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Why language scholars shouldn't use maths/science
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Gerontius
The Shire


Aug 9 2011, 1:24pm

Post #1 of 47 (1546 views)
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Why language scholars shouldn't use maths/science Can't Post

Just been reading The Hobbit and this jumped out at me:

Chapter "Queer Lodgings", about two pages from end

"Don't stray off the track! - if you do, it is a thousand to one you will never find it again..."

Reminded me of a similarly bad error in Flowers for Algernon:

"Artificially-induced intelligence deteriorates at a rate of time directly proportional to the quantity of the increase."

So, who wants to explain the errors in those excerpts? Any more maths/science errors in Tolkien or other books?

Jeg


squire
Half-elven


Aug 9 2011, 2:37pm

Post #2 of 47 (935 views)
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Fuzzy language [In reply to] Can't Post

Statistics was never my strength, but I think you are arguing that the phrase
"Don't stray off the track! - if you do, it is a thousand to one you will never find it again..."
must be read as meaning that the odds as stated are very high that they will find the track again, rather than very low, because Gandalf says "a thousand to one" rather than "one in a thousand".

But the sentence is extremely clear: "you will never find it again" can only mean one thing, forcing Gandalf's odds-making into a state of compression whereby the word "against" is clearly understood to characterize which probability he is talking about:
"Don't stray off the track! - if you do, it is a thousand to one [against that] you will [n]ever find it again..."

Tolkien was not just a language scholar but a language scientist, a philologist well-versed in quantitative methods. To me, the sentence is clear both in its math and in its meaning. The only thing notable about it is that it accurately reproduces how people talk about statistical odds that they understand perfectly, not how mathematicians do.

I'm not as sure what you see wrong about the Algernon sentence, unless it is that
"Artificially-induced intelligence deteriorates at a rate of time directly proportional to the quantity of the increase."
seems to imply that the speaker is stating that a deterioration equals an increase. But if I remember the story, the statement is referring not to an increase simultaneous with a deterioration. The increase is the increase in intelligence achieved by the initial treatment. The deterioration follows later, as the treatment wears off. What is stated by correlating "increase" with "deterioration" is that the rate of subsequent deterioration is inversely proportional to the increase achieved in the first place. As above, I think the speaker has left out an understood word "initial", as in
"Artificially-induced intelligence deteriorates at a rate of time directly proportional to the quantity of the [initial] increase."
I apologize if I've misunderstood your criticism here. I think what's going on is that everyday language is more flexible or fuzzy than mathematical language is, and even scientists are guilty of informally using the linguistic tools of context and implication to convey scientific meaning colloquially.





squire online:
RR Discussions: The Valaquenta, A Shortcut to Mushrooms, and Of Herbs and Stewed Rabbit
Lights! Action! Discuss on the Movie board!: 'A Journey in the Dark'. and 'Designing The Two Towers'.
Footeramas: The 3rd (and NOW the 4th too!) TORn Reading Room LotR Discussion; and "Tolkien would have LOVED it!"
squiretalk introduces the J.R.R. Tolkien Encyclopedia: A Reader's Diary


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Gerontius
The Shire


Aug 9 2011, 3:17pm

Post #3 of 47 (932 views)
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You're trying too hard [In reply to] Can't Post

 
I think you're trying to defend the indefensible. You've recognised where the Tolkien quote is wrong, but not WHY it is wrong. Once you realise why it is wrong, you'll see that it is a clear error.

The defence that the meaning is clear is rarely a good defence.

By the way: a thousand to one and one in a thousand a essentially synonyms, so I'm not sure what you're getting at, there.

For the Algernon quote, you don't need knowledge of the story, although I appreciate that the meaning is vague out of context. Again, it's ultimately quite straightforward, but you've so far overlooked the actual error.

Hints

Tolkien's error can be expressed in two words: it's a ___ / ___.

