## [Computational Complexity] If 50 is the new 40 then is 100 the new 80?

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• If you google 50 is the new 40 you get over 11,000 hits (fifty is the new forty gets only 961 hits). What does the phrase mean? It means that what a while back
Message 1 of 1 , Jan 30 6:10 AM
If you google 50 is the new 40 you get over 11,000 hits (fifty is the new forty gets only 961 hits). What does the phrase mean? It means that what a while back people did in their 40's they are now doing in their 50's. (Dating, Marrying, Having (perhaps more) kids, Changing Jobs, taking adult education classes, etc.) I tend to agree with this--- I often think that people in their 50's look like they are in their 40's. (The next generation won't have this problem as they will have adjusted to the shift--- unless there is another shift.)

So, if 50 is the new 40 then is 60 the new 50 ?Here is what Google says:
1. 60 is the new 50 got 3430 hits.
2. 70 is the new 60 got 788 hits.
3. 80 is the new 70 got 860 hits.
4. 90 is the new 80 got 193 hits.
5. 100 is the new 90 got 8 hits.
6. 110 is the new 100 got 2 hits.
7. 120 is the new 110 got 0 hits. You're 120! You don't look a day over 110!
(Note- these may go up because of this post.)

My intuition says that 120 is not the new 110. In fact, I think that 100 is still 100. So we are looking for a function f such that
1. f(50)=40
2. for all x&ge 100, f(x)=x
Linear? log? piecewise linear?Is there a way to really find such an f? Only if you want to replace the intuitive statment 50 is the new 40 with a more rigourous one. Here is one example. Not sure what it would yield, or if you still really have 50 is the new 40 and 100 is the new 100. Let
1. g1(x) = the life expectancy of someone who was x years old in 1950
2. g2(x) = the life expectancy of someone who was x years old in 2008
(you may pick other functions that measure something about life then and now.)

With some rigorous definition you could really answer this question. But it may be more fun to put your math hat aside and just see what your intuition tells you. Mine says
1. 50 is the new 40.
2. 60 is the new 52.
3. 70 is the new 64. (will you still need me, will you still feed me, when I'm 70?)
4. 80 is the new 76.
5. 90 is the new 88.
6. 100 is the new 100. Or the old 100.

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Posted By GASARCH to Computational Complexity at 1/30/2008 08:07:00 AM
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