Talk:Constant/Archive 1

veryopinionated says- why do u people have discusions about "constant" and other dictionary words...get out and do something fun...cus this is not fun

I removed this footnote:

There is some evidence that the speed of light is gradually decreasing, but such speed is constant over the whole universe at any given time.

Most physicists are certain that the speed of light isn't changing with time, and there isn't even agreement among them as to just what such a claim means, if anything. The issue should certainly be discussed in Speed of light, but not here. — Toby 06:16 Sep 18, 2002 (UTC)

This is pretty much moot in light of my recent changes. — Toby 07:40 Sep 18, 2002 (UTC)

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I just noticed that there are also articles titled mathematical constant and physical constant. I think some re-organization is in order. If all articles are to be kept, then constant should be the general concept, and link to the more specific articles. Or more ambitiously, someone might make one, really good article by merging all three. I don't think I'm the person to do this (mathematically stupid)! ike9898 15:23, 21 Jan 2004 (UTC)

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I find the section "Variables vs. constants" very confusing and disturbing. It doesn't match my own understanding of the terms.

Constants vs variables

A number that is constant in one place may be a variable in another.

First of all, all numbers are really constants, not variables. I believe what was intended was something about symbols that may stand for a variable in one place, constant in another. But even here, I don't really agree with the statement.

This whole distinction over "constant vs. variable" is really a matter of distinguishing between free variables and bound variables. (free variables are "constants", bound variables are "variables"). I believe that article does a much better job of explaining the distinction in practice. In general, this distinction is a fairly abstract concept that requires precise definitions, and I admit I'm not familiar with them off the top of my head, I would have to consult a logic book. But the explanation below seems misleading.

Consider the example above, with a function f defined by f(x) = sin x + c.

Now consider a functional F, a function whose argument is itself another function, defined by

F(g) = g(π/2).

Then for the function f given above, we have

F(f) = c + 1.

In the formula for f(x), we are fixing c and varying x, so c is a constant. But in the formula for F(f), we are varying both c and f, so c is a variable.

I believe this is a bit misleading. It is true that c is a variable, but it is a variable that depends on f. What this means is that f is actually a constant (free variable!) Seems ridiculous, but watch. Let's call

f_c = sin x + c

Then what we're really saying is,

F(f_c) = c + 1

To be really precise, we should say that f is a function from the reals R into the domain of F, where

f(c) = f_c

A really good way of expressing this is to say that

(f(c))(x) = sin x + c

So, f isn't a function like sin x now, it's a function that gives out a function, given a real number.

What the first statement is saying is:

(FOR ALL x) f(x) = sin x + c.

Here, clearly, x is bound, and c is free. (In other words, x is a variable, and c is a constant.)

The other statement is really saying:

(FOR ALL c) F(f(c)) = c + 1.

Here, clearly, c is bound, but just as clearly, f is free! The point is that the original "f" given in the original formula was actually f_c, not f. This dependence on c was concealed by the notation. We could have defined f differently, say

f(c) = cos x + c

and then the second statement would have been false. The second statement depends on f, so in that statement, f is a constant.

The only way f could be a bound variable was if we interpreted the statement as saying,

(FOR ALL c)(FOR ALL f) F(f(c)) = c + 1

But this is not what we mean by F, e.g. we don't mean to say that (taking c = 3, f(x) = x²)

F(9) = 4

even if we do interpret "9" to be the constant function 9. In that case, we would want

F(9) = 9

Even this statement might be false in the presence of some larger context that gives yet another point of view.

I think maybe this is supposed to be some very vague way of talking about the scope of quantifiers?

Thus, there is no precise definition of "constant" in mathematics; only phrases such as "constant function" or "constant term of a polynomial" can be defined.

Well, yes there is a precise definition, it's defining "constant" to mean "free variable". The other definitions given are really distinct from this notion, but related intuitively. The point is, they can all be defined without referring specifically to free variables, so in that sense, they are terms which have only "co-opted" the term "constant" as a matter of habit or tradition.

There is a mathematicians' joke to the effect that "variables don't; constants aren't." That is, the term variable is frequently used to mean a value that is fixed in a given equation, albeit unknown;

I never call these "variables" at all, except when I'm just being sloppy in my speech...a more accurate term would be "parameter" (or constant, or free variable, etc.)

while the term constant is used to mean an arbitrary quantity which may assume any value, as in the constant of integration.

