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Talk:Uniform continuity

This page doesn't need math mode, for anyone with a Unicode-compatible browser.

We should consider making the math renderer produce HTML for simple expressions like this that can trivially be rendered as HTML + Unicode.

 * Yes, please, in my browser the equations are about twice the font size of the rest of the article and it's quite jarring. I don't see any way to overcome this using PNG equations, since there's no way to know how any given browser will render the text. But as another option, how about a perference setting that causes equations to be displayed in MathML instead? If a browser knows how to handle MathML, then it probably knows how to make it look good as well. Bryan

 * We're not XML-clean yet, so we can't embed MathML in our output stream and expect anything to be able to use it. --Brion 08:45 Jan 7, 2003 (UTC)

The "In other words, the Slope is Bounded" comment is false. sqrt(x) is uniformily continuous on [0, infinity) but the slope can be made arbitrarily large by looking at points near 0.

$$\frac{\sqrt{x}-\sqrt{0}}{x - 0} = \frac{1}{\sqrt{x}} $$

so i'm taking down the "slope is bounded" comment. AlfredR 05:00, 6 December 2006 (UTC)

Continuous functions on a closed real interval
The introduction stated that continuous functions on a closed interval are uniformly continuous. We need compactness here, as the example $$f:\mathbb{R}\rightarrow\mathbb{R}$$, $$f(x)=x^2$$ shows: Choose $$\epsilon=1$$, let $$\delta>0$$ and set $$y=x-\delta/2$$. Then $$|x-y|=\delta/2<\delta$$, but $$|x^2-y^2| = |x-y| |x+y| = \delta/2 |2x-\delta/2| \rightarrow \infty$$ as $$x \rightarrow \infty$$. --Lacce (talk) 13:45, 22 December 2007 (UTC)

You gave a wrong definition of uniformly continous
When the author writes
 * If $$X$$ and $$Y$$ are subsets of the real numbers, $$d_1$$ and $$d_2$$ can be the standard Euclidian norm, $$|\cdot|$$, yielding the definition: if there exists a $$\delta>0$$ such that, for all $$\epsilon > 0$$ and $$x,y \in X$$, $$|x-y|< \delta$$ implies $$|f(x)-f(y)|<\epsilon$$.

s/he is trivially wrong. The right definition over the reals is
 * for every $$\epsilon > 0$$, there exists a $$\delta>0$$ (depending on $$\epsilon$$!!!) such that, for all $$x,y \in X$$, $$|x-y|< \delta$$ implies $$|f(x)-f(y)|<\epsilon$$.

It's clearly a typo, since the author gave the right definition in the case of general metric spaces. If you use the definition I'm claiming to be wrong, even the identity function f(x)=x is not uniformly continous: let suppose that such a $$\delta$$ exists, and call it D. Let's take x and x+D/2, wich are closer than D. You will have |f(x)-f(x+D/2)| = D/2, wich is far to be smaller of any possible $$\epsilon > 0$$... With the right definition, you will just take $$\delta(\epsilon) = \epsilon$$ and everything works fine. G2h2 (talk) 08:23, 7 April 2008 (UTC)

 * The comment is correct, the sentence
 * if there exists a $$\delta>0$$ such that, for all $$\epsilon > 0$$ and $$x,y \in X$$, $$|x-y|< \delta$$ implies $$|f(x)-f(y)|<\epsilon$$.
 * should become
 * if for all $$\epsilon > 0$$ there exists a $$\delta>0$$ such that, for all $$x,y \in X$$, $$|x-y|< \delta$$ implies $$|f(x)-f(y)|<\epsilon$$.
 * Stoppato (talk) 10:04, 7 April 2008 (UTC)

misleading lead?
The lead says "furthermore the size of the changes in f(x) depends only on the size of the changes in x but not on x itself". I know this is meant to be an informal statement, so maybe I should not be too picky, but I find this somewhat misleading. The changes in $$f(x)$$ do depend on x (as well as on the size of the changes to x) but they can be bounded in a way that only depends on the size of the changes. Would saying that make the lead too technical? (I think anybody wanting to learn about uniform continuity will have to be prepared to encounter some technicality anyway.) Marc van Leeuwen (talk) 16:34, 17 May 2008 (UTC)

Some revisions/additions
I made some substantial changes, mostly additions, in the section on "properties" and also added a section on the relation between uniform continuity and the extension problem.

Further edits would still be desirable. (In particular, I find the lead unsatisfactory, but didn't want to start there.) I took out the bit about nonstandard calculus and uniform continuity, but anyone who wants to add it back will find that I left an appropriate place for it in the exposition. Plclark (talk) 22:56, 7 September 2008 (UTC)

Let's discuss the place of nonstandard calculus in this article
I removed a sentence about uniform continuity in nonstandard calculus, for the second time. It seems only fair for me to discuss my reasons for doing so.

First, there is a mathematical point: it is claimed that the definition of uniform continuity in nonstandard calculus is "local." Exactly what this means is not explained, but to the extent that I understand the intended meaning I think that I disagree with it. A local property of a function f:X -> Y is a property that holds for the function iff for every point P in the domain, the property holds for the restriction of f to each element of an open neighborhood basis of that point (there are other, more elegant ways of phrasing this using things like "germs" and "stalks", but I hope the meaning is clear). In nonstandard calculus continuity is not (as I understand it) a special case of continuity in some topological space. Moreover, the definition of uniform continuity in nonstandard calculus still involves comparing two distinct points, as does the definition in standard calculus. In nonstandard calculus the points that one has to compare are "closer" than in standard calculus, but that doesn't change the logical form of the statement. This doesn't look like a local statement to me.

Second there is the encyclopedic point: we need to consider the policy WP:UNDUE of undue weight. In the lead on an article about uniform continuity, we should only be mentioning the most important core concepts related to uniform continuity. Subtle nuances, more advanced results, generalizations and so forth generally do not belong in the lead. I think the vast majority of mathematicians and students of mathematics at all levels (probably 99% or more) use the "standard" definition of uniform continuity, so the nonstandard version should not be referenced in the lead. On the other hand a section in the article on nonstandard calculus would be quite appropriate. Plclark (talk) 18:50, 26 October 2008 (UTC)

 * Please make an effort to understand the non-standard definition of uniform continuity before you make any further edits. The local nature of the definition of uniform continuity is clearly explained at uniform continuity.  For instance, in the case of the interval (0,1], in addition to checking continuity at the standard points, one needs to check continuity at a positive infinitesimal.  In other words, your assertion that you still need to deal with pairs of points rather than individual points, is incorrect.

 * The definition of nonstandard uniform continuity involves a condition that must be checked at pairs of points, just as the standard definition does. That it can be rephrased in terms of checking something at single "points" which are not points of the original space is unconvincing in regards to your claim that the property is local.  By analogy, an increasing continuous function from [0,oo) is bounded iff it has a continuous extension to [0,oo].  To say that because of this the boundedness is a 'local' property on [0,oo) is problematic. Plclark (talk) 14:29, 27 October 2008 (UTC)

As far as your "vast majority" claim is concerned, I would agree that there is a standard majority. However, there is a significant minority that disagrees with your views.

 * To say 'significant minority' is, I think, quite misleading.

Wikipedia is not a dictatorship of the majority. I am willing to discuss this further, but please try to avoid further reverts based on insufficient understanding. Katzmik (talk) 08:18, 27 October 2008 (UTC)

 * Of course it isn't. Remember that research mathematicians do not accuse other research mathematicians of insufficient understanding.  If there is something that I haven't understood well enough, then a sufficiently detailed content-related discussion will make this clear.  I am not yet convinced that this is the case.  Plclark (talk) 14:29, 27 October 2008 (UTC)

 * User Thenub followed the more elegant course of requesting a citation at (ε, δ)-definition of limit, which I duly provided. Katzmik (talk) 08:21, 27 October 2008 (UTC)

 * I agree with Plclark's points, and I have removed the contested sentence about non-standard calculus again. It should stay out of the article until and unless there is a consensus shown here for including it. Gandalf61 (talk) 09:36, 27 October 2008 (UTC)

 * It seems as though you also have misunderstood the mathematics, as you have numerous times on the talk page of non-standard calculus. Please refrain from further edits until you understand the material better.   Katzmik (talk) 09:42, 27 October 2008 (UTC)
 * Katzmik has asked me to comment, so let it be noted that I agree that the nonstandard version should not be in the lede. Algebraist 12:55, 27 October 2008 (UTC)

 * My point is not necessarily that it should be mentioned in the lead, but that if a claim is made that the notion is "global", it should also be mentioned that this is a weakness of the standard Weierstrass approach, rather than an intrinsic feature of the property in question. Perhaps the entire local/global discussion should be postponed to a later section.  Katzmik (talk) 13:03, 27 October 2008 (UTC)

 * The notion that the 'global' formulation of uniform continuity is a "weakness" seems decidedly POV to me: it would certainly need a citation. I don't understand the weakness: uniform continuity is simply not a local property in the sense that I mentioned above.  What drawbacks does this have?  Moreover, it is still not clear to me what precise definition of a local property is being used that makes nonstandard uniform continuity a local property.  Plclark (talk) 14:29, 27 October 2008 (UTC)

Katzmik, I have no idea what you mean by saying that "a local definition of uniform continuity can be given in non-standard calculus". To me the statement sounds misleading or wrong, depending on what you mean. Let's consider the function $$f(x)=x^2$$. It seems to me that: The last item contradicts your statement. Could you please explain where the error in my reasoning is? Thanks. --Hans Adler (talk) 14:34, 27 October 2008 (UTC)
 * f is not uniformly continuous.
 * This is true also in the context of non-standard calculus.
 * Every restriction of f to an interval of finite length is uniformly continuous.
 * This is true also in the context of non-standard calculus.
 * In the context of non-standard calculus, the restriction of f to the finite numbers is not uniformly continuous.
 * In the context of non-standard calculus, the restriction of f to the finite numbers is an example of a function that is not uniformly continuous even though every element of the domain (in this case: every finite number) has an open neighbourhood on which the function is uniformly continuous.
 * This shows that there is no local definition of uniform continuity.

