Tags

, , ,

This is one of the drafts that has just sat around for years, even surviving the rapid draft purge of last December. The other day, I spoke to a friend and was reminded of the quandary, which is as follows:

Tolkien, among his many and excellent descriptive narrations, loved to describe characters looking off and over vast distances, frequently espying objects at extreme distances. This always struck me as funny. Here’s one example, from The Hobbit:

“But they came to that high point at morning, and looking backward they saw a white sun shining over the outstretched lands. There behind lay Mirkwood, blue in the distance, and darkly green at the nearer edge even in the spring. There far away was the Lonely Mountain on the edge of eyesight. On its highest peak snow yet unmelted was gleaming pale.”

– Bilbo (and Gandalf) at the High Pass over the Misty Mountains, Chapter 18, The Return Journey

A lovely scene. But, was it possible? Could Bilbo, or anyone for that matter, have seen Erebor from roughly 300 miles away? Let’s, right here and now, find out.

Assumptions:

A) “300 miles” is based on my crude calculation and measurement, using the map and scale included in the deluxe boxed edition of the LOTR, from where I think the High Pass is located to where I think the peak of Erebor stands gleaming. The scale ruler is 0 – 300 miles, and it is almost an exact fit.

B) Arda was modeled after the real Earth and was spherical in the late Third Age. I will assume it is also roughly the same size and mass and with the same radius, diameter, etc.

C) I assume that this bright, sunny morning was completely free of any and all atmospheric distortion and there were no physical obstacles in the way.

D) Bilbo had better than average eyes, but I assume The Ring did not augment his visual abilities.

E) If Lonely Mountain was still snow-capped in a “fair” Spring, then it must be at least 10,000 feet tall. For convenience sake, I assume the High Pass was of similar elevation.

F) I assume my use of the simple equation, below, is sufficient. I essentially double it, thus effectively creating the measure of the more complex geometrical “offing” equation. I’m rambling about a book, not sailing a damned ship.

Now, it’s just a matter of math. Looking for distance, “d,” in miles, to the horizon:

d ≅ 1.22 x √h

h” is the height of the observation point – here, assumed to be at least or about 10,000 ft.

d ≅ 1.22 x √10,000

d ≅ 122 miles

Uh, oh…

But, wait! Tolkien never said Erebor was at or on the actual horizon, he said it was on the edge of eyesight. As mariners know, some taller objects are visible over and beyond the horizon. Keeping Bilbo’s point of observation at about 10,000 ft, let’s measure how far the horizon was would be, from Erebor, looking towards the West.

If Erebor is 10,000 feet high, then we know it’s another 122 miles. Assuming Bilbo saw the very tip of the top of the highest peak over and beyond his already 122-mile distant horizon, and allowing for simple addition (a lot of assumptions and allowances, yes), then it’s still 56 miles too far away to be seen. But, what if Erebor was taller than 10,000 feet?

If Erebor was a 20,000-foot mountain, then it’s own d to the horizon would be 172 miles, for a total line of sight of 294 miles. That is getting there. If the High Pass was really high, say 15,000 feet, then Bilbo’s d to the horizon would be 149 miles. That adds up to a total potential line of sight of 321 miles.

Thus, and I did not really expect this, given all of my assumptions, there is a distinctly plausible range of line of sight which renders Bilbo’s sighting hypothetically possible. He, in fact, could have looked across Wilderland and literally seen the tip-top of the Lonely Mountain.

To think you doubted Professor Tolkien just a little. To cure this shame, we’ll give him the benefit of the doubt as to all the other measurements. Astounding detail and accuracy.

And, happy July!