Accounting for the Numbers of the Arda

"Tall ships and tall kings
Three times three,
What brought they from the foundered land
Over the flowing sea?
Seven stars and seven stones
And one white tree."
(Gandalf to Pippin en route to Minas Tirith)

-------

Arda, Tolkien's immense and immeasurable created world, revolves around his invented languages:

"The stories were made rather to provide a world
for the languages than the reverse." (J.R.R. Tolkien, Letter 165. [8])

However, if the languages and words were responsible for the creation of the world, then it's numbers that make it go round and round. In fact, without numbers, Middle-earth as we know it would not exist. Tolkien was meticulously mathematical. From the duration of the Ages to the precise time of day, from moon phases to birthday invitations, Tolkien was a numbers man through and through. Literally, from the very genesis of Arda's creation, he used numbers to conjure a sense of power, to add emphasis to an otherwise insignificant entity:

"There was Eru, the One, who in Arda is called Ilúvatar"
(Ainulindalë - The Silmarillion)

One could also contend that Tolkien used numbers, much like his language, to anchor Middle-earth in the sea of authenticity, providing us with a calculus that we can both assimilate and comprehend. What follows is a by the numbers, comprehensive (although not completely exhaustive) compendium of the use of numbers throughout his works. In general the more prominent entries are discussed with the addition of a few of the more obscure, yet highly interesting occurrences.

ONE

• The One - As mentioned above 'Eru, the One', is most appropriately the first number that is countable. The simple, yet profound title leaves the reader with no doubt as to Eru''s lofty status. [3]
  

• The One Ring - the single, most weighty ring that ever marred the shores of Middle-earth:

"One Ring to rule them all, One Ring to find them,
One Ring to bring them all and in the darkness bind them." [5] 

• One-eyed Sauron - Sauron''s monocular view of the world was not helpful to his ultimate cause. 

TWO 

• The Two Trees - As far as the flora of Arda is concerned, nothing comes close to the hallowed and intensely radiant trees, Laurelin and Silpion. Planted on the mound of Ezellohar in Valinor, these trees became entangled with the perilous path that the unfolding history of Arda was to follow. [3] 

• The Two Towers - Tolkien never sought his books to be published as a trilogy, but rather as six books published as one volume. Unwin the publisher decided otherwise and so Tolkien was obliged to come up with three new titles. This particular title never pleased Tolkien:

"I am not at all happy about the title `The Two Towers'. It must if there is any real reference in it to Vol II refer to Orthanc and the Tower of Cirith Ungol. But since there is so much made of the basic opposition of the Dark Tower and Minas Tirith, that seems very misleading."  (Letter No. 143. [8])

• The Two Kindreds - The Elves and the Men. [3] 

• The Two Watchers - A couple of vigilant vassals of Sauron that guarded the gate of the Tower of Cirith Ungol. Between them they had six heads and twelve eyes! [7]

THREE 

• Three Rings (plus their three keepers) - Nenya, Narya and Vilya; the only three Rings of Power to be unsullied by Sauron. Their magical power preserved the realms of the Elves in Middle-earth until the destruction of the One Ruling Ring. 

• Three Silmarils - Fëanor, the Noldorian Elf, made the most-prized jewel in the history of Middle-earth. Not content with one he made three of these glorious jewels in which was sheltered the light of the Two Trees, a feat that was never to be repeated. [3]

• Three Themes of Ilúvatar - It took Eru only three themes to conjure up the world of Arda, with the third theme being arguably the most important as it revolved around the Children of Ilúvatar, whose destiny was hidden from the Valar and Melkor. [3] 

• Three Kindreds - The three hosts of the Elder (Vanyar, Noldor and Teleri) who accepted the invitation of the Valar and embarked on the arduous journey to Valinor. [3] 

• Three Houses of Men - The Edain or Men were divided up into three houses. [3]

• Three Farthing Stone - This curiously named central-Shire stone could be found by the side of the East Road and marked the precise point where the borders of the Eastfarthing, Westfarthing and Southfarthing of the Shire met. The stone stood about five miles southeast from Bywater and exactly fourteen miles west from Frogmorton. [5] 

• Three Hunters - This self-proclaimed title was first coined by Aragorn when he and Legolas and Gimli, embarked on a seemingly fruitless pursuit and rescue of the two hobbits Merry and Pippin. [5] 

• Three Tresses - Gimli requested one only but Galadriel parted with three strands of her hair. [5] 

