work. linas 02:29, 27 November 2005 (UTC)[reply]

Thanks again, this sounds enticing. Dmanin 04:16, 27 November 2005 (UTC)[reply]

I don't mean to butt in, linas, but I don't think there's actually any "contradiction" between Poincare recurrence and thermodynamics. As Boltzmann said about recurrence in a gas, "You should wait that long!" Dave Kielpinski 23:07, 18 December 2005 (UTC)[reply]

Wave-particle duality

Please take into account the comments made in Talk:Wave-particle duality#Suggestions for improvement as you proceed with your promised major edit. 66.167.253.84 18:52, 22 November 2005 (UTC).[reply]

Replied on te talk page there. linas 19:38, 22 November 2005 (UTC)[reply]

Dedekind sum

Could you please check if the formula you added under Alternative forms on Dedekind sum for s(b,c) involving cots is correct for the saw-tooth function as now (and previously) defined on the page. I've corrected the other alternative form of s(b,c) myself. Ncik 18:42, 25 November 2005 (UTC)[reply]

This formula is cited in the Beck and Robbins PDF. Do you believe its wrong? Just right now, I can't think of any quick and obvious way to verify this. Anyway, we should have this conversation on Talk:Dedekind sum linas 20:15, 25 November 2005 (UTC)[reply]

The Beverly Clock

I noticed that you reverted my recent edit to the Beverly Clock. Please read my explanation for my edit on the talk page. —Bkell 23:16, 28 November 2005 (UTC)[reply]

isospin

It's excellent! Now if only the gauge article was that good. Maury 14:34, 30 November 2005 (UTC)[reply]

Thanks! I assume you mean gauge theory. Well, if you start asking questions and commenting, it helps focus energies. Comment there, get under my skin, and maybe I could fix that up a bit. linas 23:11, 30 November 2005 (UTC)[reply]

crackpot principles of energetics

hi. I appreciate your comments. I understand the spirit of Wiki is to clean up articles rather than demonise them. I do not claim that the 3rd etc. principles were derived in 2000. They are merely references, and small statements, of the words where they have been stated. If you have the original texts where the first 4 laws were defined could you please enter them. Principles are emergent and constantly undergo revision and refinement. It would be good to have you on board as person who can clarify the principles, and support with original references. Regards, Sholto Maud 00:52, 1 December 2005 (UTC)[reply]

Hi. When appending to talk pages, please append to the bottom of the page. The spirit of Wikipedia is to create articles about valid topics. Wikipedia is not a place to conduct or publish original research. Given your comments above, I can only conclude that you are attempting to publish original research, and, based on this, this page is eligable for deletion. linas 01:54, 1 December 2005 (UTC)[reply]

My apologies for the inappropriate appendage.

Much of Odum's work is valid, published in peer reviewed journals, and worthy of historical interest for Wiki entries.
On that basis I encourage you to remove the AFD's and contribute positively to the articles, and remove any of my words that you believe is original and thus invalid, but please put them in the dicussion section where we can talk about the appropriateness of the words, and whether they are NOR.
I do not believe I have entered any details that are historically incorrect. Please see the discussion on Talk:Maximum power for example.
To "create" an article through many voices, is a creative and therefore, in some way original process, aiming at the greater clarification of the ideas. The NOR needs to be applied with wisdom not with a mallet to stamp out legitmate history of ideas, and their clarification.
Please reconsider your urgency to censor Odum and colleagues from history. 03:10, 1 December 2005 (UTC)

Hi,

I have no desire to censor Odum or his work. I skimmed a few of the articles by and about Odum that I found on google, and they are quite interesting. Odum appears to be an ecologist with many interesting ideas. However,these articles appear to be about physics, and, as physics articles, they would earn a failing grade in college freshman physics.

I strong suggest that you may find a more satisfying experience in building something at wikicities or http://math.wikicities.com which does allow original research and lively debate over the same. Copy the articles there. linas 03:24, 1 December 2005 (UTC)[reply]

E-mail

I tried to send e-mail to the address listed on your website, but I got it back with an error message. So I tried to resend it through Wikipedia's e-mail system, but you probably use the same address there. Did you receive anything? -- Jitse Niesen (talk) 17:59, 4 December 2005 (UTC)[reply]

The hardware on that server is flaking out, and the software needs improved spam filtering. I'm on a email vacation till its fixed. You can reach me at [address removed] on monday.linas 19:44, 4 December 2005 (UTC)[reply]

Got it. Thanks. -- Jitse Niesen (talk) 20:50, 4 December 2005 (UTC)[reply]

Frechet derivative

Hi Linas. Again, thank you for writing a while ago this much-needed article, which I had planned to write but never got to. I have some comments about the material in there though.

The first part is what I would expect to see there, meaning the directional derivative in real and Banach spaces, and Taylor's theorem. But then you start delving in and out of holomophic functions, and the situation becomes a bit more complicated.

First, it is not clear when the Banach space is real and when it is complex (I fixed some of that). Second, the section on "Relation to the Gâteaux derivative" seems to be not about Gâteaux derivative, at least the way Gâteaux derivative presents things. Rather, you seem to talk about defining Banach space holomorphic functions via usual holomorphic functions and how they relate to Frechet derivative (in the case of complex space).

In the last section "Entire functions" you seem to be already deep into holomorphic functions, but I could not see a mention about whether differentiable functions on complex Banach spaces are analytic or not.

In short, it looks to me that as you go along you change the topic from Frechet derivative to holomorphic functions, with an unclear transition. My suggestion would to split the part about holomorphic functions into infinite dimensional holomorphy which you redirected to Frechet derivative, and leave the current Frechet derivative with a discussion of directional derivative in real and complex Banach spaces, and maybe with an example thrown in.

