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In lugnet.general, Allan Bedford writes:
> > Allan Bedford <apotomeREMOVE-THIS@execulink.com> wrote:
> > > site (one for new browsers, one for old) you should ALWAYS design to the
> > > lowest common denominator. It's just plain rude not to. No, I really
>
> Matthew Miller <mattdm@mattdm.org> wrote in article
>
> > Greatest common denominator, probably.
> >
> > (You want to design for the highest level that people will have in common.
> > "Lowest common denominator" is meaningless.)
>
> <puzzled grin>
>
> I was expecting some contrary comments on my post, but wasn't really
> expecting a debate on semantics. :)
>
> Actually the expression "lowest common denominator" is used frequently when
> discussing how to make things appeal or be understood by a large number of
> people. You will often hear it in regards to television sitcoms that
> "cater to the lowest common denominator". In this case the expression is
> often meant as a derogatory one, in that the jokes are thought to be of a
> base level and not very intellectual. (Shows like 'Married With Children'
> are often accused of this.) By "catering to the lowest common denominator"
> you are often thought to be aiming at the greatest number of people who
> will understand your content, despite the fact that it may offend some, or
> be thought by others to be crude or vulgar.
I think the most accurate math term is actually the "greatest common
factor" or "greatest common divisor" (GCF or GCD for short), which refers to
the largest natural number which equally divides two whole numbers in
question. In non-math terms, the GCF between two objects is the maximal set
of overlapping or common traits.
The term "lowest common denominator" or "least common denominator" (or LCD
for short) refers on the other hand to the "least common multiple" (or LCM)
of the denominators of two fractions. For example, say you are asked to
compare the fractions 5/8 and 21/34. Your task is to replace the "?" below
with "=", "<", or ">". How do you do it without calculating the decimal
expansion of the two fractions?
5 21
--- ? ----
8 34
Well, first, you compute the LCM (least common multiple) of 8 and 34, which
is 136. Then, you rewrite each fraction so that the denominator is 136
(multiply the first fraction by 17/17 and the second one by 4/4):
85 84
----- ? -----
136 136
From there, you can readily see that 85/136 > 84/136. Hence 5/8 > 21/34.
Now back to the GCF (greatest common factor). If you have two numbers 231
and 294, and you're asked to compute the GCF of those two numbers, what is
the answer? It's the largest factor which is common to both 231 and 294.
What are the factors of 231? The prime factorization of 231 is 3 x 7 x 11,
so the factors of 231 are {1,3,7,11,21,33,77,231}. Similarly, the prime
factorization of 294 is 2 x 3 x 7^2, so the factors of 293 are
{1,2,3,6,7,14,21,42,49,98,147,294}. The largest factor which is common to
both 231 and 294 (in other words, the "GCF" of 231 and 294) is 21.
So GCF (not LCD) is really the term which best applies to situations in
which software is scaled back to accommodate the most users: You want to
strive for the "greatest common functionality" across situations.
However...(keep reading below :)
> [...]
> My understanding of the expression, and the way in which I meant it, was
> that you remove high level references or technologies from your
> presentation in order to allow the highest number of people possible to
> access or understand it. A site like Yahoo.com is a perfect example of
> this. Despite advances in web technology they have remained true to their
> original (and highly effective) design. And they are one of the busiest
> sites on the web.
>
> As far the expression being 'useless' I would have to disagree on that
> point. A quick string search on Altavista showed more than 10,000 web
> pages that use that expression. A similar search under the phrase
> "greatest common denominator" revealed less than 200.
The funny bit about all of this is that English has at least two meanings
for the term "common denominator." According to M-W, for example, the
phrase "common denominator" can mean "a common multiple of the denominators
of a number of fractions" and it can also mean "a common trait or theme."
When you throw the word "least" into the mix, the word bindings are a bit
ambiguous: does "least common denominator" mean the least-common (as in
most infrequent) denonimator, or does it mean the least (as in most
miniscule) denominator which is common? If it means the former, then
certainly www.yahoo.com is striving to serve the least common of all
denominators (e.g., themes or traits): plain-text, no frames, no font/link
color overriding, gracefully degrading tables, etc.
What Yahoo! is probably doing is serving the "greatest number of least-
common denominators" across situations, or, more accurately, the "union of
the set of all least-common denominators." Something like that.
Now what about "lowest"? M-W online defines "lowest common denominator" as:
1: least common denominator
2: something of small intellectual content designed to appeal to a
lowbrow audience; also : such an audience.
The 1961 dead-trees M-W defines "lowest common denominator" as:
1: the lowest common multiple of two or more denominators.
2: something (as a quality or level of taste) that typifies or is common,
acceptable, or comprehensible to all or the greatest possible number
of individuals. <the committee system...reduces all ideas to the
lowest common denominator --M.W.Straight> <broadcasting...falls into
the error of producing programs at the lowest common denominator
--Franklin Dunham> <living together in boredom, men exhibit their
lowest common denominator --Clement Greenberg> <the quest by...the
movies and radio for lowest common denominators --John Collier b.1884>
Looks like the non-math use of "lowest common denominator" goes back several
decades, at least. I don't have an OED handy to check if it goes back even
further. M-W online did say that "denominator" went back to at least the
late 16th Century.
Now, finally, an obLEGO to keep this post on-topic for lugnet.general:
the new JavaShockScriptWave www.lego.com website seems to have been designed
IMHO not for the GCF or the LCD but for the LCF (the least common factor) --
meaning that it wasn't designed to work well or at all on all systems, but
only to work well on a few systems. :-(
--Todd
[followups to lugnet.off-topic.geek]
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Message has 2 Replies:
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| (...) Matthew Miller <mattdm@mattdm.org> wrote in article (...) common. (...) <puzzled grin> I was expecting some contrary comments on my post, but wasn't really expecting a debate on semantics. :) Actually the expression "lowest common (...) (25 years ago, 17-Oct-99, to lugnet.general)
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