The Carter Catastrophe

[revolutio]

This is Professor Brandon Carter.
Dr. Carter here thinks you are all going to die. Well maybe not you, but certainly your ancestors. It will not just be any localized disaster either, no the entire human race will be wiped out.

About this time I imagine some of you are dieing (haha, get it?) to know why he would thnk such a ghastly thing. The answer lies in statistics and it doesn't even require a degree to understand.

There are three options for humanity's future. These are based on traditional observations of animal populations in the wild.

A. Constant numbers - This occurs when a population reaches equilibrium with its environment and, over long periods of time, retains virtually the same numbers.
B. Exponential growth - The population is wildly successfull and grows at an exponential rate. (think mosquitoes) There is virtually no limits to how large this population will grow.
C. Extinction - The population dies out from one means or another. Populations that are going to die out usually do so in the first 200 generations.

Alright, now where does humanity fall? Given our current rate of growth both in numbers and technologically. Humans seem quite determined to fit into the B scenario. However there is a catch, as Dr. Carter suggested first in 1983.

Consider scenario B. Humanity expands into the stars, it terraforms and settles down on tens, hundreds, thousands, and eventually millions of planets. We number well into the trillions. Suppose you want to pick a random person from the complete array of humans to ever live (from Adam & Eve to the end of time). Well over 99% of the time you will pick someone who lives in the enormously distant future.

What are the chances that, of all the times you could have lived, you are living now? Now is the veritable dawn of humanity. The total number of humans ever hasn't even topped 50 billion, a tenth of those living right now. The chances are astronomical.

However there is another way to look at things that makes it much much more likely for us to be living when we are. Complete and total extinction of the human species. In that case the chances of us living right now when we do would be a mere 1/10, for the right price most gamblers would bet on those odds. The alternative, scenario B, puts our odds of living right now at 1/1,000,000,000,000 at very least.

Carter did not make a case for how the species would die out; he didn't need to. The statistics are there. Human extinction is not only likely by those numbers, but an almost certainty.

How lucky are you feeling?

 

[David Gould]

This is bad play with numbers.

By this logic, every generation proceeding this one was the last generation.

The population of the Earth had never topped 1 billion 1,000 years ago. If you picked a person living then, the chances of them being alive at that particular time in history, given the billions of people yet to live, is so small as to be almost impossible.

But if that generation were the last generation then the chances of them being alive in it are very large.

Thus, all of humanity died out in the year 1057. Oops.

Basically, the logic is complete rubbish.

 

[revolutio]

This is bad play with numbers.

By this logic, every generation proceeding this one was the last generation.

His theory doesn't say that the next generation is going to die. That is a perversion of the words. Each generation is just increasingly likely to die.

So, yes it is improbable that we survived this long, however it is not impossible (obviously).

The logic is only rubbish if you want to see it as so.

 

[David Gould]

His theory doesn't say that the next generation is going to die. That is a perversion of the words. Each generation is just increasingly likely to die.

So, yes it is improbable that we survived this long, however it is not impossible (obviously).

The logic is only rubbish if you want to see it as so.

I still cannot see how each generation is more likely to die than the one proceeding it.

Basically, by his logic it is far less likely that the first generation of humans existed than this one as there were far less people then:

say the first generation was 10,000 people.

say humans live to gain a population of 100 trillion. If it was exponential growth, then the human population would have a limit of 200 trillion.

At our level, we have a population of 10 billion.

Thus, it means that picking a person who is alive in our generation is a million times more likely than picking someone from the first generation.

As such, it is a million times more likely that humans are alive at this time than it is that they were alive at the first generation ...


As I said, the logic is complete **** ...

 

[revolutio]

Basically, by his logic it is far less likely that the first generation of humans existed than this one as there were far less people then:

Ah you got completely confused. Yes if you had to pick someone at random you would be more likely to pick someone alive right now than at the dawn of time.

That wasn't what he was saying though. As the number of people that have existed and do exist increases, the probability of picking one person in particular becomes increasingly difficult. It doesn't matter how many people are alive now, I think that might have confused you.

It is hard to explain and I am not the best explainer obviously so here are some more links that give explanations. Also for statistical justification of this look up Baye's Theorum.

