# Talk:Lowest common denominator

Today's articles for improvement
This article was selected as Today's article for improvement on 3 June 2013 for a period of one week.
WikiProject Mathematics (Rated Start-class, Mid-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 Start Class
 Mid Importance
Field:  Basics

Needs more on usage applying to media. ReverendG 20:24, 23 June 2006 (UTC)

## Not math at all?

The article equates LCD with LCM. But a denominator is not the same thing as a multiple; in fact, they are opposite (or, more precisely, inverse). Has anyone ever heard this term in math? I have heard it only in colloquial conversation. (I think people really mean "greatest common denominator", but they substitute "least" because "greatest" sounds big.) So I propose that this article explicitly state that the concept is not mathematical at all, but a colloquial misuse of math jargon. Joshua Davis 21:09, 27 August 2006 (UTC)

I withdraw the above complaint! Somehow I did not notice the presence of fractions, which makes the concept quite meaningful indeed. Please ignore. Joshua Davis 03:35, 6 September 2006 (UTC)

I see no need to withdraw this complaint, which seems entirely correct to me in every way. Let me be the first to reinstate it. I am also annoyed that the entry under "greatest common denominator" says that it is a meaningless phrase! It is the correct phrase. ( Dr. John Krane ) —Preceding unsigned comment added by 65.112.82.28 (talk) 17:33, August 29, 2007 (UTC)

## Cleanup and stub tags

Feureau, you added a cleanup tag without explaining why on the talk page, and in this case I don't understand it. But I made some minor changes; is it cleaned up now? The grammar/spelling/writing are all fine; the concept is clearly defined, using simple language, and then examples are given, and then the greater social impact is even addressed. What's your issue?

And as for the stub tag: What do you think this article is missing? The LCD is not a large or complicated topic in math, so I don't see it having an article much longer than this. But perhaps I'm unimaginative. Joshua Davis 11:53, 5 December 2006 (UTC) punk — Preceding unsigned comment added by 112.198.234.185 (talk) 12:09, 15 August 2012 (UTC)

## Education reform

The source is Connected Mathematics 2nd edition, Bits and Pieces I. Is that sufficient as a source or do you need photocopies of the actual book? --Bachcell (talk) 23:03, 29 November 2007 (UTC)

Thank you for the source. For a proper citation of the source (so the general reader of Wikipedia's LCD article knows what book is being referred to, precisely) see Wikipedia:Citation templates. However, overriding a proper citation is the consideration that the LCD article is not the place to fight a cultural war about education reform or not. The LCD article should deal with the mathematical concept of LCD. The LCD concept is not central to education reform. (If I understand your position re. ER correctly, it seems that you should be interested first of all in a full explanantion of the LCD concept. Inserting the issue of ER only takes away from the explanation of the LCD concept.) Cheers. -- Iterator12n Talk 01:11, 30 November 2007 (UTC)

## Missing disambiguation page

I see there used to be a disambiguation page for this and it's gone away. I followed the link to the discussion of it going away and it said that I could leave follow-up comments on the discussion page for the topic, which I guess is here. My comment is simply this: There are other meanings of Lowest common denominator (or I prefer "least common denominator") that probably follow by analogy from the math definition but are social. Consider that in a pluralistic society if one group will not permit a certain kind of TV broadcast (or web page) and another group will not permit another, the result might accidentally be a publication policy that allows only the "least common denominator". Explaining my use of this term in context on a bit of writing I'm doing on the web in another venue is usually tedious and I would prefer to just use the term and hyperlink my use to a central explanation of the concept here at Wikipedia. But there is no mention here of such a usage. I would normally have considered adding an entry to the disambiguation page and starting a new article. I'd have to research the suffix, but I assume Lowest_common_denominator_(political) or some such thing. And then I'd imagine it would be linked through the disambiguation page. But given that the disambiguation page is deleted, I'm now in the awkward position of having to navigate both the mechanics and the politics of reinstating the page. I'm not up to that. I'm just a disappointed user who wishes this sort of thing were simpler to do. In sum, not all uses of this term are mathematical and there's no obvious place to acknowledge that fact. --Netsettler (talk) 08:49, 21 May 2009 (UTC)

## K-12 Balloons Standards

What is a K-12 Balloons Standard? I know K-12 (which should be a link), but I and google don't seem to know how balloons relate. DHR (talk) 15:26, 15 August 2010 (UTC)

"balloons standard" gets no relevant google hits, so I've commented out that paragraph until someone explains. Michael Hardy (talk) 17:25, 15 August 2010 (UTC)
Here it is, an old bit of vandalism. Michael Hardy (talk) 17:29, 15 August 2010 (UTC)

## Graphic glitches

I believe a contributor pasted something (the process to extract the minimum common denominator) into this article without caring about leading spaces. So it's better if somebody with better knowledge than me reviews it because it's still confusing.

