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The minute hand will be 84/60 = 1.4 years
The second hand is 1.4 / 60 = 0.023333 years = 8.5 days.
Sorry for splitting hairs and missing the big picture :). I actually watched "The Bucket List" the other day and this clock is resonating with me somehow.
The minute hand will be 1/60th of a year, say 7.3 days (close enough to a week).
The second hand will be 1/60th of this, so it ticks to the next position every 2.9 hours.
This clock also resonates with me, and I think it would be very strange and disturbing to see your life tick away each day.
Minute and second interpretation can be derived as follows:
--- 1 hour on the dial == 7 years
--- 1 minute on the dial = 1 hour / 60 == 7 years / 60 = 0.11667 years = 42.6 days
--- 1 second == 42.6 days / 60 = 0.71 days = 17 hours.
This means that you can “see” the second hand move to tick your life away every 17 hours.
-Nathir