 by -
bhcpc
(Sat Feb 22 18:37:51)
|
|
 UPDATED Sat Feb 22 18:47:08 |
It cannot be a linear correlation between human aging and Elf aging. First of all, Elves are immortal and would not die from old age. Therefore, even Cirdan, the oldest Elf in Middle-earth, who's grey and old with long beard, should never look like or have faculty of a frail, wizened old man. On the other hand, there're evidences that Elf doesn't take thousands of years to mature. For example, based on Silmarillion,
1. Maeglin could not be more than 100 years old when he reached full growth.
2. Idril was very young when she came back to Middle-earth, so she could not be more than a few hundred years old when she married Tuor.
3. Elwing (although she did have ¼ human blood) could not be more than 100 years old when she married Earendil.
Therefore, the only reasonable correlation has to be a nonlinear function, with an asymptotic (that is, when time approaches the infinitive) value of a reasonable human old age, say 60), while the full-growth of an Elf (human equivalence of say, 20 years old) should only take about 100 years. However, a single function, such as
Y (equivalent age) = Y_0 x [1 - exp(- t/t_0)], where exp stands for the Exponential function, and e.g. Y_0 = 60 and t_0 = 1000 years,
would not work well because it fails to explain how 100-yr old Elwing, 500-yr old Idril and 2700-yr old Arwen all looked young and available. Hence, I think there may be two functions -- one for Elves before they got married (having children) and one for them afterward.
For example,
*Before marriage and having children, Y_0 = 25 and t_0 = 50, an Elf who is
50 years old => 15.8 yr equivalent age
100 => 21.6 yr equivalent age
500 => 24.999 yr equivalent age
2700 => 24.999999… yr equivalent age
*After marriage and having children, Y_0 = 35 and t_0 = 5000 with an offset of 25, that is
Y (equivalent age) = 25 + Y_0 x [1 - exp(- t/t_0)]
Therefore, if an Elf gets married, by the time she's married for
500 years => 28.33 yr equivalent age
3000 years => 40.79 yr equivalent age (Erlond)
7000 years => 51.37 yr equivalent age (Celeborn and Galadriel, although she didn't look it, due to Elven Ring and …??)
16,000 years => 58.57 yr equivalent age (Cirdan)
This is of course just a theory, but a nonlinear correlation between human aging and Elf aging is quite believable and in fact necessary.
|
|
|
Very impressive, bhcpc!  Are you a mathematician?
"May the wind under your wings bear you where the sun sails and the moon walks."
|
|
|
Ahhhhh, mathematics! 
Your equations certainly work better than the simple linear ones we had before. I'll have to go investigate them more fully, but in the meantime I'd just like to offer some justification for the two different aging rates as you've outlined them. IIRC, having children takes some of the "life force" out of elven mothers (and perhaps fathers too?). This would no doubt cause them to age more quickly.
"Do you hear the call, Earth-maiden?" - "The Last Ship"
|
|
|
having children takes some of the "life force" out of elven mothers (and perhaps fathers too?). This would no doubt cause them to age more quickly.
and put on some extra pounds too, heh.
I think maybe the formula for elven aging would be somewhere along the lines of 37/(1+e^(-x+6)) for each unit of x representing one decade and they can get no older than 37 as x goes to infinity.
|
|
|
| by -
GaugeMistress
(Sat Feb 22 19:24:42)
|
|
| UPDATED Sat Feb 22 19:38:42 |
I like it! It's a little odd that it has very young elves growing faster than humans (they're born as adolescents), but you could add complexity to the model to shift and flatten out that part of the curve and retain the asymptotic behavior if you felt so inclined.
(This is a much more entertaining use of mathematics and models than those boring old high-end microprocessor designs that I spend most of my time on...)
"If you're not for yourself, then who will be for you? If you're only for yourself, what are you?"
|
|
|
Born as adolescents? By my calculations:
at t=0, Yeq=0
at t=10, Yeq=4.5
at t=20, Yeq=8.2
at t=30, Yeq=11.3 (~beginning of adolesence)
at t=40, Yeq=13.8
at t=50, Yeq=15.8 (~physical maturity)
at t=60, Yeq=17.5
at t=70, Yeq=18.8
at t=80, Yeq=20
at t=90, Yeq=20.9
at t=100, Yeq=21.6 (~full physical development)
That gives about 30 years as kids and 50 as "teens." Proportionally, they're adolescents longer than humans are (poor things!).