--Kipitis (talk) 10:30, 23 August 2011 (UTC)

## Mod to section on non-mathematical usage

I'm a bit taken aback by Nohat's comment in the revision history (16 April 2012 04:25). I grant that I had not provided a source for the remarks. But "POV"? And "rant"?

As to POV, I am sometimes a bit daunted by the things that people wish to see documented with a source. I accept full well that those who are completely nonexpert in a field might have no other basis for confidence in an assertion. The difficulty is that some assertions—and the one at issue here is a good example—are nearly self-evident, in this case based on a combination of undergraduate mathematics and passing acquaintance with contemporary usage of American English. It happens that I am a research mathematician with significant competence in the fields of linguistics and anthropology. I make that point not to lord my credentials, but merely to illuminate my quandary: I have very often heard "lowest common denominator" used with exactly the non-mathematical sense that the article describes. And any undergraduate algebra text (as well as a fair number of middle-school math texts) will support the deleted assertion: it is a simple fact that the "popular sense of the term is not faithful to mathematical usage." And yet, because this particular point has nowhere been mentioned in the scholarly literature of math or linguistics, there is no published source to cite.

Now, as to whether the deleted passage qualifies as a rant, I'd have thought that a dispassionate reading would characterize it as both simply reasoned and entirely neutral. Indeed, it even pays respect to the technically incorrect usage by noting the possibility "that the word greatest strikes non-mathematicians' intuition as suggesting the lofty, rather than the base." One might argue that that is something of a conjecture, and this is true. But the reason I had included it is a rhetorical one: presenting that hypothesis allows explicit illumination of the distinctions between the term's popular and technical senses.

So, unless somebody replies with good reasons not to restore the deleted text, I intend to do so.—PaulTanenbaum (talk) 14:03, 10 May 2012 (UTC)