Wonder what you think. I would be willing to do the work. Cheers, Oleg Alexandrov (talk) 05:16, 5 December 2005 (UTC)[reply]

I am hardly an expert on the topic; I put this together by cribbing from various notes and sources I had laying around. I wouldn't trust myself to resume editing without doing some archeology and additional study first. In particular, I can't say if the concepts of analytic and holomorphic differ in these spaces, or how they might differ. So if you want to edit, I certainly have no objections. linas 05:33, 5 December 2005 (UTC)[reply]

Great. I can't promise to do it really soon, all that stuff is quite involved and I don't know much about it either. But it seems like a cool topic to develop on. Oleg Alexandrov (talk) 20:25, 5 December 2005 (UTC)[reply]

Well, if you have a good bok reference or two, or some articles, I could study up on it a bit more. Its in the general vicinity of some problems I'm struggling to solve, so it wouldn't hurt for me to know this stuff better. I'll rekindle my interest a bit, esp. if you nag me. Really, nagging me works, as it makes me feel needed. linas 22:49, 5 December 2005 (UTC)[reply]

I don't have any books. But, searching on google books can lead to a lot of useful info (if you are prepared to the fact that the next page might not be available. :)

So you say nagging works? You know, I love to do that, I wish my wife had the same opinion as you. :) Oleg Alexandrov (talk) 01:18, 6 December 2005 (UTC)[reply]

Afshar experiment

Dear Linas,

I am currently visiting the Perimeter Institute and a colleague informed me of a series of reverts and edits on the page related to my work (http://en.wikipedia.org/wiki/Afshar_experiment) by Danko Georgiev and you. As for Giorgiev, the fact that he is absolutely wrong and does not understand even physical optics has been made clear to him by almost all of my critics including Unruh, Motl, and Drezet, so I do not see why you wish to take his side. The reference to his non-paper must be removed (as aptly acted upon by a PI colleague) simply because it reduces the legitimacy of the other expert critiques. I do not have time to delineate how many wrong ideas are contained in his non-paper, but suffice it to say that its content is mostly an incoherent copy/paste of internet articles on Fourier Optics, and wrong inferences/conclusions.

I'll remove the Danko reference; I've had occasion to chat with him, and its clear that he not only doesn't know QM, but he doesn't even understand basic undergraduate analysis.

You also say in the discussion page that I am "basically just plain wrong." Would you care to explain exactly why? I am not sure if you are a physicist or not, but usually, one expects a rather detailed critique (like Unruh's for example) to make a categorical statement like you have made. Even then, the other side should be give a chance to respond, which is clearly not the case with your remark.

Ah. I'd left a coment on the talk page some 1/2 year ago under the title Talk:Afshar experiment#Wave tank experiments in water that seemed to fail to provoke the expected response. My basic claim was that the entire experiment could be reproduced with either water waves or sound waves, and since QM is not required to explain the results, failed to see why the experiment shed any light on QM. This claim may be wrong, but I don't see how at this time. I'm willing to pursue these thoughts further; I am honestly interested in the "mystery" of QM, but I couldn't gain any new insight from the experiment.

As to my abilities, I have a PhD in theoretical particle physics, and that includes working experience with QM and QFT, as well as a smattering of higher math. I feel confident.

After my talk (movie + slides available online) at the Perimeter Institute it has become clear to me that most of the opposition to my work stems from a kind misunderstanding that more patient and thorough discussions alleviate.

At any rate, I suggest that you either remove the POV on the page, or give me a detailed critique, and a chance to respond. Otherwise, your standing in the physics community would be reduced to that of Giorgiev, i.e. null.

Please do not threaten me. Although I should mention that I have nothing to loose by being made to look foolish, so a fear of being wrong is not something that holds me back.

Finally, please find attached a preprint for a simpler yet equivalnet experiment with identical results to the original one, in which no imaging lens is used. The fact that no lens is used makes any reference to imaging and Fourier optics superfluous, rendering Georigiv's arguments entirely baseless. If you wish you can write up something for the Wikipeida page as an additional experiment (call it the Crossed-Beams version) with associated graphics from the paper (you can site the paper as "AIP Conf. Proc. 810, 2006" for now, I'll have the page numbers soon).

Looking forward to hearing from you soon.

Best regards.

Shahriar S. Afshar

Professor of Physics; Rowan University

Afshar (talk) 21:39, 6 December 2005 (UTC)[reply]

Is there a web-site I can pull the pre-print off of? linas 23:49, 6 December 2005 (UTC)[reply]

It has not been posted yet, but I e-mailed it to your address: linas@linas.org Afshar (talk) 02:04, 7 December 2005 (UTC)[reply]

Can you resend to linas@austin.ibm.com? The former site is experiencing "technical difficulties", so I'm on an email-vacation. linas 02:08, 7 December 2005 (UTC)[reply]

Dear Linas, can you please let me know if you have received my email sent on Thu 12/15/2005 at 12:38 PM? If yes, I wold appreciate your response ASAP. Thanks!Afshar 20:02, 18 December 2005 (UTC)[reply]

Friendly hello

Linas,

I hope that you don't feel bad about your rough treatment by Hillman and that I don't hold any of our previous interactions against you.

