essentialsaltes

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How does one determine 'r'? Does it somehow relate to reproductive processes of the population that would lead to an average birth rate per organism?

One could potentially measure it under controlled conditions. (Not likely for wildebeest, but maybe for aphids.)
But yes, I imagine it relates to birth rate and death rate on an arguing-from-first-principles basis.
 
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Resha Caner

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One could potentially measure it under controlled conditions. (Not likely for wildebeest, but maybe for aphids.)
But yes, I imagine it relates to birth rate and death rate on an arguing-from-first-principles basis.

This has potential, but what is the extent of the "I imagine" comment? Should I keep going?

So far, I'd say our fundamental question is: How does population size change over time?
Our measure is the organism (in units of B (beings), since O would be too easily confused with zero).
Our fundamental theorem is dN/dt = rN, where:
* N = number of organisms (B)
* t = time (s, seconds)
* r = composite birth/death rate (B/s)

We have our inside joke ... Beings don't multiply over time, because that would be Bs.

We're all set for our next 2 questions:
1. What is a fundamental principle of birth?
2. What is a fundamental principle of death?

Finally, I don't know what you meant by your initiating comment ("I don't think we're getting any closer to evolution"), but I think we're quickly heading toward evolutionary questions. For example, with respect to birth, and specifically sexual reproduction, can any given organism mate with any other organism?
 
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essentialsaltes

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This has potential, but what is the extent of the "I imagine" comment? Should I keep going?

I'm a physicist by training, so I'm not qualified to teach biology. Just trying to share some things I've stumbled across in my own learning that seemed relevant to your questions.

1. What is a fundamental principle of birth?
2. What is a fundamental principle of death?

It's not clear to me what you mean. In terms of the model:
a birth is equivalent to B --> B+1
a death is equivalent to B --> B-1
 
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Amittai

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You're using a lot of terms I don't know. You'll need to define things. Not all of them. Pick one.

In the Self and Its Brain in the section Materialism Transcends Itself (pages 27-31), we have points like: (slightly potted by me)

- first appearance of heavier elements
- beginning of life on earth (and perhaps elsewhere) (latter might happen in a different time frame IMO)
- emergence of consciousness, of language, of human brain respectively

Pauli, Monod, Wittgenstein, Jennings and von Hayek are cited in passing. Then:

" ... replace the classical ideas of possibility or potentiality or capacity or force by their new version: by probability or propensity."

Refuting a "postulate of invariance" dating from 1906, he gives the example (also raised by others), of different processes occurring before and after the emergence of chlorophyll. More detailed illustrations were given in an earlier article. (I have come across my reading matter by serendipity.)

BTW if I rebadged "intelligent design" as intelligible configuration, would the public object? Surely patterns, even incredibly complex ones, are natural. I have a gut feeling that "if it was going to happen, it would happen here - or in a place like here". The anthropic principle is not that circular, except to denial deniers. Arthur Young (designer at Bell Helicopters) in the Geometry of Meaning points out what we all knew when we were knee high, that things are "out there" as well as "in here (our minds)" at the same time: objectivity + subjectivity = projectivity.

I've only just discovered your last two (short lived) threads. I'll try and bring my "bright ideas" (as an amateur) in here unless you would like to direct me back, for some of them.
 
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Resha Caner

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I'm a physicist by training, so I'm not qualified to teach biology.

I'm not asking to be taught traditional biology, so a teaching certificate is not a necessity here. So far, you're doing better than anyone else.

It's not clear to me what you mean. In terms of the model:
a birth is equivalent to B --> B+1
a death is equivalent to B --> B-1

A dimensional analysis of the composite rate, r, would suggest the birth and death rates are additive:
r = r_b - r_d, where:
r_b = birth rate
r_d = death rate

There are other possibilities, but this is the simplest solution that maintains proper dimensionality. If we subscribe to Occam's razor, the position would be this is the form of the composite rate until given reasons it should be otherwise.

For the time being, let's leave r_d as it is. In other words, we'll leave it as an empirical quantity for now. But let's expand on r_b.

I already suggested a question that will help elucidate possible principles behind r_b: Can any organism mate with any other organism? In other words, if we enumerate the population, n_i (i=1,N), will all combinations of organisms <n_i,n_j> i/=j produce new organisms?
 
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essentialsaltes

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I already suggested a question that will help elucidate possible principles behind r_b: Can any organism mate with any other organism? In other words, if we enumerate the population, n_i (i=1,N), will all combinations of organisms <n_i,n_j> i/=j produce new organisms?

Well, we have some options. Does our population reproduce sexually or asexually (or both)?

Based on the question, I imagine we're thinking of having both male and female populations and one of each is needed for reproduction.

(Not to complicate the model too much (unless you want) but there could be different birth and death rates for males and females. And the death rate of females may be tied to the overall rate, since there can be fatal complications to giving birth. And of course the possibility of mating will be related to the number of available males and females in a population. and... )
 
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Resha Caner

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Well, we have some options. Does our population reproduce sexually or asexually (or both)?

Based on the question, I imagine we're thinking of having both male and female populations and one of each is needed for reproduction.

