Wikipedia:Scientific peer review/E (mathematical constant)

E (mathematical constant)
I'm attempting to get this core article to GA status. I previously nominated it for GA status, and the article went through several dramatic changes before being (temporarily) failed for lack of stability. I'd like to get additional feedback and suggestions for the article before I renominate. Thank you. —Disavian (talk/contribs) 14:12, 21 June 2007 (UTC)
 * Some comments:
 * I have a slight issue with the first sentence, because it appears to be using circular reasoning for the definition. e is the base of the natural logarithm, but the natural logarithm is defined as a logarithm to the base e. That doesn't seem very informative to me. The image to the right of the lead does a better job, I think, so perhaps e could also be defined in terms of the exponential function within the lead?
 * Not circular, merely complicated. "Natural log" is the basic concept here; e, and bases, can be defined in terms of it. Septentrionalis PMAnderson 22:09, 21 June 2007 (UTC)
 * It might be helpful if the "compound-interest problem" section showed how the result extended to such real-world examples as population growth, the spread of disease, and radioactive decay.
 * A substantial portion of the text consists of mathematical formulae that may not be of general interest. But I'm not sure how that could be addressed.
 * There is some redundancy between the "Alternative characterizations" and "Representations of e" sub-sections. Should they be consolidated? &mdash; RJH (talk) 15:36, 21 June 2007 (UTC)
 * I hope this was somewhat helpful. Thanks. :-) &mdash; RJH (talk) 15:36, 21 June 2007 (UTC)

I have made comments below on two of the points. These certainly merit further discussion, so I have sectioned them off accordingly. Silly rabbit 16:39, 21 June 2007 (UTC)

Exponential growth and decay
All points are worth addressing, in my opinion. But allow me to zero in one the second bullet point for a moment. While it is certainly true that exponential functions play the fundamental role in all exponential growth and decay models, it is difficult to justify in general terms why one should use the peculiar base e. This is one reason for focusing on the probability applications rather than those manifestly involving exponential growth and decay: the number e arises quite naturally. It may be reasonable to include a mention of the applications of exponential functions (these are dealt with in other articles), but I would resist placing any emphasis on them here unless someone can come up with a convincing example why one would use e as the base rather than some other number. It's important to bear in mind that this article focuses on the number e rather than the function ex. Silly rabbit 16:39, 21 June 2007 (UTC)
 * But wouldn't e naturally arise as the necessary base of the solution to certain differential equations? (E.g. Radioactive_decay.) Especially since the article spends an entire section on e in calculus. &mdash; RJH (talk) 22:02, 21 June 2007 (UTC)
 * I see. Yes, certainly.  If we are allowed to pursue the differential equations route, this could easily be worked into the e in calculus section.  Silly rabbit 22:19, 21 June 2007 (UTC)
 * I started to bring in the radioactive decay timing example you suggested, but it did not seem to be popular with the other editors. Silly rabbit 16:22, 23 June 2007 (UTC)
 * No problem. These are only suggestions, after all. &mdash; RJH (talk) 18:06, 23 June 2007 (UTC)

Mathematical formulas
It's going to be hard to get rid of the mathematical formulas in the text. Already many formulas were moved to the Representations of e article. The trouble with e is that it is so intimately tied up with ideas of calculus, and to give a proper discussion seems to involve using formulas. There are levels of general interest to consider too. I doubt there is any way to make a compelling case for the number to someone who is unfamiliar with the basic ideas of differentiation, integration, and/or limits. The derangements example may come close, but that is mathematically sophisticated in other ways. Silly rabbit 16:39, 21 June 2007 (UTC)
 * Just to clarify, I don't have an issue with the presence of the formulae in the text. But they may deter some readers. So additional clarification may be needed. &mdash; RJH (talk) 22:04, 21 June 2007 (UTC)
 * Clarification is always good. But the equations should not be trimmed; this is an encyclopedia, not Richard Feynman's publisher, who told him that every equation would halve his sales. Septentrionalis PMAnderson 22:07, 21 June 2007 (UTC)
 * I concur with Septentrionalis' points there. —Disavian (talk/contribs) 01:01, 22 June 2007 (UTC)

Redundancy
With regard to the redundancy, I'm not sure how to tackle this problem. I would like to get rid of the two redundant representations of e, since these are already discussed at length during the preceding sections. However, that would leave only the continued fraction representation, and this gives a rather misleading impression to the reader about its relative importance. It may be appropriate to reassess the inclusion of a few select candidates from the Representations of e article. It would be nice if we could say why the selected representations are important as well. Silly rabbit 10:42, 23 June 2007 (UTC)
 * Perhaps then the article could give a mathematical representation of the software algorithm used to compute the digits e? (Presumably because it is the most efficient known means to compute said digits.) I think I would find that of interest. Thanks. &mdash; RJH (talk) 17:52, 24 June 2007 (UTC)
 * Yes, I thought that was a rather odd ommission as well, given that there is a big table of the number of digits computed. ;-) Silly rabbit 18:05, 24 June 2007 (UTC)