Regards,--Carl Hewitt 05:49, 7 December 2005 (UTC)[reply]

Sigh. I regret that I make him upset; although I haven't yet figured out how I make him upset, other than by merely existing in proximity. Oh well. As to yourself, Carl, I appreciate the hello, and I see that you do understand that you will need friends for the upcoming arbitration. I'm a sociable guy, in a sociable mood, and in that mood I will encourage you to say "hi" to others as well, and to engage in constructive dialog at every opportunity. Especially if the others are challenging your edits. We are all here for the intellectual excitement, we are all serious, focused, fun-loving and creative people, and all wish to be treated with respect. Keep that in mind, and we will do well. linas 06:17, 7 December 2005 (UTC)[reply]

Maximum power

Linas,

are you interested in co-authoring the maximum power article with me? It needs a clean up and you seem to be interested in the idea. Sholto Maud 06:43, 7 December 2005 (UTC)[reply]

I would much rather see many/most of these articles merged into one, where all of these concepts can be discussed in one place. I'd also like to a strong link to references to Odum, and to the specific principle of ecology from which this all seems to extend. It needs to be made clear that Odum introduced these ideas in an attempt to solve specific problems in ecology. Trying to word these things as is they were general principles broadly applicable to physics is a mistake. linas 14:11, 7 December 2005 (UTC)[reply]

I'll take that as a no. I like your idea that Odum was attempting to solve specific problems in ecology. That's a useful approach. I'll see what I can do to make that clear. I think it is useful to understand that Odum's approach to systems ecology was more than just "ecology". The sharp boundaries between physics and ecology are not that sharp in Odum's work - you might be interested in Lotka's Physical Biology for an example. I've tried to word these things as general principles broadly applicable to physics, because it appears that they are broadly applicable to physics. I'm not sure why you consider it a mistake. If you gave more reasoning I might understand. As far as I'm aware, the debate seems to be under what conditions a theorem of physics evolves into the status of a principle. You should find numerous references to Odum and others in the articles. Best Regards, Sholto Maud 22:37, 7 December 2005 (UTC)[reply]

You should take that as a "sort-of". I'll keep an eye on it. I'm stretched thin over many projects, so I do not wish to make promises. I am encouraging you to "stick to the facts" of what Odum may have said simply because statements like "broadly applicable to physics" will continue to get snide remarks and general non-acceptance from physicists. No matter what the outcome of the AfD, it is still true that the concepts currently discussed in Principles of energetics are principles that are commonly taught in college freshman physics. As long as they are presented as "broadly applicable to physics", they will have that stink of "written by a person who washed out of physics 101", and that odor is rather unpalatable to anyone who has made the effort to graduate with a B.S in physics, never mind those who've gone yet farther. It has to be presented in a wai that doesn't make it sound like general silliness. linas 23:01, 7 December 2005 (UTC)[reply]

Wavelet edits

You added the following to the Wavelet page:

In formal terms, a wavelet series provides a complete, orthonormal set of basis functions for the set of square integrable functions.

This is only true if the wavelet series is not truncated, otherwise it is no longer complete. Also do you consider this statement meaningful in the case of discrete wavelets? Also, does this belong at the beginning of the article? You can use wavelets without using wavelet series - there are many digital imaging techniques which use convolution with single wavelets. Convolution with single wavelets, or non-orthonormal families of wavelets is also used extensively in many types of signal processing applications. - JustinWick 00:01, 8 December 2005 (UTC)[reply]

In the formal defnition, the series is not truncated. I am trying to provide a formal defnition because wavelets are also of interest in areas of so-called "pure math", such as number theory, where they have been used to derive new proofs for functions on Cantor sets, on Farey sequences, and on the convergence of functions in functional analysis. These are all formal, theoretical applications that have nothing to do with signal processing.linas 00:07, 8 December 2005 (UTC)[reply]

Pure math is great, of course, but I still do not understand why the idea of a wavelet series must be invoked to explain what a wavelet is - why can't this be in another section, or a less strong statement such as "Wavelets are often used in wavelet series to provide a complete, orthonormal set of basis functions for the set of square integrable function". Another issue I have with your definition is that (correct me if I'm wrong here) I believe there exist basises for this space (L2, right?) that are not wavelets... sin/cos come to mind here. In my mind, the key thing about a wavelet is not its basis properties, but it's spatiotemporal locality properties. - JustinWick 00:15, 8 December 2005 (UTC)[reply]

Let me rephrase that. I was trying to insert some text that would direct the pure-math types to the article on wavelet series, while leaving the engineers happily swimming in filters and what-not. If you can think of a better way to alert the reader to these two different definitions, great, please do so. The other alternative I can think of is a disambig page that links wavelet (engineering) and wavelet (mathematics) and I think that would be a shame. linas 00:21, 8 December 2005 (UTC)[reply]

And yes, there are huge numbers of bases for Lp space, besides the Fourier basis, there's Sobolev space. There's Hardy space, etc. the study whereof is known as functional analysis. I'm interested in p-adic analysis, where the dyadic of wavelets fits right in. linas 00:28, 8 December 2005 (UTC)[reply]

Resolvent formalism

Hi Linas. I saw you wrote an article at resolvent formalism. The bra-ket notation and lack of technical conditions suggests that this is written from a physicist's perspective, though it is hard to tell as there are no references (hint). However, what I was wondering is whether there is any connection with holomorphic functional calculus, another article without references, written by The Holy One. Discuss. -- Jitse Niesen (talk) 17:59, 10 December 2005 (UTC)[reply]

Hah. Yes, well, I wish I had a reference, see Talk:Hille-Yosida theorem and you'll see what lead to this. I'm hoping the hive mind will supply additional info. I was not aware of the Saint's article, but it appears to be on the same topic. linas 18:13, 10 December 2005 (UTC)[reply]

Hey people, stop taking God's name in vain. Linas, you are from Texas, you should know better than that hedonistic liberal materilistic european. Do you have any serious courses about introduction to fundamentalism in there? Have Jitse for one week for training. :) Oleg Alexandrov (talk) 18:21, 10 December 2005 (UTC)[reply]

Actually, I live in the live music capital of the world, where religious convictions lean towards Buddhism. Its been recently declared to be the "most literate city in the U.S.", and of course, was the only county in Texas that recently voted to recognize gay marriage. The only indoctrination camps we have here are comedy clubs; I guess we could do one of those. linas 18:52, 10 December 2005 (UTC)[reply]

I'm goin' down to the highway, listen to those great trucks whine.