My thoughts: Taking these points together, I don't think that the content under discussion should be included in this article. Of course it should be included in the article on nonstandard analysis. — Carl (CBM · talk) 17:03, 27 October 2008 (UTC)
 * I looked over the content in question here and in Non-standard calculus, and I agree with Plcark's thoughts dated 14:29, 27 October 2008. I don't see that a local property of an extension of a function is a local property of the original function. So it may be true that in nonstandard analysis there is a local definition of uniform continuity of a total function, but that's a much weaker statement than saying that there is a local definition of uniform continuity of an arbitrary continuous function on some open subset of the space.
 * Apart from books explicitly about nonstandard calculus, no real analysis text is going to discuss a potential local definition of uniform continuity via nonstandard analysis. It seems somewhat out of place to discuss it here, especially when it isn't clear there actually is a local definition of uniform continuity for the original function in nonstandard analysis.

 * Folks, please try to keep in mind that we are all ignoramuses to one extent or another when it comes to non-standard analysis (the two editors who have expertise in the matter don't seem interested in these nitty-gritties). For this reason, as I suggested above, it would be better actually to sort out the mathematics, before succmbing to the reverting instinct.  The point is that the non-standard definition is a pointwise definition and therefore is more accessible than the standard definition which necessarily appeals to pairs of points.  You may feel that the construction of the hyperreals is too heavy a price to pay for such improvements, but that's a separate point that could be discussed elsewhere.  Katzmik (talk) 08:51, 28 October 2008 (UTC)

 * I have again removed a statement about the local definition of uniform continuity via non-standard calculus. One could make a similar definition in the standard setting.  You could extend the domain of the function, by taking limits, to the support in the extend real numbers, and check continuity each and every point of the domain.  This does not make the definition or the property local.  I agree with many of the editors here that in either setting there is no local definition of uniform continuity.   Which was why I asked for a citation about this subject in another article. Thenub314 (talk) 04:11, 28 October 2008 (UTC)

 * That's an interesting point. Would this make the identity function f(x)=x uniformly continuous?  Apparently not.  At any rate, if one can construct a standard pointwise definition of uniform continuity in some extended setting as you suggest, I would certainly withdraw the contention that non-standard analysis furnishes an advantage in this case.  Katzmik (talk) 08:57, 28 October 2008 (UTC)

local versus global
In response to Plclark's previous comment, please let me know what you meant when you introduced the discussion of local versus global in the context of uniform continuity. Apparently you meant that in order to define continuity, it suffices to use a single point x, whereas to define uniform continuity, one needs to refer to pairs. In other words, in the standard approach, the property cannot be defined pointwise. Is that the gist of what you meant to say? Katzmik (talk) 14:34, 27 October 2008 (UTC)

7-step argument
In response to the 7-step argument above, the first six are of course correct :) The correctness of the last step depends on how you define "local", see previous section and non-standard calculus.  I perfectly admit to the possibility that I am in error in which case I would be happy if this wiki discussion clarifies my thinking, as I am an expert neither in logic nor in non-standard analysis (and would like to overcome such a shortcoming).  Katzmik (talk) 14:39, 27 October 2008 (UTC)
 * OK, I think I have understood the issue now. While I don't think non-standard analysis should be mentioned here, I would have been content with a compromise consisting of a single sentence. But it turns out the matter is so complicated (don't forget that we are at an article about advanced school-level and standard first year university level maths) that we would need several sentences to explain what the statement means, and probably still risk that people misunderstand it. --Hans Adler (talk) 19:19, 27 October 2008 (UTC)

 * One of the editors raised an interesting issue of the possiblity of a standard pointwise definition of uniform continuity in an extended domain. If this can be done, obviously that changes the picture altogether.  If not, perhaps we can talk about devising such a sentence, which in my mind should not be difficult.  Katzmik (talk) 08:59, 28 October 2008 (UTC)

Pointwise
I added a comment about the term "pointwise" without changing any substantive material here. Let's agree about the mathematics first before making any substantive changes. Katzmik (talk) 09:22, 28 October 2008 (UTC)
 * I am not sure that I can agree with using the term "pointwise" in this article. To me it sounds way too strong: To see whether two functions agree on a domain, it's enough to compare them pointwise, but to see whether a function is continuous we need to check an open neighbourhood of every point. Even though some people may use the term in a loose sense that covers this (I am not aware that anyone does), I think to minimise the potential of confusion we shouldn't do it. --Hans Adler (talk) 11:16, 28 October 2008 (UTC)

 * Oops, OK. I thought this was one uncontroversial edit.  No problem, we can take it out.  What about "pointwise germ" or something of that sort?  At any rate, it would be interesting to solve the riddle posed above about a possible pointwise germ standard definition of uniform continuity.  Katzmik (talk) 11:19, 28 October 2008 (UTC)

 * Katzmik, I realise you think I am an ignoramous with a complete lack of understanding, but perhaps you could humour me by explaining just what you mean by "pointwise" here. You say above "the non-standard definition is a pointwise definition and therefore is more accessible than the standard definition which necessarily appeals to pairs of points" - but the definition of uniform continuity in non-standard calculus says "for every pair of hyperreals x and y in I*, if $$x\simeq y$$ then $$f^*(x)\simeq f^*(y)$$". Can you explain precisely what is the "pointwise" property that the non-standard definition has and the standard definition lacks ? Gandalf61 (talk) 11:30, 28 October 2008 (UTC)

 * Hi Gandalf61, Thanks for your comment.  I am sorry I used the colorful language of "motherhood and apple pie" in an earlier discussion, but I think we should try to get over this minor episode.  At any rate I already apologized at your talk page as I recall, and I do so again to dispell any lingering doubts.  I don't happen to think you are an "ignoramus with a complete lack of understanding", either.  You asked a series of good (if somewhat naive) questions at the talk page at non-standard calculus, and I would like to remind you that I took a considerable amount of time to answer (most of) them.  To answer your specific question, the answer has to do with the order of quantifiers.  Let me state the definition in a more detailed fashion that would make the point clear:  f will be uniformly continuous if for every x in I*, whenever y\sim x, one also has f(y)\sim f(x).  Here the star above the I is the key.  I would be glad to provide further clarification if necessary.  Katzmik (talk) 17:30, 28 October 2008 (UTC)

 * Well, yes, further clarification is necessary, because I don't understand what you mean by "order of quantifiers" and I can't see how moving from the interval I to its extension I* introduces some "pointwise" property into the non-standard definition of uniform continuity that the standard definition lacks. It might help if you explained precisely what you mean by "pointwise" and/or "order of quantifiers". Gandalf61 (talk) 13:42, 29 October 2008 (UTC)

 * I am sorry I now realize my previous comment was too vague (I was sort of assuming you read the subsection Uniform continuity). At any rate, let's stick for the moment to the standard domain.  What is the difference between ordinary continuity and uniform continuity?  It is certainly the order of the quantifiers.  Namely, in ordinary continuity we choose x before we choose δ, whereas in uniform continuity it is the opposite.  Now if we apply the the definition of ordinary continuity, but on the natural extension I* instead of I, the result turns out to be equivalent to uniform continuity of f.  In other words, we still work with the pointwise germ of the function, but this germ is examined at some non-standard points in addition to the standard points.  Perhaps some of these explanations could be added at non-standard calculus, please feel free to edit (I noticed you have made some edits there before).  Katzmik (talk) 13:53, 29 October 2008 (UTC)

 * Hmmm. You said "if we apply the the definition of ordinary continuity, but on the natural extension I* instead of I, the result turns out to be equivalent to uniform continuity of f". Equivalent how ? Does that mean that any function that satisfies the non-standard definition of "ordinary" continuity everywhere in an interval I* also satisfies the non-standard definition of uniform continuity in I* ? Gandalf61 (talk) 14:44, 29 October 2008 (UTC)

 * I am sorry I am not sure what you are asking, could you clarify? Are you asking what happens when we look at the hyperreal analog of the standard definition of uniform continuity, instead of the definition that appears in Non-standard calculus? Katzmik (talk) 15:20, 29 October 2008 (UTC)

 * Oh, I give up. I was simply trying to understand what you meant by "pointwise", but this discussion has now become "pointless". Gandalf61 (talk) 15:32, 29 October 2008 (UTC)

 * That particular question is not so mysterious, please see the section on the lack of uniform continuity of x2, which is due to lack of ordinary continuity at a single infinite point, as explained there. That's what happens in general, as well.  I am sorry I did not understand your question; there are several simultaneous discussions going on, at this page alone, and I was getting confused. Katzmik (talk) 15:42, 29 October 2008 (UTC)

Comment about nonstandard uniform continuity
As far as I could see, neither of the references given at the end of nonstandard calculus discusses uniform continuity.

 * It's in Keisler's "foundations of infinitesimal calculus", page 45. Katzmik (talk) 10:35, 29 October 2008 (UTC)

 * Thanks for adding this reference. (I was initially confused by the fact that the link itself was to Keisler's "Elementary calculus", but I fixed this.)  Note that this source does not describe nonstandard uniform continuity as being "local" or "pointwise".  It would still be very useful to find a primary source which does so. Plclark (talk) 15:17, 29 October 2008 (UTC)

I think it would be helpful for all of us to see a primary source, both to see more of the mathematics itself being presented and also to see in what way the material is presented. Accordingly I added a fact tag to the nonstandard characterization of uniform continuity.

