DAGAZ THE DOOR
The Eeriness geometry conforms to the same butterfly rune dagaz which marks the Magic Door into Erebor on Thror’s map (Hobbit) and even more precisely to the rune used for dagaz in the dwarf runes on the map. We can relate dagaz to the star in I Vene Kemen via Tolkien’s early designs for Hobbit binding where dagaz appears inside the crescent moon. (A&I 147). This is replicated by the crescent moon, Smaug and star on his design for Hobbit dust-jacket, suggesting the star is being pursued. (A&I 151). In the Death of Smaug we can see that two “X” shapes seem to be escaping from the crescent moon at the moment of Smaug’s death. (A&I 144). This motif appears in Roverandom, as the dragon “chasing two perfectly insignificant butterflies among white mountains” (Tales from the Perilous Realm [Tales] 38). This image of chasing butterflies is repeated twice more. “I fell over the world’s edge chasing a butterfly. […] Luckily the moon was just passing under the world at the moment” (Tales 27). “Edge”: “Old English ecg “corner […] German Eck “corner”“. This corner I suggest is the corner of the triangle at the heart in Eeriness, the location of the Megalithic Door in Before. This makes sense as the Sun and Moon pass in and out of the World through doors and the Megalithic Door on the dust jacket design sits at the boundary separating day (right) from night (left). The “straight road” in Eeriness leads to the corner, a right-angle. The Arkenstone is the precious stone, which is “a chief corner stone, elect, precious […] the stone which the builders disallowed, the same is made the head of the corner” (THB, 1 Pet. 2.6-7). “Right”, “straight” and “rule” all share the same meaning: “PIE root *reg- “move in a straight line,” […] to rule, to lead“, straight, undeviating, morally just. We have no space to develop this here but this hypothesis leads to an understanding that the “straight road” west is only one explicit instance of a grammar which involves the “will” and different orientations and destinies.
Dagaz the door on Thror’s map is also hinted at in Tolkien’s binding design in which dagaz lines up with the Megalithic Door, Erebor and the gyfu rune “X” at the bottom of the dust-jacket design. The Megalithic Door is flanked by Sun and Moon on the dust-jacket. If dagaz lines up with the door and Erebor on the binding spine, it must also be flanked by the Sun and Moon. Therefore we can equate the quarrelling oak and birch in Eeriness with the Sun and Moon,—The Lady of the Sun and Man in the Moon (who also appears in Roverandom) of I Vene Kemen. In the Eeriness geometry (dagaz on Thror’s map) we can indeed see two dagaz runes, two butterflies at 90 degrees to one another.
Given that butterflies represent stars, these two butterflies therefore represent the quarrel over which star to follow in I Vene Kemen, The Ship of Fools. And we can relate the door in Erebor to the butterflies of the Valacirca because the butterfly rune dagaz indicates the Magic Door on Thror’s map. This 90 degree disparity in orientation between butterflies, stars, explains why the Magic Door is not pointing north, but oriented west which agrees with the positioning of the two thorn runes vis a vis dagaz in his binding design (A&I 148) being north and south of the dagaz rune, not left and right. I suggest this disparity represents the discords, the quarrel which incarnates in Thorin, Bilbo, the Arkenstone, and their very different fates. To Thorin the Arkenstone is the same precious stone, but a “stone of stumbling, and a rock of offence” to the disobedient (THB, 1 Pet. 2.8). Tolkien hints at this contrary orientation given Thror’s map has east at the top, a historical disorientation between medieval and modern maps, between Myth and History.
The two thorn runes on the spine of the binding are found on the large urn in Tolkien’s Conversation with Smaug (Pictures 17). In that picture, the middle arch which is indicated by the star-like Arkenstone at the top of the triangular mountain of treasure (serving the same function as the triangle forming the road in Eeriness), represents 
the Door on the spine of the dustjacket, Bilbo’s destiny. I will explore the evidence in an essay linked from here. Suffice to say here briefly that we can see the suggestions of a mountain in Eeriness itself. This is the same Mountain paired with the Tree in his first riddle from The Hobbit. The two are symbols of the World in ancient myth and esoteric symbolism. Left, in fig. 1.5.1 we see his drawing (A&I 99) of Gandalf and the runes he put on Bilbo’s door. The first rune is Berkanan, the birch, the second is dagaz which is the Door. The third is a diamond with a dot in the centre, referring to the Arkenstone, the “Heart of the Mountain”. Thus we can see that the presence of dagaz links Bilbo’s Door to the Magic Door of Erebor which also bears the dagaz rune identifying it, as There and Back Again. The words in runes on the map also use the version of dagaz which has the same form as the geometry of Eeriness. The Arkenstone is the Heart of the Mountain and therefore represents the mountain- the triangular mountain of treasure in Conversation with Smaug, appearing as a star at the top of the treasure. The dot represents the Arkenstone as the “heart of the mountain” and recalling the full geometry above as a diamond overlaying an “X” form, it occupies the same place as the heart in Eeriness.
Tolkien suggests a conical shaped mountain from the curved lines and the straight line through the top echoes the line “el” through the top angle of the triangle “Friend” in the Book of the Foxrook. Tolkien most obviously refers to the World as a Tree in Leaf by Niggle. Tolkien alludes to the World as the Mountain in his curious lines in the Music of the Ainur:
“And amid all the splendours of the World, its vast halls and spaces, and its wheeling fires, Ilúvatar chose a place for their habitation in the Deeps of Time and in the midst of the innumerable stars. And this habitation might seem a little thing to those who consider only the majesty of the Ainur, and not their terrible sharpness; as who should take the whole field of Arda for the foundation of a pillar and so raise it until the cone of its summit were more bitter than a needle; or who consider only the immeasurable vastness of the World” (Sil. 19).