Link
Link
Link

 

[Philosoft]

His theory doesn't say that the next generation is going to die. That is a perversion of the words. Each generation is just increasingly likely to die.

I don't think so. Why would the successive generation death probabilities be additive? Statistically speaking, a particular generation G2 is only going to carry an increased death probability over a prior generation G1 if the extinction probability of the species is known in advance.

Consider a (hopefully) analogous thought experiment: Suppose I have an opaque bag containing 20 ping-pong balls, 10 white, 10 black. If I give you the bag, tell you only that half the balls are white and half black, and have you pull one ball at a time, you'll never be able to calculate a probability of pulling a white ball or a black ball, no matter how many balls you pull or in what order. But if I tell you there are 20 balls total, you can easily calculate either probability after each pull.

So, yes it is improbable that we survived this long, however it is not impossible (obviously).

Actually, he's just deducing that we live in the "distant future." But that appears to be a deducible fact about any particular generation.

 

[David Gould]

As I read somewhere else, if you are riding an exponential curve you are always at the steepest gradient. This makes it a ridiculous way of trying to work out the likelihood of the gradient continuing. Make the calculation 500 years ago, make it 500 years from now, and you will come to exactly the same conclusion. And that proves its rubbish.

 

[David Gould]

Ah you got completely confused. Yes if you had to pick someone at random you would be more likely to pick someone alive right now than at the dawn of time.

That wasn't what he was saying though. As the number of people that have existed and do exist increases, the probability of picking one person in particular becomes increasingly difficult. It doesn't matter how many people are alive now, I think that might have confused you.

It is hard to explain and I am not the best explainer obviously so here are some more links that give explanations. Also for statistical justification of this look up Baye's Theorum.

Link
Link
Link

As the calculation is true for any generation then the calculation is worthless.

From the stuff I have seen on the Internet regarding this, all of the objections are the same as mine - that no matter what time you pick, the calculation indicates the same result.

 

[David Gould]

This is taken from http://forums.gouranga.com/iceyboard/?ibaction=topic&topic=1197&page=1

The poster Reverend Ted says:

Once again I come back to the point that we are not randomly selected from the total human population (spanning all years of human existance).
We are not a suitably random sample.

We were born when we were born, no necessarily when we were likely to be born.

That is to say:
Your vehicle is one of millions on the planet. If you randomly select a vehicle, it is VERY UNLIKELY that you will pick the 1 out of millions that is yours. However, it is unreasonable to claim that the vehicle sitting in your driveway is not yours because the probability of it being yours is very low given the total population of vehicles.

I posit that the graph of human population over time (given enough time) would resemble a sloped hill approaching a plateau, a steadily decreasing ocsillation about an equilibrium point, or a constant semi-random oscillation about that point.
This graph would likely be interrupted by a cataclysmic event at some undetermined point, very likely a point independent of any function of the population curve.

The last line is significant: unless the population causes the catastrophe event then the catastrophe event is an independent event.

As such, the size of the population cannot be used to determine the likelihood of such an event.

 

[revolutio]

As I read somewhere else, if you are riding an exponential curve you are always at the steepest gradient. This makes it a ridiculous way of trying to work out the likelihood of the gradient continuing. Make the calculation 500 years ago, make it 500 years from now, and you will come to exactly the same conclusion. And that proves its rubbish.

I really don't get where you are coming from with this calculation thing. The calculations change with each generation since the total population ever has increased. As the numbers increase it becomes less and less likely that you can pick a particular person.

Consider a (hopefully) analogous thought experiment: Suppose I have an opaque bag containing 20 ping-pong balls, 10 white, 10 black. If I give you the bag, tell you only that half the balls are white and half black, and have you pull one ball at a time, you'll never be able to calculate a probability of pulling a white ball or a black ball, no matter how many balls you pull or in what order. But if I tell you there are 20 balls total, you can easily calculate either probability after each pull.

Suppose I have a bag with some black beads in it. I tell you that there is one white bead in there. I tell you that there are either 3000 or 300 or two black beads in that bag. You start to pick beads out of the bag one at a time. Your second draw is the white bead. What assumption do you make?

 

[revolutio]

This is taken from http://forums.gouranga.com/iceyboard/?ibaction=topic&topic=1197&page=1

The last line is significant: unless the population causes the catastrophe event then the catastrophe event is an independent event.