This "paradox" arises from the conflation of terminology surrounding the term "constant". When mathematicians use the word "constant of integration", they are not using it the sense of a free variable, they are using it in the sense of a "constant function". The constant of integration doesn't vary at all, at least not with respect to the scope of the function; for any given fixed antiderivative, the constant of integration is a fixed number.

Revolver 04:44, 14 Apr 2004 (UTC)

Constint

Is Constint a good redirect? Constint 12:26, 27 February 2007 (UTC)

Huh?? Rp 18:38, 19 October 2007 (UTC)

Note

This talk page used to be at the title "Talk:Constant", before it was moved to make way for the current contents of that page. The article text that is referred to in the messages below can be found in the history of Talk:Constant/Old history. Graham87 12:03, 6 October 2010 (UTC)

Chatty and unstructured

This article has expanded tremendously, but it is chatty and unstructured. The version of a month ago looked like this, with clear links to physical constant and mathematical constant. I would prefer to revert to that version. /Pieter Kuiper (talk) 23:33, 10 December 2007 (UTC)

I must agree but please be more specific. Also, there are clear links to physical constant and mathematical constant. Randomblue (talk) 23:42, 10 December 2007 (UTC)

I have not really thought about it, but it might be best to have a disambiguation page here instead of an essay "constant" about concepts that are not really that related to eachother. Some constants are defined, others are mathematics, others are measured, etcetera. /Pieter Kuiper (talk) 23:53, 10 December 2007 (UTC)

There is a page Constant (disambiguation). I also refer to what I wrote here, including this: I am actually not convinced that it is worth having a separate article like this next to Constant (disambiguation) and the specific articles (i.e., Mathematical constant and Physical constant) and again: I remain unconvinced it has a reason to exist.  --Lambiam 01:39, 11 December 2007 (UTC)

I agree with Lambian (although the "rock"-example is a bit of an exaggeration). Users are probably served best by moving Constant (disambiguation) here. /Pieter Kuiper (talk) 08:21, 11 December 2007 (UTC)

Here are reasons why I think the article should stay:

• I don't know about Lambiam but I see that Pieter Kuiper is a "solid state physicist". Perhaps you don't appreciate enough the fact that the concept of a constant is a scientific one, and not solely a mathematical or physical concept. Chemists, biologists, cosmologists, economists, sociologists and maybe even computer scientists work with constants as well.
• Many authors (even with just a little research I found two quotes) suggest that constants have a fascinating, intriguing or beautiful aspect to them and this observation is a common observation for at the least mathematical and physical constants.
• Constants have quite a remarkable history, related in part to their notation. Also, mathematical constants and physical constants have a common history: Newton was both a mathematician and physicist, Kepler was both a mathematician and an astronomer,...
• It turns out that some constants are not discovered in a strictly orthodox way (mathematical constants while doing maths, physical constant while doing physics, etc...) Indeed, some mathematical constants (like the Feigenbaum constants that arised from studying fluids for example) are discovered not when doing mathematics and physical constants are sometimes discovered (or at least predicted) by abstract mathematical means.
• Some constants (as I've tried to suggest it) don't really fit in the classification of mathematical and physical constants because they are much more universal: we encounter them in both mathematics and physics.
• One cannot really claim that unspecified constants are of a mathematical type, of a physical type, or of any specific type. They are 'tools' that scientists use when doing modeling for example.

I must apologize if the article doesn't look pleasant. This is really my first article, I'm no kind of constant expert, and, I've only been working (from scratch) on this article for weeks. I'm ready to completely rewrite the article and apportion various parts to more specific articles. However, I really do think that the scientific concept of a constant can be dealt with as a whole before diving in the depth of the more specialized type. Randomblue (talk) 10:53, 11 December 2007 (UTC)

User:Randomblue does not present his credentials, so it cannot be ruled out that he has a much greater overview over general science than I do. The important point though is whether his essay is what a reader would expect to find in an encyclopedia. The word 'constant' does not mean very much, but it is important to note that it is often used as a contrast to 'variable'. The article constant (disambiguation) does so at the outset, while this essay never gets to such a central point.

