5 ms·

Except they don't. Populations in developing countries have now stabilized and in some cases, Japan, are well below replacement level.

by paul_f 13y ago

skj 13y ago
Population growth is a fundamentally exponential process, even if that exponent is very close to 1 in some cases, or even less than 1.
- 2stop 13y ago
  but you said exponentially growing... which typically means "doubling". You are now saying the 'exponent' could be < 1... then you aren't 'growing' anymore... so you refuted your own statement.
- gnaritas 13y ago
  > Population growth is a fundamentally exponential process No it isn't. If everyone has one or less children, the population does not grow exponentially.
  - hueving 13y ago
    skj was trolling by changing the common definition of exponential by saying the exponent could be 1 or less than one.
    - lutusp 13y ago
      > skj was trolling by changing the common definition of exponential by saying the exponent could be 1 or less than one. That's not trolling. It's called "mathematics."
      - gnaritas 13y ago
        Which is trolling in a discussion that isn't about mathematics.
        lutusp 13y ago
        Wait, what? Replying to a comment that is clearly about mathematics, with a comment that is clearly about mathematics, is trolling? The OP's comment, including " ... changing the common definition of exponential by saying the exponent could be 1 or less than one" is (a) mathematical and (b) wrong and misleading. The "common definition of exponential" accommodates any valid argument to exp(x), and to claim otherwise requires a mathematical correction to avoid misleading people.
        gnaritas 13y ago
        Trolling.
        skj 13y ago
        This is a very disappointing comment line. I know not everyone here is a CS major, but if you're even CS-knowledgable you should understand what an exponential process is. It is not, as many laypeople assume, something that is "very big". That said, I was not intentionally trolling. I do think it's possible for a SS-style benefit to sustain itself provided that an exponentially growing population, whose exponent is greater than 1, is obligated to pay in. A country with a stagnant or declining population will probably have trouble. You may disagree, that's fine. Nevertheless, any population whose growth (or lack of growth) is defined by the average number of children per member will behave exponentially.
        gnaritas 13y ago
        > behave exponentially. Behave exponentially != grow exponentially, still utterly missing the point; still trolling.
        13y ago
  - lutusp 13y ago
    > If everyone has one or less children, the population does not grow exponentially. False. An exponential function, and a growing exponential function, differ only in the value of the exponent. Here's an equation that predicts future population based on the value of an exponential term: The equation: pt - p0 e^rt pt = population at time t p0 = present population r = rate of population growth, 1% = .01 t = time A result at 40 years for a population rate of change of -1.7% per year: e^(-.017 * 40) = .5066 This result says that, for a population growth rate of -1.7%, after 40 years the population will be about half its present size. It's an exponential result, it's even an exponential growth rate, but the growth rate is negative. In this image: http://i.imgur.com/LW6bk8t.png http://i.imgur.com/LW6bk8t.png The red trace is an exponential rate of change for r = +1.7%, the green trace for r = -1.7%. Both are exponential results, and both reflect what a population would look like for given r values.
    - gnaritas 13y ago
      False. Put all your bullshit math aside because that's what it is, bullshit trying to move the goalpost. The statement I made is absolutely factually true. If everyone has one or less children, the population does not grow exponentially. We're not talking about how to model population growth, or functions, we're talking about whether every couple having one child results in exponential growth and it simply does not. If the population decreases, that is not exponential growth. An exponential result != exponential growth. You are wrong and we are done.
      - lutusp 13y ago
        > The statement I made is absolutely factually true. If everyone has one or less children, the population does not grow exponentially. You need to learn mathematics (as well as grammar). Also learn "negative growth rate" while you're about it: http://wiki.answers.com/Q/Is_it_possible_to_have_a_negative_growth_rate http://wiki.answers.com/Q/Is_it_possible_to_have_a_negative_... And, everything else aside, all the described rates are exponential. > We're not talking about how to model population growth ... WHAT?? Here is what you said: "If everyone has one or less children, the population does not grow exponentially." How exactly is that NOT talking about how to model population growth? Also, it's "one or fewer children," not "one or less children." > An exponential result != exponential growth False in a discussion about population and exponential growth rates, terms you chose.

