I was lost in the original Doomsday argument’s logic:
supposing the humans alive today are in a random place in the whole human history timeline, chances are we are about halfway through it.
This assumes that the timeline is finite, otherwise “half-way” makes no sense. The following argument
we could be 95% certain that we would be within the last 95% of all the humans ever to be born.
relies on this assumption. The remaining logic is “if we assume a finite timeline, then we can estimate how long it is with some probability, given the population growth curve so far”. The calculations themselves are irrelevant to the conclusion, which is “the total number of humans that will ever live is finite”.
So, the whole argument boils down to “if something is finite, a reasonable function of it is also finite”, which is hardly interesting.
So long as we have imprecise measurements and only a finite amount of matter and energy then time is not an issue because we eventually run out of unique (or distinguishable by any of our measurements) humans that can exist and we can just ask the nearly equivalent question: “what is the probability that I am in the last 95% of unique humans to ever exist?” At some point every possible human has been created and out of that huge finite number each one of us is an index. The question is whether the heat death stops the creation of humans in this universe before 20 times the current number of humans has been created (for the 95% argument).
However, the statement of the problem completely ignores prior probabilities. For instance it’s possible that we now have more than 5% of the total human population alive right now (that would be true if only 100 billion have ever lived). That would mean that the oldest people alive right now have a 0 probability of being in the last 95%. Additionally, we have a very good idea of whether we are in the last 99.9999999% of humans who have ever lived; the last 7 babies baby born on Earth have a slightly positive probability, everyone else has a 0 probability. What is the probability that 7 more babies will be born, replacing the current 7 who have the possibility of being the last? 1 for all practical purposes. 100 babies? Same. In fact it probably already happened while I was writing this comment. A billion? Probably still very, very close to 1. The calculation can be extended into the future based on our knowledge of our environment and society and the probability of existential risk. Unless we have a good reason for predicting the destruction of all humans we shouldn’t predict that we are in the last 95% of unique humans. Humans are built to reproduce, they have an environment that will probably last thousands if not hundreds of thousands of years, and they are learning to build their own environments anywhere they want. These facts are far more important than which particular brain is randomly selected to think of the doomsday argument.
EDIT: The part about the last 95% of humans is wrong if there are more than 5% still alive; it would have to be some of the first 5% still alive for the argument to be wrong for them today.
This is an assumption based on our current level of science and technology and failure of imagination. There are many possible ways around it: baby universes, false vacuum decay, even possibly conversion of dark energy (which appears to be inexhaustible) to normal matter, to name a few.
However, the statement of the problem completely ignores prior probabilities
I was unable to follow your logic there… Are you saying that the Doomsday argument is wrong or that it is irrelevant or what?
This is an assumption based on our current level of science and technology and failure of imagination. There are many possible ways around it: baby universes, false vacuum decay, even possibly conversion of dark energy (which appears to be inexhaustible) to normal matter, to name a few.
That may reveal a weakness in the doomsday argument itself. For instance, did any of the first hundred bllion billion humans even think of the doomsday argument? If the doomsday argument is flawed, will many future humans think of it more than briefly from historical interest? The nature of the human considering the doomsday argument significantly affects the sample space. Future humans in a free-energy universe would immediately see the falsehood of the doomsday argument and so from our perspective wouldn’t even be eligible for the sample space. It may be that the doomsday argument only has a chance of being seriously considered by a 20th/21st century human, which simply turns the question into “what is the probability that I am somewhere between the 100 billionth and 130 billionth human to ever live?” or whatever the appropriate bounds might be.
I was unable to follow your logic there… Are you saying that the Doomsday argument is wrong or that it is irrelevant or what?
The doomsday argument is correct if no other information besides the total number of humans who have lived before me and finite resources are assumed. With additional information our confidence should be increased beyond what the doomsday argument can provide, making the doomsday argument irrelevant in practice.
SSA Doomsday: You are the hundred billionth human who ever lived (or something like that). If there are two hundred billion humans total, this is not very unusual. But if there are to be a quadrillion humans, you would be in a very unlikely situation, in the first 0.0...% or something.
Analogous argument: you’re told that you’re the smartest person in your extended family. This makes it more likely your extended family is small, rather than large. Replace “smartest” with any property that distinguishes you from the rest of humanity, and the argument follows.
Isn’t it more analogous to having a child be told “you’re 5 years old!” and for this reason this makes the kid believe they’re only likely to survive to around age 10?
Imagine you’re told you’re 50 years old… is only surviving to age 100 that bad a guess for a statistical argument which takes into account close to no information whatsoever?