The objection to metaphorical use of "lowest common denominator" is a failure of imagination. It fails to recognize that in this common metaphorical usage, the metaphor is of things to fractions not of things to integers. For example, here is a quote from a letter to the editor in the Denver Post: "Obamacare, aka socialized medicine, has come to America. The effect will be to reduce us to the lowest common denominator. We'll all be the same." The big hint here is the use of the verb "reduce": one reduces fractions to a lowest common denominator, whereas one would *find* or *calculate* the lowest common denominator of a set of integers. I would have thought it obvious that in this metaphorical use, people are being compared to fractions and by "reducing us to the lowest common denominator" we are all being made the same, i.e. having the same denominator.
I removed the discussion about this usage being erroneous not only because it is an uncited claim, but also because it is just patently *wrong*. Nohat (talk) 14:55, 10 May 2012 (UTC)
Well, don't we have a difference of opinion! The lowest common denominator of 5/6 and 3/8 is "the twenty-fourth." But when we do to that pair of fractions what is colloquially called "reducing them to lowest common denomintor," we aren't changing their values at all, we are merely re-expressing the values (in this case as 20/24 and 9/24, respectively), in new forms that are equivalent to their (respective) original forms. Neither fraction (i.e, rational number) undergoes any reduction, but merely a recharacterization (into a mathematically equivalent form). The fractions—what you draw our attention to—are not, despite what you write, "all being made the same."
Now please consider the usage I was describing. For just one example of it, see | the article at Canada Free Press that includes the passage, "it is progressives who are the dedicated apostles of the 'lowest common denominator,' by which even the most minimal expectations of responsible or moral behavior must be kicked to the curb to accommodate the societal slugs among us." That quote is, exactly as I described in the passage you deleted, using the term in the sense of "debasing so low as to the level achieved by them all." But, again, the mathematical concept of "lowest common denominator" involves no such lessening of anything. The only changes involved are increases to denominators and to numerators. But a somewhat-related mathematical concept that does involve a reduction is, as I wrote, the greatest common divisor: the GCD of 6 and 8 (namely 2) is so low as the level achieved by them all (technically their infimum in the poset (Z, |)). So, where's the just patent *wrongness*?
And please note, the discussion you deleted does not, as you assert here, call the non-mathematical usage "erroneous." Instead, it describes it as "not faithful to mathematical usage."—PaulTanenbaum (talk) 19:00, 10 May 2012 (UTC)
The problem with discussions like this is that the metaphor will always break down if you analyze every detail of it. But metaphorical language has never rested upon perfect analogy, and so much of language is built on extending metaphors. The idea of reducing fractions to their lowest common denominator seems analogous enough to finding the simplest or minimal thing that some group has in common. However, like I said, if you can find some reliable source that criticizes this usage, then it might deserve mention here. Without that, however, it just sounds like original research language peeving. Nohat (talk) 20:35, 10 May 2012 (UTC)
Judging from what you write, Nohat, you are not seeing my point. Your last sentence describes the deleted passage as "peeving," and the sentence before it requests that I provide a "reliable source that criticizes this usage" [emphasis added]. All of that even though the final sentence in the comment to which you were responding pointed out explicitly that this is not a question of "erroneous," but merely of fidelity to mathematical usage.
The comment that seems to so rile you should not be interpreted as either endorsing or condemning the usage in non-technical contexts: it merely documents the popular usage and then discusses its variance from the technical usage. The intent is to help non-specialists step from their familiar (the term refers to lowering some threshold to the level of the least) to their novel (in math, the term refers to how to add or subtract fractions without introducing any unnecessary precision).
Indeed, prescriptive linguistics would be out of place here. It is true that "to the nth degree" does not strike mathematicians as superlative, and that "a quantum leap" is, for physicists, not a huge bound, but the tiniest possible nudge! But we in the technical disciplines do not hold title to language and should not aspire to legislate its usage outside the bounds of our technical bailiwicks.
So, if at this point there still remains some basis for your objection, please help me understand it so we might resolve the matter. Perhaps you think that the deleted passage's restoration could be tolerated if its neutrality were somehow further bolstered?—PaulTanenbaum (talk) 13:40, 14 May 2012 (UTC)
I still disagree that the removed commentary is even factually accurate. I would have thought that use of the word denominator would have made it plain that we're talking about fractions, not integers, and since fractions don't even have greatest common divisors, the suggestion to substitute them seems inappropriate. And as for the word "reduce", one "reduces" fractions to lowest terms—this is not "reduction" as in lowering the value, it is reduction (mathematics), where you take something that is not in some way minimal and simplify it. If you want to compare or perform some other operations on fractions with different denominators, you have to reduce them all to their lowest common denominator. I just don't understand at all how this reasonable-seeming metaphorical usage is so unfaithful to the mathematical concept that it warrants any discussion on the page. However, like I said, if you can find some reliable source that agrees with you that this is somehow an objectionable usage, I'd be willing to entertain discussing it here. Nohat (talk) 16:57, 21 May 2012 (UTC)
(1) What you write immediately above about reduction is getting precisely to my point! We agree that in the technical sense, "lowest common denominator" does not imply any lessening of value; but in colloquial usage, "lowest common denominator" often is chosen precisely to convey an idea of degradation (as illustrated by the cited example from Canada Free Press that I provided above). And that is one of the differences between the colloquial and the technical senses, which is all that the deleted passage is meant to convey.
(2) By the way, lowest common denominators are, a fortiori, denominators (of common fractions). And that makes them integers, not themselves fractions. Look at the article's lead. They are not fractions. They simply are not fractions. So when you argue that the operative metaphor is to fractions, you merely strengthen my case that that colloquial usage, based on a metaphor to fractions, can't coincide with the mathematical usage, which refers instead to integers.