The Algernon error takes just one word: it's a ___.


visualweasel
Rohan


Aug 9 2011, 4:05pm

Post #4 of 47 (869 views)
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Your point is ...? [In reply to] Can't Post

Let's set the alleged error aside for a moment. What are you really trying to achieve here? Many works of literature contain errors of a mathematical nature. So what? It goes without saying that most writers are not mathematicians. Does anybody out there really expect a work of fantasy literature to be free of errors? I think maybe your point is just: "Ha ha, look! I caught Tolkien in an error." Okay, let's grant you that — though I would side with squire if debating the point. But having granted it, so? Was that all you meant to say?

Jason Fisher
Lingwë - Musings of a Fish


The Lord of the Rings discussion 2007-2008 – The Two Towers – III.4 “Treebeard” – Part 1, 2, 3, 4, 5, 6
“On Fairy-stories” discussion 2008 – “Origins” – Part 1, 2, 3, 4, 5


Gerontius
The Shire


Aug 9 2011, 4:11pm

Post #5 of 47 (869 views)
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My point is... [In reply to] Can't Post

That ignorance should not be tolerated.

Clearly there are more people around than I expected who have something to learn about mathematics. And manners.


visualweasel
Rohan


Aug 9 2011, 5:20pm

Post #6 of 47 (851 views)
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That's not much of a point [In reply to] Can't Post


Quote
That ignorance should not be tolerated.



So I suppose you've sworn off Tolkien entirely, then, eh? Written him off as an intolerable bad job? I invited you to make a point about Tolkien (perhaps a bit brusquely), and this is your reply? What are you doing here if you don't actually want to discuss Tolkien? I'm not saying the Professor could do no wrong and should never be questioned, but one ought to have something constructive to conclude from a criticism. What's the point of a dismissive judgment like this? Oh, right, I forgot: "ignorance should not be tolerated". It's a thousand to one you'd get a better reponse maligning Tolkien in a mathematics forum somewhere. And that's all I have to say on this subject.

Jason Fisher
Lingwë - Musings of a Fish


The Lord of the Rings discussion 2007-2008 – The Two Towers – III.4 “Treebeard” – Part 1, 2, 3, 4, 5, 6
“On Fairy-stories” discussion 2008 – “Origins” – Part 1, 2, 3, 4, 5


Gerontius
The Shire


Aug 9 2011, 5:27pm

Post #7 of 47 (863 views)
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Fine [In reply to] Can't Post

If you think ignorance is an acceptable state of being, I'll leave you to wallow in it. Forgive me for thinking people might read these boards in the hope of occasionally expanding their knowledge.

Maybe squire or someone else still has a desire to learn.

And maybe authors should do some research when writing outside their comfort zone.


Darkstone
Immortal


Aug 9 2011, 6:41pm

Post #8 of 47 (968 views)
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Are they really mistakes of the authors? [In reply to] Can't Post

First of all I find it hard to believe Tolkien wrote anything he hadn't meant to write so he must have been fully aware of the meaning.

Tolkien loved to collect idioms and spring them on his friends so maybe it was a then current idiom of the sort that inverts the true meaning, like "I could care less" (originally "I couldn't care less") or "cheap at half the price" (originally "cheap at twice the price"). In any case, as squire points out, the context makes the intent clear.

Or maybe Gandalf was being logically sarcastic, such as "I should be so lucky!" (meaning "I have no hope of being so lucky”) or "Tell me about it!" (meaning “Don’t tell me about it, because I know all about it already”). Note that such sarcastic inversion is common in Yiddish culture, and Tolkien mentioned on at least two occasions that Jewish and Dwarvish cultures shared many similarities. Perhaps this sort of humorous inversion is one of them and so his "mistake" is actually him speaking to the Dwarves in (as Sir Launcelot would say) their own particular idiom?

Or maybe Tolkien was parodying the typical trope in pulp fiction that a one-in-a-million chance is a sure thing. That is, "if there's a million to one chance against something of vital importance happening in a story, then this is going to be that one time it actually happens rather than the other 999,999 times." So trope-wise Gandalf *is* correct in that if there are 999,999 chances out of a million that the Dwarves will find their way back to the path, this story is about the one-in-a-million chance they don't! (So this is a subtle tongue-in-cheek breaking of the fourth wall, like Bombadil's "Tell me, who are you alone, yourself and nameless?")

Or maybe Tolkien just wanted to show Gandalf wasn't perfect.

