Talk:Logarithm/GA1

GA Review

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Reviewer: SnottyWong ^gossip 23:21, 15 December 2010 (UTC)

I'm going to start reviewing this article. Should have some comments shortly. SnottyWong ^gossip 23:21, 15 December 2010 (UTC)

Copyedit check

Below are my initial comments on the text itself after reading the entire article, organized by section. The green text are quotes from the article. My comments on the other aspects of the article are below in the "Good Article Criteria" section.

Lead

• By the following formulas, logarithms reduce multiplication to addition and exponentiation to products: - Should "products" be changed to "multiplication"? Add wikilinks to multiplication, addition, and exponentiation.

• Done. Jakob.scholbach (talk) 00:21, 17 December 2010 (UTC)

• The first formula below the lead reads:

$\log _{b}(x\ y)=\log _{b}x+\log _{b}y,\,$

I'm not sure why there is a space between the x and the y, and it confuses the fact that x and y are being multiplied. Shouldn't this be:

$\log _{b}(xy)=\log _{b}x+\log _{b}y,\,$

• Inserted a dot to emphasize multiplication. Jakob.scholbach (talk) 00:21, 17 December 2010 (UTC)
• no need for a dot or space in a simple product like this.--JohnBlackburne^words_deeds 13:55, 18 December 2010 (UTC)

• The logarithm to base b = 10 is called common logarithm, - this should be the common logarithm, or a common logarithm. Missing the article.
  • Done. Jakob.scholbach (talk) 00:27, 17 December 2010 (UTC)
    • This now reads The common logarithm has base b = 10 and is most often used for calculation. What does that mean? Calculation of what? SnottyWong ^chat 17:12, 21 December 2010 (UTC)
      • I've clarified it: the previous formulation was confusing as, as far as I know, they are no longer used.--JohnBlackburne^words_deeds 17:24, 21 December 2010 (UTC)

I clarified it some more. I think it was unclear as stated. Dicklyon (talk) 22:01, 27 December 2010 (UTC)

• The invention of logarithms is due to John Napier in the early 17th century. This sentence is strangely worded. Also, are mathematical concepts really "invented"? Did someone "invent" addition? Perhaps "discovery" or "development" would be a better choice of wording here.

• Replaced by "development". Jakob.scholbach (talk) 00:21, 17 December 2010 (UTC)

It's better to stick to sources, and say he invented logarithms. He invented them as a computational aid; the mathematical function concept was developed later. Dicklyon (talk) 21:39, 27 December 2010 (UTC)

• Before calculators became available, via logarithm tables, logarithms were crucial to simplifying scientific calculations. If you take out the clause in the middle of this sentence, it reads "Before calculators became available, logarithms were crucial to simplifying scientific calculations." That makes no sense. What happened after calculators became available? Were logarithms any less crucial?

• hopefully fixed as part of general ce of last two paragraphs.--JohnBlackburne^words_deeds 13:55, 18 December 2010 (UTC)

• In addition to being a standard function used in various scientific formulas, logarithms appear in determining the complexity of algorithms and of fractals. "Appear" should probably be changed to "are used".

• OK. Jakob.scholbach (talk) 00:21, 17 December 2010 (UTC)

• The last two paragraphs of the lead are choppy and disjointed, and are difficult to read. Careful copyediting for cohesion would be beneficial here.

• I've copy-edited the last two paragraphs, rewriting maybe half the text and rearranging everything.--JohnBlackburne^words_deeds 13:55, 18 December 2010 (UTC)

Logarithm of positive real numbers

• For b = 2, for example, this means $\log _{2}(8)=3,\,$ - Shouldn't this read, "For b=2 and y=8, for example, this means..."
  • Sure. Jakob.scholbach (talk) 00:25, 17 December 2010 (UTC)

• Ways of calculating the logarithm are explained further down. - Could be less informal. Perhaps replace with something like "Methods of calculating the logarithm can be found in the Calculations section of this article."
  • OK. Jakob.scholbach (talk) 00:25, 17 December 2010 (UTC)