I believe that this essay includes too much original research (which includes synthesis and joining together things in creative ways) and that it is too personal for an encyclopedia. /Pieter Kuiper (talk) 12:27, 11 December 2007 (UTC)

"I really do think that the scientific concept of a constant can be dealt with as a whole". Here we clearly disagree; I think the various notions that are called "constant" are too diverse and disparate to be amenable to a meaningful joint treatment.  --Lambiam 13:12, 11 December 2007 (UTC)

User:Pieter Kuiper, if you want my credentials here they are: I'm a first year undergraduate at the University of Cambridge, studying maths. Hence, you surely have much more experience than I do. However, I am ready to do research to build a very decent article.

Contrasting constant with variable seems to be more of a "dictionary" or "thesaurus" point of view. Most people 'know' that constant contrasts with variable. However, it is the entity itself that is of interest here. What is a constant (these real numbers)? How do we define them? What role do they play in science? Why should $\pi$ be more important than 3.65?

I agree that this is an "essay" more than a proper encyclopedic article yet, but this is just the kind of work I am used to, and I wish to achieve something appropriate. I suggest you cite sentences that you find too personal (or even delete a few!) so that I can work on them.

User:Lambiam, let me rephrase my idea: "Within the scope of the definition of constant a real number with significant importance it is possible to deal with it as a whole. Indeed, with this definition we exclude the computer science term, constant functions, logical constants, etc."

Randomblue (talk) 15:27, 11 December 2007 (UTC)

Also, as I see it, the mathematical constant article is hardly more than a dry list. I find that discussion always helps grasp a concept. Randomblue (talk) 15:49, 11 December 2007 (UTC)

As a Cambridge math student, Randomblue probably knows more about mathematical constants than I do, and he certainly has a greater interest in them. I think most of this article is about mathematics. A large part of the material here could be moved to a general article about mathematical constants. /Pieter Kuiper (talk) 18:20, 11 December 2007 (UTC)

Apart from a few dimensionless physical constants, physical constants are not real numbers, and treating them together with the mathematical constants is purely artificial. The numerical values when such constants are expressed in specific units of measurement depend on decisions in defining these units that are completely irrelevant from the viewpoint of physics (such as using not-really-constant geophysical properties of the planet Earth as the basis for choosing the lengths of the second and the meter), and are therefore utterly devoid of any particular significance. And how does importance enter the concept of "mathematical constant"? Can you cite some reliable source that backs that up? Not all mathematical constants are important, as their number is without end (the largest root of x⁷−20x⁴+4, Σ n/(n³+1), √(π+1), and so on). Even many named mathematical constants have no clear significance, and it is mostly accidental that they were named at all.  --Lambiam 20:49, 11 December 2007 (UTC)

Well, it is perhaps possible to interpret Steven Finch's (the author of "mathematical constants") quote that "all constant's are not created equal" as "all constant's aren't all as important one another". I guess that examples of important constants include the truly ubiquitous and universal, those who translate nice facts (Conway's constant) and those who link different branches of mathematics (Euler-Mascheroni). Anyway, thanks for the input. I might get working on mathematical constant or some other article I'm keen about. Randomblue (talk) 22:12, 11 December 2007 (UTC)

Idea of the page is wrong, under this name

Constants don't have to be interesting; they just have to be constant. The reference for the definition is the notoriously unreliable MathWorld. I came to this page because it's listed as a "vital article" -- this very basic problem with the whole concept of the page is a serious issue that something needs to be done about. --Trovatore (talk) 16:21, 18 July 2008 (UTC)

I disagree about MathWorld being unreliable here. Rather, the person who wrote the broken definition failed to read the MathWorld article thoroughly. Fredrik Johansson 16:31, 18 July 2008 (UTC)

I haven't read that particular article either. I find MathWorld unreliable in general as a source for WP. In particular it indulges itself in neologism-making and idiosyncratic organization of information. That would be OK except for its pretensions to be a reference work. --Trovatore (talk) 18:10, 18 July 2008 (UTC)

Be bold, guys! 86.210.142.101 (talk) 17:07, 18 July 2008 (UTC)

Well, this isn't a matter of changing a line or two. The whole premise of the page is wrong, and it's a vital article, at least according to the current list. So some discussion needs to happen first. --Trovatore (talk) 18:10, 18 July 2008 (UTC)

I agree with Trovatore. Also note the first post on this page above, which references an earlier version of this article for comparison. Paul August ☎ 18:31, 18 July 2008 (UTC)

I don't want to get rid of all the nice content that Randomblue has added. It might make sense in an article called list of named constants or some such. The "list" format doesn't have to be just a collection of bullets; it can include some exposition, and (in my observation) it's a little looser about the sorts of organizing principle that it can have, even marginally "original" ones, as long as they're not aimed at pushing some sort of point.