Ohh, White Freightliner, steal away my mind. [1]

Country-western Zen-buddhist lyrics, penned by Austin native Townes van Zandt - linas 19:06, 10 December 2005 (UTC)[reply]

Did you study at UT Austin? I'm curious whether you had experience with the Moore method.

Re "one of the principle complainants User:R.Koot appears to be on an indefinite wikivacation. I'm not sure where to note this fact, but it does seem important to note.", I'd just put it on the evidence page. Ruud left a message on his user page, which you can quote. -- Jitse Niesen (talk) 18:34, 11 December 2005 (UTC)[reply]

"Topological spaces" category

Hi Linas,

I'm not too sure I agree with your recent recats of Zero-dimensional space and Polish space to Category:Topological spaces. The latter seems to be primarily for particular topological spaces, not classes of topological spaces. --Trovatore 19:53, 10 December 2005 (UTC)[reply]

OK, I'll put them back, I was scratching my head on how to sort these. I was vaguely thinking of moving any article that stated xxx is a topological space to that category. Perhaps Category:Topological spaces should be renamed Category:Examples in Topology or Category:Topology Examples?? BTW, I'm looking for the example of a double-pointed real number line; I've seen the WP article on it, but now I can't find it anywhere. linas 19:59, 10 December 2005 (UTC)[reply]

I think Linas' move was correct. Topological spaces is a good category to list topological spaces. Manifolds are a family of spaces but is a subcategory of Topolgoical spaces, as it should be. The confusion here is probably because Polish space should probably be a subcategory of Topological space. Note that I don't necessarily advocate the creation of a new category though; there would need to be more Polish space articles, although the potential for that exists. But I think that indicates why Polish space should be listed under Topological space.

Also, I believe Topological space is a relatively new category, which accounts for all the stuff in the category Topology. The latter would be more appropriate for tools and things like ~~deformation retract~~ Seven_Bridges_of_Königsberg , just like General topology is appropriate for things like paracompactness, etc. --C S (Talk) 18:42, 11 December 2005 (UTC)[reply]

It appears to me that the category Topology should probably be trimmed down. A lot of stuff could be in better subcategories. For example, deformation retract should really be in General Topology .--C S (Talk) 18:49, 11 December 2005 (UTC)[reply]

Yes, Category:Topology needs sorting (as do most categories at the higher level - I'm sure that 100 or even 50 articles in a category generaly means subcategorisation is needed). Category:Topological spaces is more problematic; general ideas like zero-dimensional space really need to be elsewhere (e.g. Category:Dimension theory), and if Polish space is a special kind of metric space then it should really be in Category:Metric spaces. Charles Matthews 19:32, 11 December 2005 (UTC)[reply]

The problem with putting Polish space in any of those categories is that there isn't a unique object called "Polish space"; it's a kind of space. So it would be fine in something called Category:Theory of topological spaces, but not, as I understand categories and their naming, in Category:Topological spaces itself. There's a separate problem with calling it a metric space, as a Polish space per se doesn't have a metric. Being a Polish space is defined in terms of having a compatible metric with certain properties, but then you apply a forgetful functor and throw the metric away. (If you remember the metric you have a Polish metric space, which is an article that should maybe be written--there's an interesting theory there.) --Trovatore 19:40, 11 December 2005 (UTC)[reply]

I'll have to meditate on this a bit more, then. One "minor" problem is that the article on topology states that "topology is the theory of topological spaces" in its very first sentence, if you see what I mean. linas 14:16, 12 December 2005 (UTC)[reply]

theta function

Sorry about that. I should have looked at the edit history and found the last non-anon editor and asked their opinion rather than try and revert. Cheers. CambridgeBayWeather (Talk) 17:55, 11 December 2005 (UTC)[reply]

CP symmetry

Hey, thanks for taking a crack at CP symmetry. That article was a huge mess. It was causing me mental anguish every time I looked at it and had to lament that I didn't have time to fix it. -- Xerxes 17:02, 13 December 2005 (UTC)[reply]

You're welcome. Its still a mess, but at least there's a bit of an outline now. linas 17:08, 13 December 2005 (UTC)[reply]

Issues with the Manual of Style

I actually have three issues with the Manual of style:

The See also policy
Capitalization of terminology that is essentially proper names
The appropriate use of blank lines, or as it is known among professional writers and editors, "white space".

-- Metacomet 00:36, 15 December 2005 (UTC)[reply]

I'd like to move this conversation over to your talk page. I'd just posted the following there:

I'm not sure that sarcasm about the Wikipedia manual of style is called for. WP is the product of thousands upon thousands of editors, over the course of many years, and there is a general, commonly agreed-upon style that is used in WP articles. While you might not agree with it, by insulting it, you insult the thousands of people who have tried to make this all work out. After you've been here for a year, and have edited several hundred articles, if you still think there are deficiencies, then you should start up a discussion in the appropriate forums. Blindly arguing about it with one or two people won't get you anywhere. linas 00:47, 15 December 2005 (UTC)[reply]

Lithuania portal

You might be interested in visting Lithuania Portal.