• The logarithm logb(y) is defined for any positive number y and any positive base b which is unequal to 1. These restrictions are explained below. This sentence could be deleted and simply explained in more detail in the appropriate section below. This section has a lot of links to other sections in the same article, which is odd. It's almost acting as a "second lead", directing the reader to various sections within the article. I don't think this is necessary or desired.
  • I removed one internal link. For the remaining one: I think we need to have up front the information what numbers the log is defined for. Otherwise it would just be incomplete and therefore partially wrong. However, justifying this is kind of less interesting for some readers and anyway seems to fit most naturally in the actual proof of well-definedness of the logs given in section 4.1. Jakob.scholbach (talk) 02:05, 19 December 2010 (UTC)
    • Agreed. SnottyWong ^chatter 17:12, 21 December 2010 (UTC)

• The name of this section isn't ideal. Being that it is the first section after the lead, I would name it something more general like "Overview" or "Overview of Logarithms". The section itself doesn't really mention anything about positive real numbers. The section as a whole also is a little bit on the WP:HOWTO side, although I think it's acceptable as is for now, and may even be a good thing for a technical article. This may need to be reviewed if the article is to progress to FA status.
  • Hm. In principle Overview is a nice name for a first section, but here it seems inappropriate to me, given that this section is just not an overview. I'm open to further suggestions, but I think we have to stick to section titles which do summarize the contents of the respective section. About HOWTO: having the examples is certainly a must for such an article, removing them would render the article useless for many readers. Jakob.scholbach (talk) 02:05, 19 December 2010 (UTC)
    • Agreed. SnottyWong ^chatter 17:12, 21 December 2010 (UTC)

Logarithmic identities

• The first is about the logarithm of a product, the second about logarithms of powers and the third involves logarithms with respect to different bases. - This sentence is entirely unnecessary and can be deleted.
  • OK. Jakob.scholbach (talk) 07:58, 17 December 2010 (UTC)
    • Rereading this section again, I noticed it starts out with an introductory sentence which says that there are three important formulas for logarithms, followed by four formulas. Are there three important formulas or four? It seems that the fourth formula (log of a root) is exactly the same as the third formula (log of an exponent), since a root is just reciprocal exponent. I'm going to attempt to fix this one myself, let me know if you have any problems with my fix. SnottyWong ^{spill the beans} 18:30, 21 December 2010 (UTC)
      • It's probably not a good idea to "fix" that. Most sources teach it this way (e.g. this book or this book); for people not familiar with a root being the same as a power, this is a way for them to see that. Dicklyon (talk) 20:04, 21 December 2010 (UTC)
        • Fair enough. Feel free to revert my changes if you like. However, either way, something needs to be fixed. Either the intro to the section needs to say that there are four important formulas, or one of the formulas needs to be deleted so that the statement that there are three important formulas is correct. Looking at Logarithmic identities#Using simpler operations, it looks like there are actually six important formulas? SnottyWong ^comment 20:51, 21 December 2010 (UTC)

• Subsection "Logarithm of product, quotient, power and root" could be more succinctly renamed to "Algebraic identities".
  • "Algebraic identities" is unspecific and tells little to people not knowing the notion of algebra, so I prefer keeping the current title. Jakob.scholbach (talk) 07:58, 17 December 2010 (UTC)

• The following formula relates the logarithm of a fixed number x to one base in terms of the one to another base: - This sentence is strangely worded and not entirely comprehensible.
  • Reworded. Jakob.scholbach (talk) 07:58, 17 December 2010 (UTC)

• As a practical consequence, logarithms with respect to any base k can be calculated with a calculator, when logarithms to any base b (often b = 10 or b = e) are available: - I understand what this sentence means because I am familiar with logarithms, but I fear someone who is not familiar will not understand. I think this sentence needs to make it clear that it is talking about situation when a certain base is not available on a calculator. Possible rewording could be: "As a practical consequence, logarithms to any base can be calculated with a calculator, even if the logarithm function to that base is not available on the calculator. For instance, to calculate a logarithm to base k with a calculator which can only calculate logarithms to base b:"

$\log _{k}x={\frac {\log _{b}x}{\log _{b}k}}.\,$

• • Reworked. Jakob.scholbach (talk) 07:58, 17 December 2010 (UTC)

• In the two formulas under the subheading of "Change of base", the first formula is solving for the logarithm of base b, and the second formula is solving for a logarithm of base k. For consistency, the left side of the equation should always be solving for the logarithm of base b, or else things get confusing.
  • Right. Jakob.scholbach (talk) 07:58, 17 December 2010 (UTC)

Particular bases

• Given a number n and its logarithm log_b(n), the base b can be determined by the following formula:

$b=n^{\frac {1}{\log _{b}(n)}}.$

This follows from the change-of-base formula above. - I'm unsure why this statement and formula appears in this section, and what relevance it has to the table below it.

