quote:

Originally posted by trancaholic Well, it's pretty much what I do for a living, and I guess I could mock up something non-fancy in Java in a couple of hours. It might even be fun. However, I would need to have the setup specified in much more detail: - What is the probability of an offspring of two extra digit-individuals being an extra digit-individual itself?

Well..Since the gene is dominant, the probability varies. If they're 65 and 65, it's 75%. If they're 66 and 65, it's 100%, and so is if they're 66 and 66. Additionally, if they're 66 and 55, it's a 100%, 65 and 55 have a 50% chance, while 55 and 55 have a 0%. However this makes it even more complicated since you'd also have to keep track of the recessive genes. If there's just 1000 people starting, I suppose you can say that each of the 2 6-fingered people has just one gene. But on larger populations, I'd say that it's best to say that 1/3 of them have a 66 and 2/3 have a 65.

quote:

- The reproduction selection mechanims is pretty unclear to me. If "the average couple" have two kids, then everyone will have to reproduce to keep the population growth from going negative (and hence answering the overall question trivially by having any such population go extinct). Additionally, it would mean that no natural selection is taking place this way.

Well, if it's just the average couple that manages to raise 2 kids, I'd say it just means that the population is neither growing nor declining. Some might have more and some less. My guess is that on average, 6-fingered people have 10% more. Now there's another problem here I'd say. If there would be 50% of the 6 fingered ppl in the population, then to maintain population equilibrium they'd have to have about 2.0952 children per couple, while 5-fingered ones would have some 1.9046 children. Mixed couples would then I suppose have 2 children exactly. But the thing is, if there's, say 10% of 6 fingered people in a group, the numbers are different, because he's closer to 2.1 children, while the rest is closer to 2.0. Ultimately, when 6 fingered people prevail, they'll have 2.0 children while the last 5 fingered couples will have about 1.81. So that's kinda one more dynamic parametar here.

quote:

Moreover, what does it mean for an individual to be "10% more likely to survive"? Does "survive" substitute for "procreate" here? And are individuals allowed to survive from one generation to the next (i.e. the same individual can compete for procreation "slots" in more than one generation)? Are individuals allowed to participate in more than one offspring generating couple in the same generation?

I don't really think the author actually thought about all these aspects, so we should make it as simple as possible. Survive does seem to substitute for procreate, and I think we should just have them be absolutely monogamous and living equal lifespans. I don't think changing that would make a big difference, aside from making the problem even more complicated.

quote:

And does "10% more" hint at "80% rather than 70% chance of surviving" or "77% rather than 70% chance of surviving". Depending on how all these questions are answered the results may vary significantly.

I'd say just substitute survive for procreate. If they all didn't have a 100% survival rate, with just 2 children per couple they'd die out pretty soon. So my guess is that the author wanted to say procreate.

Now if you actually go and do this, I'd really like to see how you did it

___________________
1+1=10

quote:

Originally posted by DrUg_Tit0 Well..Since the gene is dominant, the probability varies. If they're 65 and 65, it's 75%. If they're 66 and 65, it's 100%, and so is if they're 66 and 66. Additionally, if they're 66 and 55, it's a 100%, 65 and 55 have a 50% chance, while 55 and 55 have a 0%.

To cut it short, what I need would be the following probabilities (P(56|65,66) means "if a 65 parent and 66 parent gets a kid, then the probability of that kid being a 56 is P(56|65,66)"):

P(66|66,66)
P(65|66,66)
P(56|66,66)

P(66|66,65)
P(65|66,65)
P(56|66,65)

P(66|66,56)
P(65|66,56)
P(56|66,56)

P(66|66,55)
P(65|66,55)
P(56|66,55)

P(66|65,65)
P(65|65,65)
P(56|65,65)

P(66|65,56)
P(65|65,56)
P(56|65,56)

P(66|65,55)
P(65|65,55)
P(56|65,55)

P(66|56,56)
P(65|56,56)
P(56|56,56)

P(66|56,55)
P(65|56,55)
P(56|56,55)

P(66|55,55)
P(65|55,55)
P(56|55,55)

The last three should sum to 0.002, according to the requirement that one out of 500 kids born to normal parents would have the gene anomaly.

quote:

Originally posted by DrUg_Tit0 However this makes it even more complicated since you'd also have to keep track of the recessive genes. If there's just 1000 people starting, I suppose you can say that each of the 2 6-fingered people has just one gene. But on larger populations, I'd say that it's best to say that 1/3 of them have a 66 and 2/3 have a 65.