Here is a mathematical comment: it seems that this is related to the issue of extension properties of uniformly continuous functions (I wrote this section in the current article, although I am not completely satisfied with the exposition). It seems to me that the "local" nonstandard criterion for uniform continuity on an interval like (0,1] amounts to saying that a function on this domain is uniformly continuous iff it has a continuous extension to 0 (which is, of course, true).

 * This certainly true :) and should be mentioned. Katzmik (talk) 10:36, 29 October 2008 (UTC)

(Again, whether one decides to call this a "pointwise" criterion is up for debate, but right now I'm just talking about mathematics, not how to write the article.) On the other hand, since a metric space like [0,oo) is already complete, uniform continuity is a weaker condition then extendability to the compactification [0,oo]: consider for instance $$f(x) = x$$.  Here it seems that one needs to extend the range as well as the domain of the function, which is part of what is going on in the nonstandard version. Plclark (talk) 18:48, 28 October 2008 (UTC)

 * If we have reached a consensus that standard completion of R would not do, we can proceed further. Katzmik (talk) 10:37, 29 October 2008 (UTC)

an example
Here is a very trivial example that may be useful for comparison. Suppose f is continuous on [0,1). Extend this to a function from [0,1] to the extended real numbers by setting
 * $$f(1) = \lim_{a \to 1} \sup_{x > a} |f(x)|$$

Then the original function f is bounded on [0,1) if and only if the extension has a finite value at 1. Does this mean that if I permit myself to use extended real numbers then boundedness on an open interval is a local property of a continuous function? — Carl (CBM · talk) 12:39, 29 October 2008 (UTC)

 * I don't see anything wrong with saying so. Extending the domain works in the bounded case, so here the non-standard approach is not particularly useful.  On the other hand, extending the domain does not work for R, whereas the non-standard definition can be formulated purely in terms of the pointwise germ of f*.  Katzmik (talk) 12:42, 29 October 2008 (UTC)

 * The same procedure I just discussed would work on R. But I'm not comfortable saying that boundedness is a local property of a continuous function. After all, boundedness is one of the best examples I can think of a global, non-local property of a function... This particular extension of a continuous function to a new function involves surveying values of the original function at infinitely any points, so that examining the values of the extended function at the new points corresponds to examining the values of the original function at infinitely many points. But if I have to evaluate the extended function, it seems to me I am no longer talking about local properties of the original function, since the extension itself is a global property of the original function. — Carl (CBM · talk) 12:53, 29 October 2008 (UTC)

 * Sorry, I misread what you wrote. I thought you were still talking about uniform continuity.  I am not sure why we are discussing boundedness, but I will make the following comment.  When you define the boundary value on an extended domain, it is true that boundedness is then determined by the value at that point, but we are now dealing with a different function, whose definition is global.  Katzmik (talk) 13:00, 29 October 2008 (UTC)

 * P.S. I would like to reproduce a comment I made elsewhere: you can also define a constant C to be 0 if f is uniformly continuous, and 1 if it is not. Then uniform continuity of f indeed becomes easily computable in terms of the value of C :)  Katzmik (talk) 13:02, 29 October 2008 (UTC)

 * Yes, that's essentially what I'm doing. How is that different than the example of the extension of a function f to its nonstandard analogue f* ? Are you claiming that the value of f* on some infinite hyperreal is a local property of the original function f? That seems like a tough argument to me. I'm thinking of the potential argument that "using nonstandard analysis gives a local definition of uniform continuity for a real function f". — Carl (CBM · talk) 13:07, 29 October 2008 (UTC)

 * This is certainly a good point. I will have to think more about it, but let me make the following comment already.  In more than one sense, when we are dealing with f*, we are dealing with the same function (I can elaborate on such senses).  This is not so in the case of the objection you raised.  Katzmik (talk) 13:14, 29 October 2008 (UTC)

 * In addition to this somewhat theoretical discussion, would you care to respond to the following query: take a look at the proof of the non-uniformity of x2 at non-standard calculus, and let me know if you think a beginning student may not arrive at an intuition of what goes wrong with uniformity, at a lesser cost than reading the corresponding discussion in even the best-written standard calculus textbook? Katzmik (talk) 13:17, 29 October 2008 (UTC)

 * I would appreciate an expanded explanation on the precise way in which f and f* are related. This seems to be the main issue here. Regarding the x^2 example, I am too biased by my experience with standard calculus and my lack of experience with nonstandard analysis. I don't have any geometric image of a function on nonstandard hyperreals, and so I can't get a geometric image of uniform continuity from the definition that uses nonstandard methods. It looks to me that the main moral of the nonstandard definition is that it exploits the unboundedness of the derivative of x^2 so that at infinite hyperreals the "derivative" is actually infinite, allowing it to scale an infinitesimal to a non-infinitesimal. — Carl (CBM · talk) 13:37, 29 October 2008 (UTC)

 * As far as the issue of the exact relation between f and f*, the best solution would be to bring in some heavyweights at this point, I think. I should be able to provide adequate answers, but I think coming from the experts they may be more convincing.  Do you have any history of fruitful interactions with CSTAR or Arthur Rubin?  Katzmik (talk) 13:56, 29 October 2008 (UTC)

 * I have worked with them before, and they are both very professional. But I'm perfectly willing to accept answers from you, since I'll think through your comments the same as theirs. I do study logic, so I have quite a bit of relevant background.

 * You are ahead of me then. Katzmik (talk) 14:36, 29 October 2008 (UTC)

 * I'm just not intimately familiar with the particular ultrapower construction of the hyperreals. I'm familiar with the standard statement of Łoś's theorem but not with ultrapowers over typed languages, such as the language used to take arbitrary parameters from the superstructure V(R). But I don't think that level of technical detail is required for this particular discussion about global/local properties. — Carl (CBM · talk) 14:09, 29 October 2008 (UTC)

 * Concerning your derivative comment, there is nothing there about derivatives. Of course, we know this not to be the case cf. \sqrt{x} :)  I am not sure how the derivative enters the picture.  Add a bounded nowhere differentiable function to x^2, and exactly the same argument applies.  Katzmik (talk) 13:59, 29 October 2008 (UTC)

 * The derivative only enters at the informal level of intuitive understanding. If you asked me for the "underlying reason" why x^2 is not uniformly continuous (in the standard setting), I would say it is because the derivative of x^2 goes to infinity as x goes to infinity. The nonstandard method described in the article seems to me to be a reflection of this fact, but instead of looking at a limit as x goes to infinity we are looking at a particular infinite hyperreal. — Carl (CBM · talk) 14:09, 29 October 2008 (UTC)

 * I would say that intuitively the point is that there points that are "very close" but at the same time the values of f are "not very close". Instead of formalizing this with quadruple quantifiers, for the past fifty years only we have been able to formalize it by saying that there are infinitely close points such that the values of f are not infinitely close, which seems closer to the intuitive statement than the standard formalisation. Katzmik (talk) 14:40, 29 October 2008 (UTC)

 * Surely it's the growth rate of how "not very close" the images can be, as different pairs of points at the same distance are considered? Also, I am skeptical that any intuition involving "infinitely close" points reflects the standard view, as in the actual real line there are no infinitesimals at all, and so infinitesimals don't play any role in most mathematicians' understanding of real analysis. — Carl (CBM · talk) 14:45, 29 October 2008 (UTC)

 * Actually I have a lot of things to say about this, but I am trying to write a research paper simultaneously with this discussion. Would you mind discussing things one at a time?  Let's focus on the f/f* issue for the time being if you don't mind.  I certainly find it stimulating that people around wiki are getting more interested in Robinson's theory. Katzmik (talk) 14:48, 29 October 2008 (UTC) P.S. Perhaps this should be "Leibniz's theory"? :)

f and f*
A response to your question "I would appreciate an expanded explanation on the precise way in which f and f* are related" would seem to require a separate section :) Katzmik (talk) 14:42, 29 October 2008 (UTC)

I you don't mind I would like to start by copying some comments from the lead of transfer principle, whitten mostly by myself so all responsibility is mine:

In mathematics, the transfer principle is a concept in Abraham Robinson's non-standard analysis of the hyperreal numbers. It states that any sentence expressible in a certain formal language that is true of real numbers is also true of hyperreal numbers.

The transfer principle concerns the logical relation between the properties of the real numbers R, and the properties of a vastly larger field denoted *R called the hyperreals, constructed in terms of a standard axiomatisation of set theory such as ZFC. The field *R includes, in particular, entities that behave as infinitesimal ("infinitely small") numbers, providing a rigorous mathematical realisation of a project initiated by Leibniz.

The idea is to express virtually all of the analysis over R in a suitable language of mathematical logic, and then point out that this language applies equally well to *R. This turns out to be possible because at the set-theoretic level, the propositions in such a language are interpreted to apply only to internal sets rather than to all sets.

The theorem to the effect that each proposition valid over R, is also valid over *R, is called the transfer principle.