Except they don't. Populations in developing countries have now stabilized and in some cases, Japan, are well below replacement level.

by paul_f 13y ago

Except they don't. Populations in developing countries have now stabilized and in some cases, Japan, are well below replacement level.

skj 13y ago

Population growth is a fundamentally exponential process, even if that exponent is very close to 1 in some cases, or even less than 1.

2stop 13y ago
but you said exponentially growing... which typically means "doubling". You are now saying the 'exponent' could be < 1... then you aren't 'growing' anymore... so you refuted your own statement.
gnaritas 13y ago
> Population growth is a fundamentally exponential process No it isn't. If everyone has one or less children, the population does not grow exponentially.
- hueving 13y ago
  skj was trolling by changing the common definition of exponential by saying the exponent could be 1 or less than one.
  - lutusp 13y ago
    > skj was trolling by changing the common definition of exponential by saying the exponent could be 1 or less than one. That's not trolling. It's called "mathematics."
    - gnaritas 13y ago
      Which is trolling in a discussion that isn't about mathematics.
      - lutusp 13y ago
        Wait, what? Replying to a comment that is clearly about mathematics, with a comment that is clearly about mathematics, is trolling? The OP's comment, including " ... changing the common definition of exponential by saying the exponent could be 1 or less than one" is (a) mathematical and (b) wrong and misleading. The "common definition of exponential" accommodates any valid argument to exp(x), and to claim otherwise requires a mathematical correction to avoid misleading people.
        gnaritas 13y ago
        Trolling.
        skj 13y ago
        This is a very disappointing comment line. I know not everyone here is a CS major, but if you're even CS-knowledgable you should understand what an exponential process is. It is not, as many laypeople assume, something that is "very big". That said, I was not intentionally trolling. I do think it's possible for a SS-style benefit to sustain itself provided that an exponentially growing population, whose exponent is greater than 1, is obligated to pay in. A country with a stagnant or declining population will probably have trouble. You may disagree, that's fine. Nevertheless, any population whose growth (or lack of growth) is defined by the average number of children per member will behave exponentially.
        gnaritas 13y ago
        > behave exponentially. Behave exponentially != grow exponentially, still utterly missing the point; still trolling.
        13y ago
- lutusp 13y ago
  > If everyone has one or less children, the population does not grow exponentially. False. An exponential function, and a growing exponential function, differ only in the value of the exponent. Here's an equation that predicts future population based on the value of an exponential term: The equation: pt - p0 e^rt pt = population at time t p0 = present population r = rate of population growth, 1% = .01 t = time A result at 40 years for a population rate of change of -1.7% per year: e^(-.017 * 40) = .5066 This result says that, for a population growth rate of -1.7%, after 40 years the population will be about half its present size. It's an exponential result, it's even an exponential growth rate, but the growth rate is negative. In this image: http://i.imgur.com/LW6bk8t.png http://i.imgur.com/LW6bk8t.png The red trace is an exponential rate of change for r = +1.7%, the green trace for r = -1.7%. Both are exponential results, and both reflect what a population would look like for given r values.
  - gnaritas 13y ago
    False. Put all your bullshit math aside because that's what it is, bullshit trying to move the goalpost. The statement I made is absolutely factually true. If everyone has one or less children, the population does not grow exponentially. We're not talking about how to model population growth, or functions, we're talking about whether every couple having one child results in exponential growth and it simply does not. If the population decreases, that is not exponential growth. An exponential result != exponential growth. You are wrong and we are done.
    - lutusp 13y ago
      > The statement I made is absolutely factually true. If everyone has one or less children, the population does not grow exponentially. You need to learn mathematics (as well as grammar). Also learn "negative growth rate" while you're about it: http://wiki.answers.com/Q/Is_it_possible_to_have_a_negative_growth_rate http://wiki.answers.com/Q/Is_it_possible_to_have_a_negative_... And, everything else aside, all the described rates are exponential. > We're not talking about how to model population growth ... WHAT?? Here is what you said: "If everyone has one or less children, the population does not grow exponentially." How exactly is that NOT talking about how to model population growth? Also, it's "one or fewer children," not "one or less children." > An exponential result != exponential growth False in a discussion about population and exponential growth rates, terms you chose.