• • Moved up to base-change and reworded. Jakob.scholbach (talk) 08:06, 17 December 2010 (UTC)

• Within the table, the parenthetical statement: (in mathematics and many programming languages including C, Java, Haskell, and BASIC) is making middle column of the table very wide. Perhaps the statement could be limited to "(in mathematics and many programming languages)", or it could be wrapped onto another line, moved to a footnote, or moved to the "Used in" column.
  • OK, now in a footnote. Jakob.scholbach (talk) 08:06, 17 December 2010 (UTC)

• Within the table, we have the parenthetical statement (see decibel and see below), again directing us to another section in the article. This should be shortened to "(see Decibel)".
  • Why? (This is a general point where we seem to disagree...) Jakob.scholbach (talk) 01:58, 19 December 2010 (UTC)
    • This may just be a personal preference of mine. I took a quick look through the MOS but couldn't find a passage which discourages (or encourages) the frequent use of section links. I guess I don't find them helpful. Just saying "see below" doesn't direct the reader to any specific area of the article, and therefore isn't helpful. All it's saying is "if you're confused, keep reading and your questions might be answered later." Linking to a section is a bit more helpful, but if anyone ever changes the section name, the link will be broken (and the person who changed the section name will have no way of knowing that they broke a link). I'm ok with the reference to the decibel section, but I still don't see the need or use of "see below".

Analytic properties

• The following discussion of logarithms uses the notion of function. In a nutshell, a function is a datum that assigns to a given number another number. The first one is called variable to emphasize the idea that it can take different values. - A couple of things. First of all, any reader that has made it this far in the article probably knows what a function is already. If they don't, they're probably not going to understand the rest of the article. Second of all, the definition given for a function is extremely confusing. I understand the concept of a function but if I were explaining it to my grandmother, I wouldn't say that it is a datum that assigns to a given number another number. I think this entire statement should be removed.
  • I disagree with your first statement. Logarithms can and usually are defined at middle/high school level as we do it in the first section. The notion of function is typically introduced later in the curriculum. This group of readers will benefit from a careful introduction of the concepts. The same holds true for continuity and differentiability. This is why I gave a short explanation of these notions and I would not want to remove them just because we have of course more detailed articles. Continuous function, e.g. welcomes the reader with a cleanup tag, a choppy lead and an equally choppy main article. I fail to see how the log. article becomes better by removing the respective explanations.
  • OK, so how would you explain it to your grandmother? Jakob.scholbach (talk) 08:35, 17 December 2010 (UTC)
    • That's a tough (maybe impossible) concept to explain to your grandmother in one or two sentences. That's why I would favor linking to Function (mathematics), and if someone is truly unfamiliar with what a function is, they can learn there. If we're assuming our reader does not know what a function is, I don't think it's possible to sufficiently explain the concept to them in one or two sentences. The first two sentences of Function (mathematics) are a good start though: "The mathematical concept of a function expresses the intuitive idea that one quantity (the argument of the function, also known as the input) completely determines another quantity (the value, or the output). A function assigns exactly one value to each input of a specified type." SnottyWong ^babble 19:50, 21 December 2010 (UTC)
• The expression logb(x) depends on both the base b and on x. The base b is usually regarded as fixed. Therefore the logarithm only depends on the variable x, a positive real number. Assigning to x its logarithm logb(x) therefore is a function. It is called logarithm function or logarithmic function or even just logarithm. - This is probably the third time in this article that the logarithm has been defined at a very basic level. I really don't think any of this is necessary at this point, and the wording is very choppy and disjointed. I would suggest deleting it and rewording the following sentence to say "Logarithms can be defined indirectly by means of the exponential function..."
  • This is now reorganized. Please check again. Jakob.scholbach (talk) 01:07, 19 December 2010 (UTC)