Let me know if this helps. Katzmik (talk) 14:44, 29 October 2008 (UTC)

 * According to the article nonstandard analysis the transfer principle only holds for bounded quantifier formulas, not for arbitrary formulas in the language. But that's a minor point. It is true that f* shares many definable properties with f, and that f* is uniquely obtained from f. But I don't see that this means that a local property of f* is also a local property of f, since the definition of f* at infinite nonstandard points must depend on all of f, rather than just depending on a bounded piece of f. — Carl (CBM · talk) 14:51, 29 October 2008 (UTC)

 * Just one comment regarding the above: Admittedly, the discussion at Internal set is insufficient. Hopefully you can improve it :)  At any rate, Keisler's companion text "Foundations of infinitesimal calculus" has a section at the end where he discusses all this in detail.  The text is over 200 pages but the foundational section is only about 20 or 30 pages, as I recall.  Katzmik (talk) 14:52, 29 October 2008 (UTC)

 * I agree with your analysis of the definition of f*. Moreover, the construction is extremely global in a certain sense, since it is not sufficient to just build an ordered field with infinitesimals in it: we need a proof of the transfer principle for all the properties we would like to carry over.  Incidentally, this is the reason I was never convinced by the surreal numbers: they don't seem to have a transfer principle, therefore their construction is merely a curiosity with no relation to, for example, the definition of the derivative, as there is no guarantee that any properties of y=f(x) will be carried over to dy/dx.  At any rate, we are now talking about the construction of the hyperreals which is admittedly more difficult than anything like equivalence classes of Cauchy sequences, or Dedekind cuts.  Yet it is a rare calculus class that deals in such niceties, and you always assume something "on faith".  Even an honors calculus that does Dedekind cuts, will certainly not go over ZFC before defining derivatives.  The fact that the construction of the hyperreals comes at a certain cost was one of the first things I wrote in reaction to your comments, as you recall.  Katzmik (talk) 15:00, 29 October 2008 (UTC)

 * P.S. Similarly, the construction of the real using Dedekind cuts is extremely global: in fact, you need ALL the rationals to define a single real! I remember John Tate I think it was making the comment that if you think of a real number as an equivalence class of Cauchy sequences you will go bananas very quickly.  This does not mean that the notion of doing things pointwise is meaningless over the reals.  Similarly, when Leibniz thought about infinitesimals, he thought of individual points, even though the way they are constructed today is in terms of ultrafilters on the set of all sequences and the like.  The non-standard definition of uniform continuity would most likely have been accepted by Leibniz as a pointwise one.  Katzmik (talk) 16:41, 29 October 2008 (UTC)

 * I still can't see that a property that requires checking something at points not in the domain of a particular function would qualify as a "pointwise" property of that function. A pointwise property should only depend on what happens at points where the function is defined, not on what happens at points where the function is not defined. I think that my example about boundedness being a "local" property illustrates this.

 * Thanks for your comment. The hyperreal definition is certainly not a local definition in terms of f, but it is a local definition in terms of f*.  I think the atmosphere is too charged right now to make any changes to the article, and at any rate I am perfectly happy with Hardy's edits.  If we ever come back to this in the future, we can consider the possibility of adding a sentence to the effect that "in non-standard calculus, it is possible to give a local definition in terms of the natural extension f*".  At any rate this is a minor point and Hardy's revision is excellent.  He is also far more knowledgable about the subject matter than I am.  Katzmik (talk) 10:01, 30 October 2008 (UTC)

 * As an aside, I don't think it's helpful to refer too much to Leibniz' views on infinitesimals, as I have never seen a convincing argument that modern nonstandard analysis actually does correspond to what Leibniz was doing. That is, I think it's somewhat revisionist to reinterpret Leibniz' work in terms of 20th century methods, just as it would be revisionist to interpret Euler's work on infinite series as if he had been familiar with the modern definitions of series convergence. — Carl (CBM · talk) 16:52, 29 October 2008 (UTC)

 * You are raising an interesting point. I would reply by saying that what we are discussing is not my opinion but rather Abraham Robinson's, as stated in his published work, namely Non-standard analysis, and quoted at Robinson's page (actually it is quoted at Non-standard analysis).  Perhaps it is possible to argue that such a viewpoint is revisionist.  Are you familiar with any published work that tries to argue this?  I would certainly be interested in reading it. Katzmik (talk) 10:01, 30 October 2008 (UTC)

Out of proportion
Is this discussion on non-standard analysis not getting slightly out of proportion in terms of its significance to the concept of uniform continuity? First of all, the usual definition is simple enough: f is uniformly continuous iff in order to guarantee that f(x) and f(y) are V-close for some "measure V" of closeness, it is enough to ask that x and y are U-close, for suitable U. Supply distances for U and V into this general definition for uniform spaces, and the resulting standard definition for metric spaces is hardly difficult to grasp. I find it hard to see how this would be conceptually more taxing than the transfer principle required to really understand the non-standard definition, as I argue below.

 * The difficulty of definitions involving multiple quantifiers is not my opinion, but rather a phenomenon documented in the literature. Katzmik (talk) 10:51, 30 October 2008 (UTC)

 * True, but I think the point is understanding why there exists a model for Robinson's axioms requires more mathematical sophistication then understanding two quantifiers. Well ok, I think I am not quite hitting the point, Stca74 is making the point that understanding the transfer principle is more difficult then two quantifiers.  Thenub314 (talk) 15:43, 30 October 2008 (UTC)

Second, as far as I understand, generalising the non-standard definition to spaces more general than R and R* would not be straighforward (even possible?).

 * I think it is possible and has been done. I would mention a paper by one of the most talented topologists active today, namely Shmuel Weinberger.  His work is mostly "standard" but he recently wrote a paper using non-standard techniques.  The reference is at his page as well as at Non-standard analysis. Katzmik (talk) 10:51, 30 October 2008 (UTC)

 * I took a glance through Shmuel's paper, and it certainly doesn't directly answer this question. Maybe it can be generalized, maybe it cannot.  If it can we should include an actual reference.  On a separate subject, between me and Katzmik, Shmuel uses the terms "monad" in the sense I introduced it, on page 3. Thenub314 (talk) 15:43, 30 October 2008 (UTC)

So the non-standard definition really covers only one special case (albeit important) of the concept of uniform continuity, which itself is not essentially more complicated in its general form than it is for real-valued functions on R.

Third, on the merits and locality of the definition for real-valued functions on R: while there is a certain sense in which the non-standard definition of continuity in terms of infinitesimal differences between finite elements in the domain mapping to infinitesimal differences between their images has certain appeal, I would not be so convinced of the pedagogical benefits of the non-standard definition of uniform continuity.

 * The pedagogical benefits (based not not speculation but rather classroom experience) were detailed in a brochure Keisler wrote a couple of decades ago, partly as a response to Bishop's attack on him. I would mention at least two very significant advantages: 1. reduction of quantifier complexity, already discussed; 2. replacement of "inverse problem" by a "direct problem".  You may recall from your calculus days the way you went through the epsilon, delta exercise, obtained a certain expression in terms of epsilon as a bound for delta, and them went on to invert it so as to require an odd-looking bound for epsilon so as to end up with "delta" on the nose in the end.  Now we all enjoy this stuff enormously, but some calculus students could argue that it is an acquired taste. Katzmik (talk) 10:51, 30 October 2008 (UTC)

 * It should be noted that, despite Keisler's brochure, it does not seem to be a very popular program. Are there any curriculums using his text for introductory calculus? Are there independent verifications of it's pedagogical benefit? Thenub314 (talk) 15:43, 30 October 2008 (UTC)

The reason is the need to appeal to infinitesimally close infinite hyperreals; I would argue that gaining actual insight about them is a few magnitudes more difficult than dealing with an additional quantifier in the definition. And these insights would appear to require resorting to the transfer principle. Indeed, it is instructive to follow the proof of the equivalence of the non-standard and the usual defition in Keisler's book mentioned above, with a simple example of continuous but not uniformly continuous function such as f(x) = x2. To show that there are two infinitesimally close hyperreals x and y such that their images under f (or rather f*) are not infinitesimally close, one looks for pairs of finite ordinary reals a and b arbitrarily close to each other but such that their images are separated at least by a positive finite real number (say δ). Since these pairs can be found (by moving further and further away from zero, or "towards infinity"), one can invoke the transfer principle to claim that there is a pair consisting of infinitesimally close, necessarily infinite, hyperreals with the required property. Now it may be only me, but rather than finding the thus exhinited pair of infinite hyperrals helpful to understanding, I would need to decipher the geometric meaning of their existence, this time running through the highly non-trivial transfer principle.

 * I am sorry I did not follow the last paragraph very well. At any rate, the current state of uniform continuity is fine as far as I am concerned.  If you think this is an important point we can discuss it elsewhere.  Katzmik (talk) 10:54, 30 October 2008 (UTC)

 * I do think there is undue weight. The examples given in the non-standard section do lend much enlightenment, prehaps we could delete them. Thenub314 (talk) 15:43, 30 October 2008 (UTC)

All in all, I would leave the existence of a non-standard definition in this article as in interesting remark, wikilinking to the appropriate non-standard article, and leave it at that. Any discussion on the non-standard definition being "local" or "pointwise" would require first introducing (non-standard, I'm afraid) terminology in order to discuss an issue of only secondary importance to this article. Possibilities to elaborate on all this exist at the non-standard articles. Stca74 (talk) 20:14, 29 October 2008 (UTC)

reality versus hyperreality
Your comment "in the actual real line there are no infinitesimals at all, and so infinitesimals don't play any role in most mathematicians' understanding of real analysis" deserves a separate section, as well. What do you mean by the adjective "real" when you say "the actual real line", as well as of the related quote from Keisler at non-standard calculus and/or Bishop-Keisler controversy? Katzmik (talk) 16:14, 29 October 2008 (UTC)

 * I mean the object known as the "real line". Keisler is entitled to his own opinions, of course, but every exposition of nonstandard analysis I have seen begins with the premise that R* is not the same as R, but is an extension of it. On the other hand, in order for R to be the completion of Q, R has to be Archimedean. I'm not sure this conversation is still relevant to the article at hand; maybe it should move to a user talk page. — Carl (CBM · talk) 21:17, 29 October 2008 (UTC)

 * Fine, I was merely alluding to the somewhat epistemological remark that the "real" nature of this famous line is somewhat of a misnomer, certainly according to modern scientific theory. First of all, according to most modern accounts, the universe is finite, and therefore there is simply not enough room for R.  Even if you say that there is enough room for a big slice of it, quantum mechanics would come in to point out that the infinite divisibility that we assume in calculus simply does not agree with experiment, making it difficult (perhaps not impossible) to distinguish between Q and R, for example. Katzmik (talk) 10:05, 30 October 2008 (UTC)

Alternative characterisations
We currently have two alternative characterisations, one in terms of non-standard analysis, and one in terms of pairs of sequences. It may be helpful if someone with expertise in this area could write a sentence pointing out the equivalence of these two approaches, as sequences, together with an ultrafilter, are in fact used to define the hyperreals. Katzmik (talk) 14:44, 30 October 2008 (UTC)

Template
I don't understand why the template Calculus has been recently removed, there is no doubt that this topic is included in both advanced calculus and calculus courses and books: do we want to make a new template named Advanced calculus or a Topology one? --Jorgen W (talk) 11:40, 11 November 2008 (UTC)

I removed it because 'uniform continuity' belongs to real analysis rather than calculus ('advanced calculus' is also 'real analysis').

