At 5, I was hospitalized for a month due to pneumonia. Kids of that age have little fear of illnesses, and the discomfort is soon forgotten. What I still remember though is the intense boredom. It is during that dull month I started asking the question everyone has asked themself: "Among all the people in this world, why am I this particular one?". I still recall the ineffable yet intense feeling when thinking about it for the first time.
Eventually I realized that's a question with no answer. Out of the vast number of things in existence, the fact that I am experiencing the world from the perspective of this particular thing- a human being- has no explanation. Logic and reason are unable to ascribe any underlying cause or rationale. "I am me" is just one fundamental truth that anyone has to take as a given.
Yet this fundamental truth is different for each person. From each of our distinct perspectives, which physical thing is the "I" is different. Keeping track of such differences is both mentally consuming and often unnecessary. So there is a natural affinity to rid of the first-person and to think "objectively". Instead of basing it on one's own point of view, we organize thoughts and formulate arguments from an imaginary vantage point that is detached and impartial, with an immaterial gaze from nowhere.
Though I consider such objectivism merely a shortcut for efficiency which has often been mistakenly regarded as an ideal, there is no denying its practical success. We all use it constantly with great results. Even when we do think about something from our own perspective, we can easily transcode it to the objective. All it seems to take is exchanging the perspective-dependent self - the "I"- for the particular person. So "I'm tall" can become "Dadadarren is tall". This is required since there is no "I" in objective reasoning. It is a gaze from nowhere after all.
We all have performed these transcodings so frequently that they hardly require active thoughts anymore. Every time it subtly reinforces the idea that such transcoding is always possible, so thinking objectively can, some may even say should, supersedes thinking from any single perspective. But in some rare cases, that leads to problems. Anthropic reasoning is such a case.
Take the Doomsday Argument(DA) as an example. It proposes the uninformed prior of one's own birth rank among all human beings ought to be uniformly distributed from the 1st to the last. So learning our actual birth rank (we are around the 100 billionth) should shift our belief about the future toward earlier extinction. E.g. I am more likely to be the 100 billionth person if there are only 200 Billion humans overall rather than 200 Trillion. So the fact I'm the 100 billionth means the former is more likely.
The birth rank discussion isn't about if I am born slightly earlier or later. Nobody can physically be born more than a few months away from their actual birthday. The argument is about scenarios where "I" am altogether a different person. I.E. "If I'm the first human being" does not mean dadadarren is born so prematurely that he predates Adam, but rather "I" am Adam. There is a decoupling between the "I" and the physical person I am. Such decouplings are integral to anthropics. While normal problems discuss different ways of assigning people to rooms, anthropic problems can have only one fixed assignment while contemplating which one of those people is "me".
By focusing on "my" birth rank the Doomsday Argument uses the perspective-based "I". The argument is often expressed with more inclusive terms such as "us", or "our generation". Unsurprising since explaining the argument to someone requires the recipient to evoke their own perspective too. However, if we reason from our perspectives, then predicting the future simply involves looking at the past and present situations and, to the best of our abilities, making a forecast. That's all. Sure, there are some uncertainties regarding our birth rank since our knowledge of the past is imperfect, and there may be occasions when we learn more about it. But that won't trigger a probability update as the Doomsday Argument suggests.
The crux of the Doomsday Argument is its attempt to frame the problem objectively. From this detached viewpoint, it is impartial towards human beings of all times. Yet the argument also uses "I" which is nonsensical from the objective viewpoint. It has to be transcoded to a particular individual. But due to the decoupling mentioned earlier, the link between the "I" and the particular person is severed. There is no transcoding possible. In the end, perspective thinking would reject the supposed impartialness, while objective thinking could not make sense of the "I". No matter what, the proposed prior birth-rank distribution is inconceivable.
But the argument is deceiving because it exploits people's ingrained belief about objectivity. Its past success makes us think any perspective reasoning can also be formulated from the immaterial vantage point. We didn't question that even though it is oxymoronic to forecast "the future" from a viewpoint so detached and neutral that is fundamentally timeless. When the decoupling makes transcoding impossible, instead of taking a deep look into this ingrained belief, people choose the less effortful alternative: conjuring something up to complete the transcoding: treating the "I" as the particular person who is randomly chosen. We are susceptible to such suggestions because it minimally disturbs the question while allowing us to hold onto the old routine.
The Doomsday Argument is wrong not because it has left something out, but because it added something in. It adds the ostensibly plausible but entirely unsubstantiated assertion of treating "I" as a random sample. Making different assumptions about the sampling processes may dodge the argument's contentious conclusion. But that would create other controversies and, above all, entirely miss the point. People should be more suspicious of anthropic assumptions, they are blindly asserted answers to the age-old question: "Why am I me?".
How does the logic here work if you change the question to be about human history?
Guessing a 50/50 coin flip is obviously impossible, but if Omega asks whether you are in the last 50% of "human history" the doomsday argument (not that I subscribe to it) is more compelling. The key point of the doomsday argument is that humanity's growth is exponential, therefore if we're the median birth-rank human and we continue to grow, we don't actually have that long (in wall-time) to live.