In any case, if it was a mistake, it wasn't Tolkien's, it was Gandalf's.


As for the Algernon-Gordon Effect, remember that Charlie Gordon posited it while his artificially-induced intellect was indeed rapidly deteriorating (and to a lower IQ than he started with to boot), so I'll forgive him any mistakes.

Again, as with The Hobbit, the mistake wan't author Daniel Keyes', but the character Charlie Gordon's.

Good question, though. And welcome back to the forums! You were missed!

******************************************
Brothers, sisters,
I was Elf once.
We danced together
Under the Two Trees.
We sang as the soft gold of Laurelin
And the bright silver of Telperion,
Brought forth the dawn of the world.
Then I was taken.

Brothers, sisters,
In my torment I kept faith,
And I waited.
But you never came.
And when I returned you drew sword,
And when I called your names you drew bow.
Was my Eldar beauty all,
And my soul nothing?

So be it.
I will return your hatred,
And I am hungry.


(This post was edited by Darkstone on Aug 9 2011, 6:43pm)


FarFromHome
Valinor


Aug 9 2011, 8:06pm

Post #9 of 47 (881 views)
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Maybe it's just a typo [In reply to] Can't Post

for "it's a thousand to one you will ever find it again."

There have always been lots of small typos and editing errors in Tolkien's work. This could be one of them. You're right that most people who aren't statisticians probably just skim right past this because what is meant is so obvious. But all it takes to fix is dropping a single 'n'. Maybe you should write to the editors, and wait to see if it's fixed in the next edition!

On the other hand, maybe Tolkien was only foreseeing the subtle thought processes of Terry Pratchett:

In the Discworld book Guards! Guards!, the characters note that saying "It's a million to one chance but it just might work" practically guarantees success.
  • Needless to say, this leads to the comic relief team engaging in a painstaking process of rebalancing their odds of success to be EXACTLY one in a million. By the time they're done, the archer who's supposed to hit the dragon's weak point as it flies overhead has been handicapped to truly amazing levels. He then misses, naturally.
    • He seems to only miss because they were aiming for the Dragon's Jewels, of which it had none.
    • Rather, he was aiming for the Vulnerable Spot, which all dragons (in some traditions) have, but missed because he got the balance of probability slightly off.
    • But their chances of hitting something soft on the fall were exactly a million to one chance...
  • In fact, it's a universal law in the Discworld that million-to-one chances crop up nine times out of ten.
  • That's because Discworld runs on the Theory of Narrative Causality, therefore million-to-one chances always succeed. The problem is to get them to be that difficult.
(From a page called NeverTellMeTheOdds Tongue)

They went in, and Sam shut the door.
But even as he did so, he heard suddenly,
deep and unstilled,
the sigh and murmur of the Sea upon the shores of Middle-earth.
From the unpublished Epilogue to the Lord of the Rings



Gerontius
The Shire


Aug 9 2011, 9:46pm

Post #10 of 47 (794 views)
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That explanation doesn't convince me [In reply to] Can't Post

Hey, DS


I had thought about that, although in no way near as much detail as you! But the reason it fails to convince me is this:

Simplified into colloquial English, gandalf is saying "you won't never find the path."

It's such a brazen and jarring double negative (this being the answer I was looking for) that I can't imagine it being intentional. It isn't merely being sarcastic as in several of the examples you give, but is directly self-contradictory.

Put another way, it goes beyond idiom into gutter talk, which seems very out of place amidst all the "at your service"s and other ultra-polite grammar.


Gerontius
The Shire


Aug 9 2011, 9:50pm

Post #11 of 47 (757 views)
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Haha! [In reply to] Can't Post

Enjoyed that.

As for editing errors, I'd expected someone would have checked their own editions by now to confirm! My edition is from the 60s and contains some typos, but this is a very convenient typo!


Gerontius
The Shire


Aug 9 2011, 9:54pm

Post #12 of 47 (796 views)
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PS [In reply to] Can't Post

In Flowers for Algernon, Charlie is at the height of his intellect when he completes his paper, so I'd be surprised if he'd have made such a tautology.