• A function is continuous if it does not "jump", that is, if its graph can be drawn without lifting the pen. - This information can be found at Continuous function, which is why you linked to it in the previous sentence. Delete this sentence.
  • I disagree, see above. Jakob.scholbach (talk) 08:35, 17 December 2010 (UTC)

• Moreover, it takes arbitrarily big and arbitrarily small positive values, so that any number y can be boxed by y0 and y1 which are values of the function f. - I'm unfamiliar with the term "boxed" in this context. This term should either be changed to something more common, defined more clearly, or linked to an article which defines it more clearly.
  • Reworked. Jakob.scholbach (talk) 08:35, 17 December 2010 (UTC)

• Roughly speaking, a differentiable function is one whose graph has no sharp "corners". - This information can be found at Differentiable function, which is why you linked to it in the previous sentence. Delete this sentence.
  • I disagree, see above. Jakob.scholbach (talk) 08:35, 17 December 2010 (UTC)

• This can be derived from the definition as the inverse function of ex, using the chain rule. - Grammar is not making sense in this sentence. Do you mean "the definition of"?
  • Simplified the sentence structure. Jakob.scholbach (talk) 01:07, 19 December 2010 (UTC)

• Since this section discusses logarithms with respect to calculus, would it not be relevant to also have some discussion of the derivatives/integrals of logarithms to bases other than e? Why is this section strictly limited to natural logs?
  • It does mention it at the end of the section. More detailed formulas are found at the (linked) article List of integrals of logarithmic functions. I think these variants are not important enough to justify separate treatment here. Jakob.scholbach (talk) 01:07, 19 December 2010 (UTC)

• The figure with caption "A visual proof of the product formula of the natural logarithm." is messing up the formatting of the page because it is center-justified. This should probably be right-justified.
  • How exactly is it messing up the layout? It looks rather nice for me and I put it this way because the image is very large, so if it would be right-centered the remaining space for text would be unusually small. However, if you prefer, feel free to change it. Jakob.scholbach (talk) 01:07, 19 December 2010 (UTC)

• This relation is used in the performance analysis of algorithms such as quicksort, see below. - No need for the "see below".
  • Why not? Jakob.scholbach (talk) 01:07, 19 December 2010 (UTC)

Calculation

• One method uses power series, that is to say a sequence of polynomials whose values get arbitrarily close to the exact value of the logarithm. - Missing an article. Should be "One method uses the power series", or "..a power series".
  • Was actually supposed to be plural. Tweaked. Jakob.scholbach (talk) 09:05, 17 December 2010 (UTC)

• Finally, based on quick ways to calculate exponentials e^y, the natural logarithm of x, that is the solution a to e^a - x = 0 can also efficiently be calculated using Newton's method. Not fully understanding this sentence. I think there are too many clauses.
  • Trimmed. Jakob.scholbach (talk) 09:05, 17 December 2010 (UTC)

• While in some cases—such as log₁₀(10.000) = 4—logarithms can be easy to compute... - The long dashes here are confusing. Also, per WP:MOSNUM, the period should be a comma, i.e. it should be log₁₀(10,000) = 4.
  • OK. Jakob.scholbach (talk) 09:05, 17 December 2010 (UTC)

• ...they generally take less simple values: by the Gelfond–Schneider theorem, given two algebraic numbers a and b such as ${\sqrt[{3}]{2}}$ or ${\sqrt {-5+{\sqrt {3/13}}}}$, the ratio γ = ln(a) / ln(b) is either a rational number p / q (in which case a^q = b^p) or transcendental. - I'm not understanding this sentence at all. What does the cube root of 2 or the long radical have to do with anything? The sentence started out describing how some logarithms are easy to calculate, and ended by saying that the ratio of two natural logarithms is either rational or transcendental. This seems like a lot of random information crammed into one sentence, and there is no discernible relationship between the information.
  • Tried to improve this. Please double-check. Jakob.scholbach (talk) 00:45, 19 December 2010 (UTC)