Topology Expert (talk) 04:50, 12 November 2008 (UTC)

equivalence of definitions
As per recent edit by Thenub, I am not sure what vexes you concerning the alleged equivalence of the two definitions. I explicitly wrote that the construction presented by Keisler is in terms of sequences. Thus an infinitesimal can be thought of as represented by a sequence. Easy examples appear in Keisler's Epilogue. In this sense, there is a clear relation between the two definitions. If certain words appear weasel, why not edit the sentence instead of removing it? Katzmik (talk) 16:10, 11 December 2008 (UTC)

 * The construction outlined by Keisler also involves an equivalence relation that is not clearly the same as the condition on the sequences in the second definition. They are not clearly equivalent, which is why I removed that statement that they may be equivalent.  Thenub314 (talk) 18:38, 11 December 2008 (UTC)

 * You are right, "equivalent" was not the right word. However, there is clearly a relation here.  What do you think of a sentence of the following sort: "The two definitions below are related as both exploit sequences: the second definition explicitly, while the first, via the construction of hyperreals in terms of sequences as presented in the Epilogue".  This sounds too wordy, but it could be worked on. ?  Katzmik (talk) 20:28, 13 December 2008 (UTC)

Examples in Non-standard analysis characterization.
We currently have two examples in this section, and maybe this should be part of the out of proportion discussion above, but here goes. For the first one

 * Example 1. The trigonometric tangent function, continuous on the open interval (−π/2, π/2) fails to be uniformly continuous on that set because there are infinitely small positive real numbers δ such that tan(π/2 − δ) and tan(π/2 − 2δ) differ by more than an infinitely small amount.

Is it intended to be clear to a reader why tan(π/2 − δ) and tan(π/2 − 2δ) differ by more than an infinitely small amount?

 * Example 2. The exponential function exp, continuous on the real line R, fails to be uniformly continuous on R because there are infinitely large non-standard real numbers x and infinitely small non-standard real numbers δ such that exp(x + δ) − exp(x) is not infinitely small. A more explicit calculation in the case of the squaring function x2 appears at Non-standard calculus.

Again why is it clear (from what is said) that these two infinite quantities are not infinitely close together? I think that these two examples do not add much to the discussion of uniform continuity and should be re-worked or removed. But maybe I should get other opinions first. Thenub314 (talk) 16:00, 12 December 2008 (UTC)

 * Thanks. My personal preference is for the quadratic example, is the calculation there is very explicit.  However, Michael is the editor who made this edit and he is more experienced in wiki issues than I am, perhaps we can wait to get some input from him.  Katzmik (talk) 20:30, 13 December 2008 (UTC)

Local v Global, hyperreals
I realize I'm 4 years late to the party, but I made two clarifying edits that I believe reconciles the two competing viewpoints of the fuzzy notion of a "local" property in the sections above. 173.227.48.5 (talk) 00:17, 14 December 2012 (UTC)

"Chain of Inclusions"
The article currently states, "Continuously differentiable ⊆ Lipschitz continuous ⊆ α-Hölder continuous ⊆ uniformly continuous ⊆ continuous." But f(x) = x2 is a continuously differentiable function that is not uniformly continuous, right? Which would mean continuously differentiable does not imply uniformly continuous. 129.107.80.40 (talk) 23:38, 21 January 2016 (UTC)

 * I agree with this comment. Furthermore the article itself states that
 * "Every uniformly continuous function is continuous, but the converse does not hold."
 * GladiusMaximus34 (talk) 15:28, 30 March 2016 (UTC)

 * Did you mean that the article states "uniformly continuous = continuous"? Because that seems to be the problem you're describing, and I agree with you then. Deansg (talk) 06:23, 15 September 2017 (UTC)

Incorrect characterisation of Cauchy continuity
The "specific" statement under Other characterisations/Cauchy continuity is the incorrect statement of Cauchy continuity -- in fact, the given mathematical statement is equivalent to uniform continuity.

I made an to restate the content of the section to state that the given form of uniform continuity perhaps makes the implication clearer, but was quickly undone.

Perhaps the section should be rewritten.

Chan-Paton factor (talk) 07:16, 25 December 2019 (UTC)

 * Yes, I agree: the given mathematical statement is equivalent to uniform continuity (for arbitrary functions between arbitrary metric spaces). In contrast, Cauchy continuity is equivalent to uniform continuity on every totally bounded subset (for arbitrary functions between arbitrary metric spaces). If the first space is $$\mathbb R^n,$$ then totally bounded subsets are just bounded subsets, and in this case Cauchy continuity is equivalent to uniform continuity on every bounded subset (which is sometimes called local uniform continuity). Boris Tsirelson (talk) 09:50, 25 December 2019 (UTC)

title: Talk:Uniform continuity


text:
Reiki

Reiki (霊気) is a pseudoscientific form of energy healing, a type of alternative medicine originating in Japan. Reiki practitioners use a technique called palm healing or hands-on healing through which, according to practitioners, a "universal energy" is transferred through the palms of the practitioner to the client, to encourage emotional or physical healing. It is based on qi ("chi"), which practitioners say is a universal life force, although there is no empirical evidence that such a life force exists.

Reiki is used as an illustrative example of pseudoscience in scholarly texts and academic journal articles. The marketing of reiki has been described as "fraudulent misrepresentation", and itself as a "nonsensical method", with a recommendation that the American government agency NCCAM should stop funding reiki research because it "has no substantiated health value and lacks a scientifically plausible rationale". The Catholic Church says that reiki is based on superstition.

Clinical research does not show reiki to be effective as a treatment for any medical condition, including cancer, diabetic neuropathy, anxiety or depression. There is no proof of the effectiveness of reiki therapy compared to placebo. Studies reporting positive effects have had methodological flaws.

Etymology
According to the Oxford English Dictionary, the English alternative medicine word reiki comes from Japanese reiki (霊気) "mysterious atmosphere, miraculous sign", combining rei "universal" and ki "vital energy"—the Sino-Japanese reading of Chinese língqì (靈氣) "numinous atmosphere".

Conceptual basis
Reiki's teachings and adherents claim that qi is a physiological force that can be manipulated to treat a disease or condition. There is no evidence that qi exists as an observable phenomenon. Reiki is thus classified as a pseudoscientific practice based on metaphysical, rather than physiological, concepts.

Most research on reiki is poorly designed and prone to bias. There is no reliable empirical evidence that reiki is helpful for treating any medical condition, although some physicians have said it might help promote feelings of general well-being. In 2011, William T. Jarvis of The National Council Against Health Fraud stated there "is no evidence that clinical reiki's effects are due to anything other than suggestion" or the placebo effect.

The 22 April 2014 Skeptoid podcast episode entitled "Your Body's Alleged Energy Fields" relates a reiki practitioner's report of what was happening as she passed her hands over a subject's body: "What we'll be looking for here, within John's auric field, is any areas of intense heat, unusual coldness, a repelling energy, a dense energy, a magnetizing energy, tingling sensations, or actually the body attracting the hands into that area where it needs the reiki energy, and balancing of John's qi."

Technique
A session usually lasts for approximately one hour. A "Level 1" practitioner places their hand or hands on or near various parts of the body for several minutes. During this time, a vital energy is meant to flow from the practitioner into the client's body. "Level 2" practitioners alternatively may offer their services at a distance with no skin contact.

Research and critical evaluation
Reiki is used as an illustrative example of pseudoscience in scholarly texts and academic journal articles. David Gorski writes that reiki vies with homeopathy to be the "one quackery that rules them all" because of its "sheer ridiculousness and disconnect from reality". Jann Bellamy, a lawyer and critic of alternative medicine, has described the marketing of reiki as "fraudulent misrepresentation".

In criticizing the State University of New York for offering a continuing education course on reiki, one source stated, "reiki postulates the existence of a universal energy unknown to science and thus far undetectable surrounding the human body, which practitioners can learn to manipulate using their hands," and others said, "In spite of its [reiki's] diffusion, the baseline mechanism of action has not been demonstrated ..." and, "Neither the forces involved nor the alleged therapeutic benefits have been demonstrated by scientific testing."

Several authors have pointed to the vitalistic energy which reiki is claimed to treat,  with one saying, "Ironically, the only thing that distinguishes reiki from therapeutic touch is that it [reiki] involves actual touch," and others stating that the International Center for Reiki Training "mimic[s] the institutional aspects of science" seeking legitimacy but holds no more promise than an alchemy society.

A guideline published by the American Academy of Neurology, the American Association of Neuromuscular & Electrodiagnostic Medicine, and the American Academy of Physical Medicine and Rehabilitation states, "Reiki therapy should probably not be considered for the treatment of PDN [painful diabetic neuropathy]." Canadian sociologist Susan J. Palmer has listed reiki as among the pseudoscientific healing methods used by cults in France to attract members.

Stephen Barrett of Quackwatch describes reiki as a "nonsensical method". As a reason for why NCCAM should stop funding reiki research, he writes: "Reiki has no substantiated health value and lacks a scientifically plausible rationale. Science-based healthcare settings should not tolerate its use, and scarce government research dollars should not be used to study it further."