As such, the size of the population cannot be used to determine the likelihood of such an event.

You are right that the catastophe would be independent. Hence Carter did not make any claims about what the catastrophe would be.

However it still remains that you are more likely to be here now if humanity does become extinct than you are to be here now if humanity's growth continues undetered.

 

[David Gould]

I really don't get where you are coming from with this calculation thing. The calculations change with each generation since the total population ever has increased. As the numbers increase it becomes less and less likely that you can pick a particular person.

And I guess I can't see the connection between picking a particular person and the end of humanity. There is no causal connection. As such, the population cannot be a relevant factor in when the end of humanity comes.

 

[David Gould]

You are right that the catastophe would be independent. Hence Carter did not make any claims about what the catastrophe would be.

However it still remains that you are more likely to be here now if humanity does become extinct than you are to be here now if humanity's growth continues undetered.

You missed the point. The only way that a catastrophe event can be more likely now than say 500 years ago or 500 years into the future is if human population somehow has a causal impact on the likelihood of catastrophe events.

If the two are independent - population goes up, catastrophe event likelihoods stay the same - then I am no more likely to see a catastrophe event than any other person in history, past or future.

 

[David Gould]

The beads in a bag thing is an interesting concept but I think that it needs work.

If we take the example of a bag with one white ball and an unknown number of black balls and we draw a white ball is it reasonable to assume that the number of black balls left is likely to be very small or not? I think we are.


But this analogy is not the same because my existence at this point in time is NOT a random event.

I can only have been born after my parents. And they can only be born after their parents. And so on.

In other words, I - the individual, David Gould - have a zero chance of being born in 7890. I also have zero chance of being born in 345.


Yet the Carter Catastrophe depends on it being random. Unless I am missing something?

 

[revolutio]

You missed the point. The only way that a catastrophe event can be more likely now than say 500 years ago or 500 years into the future is if human population somehow has a causal impact on the likelihood of catastrophe events.

If the two are independent - population goes up, catastrophe event likelihoods stay the same - then I am no more likely to see a catastrophe event than any other person in history, past or future.

Okay now atleast I see where you are coming from.

I have heard this arguement before in one form or another. It is basically the reason I don't believe in the Carter Catastrophe, I just find it interesting. It holds up to scrutiny from some angles but not from others. I personally regard it as a misuse of statistics, but that is just my unedecated opinion.

However the problem is that it still leaves a paradox. Though you can "prove" that the disaster isn't more likely since it would have to be independent of population. It is also "proven" that a disaster is extremely likely based on the explanation I gave with the bag of beads. I am very tired so check my logic, but that would imply that the disaster was actually dependent on the population size.

Anyway, I don't really care one way or another. It is just a fun idea to toy around with.

 

[David Gould]

Okay now atleast I see where you are coming from.

I have heard this arguement before in one form or another. It is basically the reason I don't believe in the Carter Catastrophe, I just find it interesting. It holds up to scrutiny from some angles but not from others. I personally regard it as a misuse of statistics, but that is just my unedecated opinion.

However the problem is that it still leaves a paradox. Though you can "prove" that the disaster isn't more likely since it would have to be independent of population. It is also "proven" that a disaster is extremely likely based on the explanation I gave with the bag of beads. I am very tired so check my logic, but that would imply that the disaster was actually dependent on the population size.

Anyway, I don't really care one way or another. It is just a fun idea to toy around with.

It certainly is interesting, although I think it is an abuse of logic, not statistics

I will have another think about the bag example.

 

[revolutio]

Yet the Carter Catastrophe depends on it being random. Unless I am missing something?

I see your point. However the Carter Catastrophe only requires a consciousness, the actual origins of said consciousness do not matter. As long as the numbers in terms of populations remain the same, then the only other criteria is a single person being self-aware that they are here right now.

 

[David Gould]

I have just had a thought. If the human population became stable, say at 50 billion people, then the Carter Catastrophe calculations are still valid, although the proababilites for selecting any given human are larger as the exponential thing is not there.

The Carter Catastrophe is still valid even if the population drops to four people and remains stable, given enough time in the 'Far Future' scenario.

This to me further demonstrates that it is false.