The Equation Relating Generation Length and Time Passage -------------------------------------------------------- First, N must be strictly defined. To define it, we must think about how we count generations. Generally, you start counting sometime in one generation's lifetime (when their age is between 0 and G), and end within the current generation's lifetime. Call the generation in which counting starts generation 1 (G1 for short). Then, count down each successive generation, and the current generation will be N. For example, starting in my grandfather's lifetime, he is G1, my father is G2, and I am G3. Thus, N=3. This definition of N will work regardless of where you start counting and where you end. Let A1 be the age A of G1, and AN be the age A of GN. The equation is this: T = (G - A1) + G(N-2) +AN or, perhaps more intuitively, T = G(N-1) + (AN - A1) If you wanted to express the 1st equation in English, you would say that it is the amount of time between generation 1's current age and when generation 2 is born, plus the amount of time between generation 2's and the current generation's birth, plus the current generation's age. The second equation would be expressed as the amount of time between when generation 1 and generation N are born, plus the difference in generation 1 and generation N's ages (when counting starts and ends). Note that the above equation works whether A1 < AN, A1 > AN, or A1 = AN. If A1 = AN (i.e. if you start and end counting when G1 and GN are the same age), the equation reduces to T = G(N-1). (This type of counting I call "standard counting procedure," because normally one will start when G1 equals a certain age, and end when GN is the same age.) I think it also works if A1 > G (i.e. if the next generation has already been born), but I haven't verified this yet. Anyway, if A1 is ever greater than G, this means you have started counting one or more generations too early. You have to start the counting at 1 with somebody whose age, A, is between 0 and G. Otherwise, you aren't starting at the first generation, but at the 0th or -1st generation. Now, there is a second case: saying something happened "n generations ago." Let's say something happened 4 generations ago. Start with the first generation and label it 1. Count down to the current generation: 1, 2, 3, 4, 5. N, in this case, equals 5. However, the event could have happened any time during generation 1, i.e. when G1 was between 0 and G years old. So, in the first equation above, we will want to replace (G - A1) with a range. We want the range to run from 0 to G. So, let's define µ, such that 0 < µ < 1. The new equation is, then: T = µG + G(N-2) + AN or, if you want to express this as a range, G(N-2) + AN < T < G(N-1) + AN That's it. These equations are the only ones you need for any and all situations. Let me give one example. Take the example of Ralph and Queen Ambi in OoA. Ralph is Ambi's grandson's grandson's grandson. Let Ambi be G1. Then, counting down, Ralph is G7. So N=7. T is given to us by the Maku Tree as 400. So now we have, from equation #1: T = G(N-1) + (AN - A1) 400 = G(7-1) + (AN - A1) But we don't know AN (Ralph's age) or A1 (Ambi's age). This doesn't matter; all we need to know is the difference between their ages. Let me assume that Ambi is old enough to be Ralph's mother. Then, it is only logical to assume that Ralph and Ambi are separated by G years. Thus, AN-A1=-G. The equation becomes: 400 = 6*G - G = 5*G so G = 80 years As you can see, there was no confusion. All I did was automatically plug numbers into a formula. In mathematics, this kind of thing is ideal. Once you've derived an equation and understand it, you shouldn't have to think about it any more. You should just be able to plug in numbers and trust that the equation will give you the correct result. Mathematics, in the end, is supposed to make life easier. I'll do another example. What is Sahasrahla's age? Let's assume, for the purposes of this problem, that G for Hylians is the same as calculated above. We know that Sahasrahla has a grandson. He looks about ten years old. So, if Sahasrahla is G1, his grandson is G3. N = 3. We want to know Sahasrahla's age, so the counting will start when he is born. So, A1 = 0. Since G3 is ten years old, A3 = 10. Sahasrahla's age is given by T (because we are counting from when Sahasrahla is born to the current time). We have: T = G(N-1) + (AN - A1) = 80(3-1) + (10 - 0) = 114 + 10 = 170 years Sahasrahla is, therefore, 170 years old.