"Do you hear the call, Earth-maiden?" - "The Last Ship"
|
|
|
My apologies -- the problem here is my own temporary illiteracy. I must have seen that the exponent was 6-x to have the desired approaching-37 behavior, but somehow my brain decided it was x-6 when thinking about the value at 0. I'd better hope I'm a little more awake when determining the fate of those microprocessors...
"If you're not for yourself, then who will be for you? If you're only for yourself, what are you?"
|
|
|
Oops, I made a mistake too - I thought you were referring to the original equation rather than Goshzilla's. Doh!
Be kind to the little microprocessors. If they have a rough childhood, they take it out on us end-users when they grow up 
"Do you hear the call, Earth-maiden?" - "The Last Ship"
|
|
|
| by -
bhcpc
(Sat Feb 22 19:42:57)
|
|
That is a nice formula. However, Arwen would be like 37 years old when she met Aragorn. That's why I try to propose two formulas, instead of one.
|
|
|
This message has been deleted by the poster
|
|
|
Maybe it has to do with her not having married yet, so she's in a slo-mo aging process still.
But yeah, 3000 seems awefully young to be around 40.
Not that I'd be complaining....
|
|
|
| by -
bhcpc
(Sat Feb 22 20:36:15)
|
|
That's how my two formulas work - one for before marriage and children and the other for afterward. One formula, no matter how complicated, cannot not explain how Elwing (less than 100 yrs old) , Idril (greater than 500), Arwen (~2700) and Luthien (could be as old as 9000) could all look young (less than 25 yrs old) to mortals, while Elves like Cirdan could look aged (greater than 50 yrs old in human age).
|
|
|
Interesting...but I do not recall Cirdan having children, and what about Feanor, with seven, and still made the Silmarils...that is impressive.
Old Tom Bombadil is a merry fellow,
Bright blue his jacket is, and his boots are yellow.
|
|
|
| by -
bhcpc
(Sun Feb 23 00:32:32)
|
|
I assume he did but not mentioned in Tolkien's work. Otherwise, we are back to square one...
|
|
|
Either way...we do not have an answer now, but do you think that possibly giving up a portion of his life force affected Feanor with his 7 children, and if so, how?
Old Tom Bombadil is a merry fellow,
Bright blue his jacket is, and his boots are yellow.
|
|
|
Sweet...I hate math.
"Let us always meet each other with smile, for the smile is the beginning of love"
|
|
|
| by -
bhcpc
(Sat Feb 22 19:35:22)
|
|
By the way, this theory predicts if he's practicing abstinence, Legolas would still look young … TODAY!
Legolas lovers, rejoice!!
|
|
|
| by -
Uinen
(Sat Feb 22 20:10:54)
|
|
OH YEAH!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Gotta love a pure man!!!!!! !!!!
 "And you have my bow..."
|
|
|
Although you start to wonder why he's practicing abstinence (short of the obvious "he's waiting for me").
|
|
|
bhcpc, you're a genius. (i'm printing this out)
You have my vote as the mathmatical brainbox on this board. cheers! 
"There goes a lord who tamed a wild shieldmaiden of the North!"
|
|
|
| by -
Tarlonniel
(Sat Feb 22 21:13:07)
|
|
| UPDATED Sun Feb 23 11:51:12 |
Using an integral and something called a delta function, the two equations can be combined thusly:
/\t
Y(equivalent) = 25*(1-e^(-t/50)) + 35*(1-e^(-T/5000))* | delta(x-100)dx
0\/
where t = time since birth and T = time since birth of first child. When T = 0, this gives your first equation; however, even if T is non-zero, the second term remains zero until t > 100, in deference to Tolkien's laws about elven reproduction. The integral becomes one when t > 100.
Then there's the question of how multiple children and/or particularly mighty children (such as Feanor) affect this process....
"Do you hear the call, Earth-maiden?" - "The Last Ship"
|
|
|
| by -
Lianachan
6 days ago (Mon Jul 14 03:52:39)
|
|
I opened that expecting to see that gravity had finally been taken into the fold!
"Life is a tragedy when seen in close-up, but a comedy in long-shot."- Charles Chaplin
|
|
|
Can you explain that in English?
Old Tom Bombadil is a merry fellow,
Bright blue his jacket is, and his boots are yellow.
|
|
|
| by -
bhcpc
(Sun Feb 23 00:24:06)
|
|
| UPDATED Sun Feb 23 11:23:27 |
Sorry we are getting too mathematical now. If you are interested, I can try to explain what Tarlonniel did. Otherwise, the two formulas may be easier to understand (relatively speaking).
