Where did Cain find his wife? (his sister?)

ChetSinger

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Well, this is how reliable "Jewish traditions" are or were, etc...

This from "other stories" on your link about Cain...

In Jewish tradition, Philo, Pirke De-Rabbi Eliezer and the Targum Pseudo-Jonathan asserted that Adam was not the father of Cain. Rather, Eve was subject to adultery having been seduced by either Sammael,[21][22] the serpent[23] (nahash, Hebrew: נחש‎) in the Garden of Eden,[24] or the devil himself.[17] Christian exegesis of the "evil one" in 1 John 3:10–12 have also led some commentators, like Tertullian, to agree that Cain was the son of the devil[25] or some fallen angel. Thus, according to some interpreters, Cain was half-human and half-angelic, one of the Nephilim. Gnostic exegesis in the Apocryphon of John has Eve seduced by Yaldaboth. However, in the Hypostasis of the Archons, Eve is raped by a pair of Archons.[26]

Now do you believe "any of that", etc, because I don't, etc, and it seems like they are taking quite a bit or "liberty", and way, way too much "liberty", with the Bible and what it actually says, or rather, "does not say at all", etc...

I still think he had no sister, etc...

And the Bible specifically warns us repeatedly about "traditions" especially Old Jewish ones, etc, calling them "artfully contrived fables or false stories", etc...

God Bless!
I'm doubtful of any of it, including the part regarding Cain's wife being named Awan. After all, I just learned of her yesterday. I apologize if I gave the impression that she was included among my beliefs. And I agree that Paul told the church to beware of Jewish superstitions. After all, they can get pretty wild.

What the tradition does reveal is that the Jewish rabbis of the time did not resort to non-Adamic humans when addressing this question. They kept it in the family, so to speak.
 
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TedT

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Could you show your working please?

Not my work but a friend's:

Ted said:
I am bothered not knowing how to work out exponent growth patterns. To use a simple population pattern, no twins, no deaths, let’s consider one birth a year by one person for 13 years when the oldest child also starts having children. All children start having children at 13 years old and keep having children every year. How many people are there in 125 years?
>
> How is this for something new?

On 9/19/2014 11:20 AM, Frederick wrote:

Yeehaw. Branching processes.

Let’s do the simplest case we can first, which we can arrive at because in the case you have here, everything is deterministic and happens in 13 year increments, so you can take one generation to be 13 years and work only in terms of generations. In generation 0, there is 1 person. Each person in the previous generation produced 13 people in the next generation, plus themselves, so, notating the number of people in generation i as N_i,

N_i = 14 * N_{i-1}

with N_0 = 1, the solution to this is N_i = 14^i.

125 years is between 9 and 10 generations, so there are between 20 billion and 289 billion people in this model.

The general program is to set up a recurrence for N_i in terms of earlier values of N, and set an initial condition (N_0). Then you are into the theory of difference equations, which is a well studied area of mathematics that just happens to be rarely taught. You also don’t have to get exact solutions via difference equations. You can just plug in numbers and work your way through:

i | N_i
————
0 | 1
1 | 14
2 | 196
3 | 2744
4 | 38416
5 | 537824
6 | 7529536
7 | 105413504

This is only possible if your expression for N_i only depends on the past, not the future. If it depends on the future as well, then you actually need the difference equations. It doesn’t usually depend on the future, but that problem does show up when calculating with boundary values in physics problems (temperature is X at this end, Y at that end, calculate what it is in the middle).

Let’s take a little more complicated case and work in terms of years. The next ingredient in such problems is using a structured population, that is, dividing it into groups so that the relations for each group are simple. In this case we are going to divide into juveniles and adults, the numbers of which we will write as J_i and A_i. The total population N_i = J_i + A_i.

The number of juveniles in a given year is given by the number that existed the previous year minus those that reach child bearing age and become adults (which is the number that were born 14 years ago, which is the same as the number of adults 14 years ago), plus those born in this year, or

J_i = J_{i-1} + A_{i-1} - A_{i-14}

and the number of adults is the number that existed last year plus the number of children born 14 years ago who have now become adults, which is again equal to the number of adults 14 years ago.

A_i = A_{i-1} + A_{i-14}

When we actually calculate this, we have to specify A_i and J_i for negative values of i. We just set that to be 0 since we assume we’re starting with a single adult that popped into existence at A_0, so A_0 = 1 and J_0 = 0. Then we can work forward the same way as before

A_0 = 1, J_0 = 0
A_1 = 1, J_1 = 1
A_2 = 1, J_2 = 2

A_13 = 1, J_13 = 13
A_14 = 2, J_14 = 13
A_15 = 3, J_15 = 14
A_16 = 4, J_16 = 15
...

So this is your general approach. Break your population into subpopulations that each behave uniformly, then write down recurrence relations for each subpopulation, simulate forward with the recurrence relations, and add up the subpopulations. You can do these calculations in Excel really easily and not have to worry about solving difference equations.

There are some other fun ones you might want to play with. The classic model in epidemiology, the SIR model (for susceptible-infectious-resistant) break your population into naive individuals not affected by the disease, infectious individuals who have caught it and are spreading it, and resistant individuals who are recovered and now immune. The simple model works quite well for things like the common cold that transmit readily and don’t kill you. Its terms are

S_i = previous susceptible population - number infected = S_{i-1} - r*I_{i-1}
I_i = previous infectious population + number infected - number recovered = I_{i-1} + r*I_{i-1} - v*I_{i-1}
R_i = previous resistant population + number recovered = R_{i-1} + v*I_{i-1}

where r is the number of people infected by an infectious individual per time step, and v is the probably per time step of an infectious individual recovering.