• Here M denotes the arithmetic-geometric mean and m is chosen so that s = x / 2^m is bigger than 2^(p/2). - Not understanding this. We have to choose m such that an equation is bigger than 2^(p/2)? What has to be bigger than 2^(p/2)? s? m? It doesn't make sense to say that an entire equation needs to be "bigger" than a particular value. This needs to be clarified.
  • Reorganized. Jakob.scholbach (talk) 00:44, 17 December 2010 (UTC)

• The constants π and ln(2) can be calculated with particular series. Which series? Is it even necessary to mention this?
  • Well, there are tons of series calculating pi. I tried a rewording to make it better. Jakob.scholbach (talk) 09:05, 17 December 2010 (UTC)

• The formula goes back to Gauss. Unencyclopedic sentence. Remove or modify.
  • Reworded. Jakob.scholbach (talk) 00:44, 17 December 2010 (UTC)

Complex logarithm

• Consequently, if φ is the principal argument Arg(z), the number number - Typo. "Number" appears twice unnecessarily.
  • Goodness. Now fixed. Jakob.scholbach (talk) 09:09, 17 December 2010 (UTC)

• Accordingly, a is called complex logarithm of z. - Missing an article. "...a is called the complex logarithm of z."
  • Done. Jakob.scholbach (talk) 09:09, 17 December 2010 (UTC)

• If n = 0, a is called principal value of the logarithm, denoted Log(z). - Missing article.
  • Done. Jakob.scholbach (talk) 09:09, 17 December 2010 (UTC)

• ...hence the principal logarithm of such a number is a real number and equals the natural logarithm as defined above. - The word "above" has a link which goes to a non-existent section of this article. The link should probably be removed (as should the text "as defined above") rather than correcting the link.
  • OK, removed. Jakob.scholbach (talk) 00:26, 18 December 2010 (UTC)

• In contrast to the real case, analogous formula for principal values of logarithm of products and powers for complex numbers do in general not hold. - A bizarre sentence. Obvious number agreement problems and missing articles. Also, "do in general not hold" is a wikilink to Exponentiation. I don't understand the significance of that link, and exponentiation has been linked already (probably several times) in the article, so the link should be removed (and, if appropriate, the significance of exponentiation with regard to this statement could be elaborated upon in prose).
  • I don't see the point in removing the link. It links specifically at the section of Exponentiation explaining this. You are right that the material of the linked section might also be put to complex logarithm, but currently it is not and at this point I'm not up to reorganizing the exp. and cx. log. articles. Jakob.scholbach (talk) 00:26, 18 December 2010 (UTC)

• In general, this section is very well-worded (especially the top two-thirds of it) and should serve as a model for how the other technical sections of this article should appear.

Uses and occurences

• I.e., the amount of hard disk space on a computer grows logarithmically as a function of the size of the number to store. Didn't quite understand this example. Hard disk space increases as a function of the size of a stored number? Needs clarification.
  • Reworded. Jakob.scholbach (talk) 00:41, 18 December 2010 (UTC)

• For any given number x, the number of prime numbers less than or equal to x is denoted π(x). - Using the word "number" a lot here. Might be better to change this to "For any given number x, the quantity of prime numbers..."
  • OK. Jakob.scholbach (talk) 00:41, 18 December 2010 (UTC)

• Logarithms appear in the encoding of musical tones. - "Encoding" is a strange choice of word. Musical tones are not encoded. Maybe change "encoding" to "frequencies".
  • Reworded. Jakob.scholbach (talk) 00:41, 18 December 2010 (UTC)

• ...the interval between two notes in semitones is the base-21/12 logarithm of the frequency ratio. - Strange wording. Should be "...the interval between two semitones is..."
  • Semitones is the unit of the measurement so to say. Like "the height of the tree in yards is ...". I currently don't find a better wording for this. Jakob.scholbach (talk) 00:41, 18 December 2010 (UTC)
  • This is now reworked. Jakob.scholbach (talk) 11:10, 19 December 2010 (UTC)