Evidence quality
A 2008 systematic review of nine randomized clinical trials found several shortcomings in the literature on reiki. Depending on the tools used to measure depression and anxiety, the results varied and were not reliable or valid. Furthermore, the scientific community has been unable to replicate the findings of studies that support reiki. The review also found issues in reporting methodology in some of the literature, in that often there were parts omitted completely or not clearly described. Frequently in these studies, sample sizes were not calculated and adequate allocation and double-blind procedures were not followed. The review also reported that such studies exaggerated the effectiveness of treatment and there was no control for differences in experience of reiki practitioners or even the same practitioner at times produced different outcomes. None of the studies in the review provided a rationale for the treatment duration and no study reported adverse effects.

Safety
Safety concerns for reiki sessions are very low and are akin to those of many complementary and alternative medicine practices. Some physicians and health care providers, however, believe that patients may unadvisedly substitute proven treatments for life-threatening conditions with unproven alternative modalities including reiki, thus endangering their health.

In a December 2014 article from the USCCB's Committee on Divine Worship on exorcism and its use in the Church, reiki is listed as a practice "that may have [negatively] impacted the current state of the afflicted person".

Catholic Church concerns
In March 2009, the Committee on Doctrine of the United States Conference of Catholic Bishops issued the document Guidelines for Evaluating Reiki as an Alternative Therapy, in which they declared that the practice of reiki was based on superstition, being neither truly faith healing nor science-based medicine: "Reiki lacks scientific credibility. It has not been accepted by the scientific and medical communities as an effective therapy." They stated that reiki was incompatible with Christian spirituality since it involved belief in a human power over healing rather than prayer to God, and that, viewed as a natural means of healing, it lacked scientific credibility. The 2009 guideline concluded that "since reiki therapy is not compatible with either Christian teaching or scientific evidence, it would be inappropriate for Catholic institutions, such as Catholic health care facilities and retreat centers, or persons representing the Church, such as Catholic chaplains, to promote or to provide support for reiki therapy." Since this announcement, some Catholic lay people have continued to practice reiki, but it has been removed from many Catholic hospitals and other institutions.

Training, certification and adoption
A reiki practitioner who offers teaching is known as a "reiki master".

There is no central authority controlling use of the words reiki or reiki master. Certificates can be purchased online for under $100. It is "not uncommon" for a course to offer attainment of reiki master in two weekends. There is no regulation of practitioners or reiki master in the United States.

The Washington Post reported in 2014 that in response to customer demand at least 60 hospitals in the United States offered reiki, at a cost of between $40 and $300 per session. Cancer Research UK reported in 2019 that some cancer centers and hospices in the UK offer free or low-cost reiki for people with cancer. The cost per session for treatment vary widely, but a CNBC report found a practitioner charging $229 per session of 60–90 minutes.

History
Mikao Usui originated the practice in Japan. According to the inscription on his memorial stone, Usui taught his system of reiki to more than 2,000 people during his lifetime. While teaching reiki in Fukuyama, Usui suffered a stroke and died on 9 March 1926.

The first reiki clinic in the United States was started in 1970 by Hawayo Takata, a student of Chujiro Hayashi (who was a disciple of Mikao Usui).

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Reiki


text:
Talk:Common Object Request Broker Architecture

Interface Definition/Description Language
Modification note (7/1/2003)

I just thought I'd clear this up to avoid a mod-war. IDL stands for Interface Definition Language, *not* Interface "Description" Language. It was recently changed incorrectly to the latter. I've put it back the way that it was. See the CORBA spec p 3-1. (Derek)

I noticed that someone broke my change above when doing some edits. I've re-edited it so that it is now correct once more. (Derek)

According to [Douglas Comer]'s Book Computer Networks and Internets with Internet Applications, 4/e, both uses of the term IDL when talking about RPC stuff are valid. Subwy (talk) 18:16, 15 July 2008 (UTC)

Nick Stavros (talk) 20:33, 4 October 2013 (UTC) OMG has forked the IDL specification. The original IDL which is part of the CORBA specification remains "as-is" and untouched. The same baseline has been lifted from the CORBA specification and is available as a stand alone specification referred to as IDL 3.5.

This was done in order that IDL be allowed to evolve independently from CORBA with the caveat that the support for CORBA not be broken.

I propose that the OMG IDL link in the disambiguation page be changed to point to a new wiki page on 'OMG IDL' the stand alone IDL and that a link be placed into the new page back to this page.

IDL is now an integral part of many other OMG specifications and a new version 4.0 is expected soon.

CORBA/Common object request broker architecture
68.167.249.197 23:44, 7 Apr 2004 (UTC): I'd suggest that it is standard practice to have the main article body for CORBA/Common object request broker architecture to be under the fully expanded version of the name (cf. Remote procedure call/RPC, and File transfer protocol/FTP to name two examples).

 * That's right! I am sexy 23:46, 7 Apr 2004 (UTC)

 * I would argue that File transfer protocol should be moved to FTP, though Remote procedure call should stay as it is. This is because there is not just one file transfer protocol. Having a page title like "File transfer protocol" or "Common object request broker architecture" implies that there is more than one - for example - "a file transfer protocol is..." or "a common object request broker architecture", whilst "an FTP" or "a CORBA" is less appropriate. Dysprosia 06:40, 8 Apr 2004 (UTC)

 * 68.167.249.2 09:02, 8 Apr 2004 (UTC): Admittedly "file transfer protocol" can be generically used, but I disagree about "common object request broker architecture" which has established itself as a specific standard. That is emphasized outside of wikipedia by capitalizing all the words.  Additional examples, like OSI, DNS, SNMP, LAN, FDDI, SMTP, ICMP, RARP all redirect to the full words, though HTTP doesn't.

an exception proving the rule; disambig COBRA and CORBA
68.167.249.197 00:03, 8 Apr 2004 (UTC): One good standard practice within wikipedia is to not disambiguate misspellings. I agree that this is a good guideline to follow. As I also note at Talk:COBRA, I would contend that COBRA vs. CORBA is a case where the exception proves the rule. This is a case of two five -letter acronyms, which is unusual. For two acronyms of that length (and, to get perhaps overly analytical about it, the fact that B and R are both typed by the left index finger on a QWERTY keyboard), isn't a reasonable to anticipate our audience would appreciate such a disambiguation here? I would never advocate disambiguation for TLAs. but this seems a case where a good rule has a reasonable exception.
 * 68.167.249.2 09:02, 8 Apr 2004 (UTC): Dysprosia's suggestion elsewhere of a disambiguation block prefacing the CORBA page seems like the best of both worlds to resolve this.

KDE Using CORBA
Wasn't KDE using CORBA and then dropped it? 81.151.193.21 17:10, 9 January 2006 (UTC)

 * That was GNOME, I believe; KDE fanboys at the time often pointed to the CORBA-usage as a sign of the over-engineering which they believed plagued the GNOME project. --217.128.105.9 14:50, 3 February 2006 (UTC)
 * The CORBA in GNOME is not dropped and still used. Audriusa 07:54, 25 April 2006 (UTC)

Images?
Hi. What are these supposed to indicate? Why are they not defined? Thanks. --ChrisRuvolo 01:53, 6 Apr 2005 (UTC)

 * Developmant Status. In researching the links I found project which are not  fully developed and/or which have not been updated for many years. With the % rating on what to expect when following the link. If you know the project and find the rating unfair you are free to correct - just be honest - a project with barely make minimum feature set and has seen no update for 3 years should not be marked 100%. --Krischik 06:49, 6 Apr 2005 (UTC)

 * Ok, thanks for the info. I don't mind their use, but in the article it should be defined what they represent.. and then what the various implementations are lacking (justification of each 50% rating for example).  They won't be able to be interpreted usefully otherwise.  --ChrisRuvolo 16:23, 6 Apr 2005 (UTC)

 * I don't understand your context - what images? 68.100.20.83 (talk) 00:35, 17 November 2007 (UTC) Sorry for not logging in, I'm Seaneparker (talk) 00:36, 17 November 2007 (UTC)

Current status
Information about the current status of CORBA is needed. What alternatives are there? Is it evolving? Are there new developments that use CORBA?

 * I'd love to provide a status but I'm neither a member of the OMG nor do I work with CORBA at the moment (I did at my last job last month :-) What would you like the format to be? i.e. links to "current projects"? White papers? Conference references? New standards in process? Seaneparker (talk) 00:38, 17 November 2007 (UTC)

 * CORBA is very much alive. There are many ongoing CORBA related specifications being created - especially where quality of service issues are important. Btw, do not believe any one talking about the rise and fall of CORBA, most such talks are led by those who are trying to create new specifications created by a handful of distributed computing engineers (compare that to CORBA created over nearly 2 decades by hundreds of distributed computing specialists and domain experts). False references in this wikipedia to articles like "rise and fall of CORBA" should be deleted as they are a partial view. If some one wants to add to encyclopaedic content they can do so using a neutral subject. Today (2008) CORBA is an essential part of mission critical telecom networks, some of the most popular GUIs (GNOME). Distributed computing platforms like J2EE actually use CORBA (IIOP) in their core. Several IPTV projects require a core infrastructure powered by CORBA. To summarize, CORBA is the most successful distributed computing standard ever created. It powers many of today's software applications. There many not be too many changes in core CORBA (it is a mature standard now) however OMG is actively working on new specs. When you play a distributed mobile game, you may not know who powers it (like CORBA), does not mean it is not there :-) —Preceding unsigned comment added by 123.236.136.223 (talk) 18:12, 17 June 2008 (UTC)
 * If anyone is listening, please come up with a new, STL-based C++ binding, à la Internet Communications Engine. I wouldn't need backwards compatibility.  Thanks.  —Fleminra (talk) 18:39, 17 June 2008 (UTC)
 * TAO will soon have a prototype of a STL-based C++ binding 24.132.221.68 (talk) 19:14, 17 May 2010 (UTC)
 * I think the list of current uses, like the above with a bit more research put into it, and if available, some sort of estimation of "market share" or "market penetration" would be a good way to balance the perspective of the article while adding to the useful content.(71.233.167.118 (talk) 13:32, 9 April 2011 (UTC))

 * CORBA support is to be removed in Java 11 citing "There is no significant interest in developing modern applications with CORBA in Java." I'd say this is something which should be reflected in the article.