Phibbus
Rohan


Aug 9 2011, 10:22pm

Post #13 of 47 (806 views)
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Is it a tautology? [In reply to] Can't Post

I think I understand what you' mean... it's the same thing as saying "The train's speed is directly proportional to the distance it travels over time," correct?

But isn't the root of the problem actually the phrase "rate of time," itself? Unless we're talking about bodies moving relative to one another at near-light speeds, isn't "rate of time" meaningless?

Man is but an ass if he go about to expound this dream.


Darkstone
Immortal


Aug 9 2011, 10:52pm

Post #14 of 47 (833 views)
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"Ther nas no man no wher so vertuous!" [In reply to] Can't Post

I had thought about that, although in no way near as much detail as you! But the reason it fails to convince me is this:

Simplified into colloquial English, gandalf is saying "you won't never find the path."

It's such a brazen and jarring double negative (this being the answer I was looking for) that I can't imagine it being intentional. It isn't merely being sarcastic as in several of the examples you give, but is directly self-contradictory.

Put another way, it goes beyond idiom into gutter talk, which seems very out of place amidst all the "at your service"s and other ultra-polite grammar.


There are other times when Gandalf's manner becomes rather abrupt and gruff with the stiff-necked dwarves, so it doesn't seem out of place to me.

As for double negatives, I often use them myself when trying to make a point, even extending them into triple, quadruple, and even quintuple negatives. ("You won't never nohow, nowhere, not ever find the path!!")

Your idea of a double negative as being "gutter talk" is rather puzzling. Depending upon the culture a double negative may be negating, intensifying, or even obligatory.

Again, going back to the Dwarven/Jewish comparison, double negatives are found in the original Hebrew of the Bible, used for emphasis. Hardly gutter talk.

******************************************
Brothers, sisters,
I was Elf once.
We danced together
Under the Two Trees.
We sang as the soft gold of Laurelin
And the bright silver of Telperion,
Brought forth the dawn of the world.
Then I was taken.

Brothers, sisters,
In my torment I kept faith,
And I waited.
But you never came.
And when I returned you drew sword,
And when I called your names you drew bow.
Was my Eldar beauty all,
And my soul nothing?

So be it.
I will return your hatred,
And I am hungry.


(This post was edited by Darkstone on Aug 9 2011, 10:56pm)


Darkstone
Immortal


Aug 9 2011, 10:52pm

Post #15 of 47 (742 views)
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So he thinks. / [In reply to] Can't Post

 

******************************************
Brothers, sisters,
I was Elf once.
We danced together
Under the Two Trees.
We sang as the soft gold of Laurelin
And the bright silver of Telperion,
Brought forth the dawn of the world.
Then I was taken.

Brothers, sisters,
In my torment I kept faith,
And I waited.
But you never came.
And when I returned you drew sword,
And when I called your names you drew bow.
Was my Eldar beauty all,
And my soul nothing?

So be it.
I will return your hatred,
And I am hungry.


Gerontius
The Shire


Aug 9 2011, 10:55pm

Post #16 of 47 (793 views)
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That's it [In reply to] Can't Post

Although you don't seem to have quite realised that you've got it right.

Rate of time is the tautology since rate means "something per unit time". "Rate" by itself is sufficient or you're saying "per unit time of time".

It's like saying PIN number.

Or, using the speed example, speed is rate of travel, or travelling rate, not travelling rate of time.


Phibbus
Rohan


Aug 9 2011, 11:30pm

Post #17 of 47 (767 views)
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OK [In reply to] Can't Post

I had thought you were getting at something else. But now I'm going to ask what the author's actual intent was. I haven't read Flowers for Algernon since the eighth grade.

What I had thought you implied (and what I was trying to express in the train example) was that Charlie's rate of intellectual decline was great because the quantity of increase was great and hence was more marked than would have been that of someone whose brainpower had been boosted only a little over the same period of time. (Or, to use another example, like saying if you dropped an ant and an elephant off a tower, they would both hit at the same time, but the elephant would hit much harder.)

But the author actually is implying that Charlie's decline is rapid because they boosted his intelligence significantly—and that the loss would have occurred over a much longer period had they only boosted him to, say, mere average competence—correct?