Related notions

• The logarithm of a matrix is the inverse function of the matrix exponential. This lone sentence should at least have a minimal explanation accompanying it about what relevance this has, why it is important, and/or how this is used in mathematics.
  • It is now restructured so as to make it more smooth. Jakob.scholbach (talk) 01:01, 18 December 2010 (UTC)

History

• Napier first called L "artificial number"... - Missing an article. Napier first called L the artificial number, or an artificial number?
  • OK. Jakob.scholbach (talk) 01:56, 19 December 2010 (UTC)

• The calculation of products using logarithms stakes on the following formula: - "Stakes" is a strange verb to use here. Do you mean "depends"? Or maybe replace "stakes on" with "requires"? Some rewording is required here. It's also very unclear what this whole section (starting from this sentence down to the sentence that starts with "For different needs") has to do with the history of logarithms.
  • I tried to make it clear that log tables are an historical application/tool of logs, which is why I think they belong here (as opposed to "Uses and occurrences"). Jakob.scholbach (talk) 01:56, 19 December 2010 (UTC)

• Why is the history section at the bottom of the article? Traditionally, the history section comes right after the lead, and it would seem more appropriate in that location. Is there a particular reason that is not the case, or did it just end up that way? The overall order of the sections in the article should be re-evaluated as well. I would vote for History, then Uses & Occurences, and then all of the more technical sections after that.
  • I don't think it should come immediately after the lead, because at this point we don't even know what logs are. Also, the formulas used in the history section come up in section 2, so history is bound to appear after that. The only other place I could imagine for history is Related notions. I don't have a strong feeling about switching these two sections, but since history seems to round off the article, I slightly prefer it at the very end. For similar reasons, I would oppose moving Uses and Occurrences too far up. We have to give the reader a chance of understanding the notation etc. used there by putting the sections introducing them before. Jakob.scholbach (talk) 01:56, 19 December 2010 (UTC)
    • Fair enough. Again, this is probably just a personal preference of mine. I see some of the other technical math articles do put the history at the end, so there may be a precedent for this. SnottyWong ^speak 20:39, 21 December 2010 (UTC)

Good Article Criteria

I will evaluate the article based on the good article criteria listed at WP:GACR and list the results below:

GA review (see here for criteria)

1. It is reasonably well written.

   a (prose): b (MoS for lead, layout, word choice, fiction, and lists):

   There are numerous grammar problems, and some MOS problems, as noted in the detailed comments above. Overall, the article does not read well, consecutive sentences often don't have a relation to each other, some topics are discussed multiple times in the article, etc.

2. It is factually accurate and verifiable.

   a (references): b (citations to reliable sources): c (OR):

3. It is broad in its coverage.

   a (major aspects): b (focused):

   Article does occasionally stray into the territory of unnecessary detail, but not egregiously so.

4. It follows the neutral point of view policy.

   Fair representation without bias:

5. It is stable.

   No edit wars, etc.:

6. It is illustrated by images, where possible and appropriate.

   a (images are tagged and non-free images have fair use rationales): b (appropriate use with suitable captions):

   The article has quite a lot of images, some would say too many. The overall formatting of the images is not consistent throughout the article, resulting in a messy look. It would be worthwhile to evaluate the images in this article and delete the unnecessary ones.

7. Overall:

   Pass/Fail:

   This is a vital article on a very important subject in mathematics, and it's coming along nicely. However, it is not yet up to GA standards. The majority of the problems have to do with copyediting (as evidenced by the volume of specific comments above), however there are some other problems with the structure and content of the article. The article still needs major work, so I don't see any value in putting the GA nomination on hold. I'd encourage you to overhaul the article using some of the suggestions above, and then nominate the article again. Feel free to contact me on my talk page with any questions. Thanks. SnottyWong ^express 20:52, 16 December 2010 (UTC)

Thanks, Snottywong for the review! All detailed points above have been dealt with (most of them by following your suggestions). An entire overhaul with respect to wording, cohesion etc. of the article will follow. I have also reevaluated the pictures and removed two of them. I'm kind of disagreeing with your point that internal links should be avoided, either by simply removing them or by organising the article such that they become unnecessary. The former just removes a useful bit of information which to keep comes at virtually no cost. The latter: for a broad topic like this, the knowledge about it usually does not come linearly, i.e. a implies b implies c etc. On the contrary, facts are often (historically or factually) intertwined with each other, and I don't see the point in flattening this ontology just for its own sake. That said, I'm happy to consider more specific suggestions how to reorganize the article. Currently, though, I fail to see what major work on the content and structure of the article is needed, so I'd appreciate more specific feedback about this. Thanks again, Jakob.scholbach (talk) 02:16, 19 December 2010 (UTC)