VMCID
Is the VMCID really important enough to deserve an article? For that matter, is it even worthwhile to merge into the CORBA article? Wikipedia isn't a comprehensive reference guide for CORBA. That's what the CORBA specs are for. -- Whpq 17:34, 7 September 2006 (UTC)
 * I agree with this. An article (or section) on VMCID, in my opinion, doesn't have enough encyclopedic value to justify an article on Wikipedia. That sort of thing belongs in a programmer's handbook. --Tschel 22:10, 14 September 2006 (UTC)

The criticisms and success sections
The language of these sections seems more like an internet flame war than an encyclopedia entry. —The preceding unsigned comment was added by 194.25.80.243 (talk) 09:56, 7 December 2006 (UTC).
 * I agree, these two sections are full of contradictory statements. A neutral reader will end it up wondering if CORBA was really successful or a real failure at all. Also found the section for Success lacking for not citing enough references. (SirGalahad 21:09, 4 January 2007 (UTC))

 * I dont think the article can argue Waldo's A note on distributed computing is biased. His paper is the seminal "limitations of dist-comp" paper and was written while Sun were wholeheartedly backing CORBA -they were one of the co-founders of the OMG, after all. Java RMI came along a lot later; Java ships with a (dated) ORB and even EJB defaults to IIOP as its protocol. Admittedly the paper applies to more than just CORBA; it applies to anything that tries to make remote stuff look local (SOAP, Java RMI, DCOM). But it is valid in Corba, because a corba OID doesnt include any location hints at all; you have to use an Orb to find things. —The preceding unsigned comment was added by SteveLoughran (talk • contribs) 12:02, 27 February 2007 (UTC).

 * Also, I don't know how "fundamentally false" the notion of location transparency is. I do think its impossible to make a service on a remote system appear to be something local, and not have it fail in unusual ways (e.g NFS timeouts blocking file access operations). What may be possible is for programs to be written to talk to a system that is remote, without caring where the remote system is. Perhaps "fundamentally false" should be downgraded to "impossible to maintain in the face of network failures" SteveLoughran 17:37, 11 April 2007 (UTC)

The tone needs to be made more neutral and more examples of these supposed failures/short comings are needed; otherwise the criticism is really unsubstantiated.

 * If you look at the source of the criticisms, its quite full of commented out opinions. That discussion should be moved to the talk pages, where it belongs. SteveLoughran 22:48, 20 June 2007 (UTC)

FYI - I altered the language to be a bit more neutral (if that's possible for me to do) however I did not add any more references, etc. Please give feedback on whether improvement or detriment... seaneparker 21:26, 1 September 2007 (UTC)

Some of the language is in the past tense. This makes it sound like CORBA is no longer in use. 194.72.110.12 (talk) 11:39, 7 February 2008 (UTC)jac

 * Still in use, but it is not as ubiquitous as the vision. You can still find it in the Gnome desktop for Linux/Unix. SteveLoughran (talk) 18:39, 15 March 2008 (UTC)

 * I had a reread of the criticisms section. 1. We need to mention Microsoft and their lack of support. If all of the vendors at the time embraced CORBA, it would have stood more of a chance. As it was, MS pushed COM/DCOM. The other issue is that the criticisms says that Java RMI is the way forward. But Web Services, built on WS-*, and HTTP-based REST services have changed that. Maybe the big limitation was not the competing technologies, but the emergence of the Internet itself. CORBA was built for LAN-based distributed computing, and you now have enterprise wide and internet-scale problems, for which alternate solutions are needed. It was HTTP that stopped CORBA. SteveLoughran (talk) 18:39, 15 March 2008 (UTC)

NTCIP
I'm not sure where a link to National Transportation Communications for Intelligent Transportation System Protocol (NTCIP) would fit into this article, if anywhere. NTCIP offers CORBA as one of two possible choices for an application layer protocol. Is there a more appropriate listing for standards or other products that make use of CORBA? Squideshi 18:59, 27 June 2007 (UTC)

Red Hat delivers
"(Red Hat Linux delivers with the GNOME UI system, which has its IPC built on CORBA.)"

In addition to being grammatically unsound on several levels, this sentence is difficult to understand. . . and misleading at best. Red Hat neither engineered nor is the maintainer of GTK+ ("the GNOME UI system"). I'm looking to move/modify this, but I'd like some input on what the original intent was. Was the author merely confused as to Red Hat's responsibilities and what GTK+ is? —Preceding unsigned comment added by Brian Geppert (talk • contribs) 17:47, 12 March 2008 (UTC)

Examples
I think a code example in one of the languages where the binding is relatively standard, e.g. Java of how CORBA is used would be helpful. Since I don't know that much about how CORBA is used, I don't actually know if that makes sense, but if it does, an example should definitely be in the article. Subwy (talk) 18:20, 15 July 2008 (UTC)
 * This article also needs examples of real life applications using CORBA. --Abdull (talk) 14:07, 25 August 2008 (UTC)vnvnc
 * Java Enterprise Edition would be the primary example AFAIK. … Al least it was, 20 years ago. :) — 109.42.178.212 (talk) 13:35, 4 January 2024 (UTC)

Update on Compression paragraph?
Any update on the paragraph that ends with "the OMG meeting in September 2008 in Orlando"? trjonescp (talk) 18:40, 19 November 2008 (UTC)
 * This is now a formal standard, see http://www.omg.org Jwillemsen (talk) 19:15, 17 May 2010 (UTC)

DDS?
Why is DDS mentioned in the CORBA article? Data Distribution Service for Real-Time systems has nothing to do with CORBA, other than being sponsored by the same organization, OMG. DDS uses a subset of the IDL standard for convenience to define its datatypes, but even that IDL part is going away and will soon be XML based definitions. Some CORBA vendors offer DDS to expand their product line offerings, and re-use CORBA as a "shortcut" to create a DDS implementation, but that does not mean that the DDS standard has any relation to CORBA. A pure DDS implementation has zero CORBA under the hood. This confusion of DDS being associated with CORBA is common in industry, but we should help end the confusion. —Preceding unsigned comment added by Fpbear (talk • contribs) 08:38, 29 January 2009 (UTC)

External links (re) moved
I moved the following list of external links here. -- Marcel Douwe Dekker (talk) 20:18, 5 February 2009 (UTC)

Specific links

 * [http: //www.ciaranmchale.com/corba-explained-simply/ CORBA Explained Simply]
 * [http: //www.xs4all.nl/~irmen/comp/CORBA_vs_SOAP.html Web Services/SOAP and CORBA]
 * [http: //www.omg.org/technology/documents/formal/corba_2.htm OMG CORBA 3]
 * [http: //www.omg.org/ Object Management Group]
 * [http: //www.corba.org/ Information Board]
 * [http: //www.omg.org/technology/documents/spec_catalog.htm Catalog of OMG Specifications]
 * [http: //www.omg.org/technology/documents/idl2x_spec_catalog.htm IDL / Language Mapping]
 * [http: //www.omg.org/technology/documents/corba_spec_catalog.htm#ccm CORBA Component Model (CCM)]
 * [http: //www.omg.org/technology/documents/corba_spec_catalog.htm IIOP]
 * [http: //www.omg.org/technology/documents/corbaservices_spec_catalog.htm Services]
 * [http: //www.omg.org/technology/documents/corbafacilities_spec_catalog.htm Facilities]
 * [http: //www.omg.org/technology/documents/domain_spec_catalog.htm Domain]
 * [http: //www.omg.org/technology/documents/embed_intel_spec_catalog.htm Embedded Intelligence]
 * [http: //www.omg.org/technology/documents/formal/omg_security.htm Security]
 * [http: //www.omg.org/technology/documents/modeling_spec_catalog.htm UML, MOF, XMI, CWM]
 * [http: //cbbrowne.com/info/corba.html Description] by Christopher B. Browne
 * [http: //corbaconf.kiev.ua/ CORBA support for autoconf]
 * discussions
 * Article "[http: //cuj.com/documents/s=7993/cujcexp1907vinoski/ XML as CORBA Data]" by Douglas C. Schmidt and Steve Vinoski
 * Article "[http: //xml.sys-con.com/read/40033.htm Building Distributed Applications with Corba and XML]" by Dermot Russell and Nick Simha
 * Article "[http: //www.acmqueue.com/modules.php?name=Content&pa=showpage&pid=396 Rise and fall of CORBA]" by Michi Henning
 * Response to the Rise and Fall of CORBA here "[http: //www.orbzone.org/?p=121]"