I don't follow you here. Which gene is it that you see as recessive? Would it be somehow captured by the detailed list of probabilities listed above?

quote:

Originally posted by DrUg_Tit0 Well, if it's just the average couple that manages to raise 2 kids, I'd say it just means that the population is neither growing nor declining. Some might have more and some less. My guess is that on average, 6-fingered people have 10% more.

This I also something I don't understand. When you say that 6-fingered people have 10% more kids, do you then mean than each member of *the entire group* of 6-fingered people on the average have 10% more kids than people with five fingers? I could agree with that.

quote:

Originally posted by DrUg_Tit0 Now there's another problem here I'd say. If there would be 50% of the 6 fingered ppl in the population, then to maintain population equilibrium they'd have to have about 2.0952 children per couple, while 5-fingered ones would have some 1.9046 children. Mixed couples would then I suppose have 2 children exactly. But the thing is, if there's, say 10% of 6 fingered people in a group, the numbers are different, because he's closer to 2.1 children, while the rest is closer to 2.0. Ultimately, when 6 fingered people prevail, they'll have 2.0 children while the last 5 fingered couples will have about 1.81. So that's kinda one more dynamic parametar here.

Well, the entire thing seems highly unrealistic if everyone procreates. And it definitely clashes with the intuition of 6-digit individuals somehow having an advantage in getting to the mating stage. I would think of the reproduction mechanism in the following manner:

while (not enough new individuals to constitute a generation)
- sample two individuals from the old population, that has not already been sampled. Each individual with 6-digits on at least one hand has a 10% higher chance of being picked than someone with only 5 digits.
- generate x new individuals from these sampled individuals (the children of the couple)

Come to think of it, maybe the 10% doesn't hold for an 66-individual?

quote:

Originally posted by DrUg_Tit0 I don't really think the author actually thought about all these aspects, so we should make it as simple as possible. Survive does seem to substitute for procreate, and I think we should just have them be absolutely monogamous and living equal lifespans. I don't think changing that would make a big difference, aside from making the problem even more complicated. I'd say just substitute survive for procreate. If they all didn't have a 100% survival rate, with just 2 children per couple they'd die out pretty soon. So my guess is that the author wanted to say procreate.

I agree here. Also having equal lifetimes is a must if the question about "how many generations" is to make any sense.

quote:

Originally posted by DrUg_Tit0 Now if you actually go and do this, I'd really like to see how you did it

It won't be very deep - and I have a bad habit of not commenting my code, but of course I can post it (if I get the probabilities, that is).

quote:

Originally posted by trancaholic To cut it short, what I need would be the following probabilities (P(56|65,66) means "if a 65 parent and 66 parent gets a kid, then the probability of that kid being a 56 is P(56|65,66)"): P(66|66,66) P(65|66,66) P(56|66,66) P(66|66,65) P(65|66,65) P(56|66,65) P(66|66,56) P(65|66,56) P(56|66,56) P(66|66,55) P(65|66,55) P(56|66,55) P(66|65,65) P(65|65,65) P(56|65,65) P(66|65,56) P(65|65,56) P(56|65,56) P(66|65,55) P(65|65,55) P(56|65,55) P(66|56,56) P(65|56,56) P(56|56,56) P(66|56,55) P(65|56,55) P(56|56,55) P(66|55,55) P(65|55,55) P(56|55,55) The last three should sum to 0.002, according to the requirement that one out of 500 kids born to normal parents would have the gene anomaly.

Um, no I don't think it should work that way. You just start with 0.2% of people already having 6 fingers, and go on from there. Having 5 fingered people have a 2% chance of evolving a 6 fingered gene would necessitate having 6 fingered people with a chance of evolving a 5 fingered gene. So the last 3 should sum up to 0.

quote:

I don't follow you here. Which gene is it that you see as recessive? Would it be somehow captured by the detailed list of probabilities listed above?

I think the question said that 5 fingered gene is recessive. Lots of the possibilities you mentioned above are impossible. Mostly the ones where 55+55 give a 6 fingered child, or where xx+66 make a 5 fingered child.

quote:

This I also something I don't understand. When you say that 6-fingered people have 10% more kids, do you then mean than each member of *the entire group* of 6-fingered people on the average have 10% more kids than people with five fingers? I could agree with that.