Yes, let's focus on sexual reproduction for now.

(Not to complicate the model too much (unless you want) but there could be different birth and death rates for males and females. And the death rate of females may be tied to the overall rate, since there can be fatal complications to giving birth.

I had also suggested we focus solely on birth rate.

And of course the possibility of mating will be related to the number of available males and females in a population. and... )

True. So we have two populations: Nm, Nf (m=male, f=female). We can enumerate them n_m (i=1,Nm) and n_f (j=1,Nf). I'd suggest we put aside monogamy and infertility. Of course those would have to be dealt with at some point, but for the moment I'm more interested in drilling down to the most fundamental level.

Again, then, my question was: Will all combinations of <n_m,n_f> yield new organisms?
 
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essentialsaltes

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Again, then, my question was: Will all combinations of <n_m,n_f> yield new organisms?

Well, pregnancy does not occur with every individual act of 'combination'. Due to chance or infertility on either side.
Since(?) the model is supposed to model a single species, then at least in potentio, I would think all couplings could yield new organisms.
 
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essentialsaltes

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That was never specified.

I think that would be a useful assumption. Multiple species could be handled with parallel variables B1, B2, etc. Indeed some of the models are based on two species with separate variables for each: one predator, one prey.
 
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Resha Caner

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I think that would be a useful assumption. Multiple species could be handled with parallel variables B1, B2, etc. Indeed some of the models are based on two species with separate variables for each: one predator, one prey.

I was thinking more in terms of why two organisms can't produce offspring. Suppose male1 and female1 produce offspring; male2 and female2 produce offspring; but male1 and female2 can't; male2 and female1 can't.
 
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essentialsaltes

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I was thinking more in terms of why two organisms can't produce offspring. Suppose male1 and female1 produce offspring; male2 and female2 produce offspring; but male1 and female2 can't; male2 and female1 can't.

If male1 and female1 are cats and male2 and female2 are dogs, then the why is obvious.

If(?) we are talking about a single species, then I can see how that situation might arise in a ring species, and vaguely see why.

I don't even know if such a thing can happen among individuals in a 'normal' population, and if it can I feel pretty lost about why.
 
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Hans Blaster

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Yes, let's focus on sexual reproduction for now.



I had also suggested we focus solely on birth rate.



True. So we have two populations: Nm, Nf (m=male, f=female). We can enumerate them n_m (i=1,Nm) and n_f (j=1,Nf). I'd suggest we put aside monogamy and infertility. Of course those would have to be dealt with at some point, but for the moment I'm more interested in drilling down to the most fundamental level.

Again, then, my question was: Will all combinations of <n_m,n_f> yield new organisms?

These sorts of equations ( dN/dt = r * N ) don't apply to individuals, but rather to populations. That's what the N is for. Given N organisms, how many will die in a year? How many will be born?

These are the kind of things that can be measured and plugged into the equations. They can be solved coupling a "prey" version to a "predator" version. (More predators = more more prey deaths; more prey = larger "r" for the predator, etc.)

BTW, these are the types of equations at the heart of the COVID-19 growth projections.
 
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essentialsaltes

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I didn't think anything in science was decided on the basis of what seems obvious.

It's statements like this, without any other way of moving the discussion forward, that make me suspect your sincerity in this dialogue. In science? You seem to have mistaken discussions on this forum for science. I have already disavowed any expertise in biology. If you wish to take me to task for my failings, please feel free to enjoy yourself. Regardless...

Response A: since you were unwilling to restrict the discussion to a single species, then the common understanding that a species is a population that can interbreed would seem to make my comment apt.

Response B: since I know a lot of people with both dogs and cats, and know none that have cross-breeds, I have empirical evidence that my comment was apt.
 
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Resha Caner

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It's statements like this, without any other way of moving the discussion forward, that make me suspect your sincerity in this dialogue. In science? You seem to have mistaken discussions on this forum for science. I have already disavowed any expertise in biology. If you wish to take me to task for my failings, please feel free to enjoy yourself. Regardless...

Response A: since you were unwilling to restrict the discussion to a single species, then the common understanding that a species is a population that can interbreed would seem to make my comment apt.

Response B: since I know a lot of people with both dogs and cats, and know none that have cross-breeds, I have empirical evidence that my comment was apt.

Oh, I'm sorry. It was just a joke. It didn't seem this was a serious discussion, so I didn't think it would matter. I guess it's best I step back.
 
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Resha Caner

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For what it's worth, each of the latest threads was begun sincerely. But I must be getting old because I let myself be taken off-topic. Anyone who's been at CF more than 12 minutes knows who the trolls are, but ... well ... as it's been said: once the damage is done, it's done.

So, I can either play the jester or exit the stage. I've heard there's a 12-step program for this - maybe I'll check it out.
 
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muichimotsu

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I interpreted you to say my question was ill-formed, and therefore could not be answered. If you cannot answer, there's nothing more to say.
You could say that you'll think about it rather than the almost dismissive notion that it's just my opinion. Something mildly constructive, acknowledging a flaw in your question, very honest and humble
 
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