CORBA implementations

 * [http: //www.puder.org/corba/matrix/ An overview of available CORBA implementations]
 * [http: //www.bea.com/framework.jsp?CNT=index.htm&FP=/content/products/tux BEA Tuxedo] - [[Image:100%.svg]] - A CORBA 2.5–compliant commercial ORB for Java and C++ from BEA Systems
 * [http: //www.borland.com/us/products/visibroker/index.html Borland Enterprise Server, VisiBroker Ed.] - [[Image:100%.svg]] - A CORBA 2.6–compliant commercial ORB for Java and C++ from Borland.
 * [http: //www.fpx.de/Combat/ Combat] - A Tcl ORB, and a Tcl layer for C++ ORBs.
 * [http: //sourceforge.net/projects/fnorb Fnorb] - A CORBA 2.0 ORB for Python
 * ILU - An open software object interface system from Xerox PARC.
 * GNU Classpath - Contains the Free Software (GPL+linking exception, including newly written org.omg packages) implementation for Java.
 * [http: //iiop-net.sourceforge.net/ IIOP.NET] - [[Image:50%.svg]] - A Free Software (LGPL) ORB for Microsoft .NET.
 * [http: //www.jacorb.org/ JacORB] - [[Image:50%.svg]] - A Free Software (LGPL) ORB implemented in Java.
 * [http: //j-integra.intrinsyc.com/products/espresso J-Integra Espresso] - commercial Microsoft .NET ORB by Intrinsyc J-Integra
 * [http: //www.mico.org/ MICO] - [[Image:100%.svg]] - A Free Software (LGPL) ORB implemented in C++.
 * [http: //omniorb.sourceforge.net/ omniORB] - [[Image:75%.svg]] - A Free Software (LGPL) ORB for C++ and Python.
 * [http: //www.prismtech.com/ PrismTech's OpenFusion CORBA] - C, C++, Java, Java Real-Time, Ada CORBA solutions from hard real-time embedded to enterprise level, including CORBA services, training, consulting and industrial-grade support
 * [http: //openorb.sourceforge.net/ OpenORB] - [[Image:100%.svg]] - A Free Software (BSD) ORB for Java.
 * [http: //www.orbacus.com/ Orbacus] - commercial C++ and Java ORB by IONA Technologies
 * [http: //www.ois.com/ ORBexpress] - standard and real-time commercial Ada, C++, and Java ORBs by Objective Interface Systems
 * ORBit2 - [[Image:100%.svg]] - A Free Software (LGPL) ORB for C, C++ and Python.
 * [http: //www.iona.com/products/orbix/welcome.htm Orbix] - commercial ORB by IONA Technologies
 * [http: //opalorb.sourceforge.net opalORB] - [[Image:100%.svg]] - A CORBA implementation written completely in Perl.
 * [http: //sf.net/projects/perlorb/ Perl ORB] - [[Image:25%.svg]] - An open-source (Artistic License) ORB implemented in Perl.
 * PolyORB - [[Image:100%.svg]] - A Free Software (MGPL) ORB implemented in Ada.
 * Python ORB - [[Image:50%.svg]] - A Free Software (Python license) ORB implemented in Python.
 * [http: //www.sankhya.com/info/varadhi.html SANKHYA Varadhi] - [[Image:100%.svg]] - A commercial ORB for C++
 * [http: //www.dre.vanderbilt.edu/~schmidt/TAO.html TAO] - [[Image:100%.svg]] - The ACE ORB, an open-source ORB for C++
 * [http: //www.taox11.org TAOX11] - [[Image:100%.svg]] - A open-source ORB for C++11
 * [http: //www.martin-both.de/vborb.html VBOrb] - [[Image:100%.svg]] - A Free Software (LGPL) ORB for Visual Basic
 * [http: //www.franz.com/support/documentation/5.0.1/orblink/doc/ ORBLink] - A commercial ORB for Allegro Common LISP
 * [http: //clorb.sourceforge.net/ CLorb] - for Common Lisp
 * [http: //www.remedy.nl/ R2CORBA] - [[Image:100%.svg]] - An open-source ORB for Ruby by Remedy IT
 * [http: //www.remedy.nl/ JR2CORBA] - [[Image:100%.svg]] - An open-source ORB for JRuby by Remedy IT
 * [http: //oil.luaforge.net/ OiL] - A free ORB in Lua, supports currently only part of the CORBA specification
 * [http: //forge.morfeo-project.org/projects/tidorbj/ TIDorb for Java] - An open source CORBA 2.6 ORB implementation for Java Language from [http: //morfeo-project.org Morfeo Community]
 * [http: //groups.google.com/group/comp.object.corba/msg/901730022f43f98f PocoCapsule for CORBA] A C++ IoC component framework for CORBA, Event, DDS, RTC, and SDR/JTRS-SCA applications.

Further comments
This doesn't fit in the Wikipedia article. -- Marcel Douwe Dekker (talk) 20:19, 5 February 2009 (UTC)

Timeline
Could someone with the knowledge discuss the general timeline of CORBA and it's advancements? I know Vinoski wrote a paper back in 1993.Mojodaddy (talk) 19:34, 19 August 2009 (UTC)

Corba Location (CorbaLoc) section
IMO this section is not clear. What does "must support" mean in "[...]All CORBA products must support two OMG-defined URLs:[...]"? What about software whose use case doesn't involve the concept of a URL? One could just read the spec, but that defeats the purpose of mentioning it in the article. Sojourner001 (talk) 18:57, 17 January 2012 (UTC)

C++11 mapping implementation
Following sentence is lacking source of information, most notably which CORBA implementation is meant.

"By contrast, the C++11 mapping is very easy to use, as it uses Standard Template Library (STL) heavily." — Preceding unsigned comment added by 2001:1488:AC14:1400:1AA9:5FF:FEF6:7AA9 (talk) 13:30, 29 October 2013 (UTC)

Structure of this article needs some work
As of now there is a lot of detail in the Overview section. Essentially most of the article are sub sections under Overview. I think it needs to be re-structured. E.g., make some of those sub-sections top level sections and/or create additional top level section(s) with a more reasonable title than "Overview" and group the sub-sections under them. I may take a shot at that but at a minimum I wanted to document I think it needs to be done. --MadScientistX11 (talk) 16:05, 9 January 2014 (UTC)
 * After looking a bit more one of the things that jumps out at me is that Features could definitely be it's own major heading and I think it should be called Benefits instead. The difference is subtle but to me a feature is some technical capability that the system has. A benefit is something of value a user gets as a result of the feature. That list seems more like benefits (other things in the article are what I would consider features). I plan to change it unless anyone objects. --MadScientistX11 (talk) 19:57, 9 January 2014 (UTC)
 * I made the change. Also, changed some wording. There was an unsourced claim about how "no other system provides what CORBA provides" which I just removed. IMO those kinds of claims are more appropriate for vendor marketing materials then for an encyclopedia anyway. There was also a direct link to an external site which I removed and turned into a reference. --MadScientistX11 (talk) 20:24, 9 January 2014 (UTC)

Funny, but doesn't CORBA look a bit like the IPC architecture of a host operating system?
Well, yeah, which is not surprising as it was more or less abstracted from a host operating system:

https://en.wikipedia.org/wiki/Spring_%28operating_system%29

That might be worth a mention. — Preceding unsigned comment added by 69.116.92.84 (talk) 18:42, 6 June 2014 (UTC)

So where do we stand?
What's the status of CORBA today? Are old CORBA based systems being maintained or transitioned? Are new CORBA based systems being built? If so, in what contexts? — Preceding unsigned comment added by 69.116.92.84 (talk) 18:44, 6 June 2014 (UTC)
 * Corba is dead as a doornail. — Preceding unsigned comment added by 148.225.103.2 (talk) 20:10, 1 July 2014 (UTC)

Merging the Incarnation article
I'm merging the Incarnation article into this one. I'm not going to do much editing to make them fit together, I've done a little editing on the Incarnation text and I'm just going to add a new section called Incarnation after the Overview. It's not a great solution but my CORBA knowledge is kind of rusty and I would have to do more work than I have time for now to read up on it in order to really do justice to the article. But I think at least doing the merge is a step in the right direction: there were no refs on the Inception article at all and it's just a short block of text. --MadScientistX11 (talk) 18:33, 17 September 2014 (UTC)

 * Thanks User:MadScientistX11 ~KvnG 14:20, 20 September 2014 (UTC)

Merging Servant (CORBA)
I support merging.. I may do that if I bother.. I'm not an expert on CORBA, and do not really know "Servant" in CORBA or similar context, but it seem it belongs here and not needing a separate page.. It's been a year.. Either nobody cares to much about this/that article and/or it supports CORBA as "dead".. comp.arch (talk) 16:52, 7 September 2015 (UTC)
 * CORBA is not "dead". I was on a mailing list just yesterday where people were talking about it quite a lot in relation to a Semantic Web project. In any case even if CORBA were "dead" it was still extremely influential in the history of IT so the articles about it should be accurate. BTW, if you don't even know what a Servant is I don't see how you can responsibly edit that part of the article without first doing some serious study on the topic. I DO know what a Servant is but I don't feel I understand it well enough to edit further without doing more research first.  --MadScientistX11 (talk) 18:46, 7 September 2015 (UTC)
 * You are right, I'm not sure what Servant is in the CORBA context (I said I would "support merging", I would be careful if I did it myself), but it would not disallow merging to this article? Shown by "(CORBA)" in the title.. (one other thing, people wouldn't know what that is, so it's kind of disallowed while "(software)" isn't).. I'm not saying CORBA isn't notable, it is and I remember it. This article is 30,094 bytes and there is room, and the other article is very short and it has hardly been edited since 2009 and not at all since the merge proposal a year ago.. Even if CORBA isn't dead, CORBA is notable, but Servant (CORBA) on it's own? I doubt it. comp.arch (talk) 21:03, 7 September 2015 (UTC)

✅ by ~Kvng (talk) 14:14, 17 February 2016 (UTC)

Relation to JSON & co
CORBA just seems like an over-engineered enterprisey (as defined by thedailywtf.com) and painful earlier alternative to easy-to-use things like JSON. But I came here, to look for what CORBA brings to the table in comparison… Aside from the article ringing all the alarm bells of enterprise-speak, I could not find a mention of how it relates to such protocols. If anyone knows, adding this would be welcome. :) — 109.42.178.212 (talk) 13:33, 4 January 2024 (UTC)