But I really don't think that content can stay under an article called "constant" (and while it's not really on point, I also sort of doubt that any article with "constant" in the name really belongs under "vital articles" for mathematics). --Trovatore (talk) 09:13, 19 July 2008 (UTC)

This article was nominated for deletion on 7 March 2008. As you can read at the top of this talk page, the result of the discussion was: merge content to Mathematical constant, then redirect page to Constant (disambiguation). It's just that nobody has executed this (yet).  --Lambiam 21:55, 24 July 2008 (UTC)

Hmm, but mathematical constant kind of has the same issue, wouldn't you say? --Trovatore (talk) 21:57, 24 July 2008 (UTC)

When I use the term "mathematical constant" rather than just "constant", it means a number such as e or π, not just any constant such as, e.g., log(34211/16231). As far as I'm aware that is the common use. Our page Constant (disambiguation) agrees – which is not surprising since I authored the relevant bit.[1] For another position note that Plouffe's inverter identifies itself as "a database of more than 215,000,000 mathematical constants like Pi, E, Catalan or Euler-Mascheroni constant", where of course not all 215,000,000 entries are equally "significantly" interesting as the four ones named.  --Lambiam 22:44, 24 July 2008 (UTC)

Hmm -- there is certainly a better case for that view for the name mathematical constant as opposed to just constant. But I'm still uncomfortable with giving a definition that requires the object to be "interesting". Maybe my discomfort would be eased somewhat if there were a way to clarify that this is not a mathematical definition. --Trovatore (talk) 23:10, 24 July 2008 (UTC)

I've edited the lede of Mathematical constant a bit to clarify that "interesting" is a matter of taste, assuming that readers will understand that applying mathematical definitions will not require one to exercise taste. Please review and see if this assuages your unease.  --Lambiam 16:22, 25 July 2008 (UTC)

Ahad's Constant

The article opens with this paragraph: "Constants are real numbers or numerical values which are significantly interesting in some way. The term "constant" is used both for mathematical constants and for physical constants, but with quite different meanings."

Well, here's one that has been floating around since c. 2004 and hugely discussed in lots of places and it seems "significantly" interesting and is both a *http://en.wikipedia.org/w/index.php?title=Talk:Constant&action=edit&section=3physical* as well as a *mathematical* constant:

File:Ahads constant public domain image.jpg

The article would be more complete if Ahad's Constant were added. Discuss? :-) —Preceding unsigned comment added by 86.133.83.119 (talk) 12:08, 5 August 2008 (UTC)

This constant is not notable. The only publication is in the "Letters" column journal of the BAA, an association of amateur astronomers. Such "Letters to the Editor" are not peer-reviewed and are not "reliable sources". The "surrounding cosmic illumination", not counting the contribution of the Sun, actually depends on where you are in the universe – although the variation will not be very large in the vicinity of the Solar system.

A small correction: that is not the *only* publication, albeit in non-refereed journals. There's an inordinate amount of mainstream media and popular culture publications that support this constant and Mr. Ahad's astrophysical theorem of the Sun's radiative zone of pre-eminence. They include the following on and (known) off-line publications: The Mathaba News Network (February 1st, 2007), The American Chronicle, The Daily Star, Writewords.org.uk, Whosreadit.Com, The Muslim Writers Society (July 30th, 2005), Muktadara.Net (Page 71 - "Notable Scientists"), The Luton Herald & Post (August 4th, 2005, p. 29), the Janomot (London: Sep 30-Oct 06, 2005, p. 19) and Bangla Mirror newspapers. From [2] —Preceding unsigned comment added by 217.36.214.12 (talk) 14:52, 18 August 2008 (UTC)