(2) Now, for what may be the fourth or fifth time, I'll try to convey a point that I've not been able to get you to see. I've nowhere called the colloquial usage erroneous or worthy of criticism or "somehow objectionable." No, all I have said—and tried to clarify repeatedly to you that I said—is that it is not faithful to mathematical usage. Lowest common denominators (in arithmetic) are not debased, degraded, compromised, or despoiled. So when people use the term with any of those connotations, they are using it in a way that does not happen to be faithful to mathematical usage. Not wrongly. Not badly. Not evilly. Not meriting criticism. Merely in a way that is not faithful to mathematical usage. My previous posting (just above) went to length to disavow prescriptive linguistics, so please do not accuse me of pronouncing the colloquial usage "somehow an objectionable [one]."—PaulTanenbaum (talk) 20:55, 25 May 2012 (UTC)
I understand that sometimes writers stretch the analogy beyond your comfort level. However, I could charitably interpret pretty much any use for my own sense of "faithful" and at the same time one could uncharitably interpret every non-mathematical use as "unfaithful". I just don't see how you could define usage of a metaphor as "faithful to mathematical usage" in a neutral way that would be suitable for inclusion in an encyclopedia article. Nohat (talk) 22:08, 25 May 2012 (UTC)
OK, Nohat, first consider this. The technical usage of the verb accelerate (from physics) covers what happens if the driver of an automobile depresses either the gas pedal or the brake. But in its colloquial usage, accelerate is the antonym of the verb slow. If a passenger were to glance at a falling speedometer and remark, "Wow, you're braking so hard that my head nearly hit the dashboard. Your car can really accelerate!" then that speaker would be using the verb in a way that is faithful to mathematical usage and surprising to most speakers of English.
Next I'll come closer to your last remark by introducing a metaphor. Imagine a very simple biological species that reproduced sexually and with genetics exhibiting pure Mendelian inheritance. If an individual organism, O, of that species happened to be homozygous recessive for every trait, then one could muster a mathematical metaphor to label that organism (or perhaps its genome) "the identity element" of the species. I'd call this metaphor faithful to mathematical usage because there would exist a broad-based correspondence as follows:
 Biology Group Theory Organisms O and X Elements O and x of a group G O and X produce offspring Y Element O + x of G No matter X's genome, Y inherits it For all x, O + x = x
Of course, like every metaphor, this one would be imperfect. One reason is that such a species would not be "closed" under reproduction: indeed, for any organism Y of the same sex as O, it would be impossible for there to exist a C that was the child of O and Y. OK, big deal. So metaphor is a weaker concept than isomorphism, we already knew that. Anyway, given all of this, I do find the metaphor described here to be faithful to mathematical usage.
By contrast, imagine somebody, Joe, who was vaguely familiar with the term "identity element" but who no longer quite recalled its technical meaning. If Joe latched onto the word identity, then he might think, "I could use metaphor to apply the term 'identity element' to any organism O${\displaystyle \star }$ who was homozygous dominant for every trait." Recall that our friend O was homozygous recessive. Anyway, Joe might like his idea because O${\displaystyle \star }$ would have the property that no matter which other organism it mated with, the resulting offspring would inherit O${\displaystyle \star }$'s entire genome. So Joe might conclude, "Yes, 'identity element' would be a good metaphor for O${\displaystyle \star }$ because he always manages to pass along his genetic identity intact." Well, that would be an application of the term "identity element" that is not faithful to mathematical usage. Indeed, if one were judging only by fidelity to mathematical usage, then one might sooner choose to label O${\displaystyle \star }$ metaphorically an attractor. OK, we switch from group theory to dynamical systems theory, but the attractor metaphor might be particularly apt if the population genetics were such that O${\displaystyle \star }$'s alleles would come to replace all others; this is what population geneticists call fixation.
Now, finally, I'm not sure whether you were being literal above when you challenged me to produce a definition of metaphors' fidelity to mathematical usage. In any event, I hasten to say that I cannot offer any rigorous definition. But the fact that there cannot exist a definition of greatness of poets does not prevent encyclopedia articles from labeling Shakespeare the greatest writer in English literature.
Anyway, the whole reason the infamous deleted passage even mentions fidelity to mathematical usage is to help those readers of Wikipedia who, like Joe, might not grasp the meaning of a technical term at its deepest, richest level. Consider my accelerate example above. When explaining the physics concept, it can be very beneficial to discuss the differences in meaning between the technical and colloquial senses of the verb. People for whom slowing down can only be described as deceleration can find it mind-opening to consider that there might be good reason to speak of acceleration as sometimes being negative. No good physics teacher would chastise them for feeling that accelerate means "speed up." Indeed, most physics teachers probably use English the same way when they're not in the lecture hall but out driving their cars. My point is that although tidy, formal definitions of acceleration in terms of second derivatives do logically imply all that one might need to know about the concept, those formal definitions do not yield their full significance without a learner's investing significant thought. So it can be very helpful to compare and contrast for learners the formal and colloquial concepts, because that makes it easier for them to get the subtleties of the relationship between the two usages, and thus better understand the technical usage they're learning about. And that's a worthy goal for an encyclopedia article.—PaulTanenbaum (talk) 03:40, 27 May 2012 (UTC)

## Reliable, non-dictionary sources for the metaphorical meaning?

I removed the "Non-mathematlcal usage" section because it only described a figurative usage of the word and searching didn't turn up sources that covered it any serious way beyond documenting that the metaphorical usage exists. Since Wikipedia is not a dictionary, I removed it. A couple people added it back because the lead had a link to it. I'm thinking that rather than restore the section, we should remove the link. On the other hand, if there are some good sources about the non-mathematical kind of lowest common denominator, then I'd like to cover them well (perhaps in a separate article since it's really a separate topic). I did find this book, but it appears to be a self-indulgent rant rather than a reliable source of information. Does anyone know of any good sources? I can imagine that there might be. —Ben Kovitz (talk) 16:02, 11 August 2013 (UTC)

The least common denominator is when you use one of the denominators you are adding, the answer should be correct, the greatest common denominator, is not correct, and the greater it is, the further away it is from the truth, unless you take two further actions to correct the problem. I guess you can call it the top 1% that pays all the taxes, unless the top 1% is considering being charitable.173.62.160.246 (talk) 19:03, 8 September 2017 (UTC)Cite error: A `<ref>` tag is missing the closing `</ref>` (see the help page). </ref>a copy of a free will. Which wasn't so free after all.