It is an attempt to gather all Wikipedians interested in Lithuania and Lithuania-related topics. It could be a central place for discussions. If interested, put yourself on the guest book and add the portal, portal talk, and Portal:Lithuania/Questions to your watch list. I would welcome any suggestions or any actual improvements to the portal.

Esperanza elections

File:Voting box clipart.gif

Hi Linas/Archive5: This is a quick note just to let you know that there's an election under way at Esperanza. If you'd like to become a candidate for Administrator General or the Advisory Council, just add your name here by 15 December 2005.

Voting begins at 12:00UTC on 16 December and all Esperanza members are encouraged to join in.

This message was delivered to all Esperanza members. If you do not wish to receive further messages, please contact Flcelloguy. Thank you.

➨ ❝R E DVERS❞ 10:01, 14 December 2005 (UTC)[reply]

Permutation group

Sorry about that. I had a bunch of pages up and wasn't really paying attention. Deltabeignet 00:32, 15 December 2005 (UTC)[reply]

Depleted uranium RfC

Your input to an RfC at Talk:Depleted uranium would be appreciated. DV8 2XL 04:06, 15 December 2005 (UTC)[reply]

Your comments are appreciated. Badagnani 01:58, 17 December 2005 (UTC)[reply]

Original research wiki

Ok, so I have ended my argument for WikiScience. The concept is simply to big and spanning to be implemented all at once, plus without offending all of the math contributers here at wikipedia. So I have decided to go forth with a original research math wiki only. I will call this tentively WikiPOLIS. Visit the page at Meta where we can share ideas so we can make this happen! --Hypergeometric2F1[a,b,c,x] 05:36, 15 December 2005 (UTC)[reply]

No,the problem was not that your idea was "too big", its that you didn't take the time to figure out what WP was, and how it worked, before you started launching into criticisms of it. There are in fact hundreds of highly informed conversations going on about how to make WP better. A tiny portion of them can be found at Category:Editorial validation but also in other places as well. The fact that you made some blatently false assertions didn't help your cause either.

Please do go forwards on the original research bit. As I mentioned before, a fundamental problem is the technical problem of editorial control. Have you actually done the research to see if this software can support editorial control? Without that, the whole effort founders.

My vision would work something like this: users would have the right to publish an unlimited amount of original research in their personal namespaces. For example, I could create an unlimited number of User:Linas/Whiz-bang theory pages. I and my friends could edit these pages. When I thought that I was "done", I could ask for a "peer review" and "publication", at which point, if it passes, the article could be moved out of the "user pages" section and into the "published" section. Once an article was "published", the number of allowed edits would be kept minimal. Possibly a process similar to Wikipedia:Stable versions might be used to publish. Standard escalation mechanisms might be applied to de-publish a page. There are four barriers to my vision for this: (1) the Wikipedia:Stable versions process has not yet been defined, (and once it is, it might still not be suitable), (2) we need a place that would allow OR, and that place is not WP, (3) software enhancements to the mediawiki software to support this new usage, and (4) a system of credible peer reviewers. The last part might easily be the hardest. I'm thinking that starting such a thing is not unlike launching a peer-reviewed on-line journal: it is a major undertaking. As experience shows, most on-line journals eventually collapsed. However, if done under the wing of WP, and with the explicit support of Jimbo Wales, we could leverage the growing reputation of WP to attract the needed peer reviewers. I figure it would take maybe 5 years to get it going.

Put another way: this thing would be part pre-print server, part-blog, and part-online-journal, with the elements of each that has made each of these things so successful.

The biggest question mark is reputation. The journal Foundations of Physics is peer reviewed, but also has an editorial policy that explicitly welcome "crackpot" articles. Although most of the articles published there are "nuts", a few have been highly important papers by highly respected researchers. By contrast, Nature and Science are impeccable. What, exactly, shall the editorial policy of this on-line thing be? Maybe there would be several "levels of impeccability"? linas 06:22, 15 December 2005 (UTC)[reply]

May I chime in? I like this emergent vision, and encourage this "preprinblonal". I've been imagining something like this, something which school students and university students could also contribute their science experimental results to in order to give a world wide verification and definition of the "laws" of science. In this way the more that some proposition is verified by experiences of the students of the world, the less crackpot it seems to become. In this I'd like to suggest

1. an impeccable definition of the notion of "crackpottery". If we can come to a better specification of this thing that we fear will take away from the authoritative reputation of Wiki, then we might understand how it fits into the generation of "impeccability".

1.1. The notion that something is verified by many people would make it less crackpot.

This is a point I try to address in my proposed idea to create a system where people may "subscribe" or "own" the article, allowing them to contribute to it. The less "crackpot" of an idea, the more people would subscribe to it (presumably), creating a darwinian seperation of the most interesting and relevant research. This would also create a crude form of peer-review, with the strongest of articles requiring greater review by many people (since more ppl own it). Linas wants a stronger more traditional peer-review however.--Hypergeometric2F1[a,b,c,x] 08:39, 15 December 2005 (UTC)[reply]

2. I'd also like to see Wiki enabled to generate dynamic graphs from math formulas, so that we can simulate mathematical models to test any claims to original research. Sholto Maud 08:25, 15 December 2005 (UTC)[reply]

Doesn't the wikipedia software include gnuplot to plot equations?--Hypergeometric2F1[a,b,c,x] 08:42, 15 December 2005 (UTC)[reply]

I don't know about Linas, but I was imagining it mainly as a math wiki, are you saying it should include physical sciences also? I created a proposed wiki page for this idea, which I am dubbing "Wikipolis". Feel free to add ideas to it there or here, whichever.--Hypergeometric2F1[a,b,c,x] 08:34, 15 December 2005 (UTC)[reply]

Partitions of Poland

Would you take a look at talk:Partitions of Poland. We are discussing a possible change of the name of the article there and I believe that a Lithuanian perspective view would be helpful. --Lysy ^(talk) 10:22, 16 December 2005 (UTC)[reply]

Nemesis

Hi Linas. As regards Muller (et al.) hypothesis about Nemesis, there's a paper in the same issue of Nature as the one cited in the article ...