Yes, on average the 6 fingered group has 10% more children than the 5 fingered group. I suppose mixed couples have it half-way in between.

quote:

Well, the entire thing seems highly unrealistic if everyone procreates. And it definitely clashes with the intuition of 6-digit individuals somehow having an advantage in getting to the mating stage.[quote] As long as the procreation average of a group is the same, it doesn't matter if every individual has 2 kids, or if one individual has 4 kids while another one has none. [quote] I would think of the reproduction mechanism in the following manner: while (not enough new individuals to constitute a generation) - sample two individuals from the old population, that has not already been sampled. Each individual with 6-digits on at least one hand has a 10% higher chance of being picked than someone with only 5 digits. - generate x new individuals from these sampled individuals (the children of the couple)

Hm..I suppose a 65 or a 56 individual will have 6 fingers on both hands, that there won't be ones with 6 fingers on just one hand only. I suppose picking chance is more realistic than just arbitrarily saying they have 10% more children, and that may be what the author actually meant. I was thinking of giving them all a same chance and just having 6 fingered ones 10% more kids. But I suppose it shouldn't matter much in the end.

quote:

Come to think of it, maybe the 10% doesn't hold for an 66-individual?

It should, since he's externally no different than a 5 fingered person.

quote:

It won't be very deep - and I have a bad habit of not commenting my code, but of course I can post it (if I get the probabilities, that is).

Yeah..well at least you have some idea about it..Although I might start working on it too now, I'm kinda getting intrigued..

___________________
1+1=10

So I'm really curious as to what the hell time is. Does it even exist? I'm not very well read in this area of physics. Are there any books or something you guys could recommend that could provide some insight? I'm guessing Drug_Tito, trancaholic, and Renegade have probably read plently of material related to this subject. So if you guys could direct me to something that would help, that would be much appreciated.

___________________
"The Greatest enemy of knowledge is not ignorance, it is the illusion of knowledge." -Stephen Hawking
"First they came for the communists, and I did not speak out— because I was not a communist;
Then they came for the socialists, and I did not speak out— because I was not a socialist;
Then they came for the trade unionists, and I did not speak out— because I was not a trade unionist;
Then they came for the Jews, and I did not speak out— because I was not a Jew;
Then they came for me— and there was no one left to speak out for me." -Martin Niemöller

So here's some stuff from wiki:

quote:

Many ancient philosophers wrote lengthy essays on time, believing it to be the essence around which life was based. A famous analogy was one comparing the time of life to the passing of sand through an hourglass. The sand at the top is the future, and, one tiny grain at a time, the future flows through the present into the past. The past ever expanding, the future ever decreasing, but the future grains being moulded into the past through the present. This was widely discussed in around the 3rd century CE. ..... Newton believed time and space form a container for events, which is as real as the objects it contains. In contrast, Leibniz believed that time and space are a conceptual apparatus describing the interrelations between events. These differences came to a head in the famous Leibniz-Clark Correspondence. Leibniz and others thought of time as a fundamental part of an abstract conceptual framework, together with space and number, within which we sequence events, quantify their duration, and compare the motions of objects. In this view, time does not refer to any kind of entity that "flows," that objects "move through," or that is a "container" for events.

I tend to lean towards Leibniz's understanding of time. Ofcourse, this still doesn't satisfy my curiousity. There also seems to be great disagreemnt amongst scientists and philosophers alike on what time is...

bah...

I guess I'll wait for a response from one of you guys before I post more stuff.

___________________
"The Greatest enemy of knowledge is not ignorance, it is the illusion of knowledge." -Stephen Hawking
"First they came for the communists, and I did not speak out— because I was not a communist;
Then they came for the socialists, and I did not speak out— because I was not a socialist;
Then they came for the trade unionists, and I did not speak out— because I was not a trade unionist;
Then they came for the Jews, and I did not speak out— because I was not a Jew;
Then they came for me— and there was no one left to speak out for me." -Martin Niemöller

quote:

Originally posted by shaolin_Z So I'm really curious as to what the hell time is. Does it even exist? I'm not very well read in this area of physics. Are there any books or something you guys could recommend that could provide some insight? I'm guessing Drug_Tito, trancaholic, and Renegade have probably read plently of material related to this subject. So if you guys could direct me to something that would help, that would be much appreciated.

time Audio pronunciation of "time" ( P ) Pronunciation Key (tm)
n.