(Reminds me of the reaction to the sunrise example for Laplace’s law.)
Let’s imagine that I’m an immortal being who has lived since prehistorical times—except that I lose all memories every 50 years or so, and my body and my mind reverts to the form of an infant, so that for all intends and purposes I’m a new person.
From prehistorical times, I can therefore think the Doomsday argument to myself—if I had the knowledge to do so. So when I’m Urgh the caveman, among the first 10,000 people I think that mankind is only likely to survive to around double that size, and when I’m Marconius the Roman, I think it likely that mankind is only likely to survive to around double that present size, and when I’m Aris Katsaris the modern Westerner, I think it likely that mankind is only likely to survive to around double this present size...
And each time, I effectively die and forget all my thoughts about Doomsday, and get born anew and reconstruct the Doomsday argument for myself. And can do so for as long as humanity lasts, and it never actually provides me any new information about how long humanity will last.
Until the point where I’m made physically or mentally immortal I guess, and no longer die, at which point I no longer ask the Doomsday argument again, because I first asked it millenia back and remember it.
I don’t know. This chain of thought above makes me intuitively think the Doomsday argument is bollocks, but I don’t know if it will have the same effect on anyone else.
Why does one example matter? The Doomsday argument is over billions of people (something like >100b so far), so one immortal—who doesn’t even exist—shows nothing. He’s wrong a few hundred times, so what—your immortal adds nothing at all to just pointing out that Romans or cavemen would’ve been wrong.
Shouldn’t it be either over all lifeforms or only over people who’ve heard and are able to appreciate the Doomsday argument?
so one immortal—who doesn’t even exist—shows nothing
The example of the immortal is just a trick helpful of thinking about individual lives as not especially meaningful to probabilities in an external sense. Your brain loses cognition and memory, its atoms eventually become part of many other people—in a sense, we’re all this “immortal”—is it meaningful in a mathematical sense to label one particular “life” and say “I was born early” or “I was born late”?
I don’t know. I admit myself just confused over all this.
But if there are to be a quadrillion humans, you would be in a very unlikely situation, in the first 0.0...% or something.
Again the finiteness assumption, which presumes the Doomsday (barring infinite lifespan, which is just another infinity) to begin with. This is a trivial tautology. I’m growing more and more disenchanted with this area of research :(
I was lost in the original Doomsday argument’s logic:
This assumes that the timeline is finite, otherwise “half-way” makes no sense. The following argument
relies on this assumption. The remaining logic is “if we assume a finite timeline, then we can estimate how long it is with some probability, given the population growth curve so far”. The calculations themselves are irrelevant to the conclusion, which is “the total number of humans that will ever live is finite”.
So, the whole argument boils down to “if something is finite, a reasonable function of it is also finite”, which is hardly interesting.
Am I missing something?
So long as we have imprecise measurements and only a finite amount of matter and energy then time is not an issue because we eventually run out of unique (or distinguishable by any of our measurements) humans that can exist and we can just ask the nearly equivalent question: “what is the probability that I am in the last 95% of unique humans to ever exist?” At some point every possible human has been created and out of that huge finite number each one of us is an index. The question is whether the heat death stops the creation of humans in this universe before 20 times the current number of humans has been created (for the 95% argument).
However, the statement of the problem completely ignores prior probabilities. For instance it’s possible that we now have more than 5% of the total human population alive right now (that would be true if only 100 billion have ever lived). That would mean that the oldest people alive right now have a 0 probability of being in the last 95%. Additionally, we have a very good idea of whether we are in the last 99.9999999% of humans who have ever lived; the last 7 babies baby born on Earth have a slightly positive probability, everyone else has a 0 probability. What is the probability that 7 more babies will be born, replacing the current 7 who have the possibility of being the last? 1 for all practical purposes. 100 babies? Same. In fact it probably already happened while I was writing this comment. A billion? Probably still very, very close to 1. The calculation can be extended into the future based on our knowledge of our environment and society and the probability of existential risk. Unless we have a good reason for predicting the destruction of all humans we shouldn’t predict that we are in the last 95% of unique humans. Humans are built to reproduce, they have an environment that will probably last thousands if not hundreds of thousands of years, and they are learning to build their own environments anywhere they want. These facts are far more important than which particular brain is randomly selected to think of the doomsday argument.
EDIT: The part about the last 95% of humans is wrong if there are more than 5% still alive; it would have to be some of the first 5% still alive for the argument to be wrong for them today.