Title: ARE PERIODIC MASS EXTINCTIONS DRIVEN BY A DISTANT SOLAR COMPANION

Author(s): WHITMIRE DP, JACKSON AA

Source: NATURE 308 (5961): 713-715 1984

I can't access it to check up on it (it's beyond the window of Nature I can see), but as it immediately precedes the cited paper, it might be of interest. Suggests that Muller (et al.) was one of many. Anyway, thought you might be interested. Cheers, --Plumbago 15:55, 16 December 2005 (UTC)[reply]

P.S. Strictly speaking, Nemesis doesn't have anything to do with punctuated equilibrium. I think you're conflating mass extinctions with that. --Plumbago 15:58, 16 December 2005 (UTC)[reply]

News from Esperanza

Hello, fellow Esperanzians! This is just a friendly reminder that elections for Administrator General and two advisory council positions have just begun. Voting will last until Friday, December 30, so make sure you exercise your right to vote! Also, I'm pleased to announce the creation of the Esperanza mailing list. I urge all members to join; see Wikipedia:Esperanza/Contact for more information. All you need to do is email me and I will activate your account. This will be a great way to relax, stay in touch, and hear important announcements. Thanks! Flcelloguy (A note?)

This message was delivered to all Esperanza members by our acting messenger, Redvers. If you do not wish to receive further messages, please list yourself at WP:ESP/S. Thanks.

Thanks for your kind words

Thanks for your message on my talk page. I'm pretty new to Wikipedia, and though I've read most of the help documentation, I'm still trying to be cautious... probably too much time spent writing for the peer-reviewed literature. If I screw up egregiously, could you please let me know? Also, I'm glad you drew my attention to other articles and categories that I hadn't run into yet. The category structure still seems a little incomplete.

I actually had received an email from CT before, after the Bell experiment I was involved in. I had concluded it wasn't worth writing back, but I had since forgotten about it. She was kind enough to remind me with a couple emails about how all mainstream physicists were wrong. I'm not really intending to engage her further, at least without citing her crackpot index, which I'm currently estimating at an impressive 90. Dave Kielpinski 02:30, 17 December 2005 (UTC)[reply]

You will find a wide variety of article quality here, and a wide variety of editorial styles. For every careful editor we have one incautious editor, and the combination can be volatile. Many of the "pop-physics" articles attract well-meaning but completely misguided edits from high-school or college students and it can be a trial to deal with this. I initially avoided this mess by making well-meaning but misguided edits to abstract and arcane topics for which there are few experts: you might try that route to get your bearings. The more arcane topics are written by grad students and young postdocs, and so tend to be more scholarly. We seem to be getting more full professors all the time; there's at least one famous mathematician working here, anonymously. And non-anonymously, John Baez caught an error of mine; although perhaps more embarassing was that at first I didn't recognize him by name, and said "gee your name sounds familiar, do I know you?"

Anyway: I monitor articles, not people, so if you screw up outside my field of vision, I won't know. Technical mistakes happen and are forgivable and correctable. The only real screw-up you can make at WP is to get into bad arguments, show disrespect, fail to listen to advice & opinion from others, etc. These are the true egregious crimes here, and are the things that will get you into big trouble. All else is secondary. For general help and advice, appeal on the talk pages of the math and physics wikiprojects. Good luck! linas 04:42, 17 December 2005 (UTC)[reply]

Reference

Thanks for your message Iinas. I saw that page previously. For what it is worth, I'll say the following in the hope that I can help reestablish some firmer footing for you. My first impression was one of crackpottery. But when my Wikipedia additions on emergy & energy quality & maximum power were called crackpot, it shook my world a little, and so I've become a quite sympathetic to those who are trying to put up a page describing divergent uses of "laws". For myself I have tried to keep my contributions as close to the peer-reviewed texts in ecology and general systems theory as possible, but the texts are sometimes quite opaque, so I find I have to add a layer of interpretation to make the meaning clear in small amount of words to an assumed lay audience. But interpretation appears to be a process of putting what one wants there, rather than what is just there. Nevertheless a list of quotes from peer-review texts doesn't really fit the idea of a Wikipedia article, so we seem to be stuck with a level of interpreation in an article. The article that you referred me to, in my books has more of what one wants to be there than is actually there. I am probably guilty of this at times, but it is a fine line. I am sympathetic to what wavesmikey is doing, simply because H.T.Odum referred to a concept of biological "thrust" - such as the "thrust" of a tree as it grows and raises mass up from the soil, into the air against the force of gravity, and transforms it into an apple which then could hit Newton on the head. This has implications for our understanding of evolution in terms of thermodynamics. But in the context of thermodynamics there is a massive issue, and that is with the notion of "neg entropy". This concept, which was discussed by Schrodinger in the context of the physical definition of "life", and seems to be equivalent to the concept of "exergy", and appears to be in contradiction with the first law of the conservation of energy, I.e. exergy algorithms are, in some instances, non-conservative. To return to the article under question on evolution and thermodynamics, there are peer-reveiwed publications which discuss these matters. However I believe that the article is more on the site of what one wants to be there. Nevertheless I think that it should be there with better references and linked up to Lotka's work and the work of Schrodinger. I hope this might help?? Sholto Maud 09:28, 18 December 2005 (UTC)[reply]