And isn't Darkstone right? Don't we start to see other minor slips right around this point?

(A sad little OT anecdote: My mom has never been much of a reader. When I was assigned the story in eighth-grade English, she felt sorry for me because, she said, it was one of the things she had read that had depressed her enough to want to stop. Unimpressed)

Man is but an ass if he go about to expound this dream.


Pryderi
Rivendell

Aug 9 2011, 11:36pm

Post #18 of 47 (830 views)
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Well you will find me intolerable.... [In reply to] Can't Post

....because I am ignorant. In particular of Mathematics. (Please note the lack of verb there: Another sign of ignorance.) I obtained my first degree in Maths from Tolkien's Oxford University in 1971. It was then or shortly thereafter that, with great pride, I felt I had understood the extent of my own ignorance. I went on to gain two post graduate degrees in Maths during which time, sadly, I became ignorant once more of the extent of my own ignorance. I was specialising and the general Mathematical world was moving on. I have continued to study Maths all my life, partly for my work, and since my retirement for recreation.
My younger son recently graduated with a good Maths degree and it was interesting to see the courses he chose in "Non Linear Dynamics" and "Graph Theory" and such like. Things that were not on the syllabus in my day (note verb but no sentence, I'm incorrigible!). Sadly I was so ignorant that he had to explain them to me rather than the other way around.
Well I could continue in that vein but perhaps I should speak from the point of view of a Mathematician on your original point. We do not describe probabilities in terms of "odds". It makes life too complicated as you point out. Probabilities are numbers between nought and one, where one means certainty and nought means impossibility. So if the odds "on" a horse winning are 2-1 "against" I know to translate this as as a probability of 1/3 that the horse will win. If the odds are 2-1 "on" that is a probability of 2/3 that the horse will win. Tolkien is certainly guilty of of omitting to say whether his odds are "on" or "against" although, as Squire says, it is clear from the context that he means "on". I do not think that this sort of thing is either unusual or undesirable in literature.
"We thought we could live there together in fun/ But our chances really were a million to one." Bob Dylan's Dream. Here again the listener seems to know whether the odds were on or against, as the reader does with your quote from the Hobbit. Surely the point is that Mathematical language is supposed to be precise and concise, with great benefits for Mathematics. Natural language is neither intended nor suitable for Mathematics because it expresses meaning in a different way. It uses metaphor ( including oxymoron: "He looked so immaculately frightful") which would be totally out of place in Maths. I conclude that we should not judge the written word by Mathematical standards.
I will finish with a quote from the the Prologue to Chaucer's Canterbury Tales which will demonstrate that, despite my ignorance, I have no manners either.

"And Frensh she spak ful faire and fetisly,
After the scole of Stratford-Atte-Bowe,
For Frensh of Paris was to hir unknowe."

Pryderi.


Phibbus
Rohan


Aug 10 2011, 12:02am

Post #19 of 47 (785 views)
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Yay, more Chaucer [In reply to] Can't Post

How about...
A Clerk ther was of Oxenford also
that unto logyk hadde long ygo.
[…]
But al be that he was a philosophre,
Yet hadde he but litel gold in cofre.


Man is but an ass if he go about to expound this dream.


Pryderi
Rivendell

Aug 10 2011, 12:40am

Post #20 of 47 (853 views)
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The Clerk of Oxenford [In reply to] Can't Post

Two things spring to mind

One is "The Four Wise Clerks of Oxenford" who had defined (inappropriately) the blunderbuss that Farmer Giles used against the giant. Recently (2006) a gang of three "Wise Clerks", apparently the inheritors of Tolkien's Four, published "The Ring of Words: Tolkien and the Oxford English Dictionary". A case of gamekeeper turned poacher if ever there was one. Anyway I recommend it as a brilliant read to anyone who hasn't come across it.

The second: Don't you think that Ori, as illustrated in the recently published Hobbit Movie images, is going to be portrayed as a cross between Private Pike from Dad's Army and The Clerk of Oxenford? That's what I thought.

Thanks for responding, Pryderi.