• Thrihyrne - The three peaks of Ered Nimrais behind the Hornburg in which Helms Deep could be found. [6] 

• Three Trunks of Hirilorn - The great beech tree that Luthien was imprisoned in by her father Thingol, so as to prevent her from aiding Beren. Not only that but her little cubby had three corners and three windows and she sang three songs of magic to grow her hair! [3]

• Huan - A handy hound who was given the gift of speech three times during his lifetime. [3] 

• Fingolfin - Three times Fingolfin was crushed to his feet by Morgoth and three times he rose again. [3] 

• Three Towers - On the Tower Hills in western Middle-earth there were three towers, the tallest of which - Elostirion, was home to a palantir. [5] 

• Three Blind Mice - Or to be more accurate - the three mice that blind! In the original Tale of Beren and Luthien, Tevildo the Cat ordered Beren to hunt and capture three mice. He took three days but his efforts were futile, earning only a single nip to one of his fingers. [2] 

• Three Stretches - Perhaps trivial but Tevildo the Cat stretched three times while listening to Luthien''s tall tale about Huan''s fictional predicament. [2] 

• Maeglin - Tuor''s herculean throw caused Maeglin''s body to 'smote' the hill of Amon Gwareth three times on it's way to the bottom. [3] 

• The swans that Tuor followed during his journey to Gondolin originally numbered three but eventually Tolkien increased their number to seven. [2] 

• Three Eagles went to the rescue of Sam and Frodo from Mount Doom. [7]

FOUR 

• Four hobbits - Sam, Frodo, Pippin and Merry were the four hobbits that were instrumental in Sauron's destruction. 

• Four Ages - the History of Aman and Middle-earth was divided into four ages, although it''s only the first three that we know a great deal about. 

• Four Farthings - The Shire was divided up into four geographic regions. [5]

FIVE 

• The Five Istari - These five important Maiar were of course the all-important wizards that came to Middle-earth in the Third Age. These were Gandalf, Saruman, Radagast, Alatar and Pallando. [3]
  

• Battle of the Five Armies - This crucial battle was fought in the Third Age (III 2941) in the valley of Dale and on the slopes of Erebor. On one side were the Elves, Men and Dwarves, while the losing side was made up of the orcs and wargs. Unfortunately, for the Eagles and Beorn  - the tide-swinging avians and bear-man, they were not included in this celebrated title. [4]

SIX 

• As mentioned above Tolkien wrote The Lord of the Rings as six books. 

• The Eldar seemed to prefer working with sixes and twelves. [6 - appendix] 

• An ideal day for a Hobbit was one in which he or she dined on six meals. [5] 

• The number of dwarves that was required to lift an aging, portly Bombur! [5]
  

SEVEN 

Without question, the number seven (followed by the number '"three"') is the most frequent number that Tolkien uses. It''s also a number that has historical and religious significance. In almost every system of antiquity there are frequent references to the number seven. The Pythagoreans called it the perfect number, three and four, the triangle and the square, being the perfect figures. The Arabians had seven Holy Temples. In Persian mysteries there were seven spacious caverns through which the aspirants had to pass. The Goths had seven deities, as did the Romans, from whose names are derived our days of the week. There were also seven ancient planets. In Scriptural history there is a frequent recurrence of this number (528 occurrences in fact) where it abstractedly symbolises completion, fullness, or perfection. Richard Trench, the famous Arch-Bishop of 19th Century Ireland, who was renowned for not only his biblical studies but also his philology, said of the number seven:

"There is no doubt that it claims, throughout Scripture, to be considered as the covenant number, the sign and signature of God's covenant relation to mankind, and above all to that portion of mankind with which this relation is not potential merely, but actual-namely, the Church."  (Commentary on the Epistles to the Seven Churches in Asia. Revelation i-iii. (London, 1861))

It is no wonder then that this sacred Christian number is reflected throughout Tolkien's works.

* Gondolin, especially 'The Fall of Gondolin' that can be found in The Book of Lost Tales 2, [2] deserves it''s own special seven section:

• Gondolin was also known as the City of Seven Names, although this must be the seventh name. The remaining six names are: Gondobar, Gondothlimbar, Gondolin, Gwarestrin, Gar Thurion, and Loth.[2]

• The seven Gates of Gondolin - Wood, Stone, Bronze, Writhen Iron, White marble, Gold, and Steel.[2] 

• The Folk of the Heavenly Arch who fought valiantly but in vain during the Fall of Gondolin, bore shields embedded with seven gems - ruby, amethyst, sapphire, emerald, chrysoprase, topaz, and amber.[2] 

• During the Fall of Gondolin each man of the Hammer of Wrath took seven enemies in payment for the loss of their own lives.[2] Compare this to Genesis 4:15 ''But the Lord said to him, "Not so, if anyone kills Cain, he will suffer vengeance seven times over."' 