This is an assumption based on our current level of science and technology and failure of imagination. There are many possible ways around it: baby universes, false vacuum decay, even possibly conversion of dark energy (which appears to be inexhaustible) to normal matter, to name a few.
I was unable to follow your logic there… Are you saying that the Doomsday argument is wrong or that it is irrelevant or what?
That may reveal a weakness in the doomsday argument itself. For instance, did any of the first hundred bllion billion humans even think of the doomsday argument? If the doomsday argument is flawed, will many future humans think of it more than briefly from historical interest? The nature of the human considering the doomsday argument significantly affects the sample space. Future humans in a free-energy universe would immediately see the falsehood of the doomsday argument and so from our perspective wouldn’t even be eligible for the sample space. It may be that the doomsday argument only has a chance of being seriously considered by a 20th/21st century human, which simply turns the question into “what is the probability that I am somewhere between the 100 billionth and 130 billionth human to ever live?” or whatever the appropriate bounds might be.
The doomsday argument is correct if no other information besides the total number of humans who have lived before me and finite resources are assumed. With additional information our confidence should be increased beyond what the doomsday argument can provide, making the doomsday argument irrelevant in practice.
Thanks, this makes sense.
SSA Doomsday: You are the hundred billionth human who ever lived (or something like that). If there are two hundred billion humans total, this is not very unusual. But if there are to be a quadrillion humans, you would be in a very unlikely situation, in the first 0.0...% or something.
Analogous argument: you’re told that you’re the smartest person in your extended family. This makes it more likely your extended family is small, rather than large. Replace “smartest” with any property that distinguishes you from the rest of humanity, and the argument follows.
Isn’t it more analogous to having a child be told “you’re 5 years old!” and for this reason this makes the kid believe they’re only likely to survive to around age 10?
That seems like a reasonable conclusion for the child to draw, in the absence of other evidence (like, say, the ages of the people around them).
Actually, I think the right conclusion is that they’re likely to live to about 5*e years, not 10, but the idea is similar.
Imagine you’re told you’re 50 years old… is only surviving to age 100 that bad a guess for a statistical argument which takes into account close to no information whatsoever?
(Reminds me of the reaction to the sunrise example for Laplace’s law.)
Let’s imagine that I’m an immortal being who has lived since prehistorical times—except that I lose all memories every 50 years or so, and my body and my mind reverts to the form of an infant, so that for all intends and purposes I’m a new person.
From prehistorical times, I can therefore think the Doomsday argument to myself—if I had the knowledge to do so. So when I’m Urgh the caveman, among the first 10,000 people I think that mankind is only likely to survive to around double that size, and when I’m Marconius the Roman, I think it likely that mankind is only likely to survive to around double that present size, and when I’m Aris Katsaris the modern Westerner, I think it likely that mankind is only likely to survive to around double this present size...
And each time, I effectively die and forget all my thoughts about Doomsday, and get born anew and reconstruct the Doomsday argument for myself. And can do so for as long as humanity lasts, and it never actually provides me any new information about how long humanity will last.
Until the point where I’m made physically or mentally immortal I guess, and no longer die, at which point I no longer ask the Doomsday argument again, because I first asked it millenia back and remember it.
I don’t know. This chain of thought above makes me intuitively think the Doomsday argument is bollocks, but I don’t know if it will have the same effect on anyone else.
In an argument made confusing by manipulating the sample, I don’t think it’s very helpful to make an even weirder sample.
Why does one example matter? The Doomsday argument is over billions of people (something like >100b so far), so one immortal—who doesn’t even exist—shows nothing. He’s wrong a few hundred times, so what—your immortal adds nothing at all to just pointing out that Romans or cavemen would’ve been wrong.
Shouldn’t it be either over all lifeforms or only over people who’ve heard and are able to appreciate the Doomsday argument?
The example of the immortal is just a trick helpful of thinking about individual lives as not especially meaningful to probabilities in an external sense. Your brain loses cognition and memory, its atoms eventually become part of many other people—in a sense, we’re all this “immortal”—is it meaningful in a mathematical sense to label one particular “life” and say “I was born early” or “I was born late”?
I don’t know. I admit myself just confused over all this.
Again the finiteness assumption, which presumes the Doomsday (barring infinite lifespan, which is just another infinity) to begin with. This is a trivial tautology. I’m growing more and more disenchanted with this area of research :(
Which is one of the reason I recommend sidstepping the whole argument, and using “Anthropic decision theory” http://lesswrong.com/lw/891/anthropic_decision_theory_i_sleeping_beauty_and/