Mixel
The Shire

Aug 10 2011, 2:24am

Post #21 of 47 (798 views)
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Nameless [In reply to] Can't Post

Why is "Tell me, who are you alone, yourself and nameless?" breaking the fourth wall?



Darkstone
Immortal


Aug 10 2011, 3:02am

Post #22 of 47 (835 views)
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Consider: [In reply to] Can't Post

“Don't you know my name yet? That's the only answer. Tell me, who are you alone, yourself and nameless? But you are young and I am old. Eldest, that's what I am. Mark my words, my friends: Tom was here before the river and the trees; Tom remembers the first raindrop and the first acorn. He made paths before the Big People, and saw the little People arriving. He was here before the Kings and the graves and the Barrow-wights. When the Elves passed westward, Tom was here already, before the seas were bent. He knew the dark under the stars when it was fearless - before the Dark Lord came from Outside.”

Who is the eldest in any story, the one who existed before *everything*?

Answer: The author.

And who is the youngest in any story?

Answer: The reader.

So "Tell me, who are you alone, yourself and nameless?" is Tolkien stopping the story for a moment and conducting a proper British introduction: "Hello, dear reader, sitting alone reading my book. I am pleased to meet you. My name is JRR Tolkien. And you are....?"

That is, he's breaking the fourth wall.

A wonderful "easter egg"!!

******************************************
Brothers, sisters,
I was Elf once.
We danced together
Under the Two Trees.
We sang as the soft gold of Laurelin
And the bright silver of Telperion,
Brought forth the dawn of the world.
Then I was taken.

Brothers, sisters,
In my torment I kept faith,
And I waited.
But you never came.
And when I returned you drew sword,
And when I called your names you drew bow.
Was my Eldar beauty all,
And my soul nothing?

So be it.
I will return your hatred,
And I am hungry.


Gerontius
The Shire


Aug 10 2011, 7:39am

Post #23 of 47 (769 views)
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In my experience [In reply to] Can't Post

Only scientists understand true ignorance. The key is to rail against it after accepting it, but to also have faith in those small parts you do understand.

As for "on" and "against", I was of the understanding that odds always meant against unless specified otherwise. It's the same with "rate", which means a time ratio unless otherwise specified. Of course, there is s chance this is a failure on my part... Wink


Gerontius
The Shire


Aug 10 2011, 7:59am

Post #24 of 47 (858 views)
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double negatives... [In reply to] Can't Post

I have always seen double negatives as the bastard child of good Lady English. Yes, seen culturally but not really accepted by the higher classes, and the hobbit, to me, reeks of the higher classes with it's gentle tone addressing a presumed intelligent reader.

To me, double negatives are more often used for comic effect than real literary emphasis. There are some rowan atkinson sketches that use it, although the only one I can recall now is him warning people to be purposelessnessless.

Other than that, perhaps if the dwarfs, singing of their lost gold, had burst into a refrain of 'aint no sunshine when she's gone, I'd be convinced. But it's not a writing form that I've seen anywhere else so it stands stark and alone.

The song reference brings me back to the bible. As with the lyrics if a singx the bible was "written" to sound good, at least some if the earlier books. As a collection of tribal stories told and retold by word of mouth before being put down on paper, the sound would be everything and double negatives, much like split infinitives, can sound good. But the bible should never be held up as an example of good grammar.

I'd be intrigued to know whether the double negatives made it into the KJV, or if the editors of that version felt they were inappropriate.

For flowers for Algernon, Charlie has several arcs. Physical, intellectual and emotional, all developing differently. I'm pretty sure the intellectual arc is at it's height at that moment, even if he's still struggling emotionally.


dernwyn
Forum Admin / Moderator


Aug 10 2011, 11:15am

Post #25 of 47 (762 views)
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So Tom is a Mary Sue? [In reply to] Can't Post

Well, that does explain the singing then, and why "Goldberry" (Edith) was always doing laundry...


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


"I desired dragons with a profound desire"

"It struck me last night that you might write a fearfully good romantic drama, with as much of the 'supernatural' as you cared to introduce. Have you ever thought of it?"
-Geoffrey B. Smith, letter to JRR Tolkien, 1915



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