Sholto, I am rather frustrated to read what you just wrote. Firstly, almost everything Schrodinger wrote has passed into history. No modern physicist writing about current physics is going to say "Schrodinger said this or that". They may do this in a historical review, but not in modern research. Physics has moved on by 75 years since his time. Concepts have changed. Old ideas have been polished and revised. We understand things better. So, to listen to you try to reference old thoughts of Schrodinger's (such as negentropy, which he introduced in a pop-sci book, and not as a scientific concept) as if they were principles or "laws" of ecology and evolution is really grating. If you were writing about the historical development, and started 400 years ago, moving to modern times, that would be acceptable. However, it is not acceptable to reference Schrodinger's thoughts as having relevance to modern concepts of entropy and thermodynamics. These fields have had a huge amount of development in the last 75 years. Among other things, thermodynamics has become highly abstract and mathematical. You have to either write about it in terms of history, or forgo the references. linas 18:03, 18 December 2005 (UTC)[reply]

Sorry to frustrate you linas. I merely meant to give some historical context to the discussion, rather than to reference Schrodinger as gospel, and to say that, as I understand it the term 'exergy' (which has current use) refers to the same thing as 'neg entropy'. Thermodynamics may have undergone a large amount of development, but yet the "laws" have remained pretty much the same haven't they? I'm not sure about the claim that the mathematical treatment of things like the "neg entropy" concept started 400 years ago. As far as I understand it Clausius formalised the entropy theorem in the mid 1800's. So that would make the history about 150 years. Abstract mathematics does not deter me from trying to understand or comment, because in the literature that I have been reading people claim that highly abstract mathematics has a tendency to become removed from thermodynamic reality - even though it may be insulting to mathematical thermodynamacists, it appears that we can concot all sorts of novel maths equations with novel symbols that are energetically invalid. So what is the basis of right and wrong and legitimate authority in this area? Maybe I am a fool, but I believe one must tread without fear or favour, and be willing to make and acknowledge errors of logic and math if doing so helps uncover the energetic truth. Sholto Maud 21:04, 18 December 2005 (UTC)[reply]

I picked 400 years, since I hoped that you would be writing about evolution or ecology or something. My suggestion is to leave the statement of physical principles to physicists. We have a few dozen PhD's and grad students, and even a few professors, working at Wikipedia:WikiProject Physics, and they can be consulted there. We even have a postdoc in the history of science and the history of physics.

There is a canon of teachings regarding entropy that undergraduate physics majors are taught. The theory has many facets, and the terms have very specific, highly detailed meanings, see, for example, the Kolmogorov-Sinai entropy, or the information entropy, which is a quantity I (personally) can calculate to many decimal places of precision for many systems. By contrast, exergy and negentropy and emergy and transformity are not part of this canon. I have absolutely no idea how to calculate these values for any given system. This may be personal ignorance on my part, but I note that the WP articles fail to provide a definition. There's nothing there that a practicing physicist or mathematician could apply to a real-world system. Instead, there's a bunch of interesting-sounding words, but its not clear that these can be used for anything. Can one predict anything? Can one calculate? Is this stuff actually useful for anything?

Ok. Looks like we can cut some of the rhetoric and ad hominem and work on 4 points:

Its not rhetoric or ad-hominem when I state that I can't figure out what maximum power is about; it appears to be word salad to me. I also believe that most others with a formal training in math/physics will perceive it in a similar manner. I've said this to you more than three times now, I fail to see why you persist in taking this to my front door. Can't this article just be fixed?

Ok You are not enjoying this. So I'll leave this thread alone. But I've found it very useful. Thankyou for your time linas. I'm not sure which of us is knocking on the other's door. We seem to be bumping into each other in the street. It seems like we both want to understand each other but have trouble bringing each other along for the ride. I'll finnish by saying that I don't think I can "just fix" the maximum power article because as I understand it, it seeks the maximum power theorem in biological and ecological systems, but most people who object say that max power theorem is physics and has nothing to do with ecology - so my hands are tied by those who don't want the maximum power theorem to have wider application than in electronics alone. I can't take it any further. Have a good Xmas. Sholto Maud 09:45, 19 December 2005 (UTC)[reply]

1.Agreed there is not a statement of how to calculate transformity etc. I ask that you give me alot of time to fill out the details the best I can.
2. The information entropy article you refer to is in the same territory as my current readings. I've been reading M.Tribus and E.T.Jaynes on thermodynamics and information. Tribus refers to Odum on maximum power. So it seems that we may have some overlap in the territory of our languages. Maybe we can help each other? Maybe not.

2.1 Interesting to note that the entropy of a Bernoulli trial (as a function of success probability) is a maximum when the sucess probability is 0.5 (= maximum entropy sucess probability efficiency of 50%). Look I might be stepping way out of line but this seems to be a similar pattern to the maximum power theorem which is what Odum considered/proposed as a biological/ecological, and evolutionary law.

No. There are zillions of things that are parabola or sine-wave shaped with a peak at 0.5. The maximum power theorem is a statement about electronics and the sorts of things that happen when complex analysis is applied to continuous media, such as optics. Its a very very classical kind of mathematics that bears no resemblance to the kind of math used in the study of ergodic systems and mixing systems whose underlying theory anchor modern views of thermodyanmics. The resemblance is purely accidental.

