No, I don’t use bell curve distribution. By saying “middle in the year” I mean everything which is not 1 of January or 31 of December. Surely I understand that people have the same chance to be born in July and in December.
The example was needed to demonstrate real (but weak) predictive power of mediocrity reasoning. For example, I could claim that it is very unlikely that you was born in any of these dates (31 December or 1 of Janury), and most likely you was born somewhere between them; the same way I could claim that it is unlikely that it is exactly midnight on your clock.
And this is not depending on the choice of the starting point or framing. If our day change will be in 17.57, it would be still unlikely that your time now is 17.57.
I interpreted “the middle” as a point and its near surroundings, which explains some of the disagreement. (All of your specific examples in your original post were near the midpoint, which didn’t clarify which interpretation you intended.)
I think that the more fundamental rule isn’t about middles, and (as demonstrated here) that’s easily misinterpreted without including many qualifiers and specifics. “Larger intervals are more likely, to the extent that the distribution is flat” is more fundamental, but there are so many ways to define large intervals that it doesn’t seem very useful here. It all depends on what you call a very unusual point—if it’s the middle that’s most unusual to me, then my version of the doomsday argument says “we will probably either die out soon or last for a very long time, but not last exactly twice as long as we already have.” (In this case, my large interval would be time-that-civilization-exists minus (midpoint plus neighborhood of midpoint), and my small interval would be midpoint plus neighborhood of midpoint.)
No, I don’t use bell curve distribution. By saying “middle in the year” I mean everything which is not 1 of January or 31 of December. Surely I understand that people have the same chance to be born in July and in December.
The example was needed to demonstrate real (but weak) predictive power of mediocrity reasoning. For example, I could claim that it is very unlikely that you was born in any of these dates (31 December or 1 of Janury), and most likely you was born somewhere between them; the same way I could claim that it is unlikely that it is exactly midnight on your clock.
And this is not depending on the choice of the starting point or framing. If our day change will be in 17.57, it would be still unlikely that your time now is 17.57.
I interpreted “the middle” as a point and its near surroundings, which explains some of the disagreement. (All of your specific examples in your original post were near the midpoint, which didn’t clarify which interpretation you intended.)
I think that the more fundamental rule isn’t about middles, and (as demonstrated here) that’s easily misinterpreted without including many qualifiers and specifics. “Larger intervals are more likely, to the extent that the distribution is flat” is more fundamental, but there are so many ways to define large intervals that it doesn’t seem very useful here. It all depends on what you call a very unusual point—if it’s the middle that’s most unusual to me, then my version of the doomsday argument says “we will probably either die out soon or last for a very long time, but not last exactly twice as long as we already have.” (In this case, my large interval would be time-that-civilization-exists minus (midpoint plus neighborhood of midpoint), and my small interval would be midpoint plus neighborhood of midpoint.)