Lara documents/Lara 001.001
Translated by tobyas
My longtime friend,
I pray that the Guild of Maintainers is treating you well. I have enjoyed my first few hahrtee with the Guild of Surveyors. I trust that you have learned much about your trade from your instructors, as have I[1].
However, I feel that there is something that I am not being told, things that seem almost deliberately ignored or, worse, hidden. When I attempt to inquire about such things I am met with blank stares at best and lengthy, angry lectures at worst. In younger times, you were always good at seeing through cover ups. I am hoping that you could help me. One of the most useful tools that we have in the Guild of Surveyors is the "fah-lahn Triangle." The use of the "fah-lahn Triangle" is simple. You simply need to draw squares on each side of a triangle and then measure the area of the squares. It works that simply so long as one angle has measure 15,625[2] torans. What you find is that the sum of the areas of the two smaller squares is equal to the area of the larger square[3].
This technique is useful mostly for determining the distance between two landmarks when there is some other object, like a large boulder, in the way. My problem, however, arises rather quickly. Surely it is not difficult to realize that it is possible to draw a line accurately measuring 1 span. It is equally easy to draw a second line, also of measure 1 span, 15,625 torans away from it. Finally, using a straight piece of metal, I can connect the ends of those two lines. The problem arises when I ask the length of the third line.
Using the "fah-lahn Triangle" I created, we can see that the two smaller squares have measure of 1 square-span and so the larger square has measure of 2 square-spantee. This means that the side of the larger square is some number that when times itself becomes 2. I won't bore you with the details, but it I can show that this number does not actually exist, yet the line obviously measures it. When we encounter this while working, we approximate by picking two numbers and saying it is a certain number of parts of a whole. For the number that multiples by itself to 2, we usually say that it is 1 whole and 6,469 parts of 15,625. We can measure to more parts if we are doing higher precision work, but the truth remains that the actual calculated length of the line cannot be said as parts of a whole even though it is obvious that everything is either a whole or a part of a whole.
All the members of the Guild of Surveyors I have discussed this with have simply shrugged it off saying that I simply have not been accurate enough in either my measurement or my expression of the parts. I now come to you, my trusted friend. Surely the Guild of Maintainers also makes use of calculation in the course of their activities. Have you encountered such similar problems as this?
Truthfully, I hope that I am wrong. If we are finding lengths of paths that shouldn't exist, what does this mean of the Age we live in? I know that contradictions make an age unstable and thus unsuitable for life. Does a contradiction like this mean that D'ni is unstable?
Fondly,
Cahy'leh
Footnotes[edit]
- ↑ This comment indicates that the author is young. However, his command of language indicates he’s quite a bit older than the age of admittance at the time of the Fall, which was four hahrtee old. The age of which one began in a Guild must have been different at that time. –J.D
- ↑ In this translation, decimal numbers have been used instead of D'ni base-25 numbers, for ease of reading. –J.D
- ↑ After careful consideration I have determined that this is the D'ni equivalent of the Pythagorean Theorem. At first the number 15,625 seems a bizarre choice, even if it does become 1,000 in the D'ni number system. However, we can see that 15,625 is exactly one quarter of 62,500 which corresponds to 4,000 in the D'ni number system. So one quarter of 62,500 torans is equivalent to one quarter of 360 degrees. Since it is obvious that the author is talking about a right triangle because of the use of the right angle, we can see that the technique described here is fairly similar to one of the many proofs that we have for the Pythagorean Theorem. –tobyas
