Wednesday 10 August 2016

'Thirty' white horses on a red hill? The insoluble riddle

In The Hobbit chapter Riddles in the dark, Bilbo asks Gollum the riddle

Thirty white horses on a red hill, 
First they champ, 
Then they stamp, 
Then they stand still.

But people have thirty-two teeth, assuming there is a full set - and not 'thirty'!

Indeed, it would be unlikely to have thirty teeth, since the number is not divisible by four, which means that two of the teeth would (presumably, if the upper and lower jaws have the same kind of teeth) be unopposed and bite onto gum.

Interestingly, this error was missed in The Annotated Hobbit by Douglas A Anderson (2002). although I noticed, and was puzzled by, it decades ago (and plenty of other people on the internet have noticed the discrepancy).

Therefore, the riddle is - strictly, insoluble - unless we allow for congenital abnormality, dental surgery, or traumatic loss (of lesser severity than that which led to Gollum having 'only six' teeth)...

Note: I should clarify that Tolkien didn't invent this riddle - which is 'traditional'; as are most of theother riddles in this chapter.


Craig said...

Indeed, my youngest sister is having a couple teeth pulled before her birthday because they are unopposed.

Bruce Charlton said...

@Craig - But maybe Hobbits have an extra molar on just the lower jaws, to oppose the two upper pre-molars - or something...

But I imagine that Hobbits need all the teeth thay can fit-in...

Karl said...

Forward, the Light Brigade!
Was there a man dismayed?
Not though the soldier knew
   Someone had blundered.
   Theirs not to make reply,
   Theirs not to reason why,
   Theirs but to do and die.
   Into the valley of Death
   Rode the six hundred and seven.

(Russell's report in The Times recorded that just short of 200 men were sick or for other reasons left behind in camp on the day, leaving "607 sabres" to take part in the charge.)

Samson J. said...

Rode the six hundred and seven.

(Russell's report in The Times recorded that just short of 200 men were sick or for other reasons left behind in camp on the day, leaving "607 sabres" to take part in the charge.)

Ha, ha, good find. Exactly - it's clearly poetic license, to make the verse flow better, nothing more. (I HATE it when people nitpick stuff like this!)

It's worth noting that the bible itself frequently employs this sort of "rounding-off". As anthropologists observe, in many ancient cultures they simply didn't care about being strictly accurate about these things; ergo, just about any number you come across in the bible is going to be somewhat open to interpretation. Did Jesus really feed exactly five thousand people? Was there really a remnant of exactly seven thousand who hadn't bowed the knee to Baal?

(And hence the JWs who think precisely 144,000 people are going to heaven are off the mark...)

Bruce Charlton said...

@Karl and SJ - OK guys, point taken -- but this is not poetic license - it's a riddle! More like a crossword puzzle clue than a poem.

Thirty two horses on a red hill,
White and champing -
Then they stamp -
And then they stand still.

See, even I can make it scan AND be accurate!

Karl said...

You have inspired me to review my favorite verse collections for accuracy.

Housman's Shropshire lad knows the price of a knife. He knows the difference between one-and-twenty and two-and-twenty. And at Eastertide, when he sets out to calculate his future life expectancy, his arithmetic is quite correct:

Loveliest of trees, the cherry now
Is hung with bloom along the bough,
And stands about the woodland ride
Wearing white for Eastertide.

Now, of my threescore years and ten,
Twenty will not come again,
And take from seventy springs a score,
It only leaves me fifty more.

And since to look at things in bloom
Fifty springs are little room,
About the woodlands I will go
To see the cherry hung with snow.

But of course modern improvements have made the seventy-year estimate of life expectancy obsolete, and even apart from that, the calculation is actuarially unsound. The longer you survive, the greater your expected age at death; this is why you are never really too old to buy green bananas.

We must, however, not neglect
To add some supplemental terms
Like the survivorship effect,
Plus better diet, fewer germs.

So fifty’s just a lower bound
On years to expect before life’s ebb.
Now, therefore, I shall turn around
And go indoors and surf the Web.

Anonymous said...

Hmm... even if it's a 'traditional' riddle, perhaps Tolkien is enjoying a subtle implicit excursus into Middle-earth dental anthropology whereby hobbits are characterized by hereditary hypodontia in the form of agenesis of two permanent teeth, in which both Smeagol and Bilbo think in terms of having thirty teeth because both are members of hobbit(-like) races in which this is the norm.

I read a fascinating account by Gustav Heinrich Ralph von Koenigswald of his discovery of various distinctive specimens of early human teeth by going around purchasing 'dragon's teeth' from vendors of traditional medicines in the Far East - something (conjecturing with wild abandon) I can imagine would have struck Tolkien had he read about it while writing The Hobbit and which might have turned his thoughts to dental palaeoanthropology in the context of this "thirty" and the distinct 'humanity' of hobbits.

David Llewellyn Dodds