The argument is so simple that it has been invented several times in the course of history.
People estimate that ~ 100 billion individuals of homo sapiens have lived on Earth in the past 250,000 years. Suppose that I was "chosen" by some mechanism to be a random individual among all the homo sapiens who will ever live.
Then it is likely that the total number of homo sapiens who will ever live will be something like ~ 200 billion. If we assume that the population of Earth will stay at 10 billion, then homo sapiens is expected to go extinct in ~ 700 years.
How could the number future homo sapiens could be so low, only 10¹¹? If humans will colonize exoplanets, there might be 10¹⁷ humans living in the next 10,000 years.
The doomsday argument is an example of anthropic reasoning.
Could it be that humans will be replaced by artificial intelligence machines?
What if artificial intelligence machines will replace humans in the future? Communication between exoplanets is slow. Each colonized exoplanet must have at least one instance of AI, autonomous from other instances. If the AI sends space probes, each probe must have an autonomous AI instance.
If humans are replaced by AI machines, we expect a very large number of autonomous, individual AI machines to exist in the future.
Why was I born as an instance of homo sapiens and not an instance of an AI machine? Or is it so that only ~ 100 billion AI machines will exist in the future?
Why was I born as homo sapiens, and not a random vertebrate?
Vertebrates appeared on Earth 530 million years ago. There has been a huge number of individuals in the past. The 100 billion instances of homo sapiens is an extremely tiny fraction of all instances of vertebrates which have lived.
Why am I not a random instance of a vertebrate, living some time in the past 530 million years?
Maybe I was destined to be born as a "self-conscious" being? But I was not born that way: a fetus or a newborn child is not self-conscious in the way that an adult is.
The self-indication assumption objection refutes the doomsday argument
The self-indication assumption is one way to refute the doomsday argument. Suppose that I am one of an almost infinite number N of "souls" who may be born as homo sapiens, or not be born at all. If I then find myself born as homo sapiens, I cannot deduce anything about the number of homo sapiens who will ever live.
Let us have two possible worlds:
- A: 200 billion homo sapiens will live;
- B: 10¹⁰⁰ homo sapiens will live.
Let, a priori, the probability of A and B be both 0.5.
Let me find myself living as the 100 billionth instance of homo sapiens in the world. Can I now deduce anything more about the probabilities of A and B?
No. In both cases, A and B, the probability of me being born as the 100 billionth instance is the same.
Self-indication assumption and vertebrates
The self-indication assumption does not answer the question: why was I born as an intelligent vertebrate (homo sapiens), and not as an average vertebrate (a small fish)?
There may exist a huge number of homo sapiens in the future, but that does not explain why I was born as homo sapiens at a time when only a tiny fraction of all instances of vertebrates have been homo sapiens.
I was not born as a random instance of a vertebrate?
This is the natural hypothesis: I was somehow predestined to be born as a being which becomes self-aware as an adult. There was no randomness in this.
Then it is also natural to assume that I was not born as a random instance of homo sapiens.
The doomsday argument is refuted because there is no randomness.
If there is no randomness, then there is some law of nature outside our universe. That law of nature brought me here.
The doomsday argument itself assumes that there is a law of nature outside our universe: that a "random process" causes me to be born as an instance of homo sapiens.
Criticism of the self-indication assumption
Nick Bostrom (2002) argued that the self-indication assumption leads to absurd consequences. Bostrom's argument is called the "presumptuous philosopher".
Suppose that we have two possible cosmologies:
- A: there are only 10¹¹ conscious observers in the universe;
- B: there are 10¹⁰⁰ conscious observers in the universe.
A priori, A and B have a probability 0.5. I am a conscious observer. Can a I deduce if I am in A or B?
Let us use the self-indication assumption. Let us assume that "souls" are assigned at random from the very large pool of N souls to the universe. Let us assume that I am a random soul in the pool. I realize that I was born. This implies that I am almost certainly in the universe B, not in A. Let us call the reasoning in this paragraph P.
Nick Bostrom is quoted in Wikipedia saying that it is "absurd" if one can draw the conclusion above in the reasoning P. He believes that the absurdity discredits the self-indication assumption.
We in our blog do not think that the reasoning P is absurd – rather, P is the natural conclusion if the randomization model and the pool of N souls is correct.
The weakness in P is that we do not know if the assumptions are correct. It certainly does not look like that my soul was assigned randomly into the universe.
Conclusions
The doomsday argument probably does not hold. It is easily refuted by the self-indication assumption. It is also refuted if there is no randomness. We cannot claim that only ~ 200 billion humans will ever live.
There seems to be a law of nature which is outside our universe. That law of nature decides in what role I am born.
In quantum mechanics, the collapse of the wave function, or in the many-worlds interpretation, how we choose the branch in which we live, is an unsolved mystery. The mystery looks like the question "why I was born as this instance of homo sapiens?"
We have to think about this: what kind of a law of nature outside our universe could possible solve the mystery in quantum mechanics?
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