• Seven Balrogs - In a late marginal note Tolkien wrote about Balrogs: '"There should not be supposed more than say three or at the most seven ever existed."[10] 

• Seven Dragons of Fire contributed to Gondolin''s downfall.[2] 

• Idril watching her father Turgon''s fate unfold before her eyes exclaimed: "Woe is me whose father awaiteth doom even upon his topmost pinnacle; but seven times woe whose lord hath gone down before Melko and will stride home no more!"[2] 

• Seven chains - After fleeing Gondolin, Tuor and company came to lofty Cristhorn, home of Thorondor, whose eyries were ''nigh seven chains'' from the path they followed.[2]

-------

• The Tale of Earendel was originally going to be divided into seven parts: 'It is a mighty tale, and seven times shall folk fare to the Tale-fire ere it be rightly told;'[2] 

• There are several examples of Tolkien wavering between the number three and the number seven. This includes the number of mariners that accompanied Ælfwine in his quest for the West. 

• Sauron - At the end of the Second Age the last Alliance of Men and Elves, under the direction of Gil-galad and Elendil, overcame Sauron but only after a seven year siege of Barad-dûr in Mordor.[3] 

• Eowyn was instructed to stay in bed for a further seven days during her recovery period.[7] 

• Aragorn''s crown was adorned with seven gems of adamant.[7] 

• Saruman referred to the ''crowns of seven kings'' in his address to Gandalf at Isengard.[6] 

• The Valacirca - a constellation made up of seven stars, also called ''The Sickle of the Valar'', that was set in the night-sky as an ever-present notice to Melkor and all his vassals, that the Valar were untouchable.[3] This has a biblical echo too; Revelation 1:20 '"The seven stars are the angels of the seven churches". These seven stars were a common motif in Middle-earth appearing on Aragorn's standard and his sword Anduril. 

• Tuor followed seven swans from Nevrast to the halls of Vinyamar.[3] 

• The Seven Sons of Fëanor and Nerdanel - Maedhros, Maglor, Curufin, Celegorm, Caranthir, Amrod and Amras.[3] 

• Seven Fathers of the Dwarves - Aulë''s stoney stoic creations who went on to found the Seven Houses of the Dwarves as well as the Seven Hoards.[3] 

• Seven Rivers - These waters are to be found in the south of Gondor and include the Anduin. The remaining six are Lefnui, Morthond, Ciril, Ringló, and Gilrain-Serni.[11] 

• Ossiriand - The region of Beleriand that actually means ''seven-rivers land''.[3] 

• The Seven Seeing Stones or the Palantíri. In fact, if you include the Master Stone there were actually eight stones wrought by Fëanor. 

• Haldir said to Frodo on Cerin Amroth that he feared Dol Guldur was inhabited again, '"and with power sevenfold."'[5] 

• Under instruction by Turgon, Círdan the shipwright built seven ships to sail to Valinor, only one of which ever returned to Balar.[3] 

• Eärendil was seven years old when Morgoth attacked Gondolin.[3] 

• Seven ships built by Círdan were sent to Valinor by Turgon - none made it and only one returned to Middle-earth.[3] 

• 'The Lords of the Valar are seven; and the Valier, the Queens of the Valar, are seven also'.[3] 

• The Seven Names of Túrin - An identity crisis for sure. No one in the history of Middle-earth had as many pseudonyms as this man: Túrin - Neithan - Gorthol - Agarwaen - Adanedhel - Mormegil - Wildman of the Woods. Never happy with his name the end result was seven names, which in anyone''s lifetime is more than enough.
  

• The Seven Wounds of Fingolfin - In the David and Goliath duel between Fingolfin and Morgoth, Fingolfin managed to inflict seven wounds with his sword Ringil causing Morgoth to cry out in anguish seven times.[3] 

• Highdei (or Friday) was the 7th and chief day of the week in Shire-reckoning. 