3. In the information entropy article there is the proposition that "Maxwell's demon reverses thermodynamic entropy with information". Can you please clarify what the reversal of thermodynamic entropy with information is. Does this mean that thermodynamic entropy (the arrow of time) can go backwards and forwards? If so would backwards thermodynamic entropy have a negative value? And if so would you be happy to call this negative thermodynamic entropy, or neg entropy for convenience?

No. Your asking me to tutor you is a bit of an imposition.

Maxwell's daemon decreases the entropy of a system. In information theory, systems with low entropy are said to have a high information content.

The arrow of time cannot go backwards. The entropy of a closed system cannot decrease. Maxwell's daemon is not about closed systems. The entropy of open systems may decrease.

Entropy cannot have a negative value, by definition. Entropy is, by definition, $S=-\sum _{i}p_{i}\log p_{i}\,$ with $\sum _{i}p_{i}=1\,$ and $0\leq p_{i}\leq 1$ . There is no way that S can go negative.

Schroedinger knew that the entropy cannot be negative. The concept of negentropy is about the direction of a "flow" of entropy, and not its magnitude.

4. You say you can calculate information entropy for many systems. Can you calculate information entropy of any refrigeration, biological or ecological systems? If so what predictions can you make about these systems?

Sholto Maud 23:32, 18 December 2005 (UTC)[reply]

I don't particularly like the tone of this conversation, and I don't find this conversation enjoyable.

For refridgeration, yes. For the others, not really, no. I did refrigeration back in college, and have forgotten most of it. I can calculate the information entropy for the Bernoulli scheme and the Potts model. In the past, I've calculated the entropy of the communications channel used in the Global Positioning System. I have numerically calculated the entropy of a collection of interacting cellular automata, which was being used to model a biological system. Other than this, and some abstract theoretical work on gene populations and neural nets, I know very few biological or ecological models and would thus be unable to make any predictions. I could probably numerically compute the entropy of a neural net, but have never tried.

You ask "...it appears that we can concot all sorts of novel maths equations with novel symbols... So what is the basis of right and wrong and legitimate authority in this area?", and I am flabbergasted. The answer is very simple: science. If an "idea" can be used to make a prediction, then the idea is called a "theory". If the theory is upheld in experiment, it might be promoted to being a "good theory". If you refer only to formulas, then mathematicians have their own unique way of determining truth and falsehood. There is no ambiguity. If some idea, say exergy, cannot be used to make any concrete predictions, then it is philosophy or literary criticism or hermeneutics or structural anthropology or something, but its not "hard science".

But maybe I misunderstood your question. It seems that the words exergy and energy quality were invented by Odum, in which case Odum is the "authority in this area". The article energy quality still reads like pure and utter crackpot research, and I find it embarrassing to have this kind of stuff on WP. These need to be re-written so that they talk about ecology, the way Odum did, instead of pretending to be about physics, which, most emphatically, they are not. linas 22:06, 18 December 2005 (UTC)[reply]

As I go through my books and those in the library that I've read, I've been ablel to update the articles I've been writing (which I hope others will constribute to). The exergy article was there before I started on Wiki. I've updated the energy quality article. Hopefully it is less embarassing for us both. Odum did not invent either of the terms exergy or energy quality. One problem might be is that I turned to Odum first in the writing of the various articles. I did this because his work appears to be that which is most unified and general in the treatment of energy and formalisms. I was then aiming to fill out other references as time goes on.

Lastly. Odum was a radiation ecologist turned systems ecologist. So how does one classify radiation ecology? Physics or ecology, or both? An if the latter what consequences does this have for our understanding of the domain of phyiscs? Sholto Maud 23:44, 18 December 2005 (UTC)[reply]

I've never heard of radiation ecology. linas 07:20, 19 December 2005 (UTC)[reply]

""**There was alot of work done in radiation ecology with the U.S. Atomic energy commission. See H.T.Odum's 'a tropical rainforest' for example. By the way with respects to a reference to exergy in thermodynamic literature you can find such in P.K.Nag (1984) Engineering Thermodynamics, Tata McGraw-Hill Publishing Company. Best regards, Sholto Maud 09:52, 19 December 2005 (UTC)[reply]

User talk:Linas/Archive5

Scientific Community Methaphor

Hamiltonian Mechanics

Prime number theorem

Organization of Category:Physics

insanely fractal

Wave-particle duality

Dedekind sum

The Beverly Clock

isospin

crackpot principles of energetics

Categories

E-mail

Frechet derivative

Afshar experiment

Friendly hello

Maximum power

Wavelet edits

Resolvent formalism

"Topological spaces" category

theta function

CP symmetry

See also

Issues with the Manual of Style

Lithuania portal

Esperanza elections

Permutation group

Depleted uranium RfC

Original research wiki

Partitions of Poland

Nemesis

News from Esperanza

Thanks for your kind words

Reference

Navigation menu

User talk:Linas/Archive5

Scientific Community Methaphor

Hamiltonian Mechanics

Prime number theorem

Organization of Category:Physics

insanely fractal

Wave-particle duality

Dedekind sum

The Beverly Clock

isospin

crackpot principles of energetics

Categories

E-mail

Frechet derivative

Afshar experiment

Friendly hello

Maximum power

Wavelet edits

Resolvent formalism

"Topological spaces" category

theta function

CP symmetry

See also

Issues with the Manual of Style

Lithuania portal

Esperanza elections

Permutation group

Depleted uranium RfC

Original research wiki

Partitions of Poland

Nemesis

News from Esperanza

Thanks for your kind words

Reference

Navigation menu

Search