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Assuming that the user is looking at the clock at any given moment, we know that the user is still alive. Thus, we must update the expected remaining days of life upwards, given that additional information. For example, if the user is an infant, the output might read "76 years". However, once the user is 75 years old, the output should now read around "11 years", as the average 76 year old still has another 10 years or so of life left. Similarly, once the user reaches 110, the clock should still be counting down (and display around half a year).
For U.S. humans, here's a reasonable basis for calculating remaining days: https://www.ssa.gov/oact/STATS/table4c6.html
mattcan, adamtait, itsJoKr and pwab
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