Here goes:
delta function y = delta(x - c) has the following properties
1. when x = c exactly, y goes to infinitive
2. Otherwise, y = 0
3. Integration of delta(x - c)
/b
| delta(x - c)dx = 1 if a<c<b (a and b on either side of c), and 0 if a<b<c or c<a<b
/a
As you can tell, nothing in "real world" would behave like it. However, it is very useful in formulation for theoretic physics or electrical engineering.
In Tarlonniel's case(I don't think the term "x/100" is necessary),
/t
| delta(x-100)dx = 1 if 0<100<t and 0 if 0<t<100
/0
Therefore, two formulas can now be written as one formula (it should be 35 for the 2nd term to make the total asymptotic age of 60).
/t
Y(equivalent) = 25*(1-e^(-t/50)) + 35*(1-e^(-T/5000))* | delta(x-100)dx
/0
Like I said, this is getting too mathematical. The bottom line is that by introducing marriage/child birth into consideration, we may be able to explain this seemingly conflicting Elf aging process.
|
|
|
| by -
Tarlonniel
(Sun Feb 23 07:35:03)
|
|
| UPDATED Sun Feb 23 11:39:12 |
Oops, you're right, the x/100 isn't needed.
I wasn't sure what the initial values of the second term should be. I tried to find another elf to calibrate them by (along with Cirdan), but those darned elven rings complicate things, and I also don't have the books with me so I can't look up character descriptions. Oh well - 35's okay.
Too mathematical? What's that? 
"Do you hear the call, Earth-maiden?" - "The Last Ship"
|
|
|
| by -
bhcpc
(Sun Feb 23 11:34:08)
|
|
Actually, the numbers 25, 35 and the total of 60 are somewhat arbitrary, and they are merely used to represent to the notion of young looking and old looking. As you know, other numbers would work just as well, as long as the assumption of the 2nd aging process starting after marriage/child birth is valid.
By the way, Tolkien described Cirdan as follows.
"Very tall he was, and his beard was long, and he was grey and old, save that his eyes were keen as stars."
|
|
|
Hmmm, "grey" and "old" - thanks for being so specific, J.R.R.! 
"Do you hear the call, Earth-maiden?" - "The Last Ship"
|
|
|
If it makes sense to someone else, I will take your word for it. The math is beyond me.
Old Tom Bombadil is a merry fellow,
Bright blue his jacket is, and his boots are yellow.
|
|
|
How's this - it's not entirely accurate, but it should get the point across.
Pretend a little robot has five apples and an orange, lined up like this: A A A O A A. It's programmed to register "0" when it comes across an apple and "1" when it encounters an orange.
Now you tell it to look at the first three fruits and add up the result. It'll get 0 + 0 + 0 = 0, because there's no orange in that bunch. If you tell it to look at the first four, then you get 0 + 0 + 0 + 1 = 1. If it looks at all six, it returns 0 + 0 + 0 + 1 + 0 + 0 = 1.
Whenever the orange is included in the robot's range, you get 1. If it's not, you get 0.
Now pretend we have delta(x - 3). If we use this to integrate (which means add up) all the numbers from negative three billion to 2, we'll get zero, because this little delta function only gives 1 when our range includes 3. As long as there's no 3 among the numbers being added, the function gives 0; if 3 is in there somewhere, we get 1.
My elven aging equation adds up all of the numbers from 0 to the age of the elf. If the elf is under 100, the integral of delta(x-100) will be zero. If the elf is over 100, the integral is 1!
"Do you hear the call, Earth-maiden?" - "The Last Ship"
|
|
|
How is it that you figured out you could make it make sense by using food?
Old Tom Bombadil is a merry fellow,
Bright blue his jacket is, and his boots are yellow.
|
|
|
Easy - everyone understands food! 
"Do you hear the call, Earth-maiden?" - "The Last Ship"
|
|
|
I thought I did!
"Do you hear the call, Earth-maiden?" - "The Last Ship"
|
|
|
| by -
bhcpc
(Sun Feb 23 21:38:03)
|
|
nm
|
|
|
"I sang of leaves, of leaves of gold, and leaves of gold there grew..."
|
|
|
Old Tom Bombadil is a merry fellow,
Bright blue his jacket is, and his boots are yellow.
|
|
|
...the angels had guitars even before they had wings...
|
|
|
A friendly bump from Sponsor #11593: Lady Éowyn
 You are a daughter of kings. A shieldmaiden of Rohan.
|
|
|
A friendly bump from Sponsor #11593: Lady Éowyn
You are a daughter of kings. A shieldmaiden of Rohan.
|
| |
| | |
company.
Advertise on IMDb.
License our content.
@~~ Renee @~~