1.
1. A nonspatial continuum in which events occur in apparently irreversible succession from the past through the present to the future.
2. An interval separating two points on this continuum; a duration: a long time since the last war; passed the time reading.
3. A number, as of years, days, or minutes, representing such an interval: ran the course in a time just under four minutes.
4. A similar number representing a specific point on this continuum, reckoned in hours and minutes: checked her watch and recorded the time, 6:17 A.M.
5. A system by which such intervals are measured or such numbers are reckoned: solar time.

what's unsatisfactory about this definition to you?


what could the thing we refer to as "time" be, if not time? what are our clocks measuring?

another approach, hopefully you know some basics about music production for this one:

you have a track playing a pattern at 120bpm (beats per minute), the pattern has only one short note on it's first step (in it's begining), and it cycles every 16 steps. what happens between the soundings of the note? what separates them? is it three dimensional space?

___________________
People who own my ass: Citric Acid, Boomer187, Tribu, Sand Leaper,
Jackson, venomX, jamie, Renegade, Konjin, Akridrot, Miss Bliss.
Psy-T - Down The Rabbit Hole (400minute long acid set)

^^ I think you misunderstood my question. Is time even real or is it a function of our mind that shapes our perception of the universe? I don't know if I expressed it really well just here so let me know if you need some clarification .

___________________
"The Greatest enemy of knowledge is not ignorance, it is the illusion of knowledge." -Stephen Hawking
"First they came for the communists, and I did not speak out— because I was not a communist;
Then they came for the socialists, and I did not speak out— because I was not a socialist;
Then they came for the trade unionists, and I did not speak out— because I was not a trade unionist;
Then they came for the Jews, and I did not speak out— because I was not a Jew;
Then they came for me— and there was no one left to speak out for me." -Martin Niemöller

quote:

Originally posted by shaolin_Z ^^ I think you misunderstood my question. Is time even real or is it a function of our mind that shapes our perception of the universe? I don't know if I expressed it really well just here so let me know if you need some clarification .

define "real".

___________________
People who own my ass: Citric Acid, Boomer187, Tribu, Sand Leaper,
Jackson, venomX, jamie, Renegade, Konjin, Akridrot, Miss Bliss.
Psy-T - Down The Rabbit Hole (400minute long acid set)

Oh boy, somehow I expected your philosophical ass to say something like that . Well, real in the sense that the existence of it is independent of how our brain functions.

But that was only one aspect to my question. I'm also interested in having a better understanding of what it is (and by that I don't mean a dictionary definition or a mechanics text book definition).

___________________
"The Greatest enemy of knowledge is not ignorance, it is the illusion of knowledge." -Stephen Hawking
"First they came for the communists, and I did not speak out— because I was not a communist;
Then they came for the socialists, and I did not speak out— because I was not a socialist;
Then they came for the trade unionists, and I did not speak out— because I was not a trade unionist;
Then they came for the Jews, and I did not speak out— because I was not a Jew;
Then they came for me— and there was no one left to speak out for me." -Martin Niemöller

I remember something about it gravity being the curve of space-time.... hmm is time not actaully another part of space. Like spacetime basicly? Just another (invisable to us) dimention?

quote:

Originally posted by shaolin_Z Oh boy, somehow I expected your philosophical ass to say something like that . Well, real in the sense that the existence of it is independent of how our brain functions.

cogito ergo sum can only lead us so far...
in other words.. name one thing which is definitely independent of our brain functions and explain how it is independent.

quote:

Originally posted by shaolin_Z But that was only one aspect to my question. I'm also interested in having a better understanding of what it is (and by that I don't mean a dictionary definition or a mechanics text book definition).

while we're rejecting time, why not reject space aswell? it conforms to the same definition...

___________________
People who own my ass: Citric Acid, Boomer187, Tribu, Sand Leaper,
Jackson, venomX, jamie, Renegade, Konjin, Akridrot, Miss Bliss.
Psy-T - Down The Rabbit Hole (400minute long acid set)

quote:

Originally posted by Dervish I remember something about it gravity being the curve of space-time.... hmm is time not actaully another part of space. Like spacetime basicly? Just another (invisable to us) dimention?

with time being A nonspatial continuum in which events occur in apparently irreversible succession from the past through the present to the future, and continuum being A continuous extent, succession, or whole, no part of which can be distinguished from neighboring parts except by arbitrary division... space doesn't seem that far off...

___________________
People who own my ass: Citric Acid, Boomer187, Tribu, Sand Leaper,
Jackson, venomX, jamie, Renegade, Konjin, Akridrot, Miss Bliss.
Psy-T - Down The Rabbit Hole (400minute long acid set)