4 ms·

The mathematics of life is exponential growth. Two begets four begets eight and so on. So if you happen to die from old age after the fifth or sixth generation,

by jostmey 12y ago

The mathematics of life is exponential growth. Two begets four begets eight and so on. So if you happen to die from old age after the fifth or sixth generation, the effect on how many copies your genes make of themselves is marginal.

ars 12y ago
You are completely forgetting that if the parent organism has extra copies so do all the children. Compare 2^100 vs 3^100: 2^100: 1267650600228229401496703205376 3^100: 515377520732011331036461129765621272702107522001
- jostmey 12y ago
  No, I am not. I assumed that the offspring will die of old age too. You neglected the variable of time. That third offspring will be born after the second one, which is born after the first one. You need to use the Euler-Lotka equation. The mathematics was worked out centuries ago. Here is the wikipedia article http://en.wikipedia.org/wiki/Euler%E2%80%93Lotka_equation http://en.wikipedia.org/wiki/Euler%E2%80%93Lotka_equation
  - ars 12y ago
    > No, I am not. I assumed that the offspring will die of old age too. How does that change the conclusion? 3 children vs 2 is still immensely more children, not just a marginal amount as you thought.
    - jostmey 12y ago
      When that third child is being born the second child is already beginning to reproduce (if you reproduce like Yeast). Clearly, that second child is more important because it has already given you a grandchild when your third child is still in the process of being born. That second child has already resulted into two offspring, and counts for twice as much.
      - ars 12y ago
        That only matters at a specific moment in time, but if you take a slightly longer view that 3rd child had an enormous impact. > That second child has already resulted into two offspring, and counts for twice as much. Only for one generation, but we care about many many generations. 10 generation down the line the slight difference in timing makes no difference. But the increase in number made an enormous difference. You really need to sit and run some numbers and you'll see you are mistaken. Maybe your intuition will help you if think of it as a steady state - babies in (born), babies out (die), rather than thinking about one moment in time. In a steady state the timing make no difference (because you've already waited out the time) - only the number matters.
      - thaumasiotes 12y ago
        > Clearly, that second child is more important because it has already given you a grandchild when your third child is still in the process of being born. That second child has already resulted into two offspring, and counts for twice as much. Well, to pull the idea from my own other comment... a child+grandchild pair is not twice as good as a child even if all you care about is that specific moment in time). It's 1.5 times as good, because a grandchild is only half as good as a child. And (as ars says) once all concerned have died, the timing offset is of no significance whatever. However, for the impact on your total representation in the world of the present (no particular present), which does have significance... see my other comment, where you're still quite wrong. The Euler-Lotka equation values all members of the population equally; that has no relationship to reality when you're talking about (in your own exact words) "how many copies your genes make of themselves".
deleted 12y ago
[deleted]
thaumasiotes 12y ago
But that's total nonsense. Taking the model you describe, where everyone has two children, look at two scenarios: 1. You, and only you, have a magically extended life, such that if you choose you can reproduce at any point. In scenario (1), every generation after you represents one copy of your genes. When you have a third child in the fifth generation, the world goes from one additional copy of you to 1.5 copies, a 50% increase. 2. You, and all of your descendants, never die. In scenario (2), every generation after you is still one full copy of your genes, but they add up over time because they never die. When you have an extra child in the fifth generation, the number of copies of your genes (again, not counting you) goes from 5 to 5.5, a 10% increase. That's still hugely significant. Let's imagine a third scenario: 3. Your genes are so massively successful that people in your family line have three children, not two children. But except for you, they die like normal. In scenario (3), after 5 generations your 243 generation-5 descendants represent 7.6 copies of your genes. An extra child at this point would increase your representation to 8.1, a 6.6% increase. The mistake you appear to be making is in not realizing that the exponential increase in your descendants is offset by an exponential decay in how related they are to you. Another child, at any point, is hugely valuable, because your child is 16 times more strongly related to you than your great-great-great-grandchild.

by jostmey 12y ago

ars 12y ago

You are completely forgetting that if the parent organism has extra copies so do all the children. Compare 2^100 vs 3^100: 2^100: 1267650600228229401496703205376 3^100: 515377520732011331036461129765621272702107522001

jostmey 12y ago
No, I am not. I assumed that the offspring will die of old age too. You neglected the variable of time. That third offspring will be born after the second one, which is born after the first one. You need to use the Euler-Lotka equation. The mathematics was worked out centuries ago. Here is the wikipedia article http://en.wikipedia.org/wiki/Euler%E2%80%93Lotka_equation http://en.wikipedia.org/wiki/Euler%E2%80%93Lotka_equation
- ars 12y ago
  > No, I am not. I assumed that the offspring will die of old age too. How does that change the conclusion? 3 children vs 2 is still immensely more children, not just a marginal amount as you thought.
  - jostmey 12y ago
    When that third child is being born the second child is already beginning to reproduce (if you reproduce like Yeast). Clearly, that second child is more important because it has already given you a grandchild when your third child is still in the process of being born. That second child has already resulted into two offspring, and counts for twice as much.
    - ars 12y ago
      That only matters at a specific moment in time, but if you take a slightly longer view that 3rd child had an enormous impact. > That second child has already resulted into two offspring, and counts for twice as much. Only for one generation, but we care about many many generations. 10 generation down the line the slight difference in timing makes no difference. But the increase in number made an enormous difference. You really need to sit and run some numbers and you'll see you are mistaken. Maybe your intuition will help you if think of it as a steady state - babies in (born), babies out (die), rather than thinking about one moment in time. In a steady state the timing make no difference (because you've already waited out the time) - only the number matters.
    - thaumasiotes 12y ago
      > Clearly, that second child is more important because it has already given you a grandchild when your third child is still in the process of being born. That second child has already resulted into two offspring, and counts for twice as much. Well, to pull the idea from my own other comment... a child+grandchild pair is not twice as good as a child even if all you care about is that specific moment in time). It's 1.5 times as good, because a grandchild is only half as good as a child. And (as ars says) once all concerned have died, the timing offset is of no significance whatever. However, for the impact on your total representation in the world of the present (no particular present), which does have significance... see my other comment, where you're still quite wrong. The Euler-Lotka equation values all members of the population equally; that has no relationship to reality when you're talking about (in your own exact words) "how many copies your genes make of themselves".

deleted 12y ago

[deleted]

thaumasiotes 12y ago

But that's total nonsense. Taking the model you describe, where everyone has two children, look at two scenarios: 1. You, and only you, have a magically extended life, such that if you choose you can reproduce at any point. In scenario (1), every generation after you represents one copy of your genes. When you have a third child in the fifth generation, the world goes from one additional copy of you to 1.5 copies, a 50% increase. 2. You, and all of your descendants, never die. In scenario (2), every generation after you is still one full copy of your genes, but they add up over time because they never die. When you have an extra child in the fifth generation, the number of copies of your genes (again, not counting you) goes from 5 to 5.5, a 10% increase. That's still hugely significant. Let's imagine a third scenario: 3. Your genes are so massively successful that people in your family line have three children, not two children. But except for you, they die like normal. In scenario (3), after 5 generations your 243 generation-5 descendants represent 7.6 copies of your genes. An extra child at this point would increase your representation to 8.1, a 6.6% increase. The mistake you appear to be making is in not realizing that the exponential increase in your descendants is offset by an exponential decay in how related they are to you. Another child, at any point, is hugely valuable, because your child is 16 times more strongly related to you than your great-great-great-grandchild.