Reproduction Issue: Polynomial or Exponential?

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Discussion Overview

The discussion revolves around a hypothetical scenario involving the reproduction of organisms within a universe characterized by exponential and polynomial sizes. Participants explore the implications of these size definitions on the potential for population growth, specifically whether a polynomially large subset can lead to an exponentially large population through reproduction.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant presents a scenario where organisms reproduce within a universe that is exponentially large in n, while the subset is polynomially large, questioning if exponential growth in population is possible.
  • Several participants seek clarification on terms like "exponentially large," "polynomially large," and "compatible," indicating a need for precise definitions.
  • There is a suggestion that the concept of time may affect the growth dynamics, with one participant questioning if time flows independently of n.
  • Another participant argues that if the total population is fixed, then exponential growth cannot occur, while another counters that it is still possible to have exponentially many organisms within the subset.
  • Concerns are raised about the limitations imposed by the polynomial compatibility of organisms for reproduction, questioning the implications for population growth.

Areas of Agreement / Disagreement

Participants express differing views on the implications of fixed total population size on the possibility of exponential growth in the subset. There is no consensus on whether exponential growth can occur under the given conditions, and the discussion remains unresolved.

Contextual Notes

Participants highlight the need for clarity on definitions and the assumptions regarding population dynamics and reproduction constraints, which may affect the conclusions drawn from the scenario.

twoflower
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Hello,

let's have this scenario. We have a parameter n and a exponentially large (in n) universe of organisms. We are given a subset of this universe, which is only polynomially large. The only action which the organisms are able to do is that two compatible organisms join together and a new organism is created (the two original organisms remain there as well). The fact is that each organism is compatible with polynomially many other organisms from the universe and this polynom is the same for all the organisms.

The question is: if we let the given organisms reproduce as long as they are able to, may it happen that we end up with exponentially many organisms?
 
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What do you mean by "exponentially large in n", "polynomially large", and "compatible"?
 
twoflower said:
The question is: if we let the given organisms reproduce as long as they are able to, may it happen that we end up with exponentially many organisms?

You need to re-think your question. Does time flow independently of n?
 
Dragonfall said:
You need to re-think your question. Does time flow independently of n?

As I'm thinking about it again, now it seems clear to me that yes, we can end up with exponentially many organisms. I'm not sure what you mean for time to flow "independently of n", but we can imagine that time "happens" in discrete moments and only one thing can happen in each moment: two organisms join together and a new one emerge.
 
"Time flows independently of n" means that the total population does not grow. This is as opposed to the total population growing wrt time. If the total population grows exponentially wrt time, then the subpopulation will never catch up.
 
Dragonfall said:
"Time flows independently of n" means that the total population does not grow. This is as opposed to the total population growing wrt time. If the total population grows exponentially wrt time, then the subpopulation will never catch up.

I see. The universe (total population) is fixed and of the same size the whole time. It's only the subset which is growing.
 
If the total population is fixed, then you can't talk about "exponential growth". And it's obvious that in this case, even if 1 new specimen appears every 500 years, eventually the subpopulation will eclipse the total population.
 
Dragonfall said:
If the total population is fixed, then you can't talk about "exponential growth".

Why not? I can, indeed, end up with exponentially many organisms (exponentially many in n) - that was my concern.

Dragonfall said:
And it's obvious that in this case, even if 1 new specimen appears every 500 years, eventually the subpopulation will eclipse the total population.

Is it really so obvious even if we take into account the limitation that each organism can reproduce only with polynomial (in n) amount of other organisms?
 
  • #10
twoflower said:
Is it really so obvious even if we take into account the limitation that each organism can reproduce only with polynomial (in n) amount of other organisms?

Since the original organisms remain, all you need is for tow to find each other... right?
 

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