At the top of this mountain (at the centre of Eeriness) sits Eden, paradise, heaven on earth. The line through the top angle in his triangle “Friend” in Foxrook corresponds to the “needle”. Tolkien invites us to visualize a mountain as a triangle in his images Halls of Manwe (Taniquetil)(A&I 56) and The White Dragon Pursues Roverandom & the Moondog(A&I 81) here. In this way we have the World Soul evident in Eeriness represented as both a Tree (in the two trees at the centre and outside), and the Mountain.
The equation of a mountain with a triangle is supported if we consider that the two butterflies being pursued by the White Dragon have been equated with the two butterflies evident in the triangular geometry of Eeriness, which itself can be regarded to have a mountain. Indeed we can extend this understanding to include the other triangles in Eeriness to be the other three sides of the mountain if we climb it from other directions,—the mountain in fact as a pyramid. Therefore the mountain with four triangular sides equates to the two butterflies with two wings each.
The ladder in Conversation with Smaug points to the unwelcoming left arch and leads between the two runes. As such the thorn runes on the urn represent the two trees to either side of Thorin’s path of destiny, in accordance with Before and Afterward and all of the other imagery and symbolism presented here. Because of his disobedient wilfulness the (Arken)stone is a stumbling block to him, a “rock of offence”. “Stumble”: “Middle English Compendium compares Middle Dutch stommelen “to overturn”“. Thorin turns away from the path to the Door north-south towards the path west-east because the Devil by guile, turns the spirit, makes it crooked. As a hint Smaug’s tail (a spiral ending in a tripartite form) is pointing at the left arch. This “turn” echoes the narrative: Bilbo becomes afraid of Thorin’s behaviour and gives the Arkenstone (the guiding star) to Bard and Thorin perishes. Therefore on the dust-jacket spine the east-west dagaz represents Bilbo’s path between them leading north. The two thorn runes represent Thorin’s path.
When the river finally takes Bilbo into Long Lake we see a turn, a gate, and the Seven Stars associated with Erebor which has a Megalithic Door:
“The sun had set when turning with another sweep towards the East the forest-river rushed into the Long Lake. There it had a wide mouth with stony clifflike gates at either side whose feet were piled with shingles. […] it was so long that its northerly end, which pointed towards the Mountain, could not be seen at all. Only from the map did Bilbo know that away up there, where the stars of the Wain were already twinkling” (Hobbit 10.155-156).
If this path leading up the spine of the cover to the Megalithic Door is Bilbo’s path, we can see that Thorin’s leads at right angles across it between the two thorn runes. “Dawn” is from “Proto-Germanic *dagaz “day”“. Dawn and dusk are twilight, the time of “two lights”. Tolkien tells us “The presence of the sun and moon in the sky together refers to the magic attaching to the door” (Letters 19, #12). We can understand the door as consisting of two halves because, “The oldest forms of the word in IE languages frequently are dual or plural, leading to speculation that houses of the original Indo-Europeans had doors with two swinging halves” (Door | Search Online Etymology Dictionary). We note that they would swing in contrary directions like the two oars, two wings, the winged door in Before, and the two spirals. The two halves are Tolkien and Edith, Moon and Sun on the sail of I Vene Kemen (“sail”: “Old English segl “sail, veil, curtain”“).
When the Grey Company pass into the West over the “edge of the world” we read: “the grey rain-curtain turned all to silver glass and was rolled back, and he beheld white shores and beyond them a far green country under a swift sunrise” (LotR 9.VI.1030). Thus we see twilight, a curtain of silver glass suggesting the silvered glass of a mirror and a veil at the edge or corner where the Door is. The curtain and hand appear in his images Wickedness (A&I 37) and Maddo (84). Wickedness (fig. 1.6 below) has two spirals and two triangles. A dagaz form across the curtain is implied. The triangles are not turned towards each other which I propose represents “wickedness”. In fig. 1.2 we saw the diamond (lozenge) in the lattice and in Undertenishness. We have no space to discuss its symbolism but it represents the discords (pun on “quarrel”: “square or diamond-shaped plane of glass” which Tolkien mentions in his essay Middle English losenger where Tolkien continues his 
riddling game with the audience) of Melkor, the stone over the door,—fundamentally the tomb of Christ which is rolled away. The “X” figure (also representing the Chi-Rho of Christ) appears on the curtain of Maddo: specifically a combination of “butterfly” and “lozenge” as “※” (“a diamond “◊” overlaying a chi “X”) which is the fundamental element of the lattice: a door and the means to open and close it. This appears in bold in fig. 1.2. In Maddo we also see the crescent moon with its star—this time it appears to be the Sun, suggesting the Moon is hunting the Sun, echoing the story of Tilion and Arien. Maddo repeats the imagery of Wickedness,—a hand moving back a veil. The window represents the veil, the Door. This agrees with the implied dagaz rune marked in fig 1.6 which centres on the threshold. If we consider the Chi-Rho, the letter Rho appears where the heart is in Eeriness and we can regard it as the Sacred Heart of Jesus and the Immaculate Heart of Mary given the heart is created by the outline shapes of the two trees “You and I”,—echoing the precious stone as referring to Jesus and Mary.