• Treebeard claimed he could of watched Saruman in Orthanc for ''seven times the years in which he (Saruman) tormented us''. This was not to be however, for seven days after he let Saruman depart, Gandalf and company arrived at Isengard to discover Treebeard''s heart of warm soppy sap had set him free.[7] 

• This number even occurs outside Arda, in the adventures of a little dog called Rover in Roverandom. During one of these adventures while visiting the Pacific and Atlantic Magician Arterxarxes in his ocean abode: "He was looking into a vast ballroom with seven domes and ten thousand coral pillars."[9]

EIGHT

• Aratar - The title bestowed on the eight greatest of the Valar and Valier, these being Manwë, Varda, Ulmo, Yavanna, Aulë, Mandos, Nienna and Oromë.[3]
  

NINE 

• Nine Rings - The nine rings given to men, worn by the nine Nazgul who were indirectly responsible for the Fellowship numbering nine.[5] 

• Nine Fingered Frodo - The ultimate destruction of the One Ring relied upon a somewhat gnawing Gollum, who unceremoniously detached Frodo''s ring-finger.[7] 

• The One Ring was held or worn by nine historical individuals. In chronological order these were: Sauron, Isildur, Deagol, Sméagol, Bilbo, Frodo, Gandalf, Tom Bombadil and Samwise Gamgee. 

• In actual fact the Aratar were originally nine, and included Melkor, but he was unceremoniously removed from this 'order' after his inevitable insurgence: 

"Among [the Valar] Nine were of chief power and reverence; but one[Melkor] is removed from their number, and Eight remain, the Aratar, the High Ones of Arda..."[3]

TEN 

• The spiders of Mirkwood could grow up to ten feet wide![4]
  

THIRTEEN 

• The number of the Company that embarked on the treasure hunt in The Hobbit.[4] 

• Samwise Gamgee was not just a hero and a model Mayor - he and Rose were fruitful procreators - turning out thirteen children.[7] 

FIFTEEN 

• Fifteen Birds in Five Fir Trees - at least this is how the goblins in The Hobbit saw Bilbo, Gandalf and the thirteen dwarves when they had them surrounded. [4]
  

NINETEEN 

• Number of Hobbits killed in the Battle of Bywater.[7]
  

TWENTY 

• Total number of Rings of Power (ie. The 1 + 9 + 7 + 3).[3]
  

TWENTY-SEVEN 

• From the bottom of Orthanc to the great door above was a flight of 27 steps.[8]
  

THIRTY-THREE 

• Coming of age for a Hobbit occurred at the rambunctious age of 33. Almost certainly by design, this is also the age that Jesus Christ was said to have been when he was crucified and resurrected.[5]
  

ONE HUNDRED AND FORTY-FOUR 

• This notorious number we meet early on in the preparations for Bilbo and Frodo''s unique birthday party. The number of people invited totalled one gross (144), or as Belladonna Took described it: '"a nasty vulgar expression"'.[5] 

• The Quenya word 'yén', meaning 'year', actually lasts for 144 of our years. (Appendix G)

THOUSAND 

• The Thousand Caves (Menegroth) - This refuge of Thingol was found on the southern banks of the River Esgalduin, in the Forest of Region. Whether there were a thousand caves exactly or not, we will never know since this part of the world is now under the sea.[3]
  

REFERENCES: Works by J.R.R. Tolkien

(1) The Book of Lost Tales. Part I. Edited by Christopher Tolkien. London: George Allen & Unwin, 1983.

(2) The Book of Lost Tales. Part II. Edited by Christopher Tolkien. London: George Allen & Unwin, 1984.

(3) The Silmarillion. First Edition London: George Allen & Unwin 1977; cited here from second edition, 1983.
(4) The Hobbit. First edition London: George Allen & Unwin 1937; cited here from fourth edition, 1981.

(The Lord of The Rings) in three volumes:

(5) I,  The Fellowship of the Ring. First edition London: George Allen & Unwin 1954; cited here from fourth edition, 1981.
(6) II,  The Two Towers. First edition London: George Allen & Unwin 1954; cited here from fourth edition, 1981.
(7) III,  The Return of the King. First edition London: George Allen & Unwin 1955; cited here from fourth edition, 1981.
(8) Letters of J.R.R. Tolkien. Edited by Humphrey Carpenter with the assistance of Christopher Tolkien, London: George Allen & Unwin 1981; cited here from second edition, 1995.
(9) Roverandom. First Edition London: HarperCollins Publishers, 1998.
(10) Morgoth's Ring: The Later Silmarillion, Part One: The Legends of Aman. Edited by Christopher Tolkien, London, Harper Collins, 1993.
(11) The Adventures of Tom Bombadil. With illustrations by Pauline Baynes. London: George Allen & Unwin, 1962.