Once you’re comfortable running simulations like this in Excel, you can plot S, I, and R vs time and see the dynamics of a disease. Then you can try adding terms for other things. For example, something like flu or plague would add a term to I_i of the form -d*I_{i-1} which captures people dying. Then d is the probability per unit time of an individual dying. Tuberculosis is really interesting because it is very, very slow. You have to add birth and death rates to S, and death by other causes rates to I and R. Common cold mutates very fast, and you can simulate that by having resistant people become susceptible again at some rate, as the cold mutates and their resistance becomes useless.

This can all be pushed into much more detail in various interesting ways, mostly to account for things like randomness, partial mixing of people in the population (if you never go north of the river and the other guy never goes south, then you can’t be infected by him, and you have to further structure your population to account for this).

Fred
 
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Kylie

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Not my work but a friend's:



On 9/19/2014 11:20 AM, Frederick wrote:

Yeehaw. Branching processes.

Let’s do the simplest case we can first, which we can arrive at because in the case you have here, everything is deterministic and happens in 13 year increments, so you can take one generation to be 13 years and work only in terms of generations. In generation 0, there is 1 person. Each person in the previous generation produced 13 people in the next generation, plus themselves, so, notating the number of people in generation i as N_i,

N_i = 14 * N_{i-1}

with N_0 = 1, the solution to this is N_i = 14^i.

125 years is between 9 and 10 generations, so there are between 20 billion and 289 billion people in this model.

The general program is to set up a recurrence for N_i in terms of earlier values of N, and set an initial condition (N_0). Then you are into the theory of difference equations, which is a well studied area of mathematics that just happens to be rarely taught. You also don’t have to get exact solutions via difference equations. You can just plug in numbers and work your way through:

i | N_i
————
0 | 1
1 | 14
2 | 196
3 | 2744
4 | 38416
5 | 537824
6 | 7529536
7 | 105413504

This is only possible if your expression for N_i only depends on the past, not the future. If it depends on the future as well, then you actually need the difference equations. It doesn’t usually depend on the future, but that problem does show up when calculating with boundary values in physics problems (temperature is X at this end, Y at that end, calculate what it is in the middle).

Let’s take a little more complicated case and work in terms of years. The next ingredient in such problems is using a structured population, that is, dividing it into groups so that the relations for each group are simple. In this case we are going to divide into juveniles and adults, the numbers of which we will write as J_i and A_i. The total population N_i = J_i + A_i.

The number of juveniles in a given year is given by the number that existed the previous year minus those that reach child bearing age and become adults (which is the number that were born 14 years ago, which is the same as the number of adults 14 years ago), plus those born in this year, or

J_i = J_{i-1} + A_{i-1} - A_{i-14}

and the number of adults is the number that existed last year plus the number of children born 14 years ago who have now become adults, which is again equal to the number of adults 14 years ago.

A_i = A_{i-1} + A_{i-14}

When we actually calculate this, we have to specify A_i and J_i for negative values of i. We just set that to be 0 since we assume we’re starting with a single adult that popped into existence at A_0, so A_0 = 1 and J_0 = 0. Then we can work forward the same way as before

A_0 = 1, J_0 = 0
A_1 = 1, J_1 = 1
A_2 = 1, J_2 = 2

A_13 = 1, J_13 = 13
A_14 = 2, J_14 = 13
A_15 = 3, J_15 = 14
A_16 = 4, J_16 = 15
...

So this is your general approach. Break your population into subpopulations that each behave uniformly, then write down recurrence relations for each subpopulation, simulate forward with the recurrence relations, and add up the subpopulations. You can do these calculations in Excel really easily and not have to worry about solving difference equations.

There are some other fun ones you might want to play with. The classic model in epidemiology, the SIR model (for susceptible-infectious-resistant) break your population into naive individuals not affected by the disease, infectious individuals who have caught it and are spreading it, and resistant individuals who are recovered and now immune. The simple model works quite well for things like the common cold that transmit readily and don’t kill you. Its terms are

S_i = previous susceptible population - number infected = S_{i-1} - r*I_{i-1}
I_i = previous infectious population + number infected - number recovered = I_{i-1} + r*I_{i-1} - v*I_{i-1}
R_i = previous resistant population + number recovered = R_{i-1} + v*I_{i-1}

where r is the number of people infected by an infectious individual per time step, and v is the probably per time step of an infectious individual recovering.

Once you’re comfortable running simulations like this in Excel, you can plot S, I, and R vs time and see the dynamics of a disease. Then you can try adding terms for other things. For example, something like flu or plague would add a term to I_i of the form -d*I_{i-1} which captures people dying. Then d is the probability per unit time of an individual dying. Tuberculosis is really interesting because it is very, very slow. You have to add birth and death rates to S, and death by other causes rates to I and R. Common cold mutates very fast, and you can simulate that by having resistant people become susceptible again at some rate, as the cold mutates and their resistance becomes useless.

This can all be pushed into much more detail in various interesting ways, mostly to account for things like randomness, partial mixing of people in the population (if you never go north of the river and the other guy never goes south, then you can’t be infected by him, and you have to further structure your population to account for this).

Fred

Does this take into account things like the infrastructure needed to support such a huge population growth, like being able to produce enough food?
 
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