Thanks for addressing my comments above. I stopped my review at the copyediting problems, because there were so many of them and I wasn't sure if anyone was even going to address those comments. I think you have addressed most of the points I brought up satisfactorily, however the article still has some ways to go before it will pass as a GA. Here are a couple of larger issues to address with the article before renominating it:

• There are likely some copyediting issues that I've missed. I was going to recommend you list the article at WP:GOCE/REQ, but it appears you've already done that, which is great.
• Wikipedia articles are written by multiple editors, often with little or no coordination between them. The result often becomes a mish-mash of topics with poor cohesion or a "basket of sentences" that have little or no relation to one another, and no logical transition from one to the next. Now that you've gotten all or most of the small copyedit problems (i.e. single-word or single-sentence problems) corrected, it's time to look at the bigger picture. I think that what this article needs is a "meta-copyedit", a process which will rearrange and modify the material in the article such that it reads like it was written by one person. Information needs to be presented in a logical order, with transitions between different subjects. Random interjections of information need to be woven into the article so that they are no longer random interjections.
• The History section in particular needs a lot of work. Use articles like Integral#History and Calculus#History as examples of how this section should be structured. The History section needs to read like a narrative, telling the story of the logarithm from its origin to present times, with a strong sense of the chronology. The section currently is riddled with formulas and equations and various overly-specific trivia like the derivation of how Napier calculated 10⁷(1 − 10⁻⁷)^L, etc. The section also has several one sentence paragraphs that have no relation to the other material (i.e. the random interjections mentioned above), and are not woven into a narrative about the history of the logarithm. For instance, The work of Cavalieri (Italy), Wingate (France), Fengzuo (China), and Kepler's Chilias logarithmorum (Germany) helped spread the concept further. This sentence should be expanded into multiple paragraphs, showing specifically how their work helped spread the concept further. Overall, the section starts off well, talking about the origin of the logarithms with Virasena in the 8th century, but then jumps to 1544 (nothing happened in between?), then jumps to John Napier and gets into an overly specific description of his work, and then we lose a sense of time altogether and start talking about log tables and slide rules.

—SnottyWong ^chatter 20:33, 21 December 2010 (UTC)

From studying the historical references, it seems that the history of logarithms is by and large incomparable to the one of, say, calculus. Basically, logarithms appeared "over night" (or, after Napier calculating them for 20 years). There is not so much to tell. In particular, no reference notes anything between the "precursors" (most don't even mention them) and Napier/Bürgi. Also, the influence of the four mathematicians your quote refers to is barely mentioned in the books, so I don't know how to write a whole section about this. I'll think about a more historically engaging way of telling the stuff that is to be told, but we can't just invent things. The more I think about it, the more I'm convinced that your expectations in this respect are neither part of GA criteria and nor satisfiable independently of the criteria. Jakob.scholbach (talk) 21:08, 26 December 2010 (UTC)

I disagree. The GA criteria require (among other things) that an article be written in a clear and concise manner, with cohesive paragraphs, and without spelling and grammar errors. It also requires that the article is broad in its coverage, addressing all of the important points without straying into unnecessary details. I believe that portions of this article continue to fail these criteria, per my comments above. You may have a point that there isn't much more of a story to tell in the history section; I don't pretend to have studied the sources in great enough detail to argue. However, I still believe that what story there is to tell must be told better. Excessive derivations and equations don't have a place in the history section of the article, in my opinion. I think we've made a good amount of progress in this process, and there is still some to go. I would encourage you to continue making improvements, and the renominate for GA. If you believe the article currently satisfies the GA criteria and you disagree with my assessment, you may also apply for reassessment. SnottyWong ^{spill the beans} 18:56, 27 December 2010 (UTC)