Computational Complexity

Wednesday, January 30, 2008

 
If 50 is the new 40 then is 100 the new 80?

Posted by GASARCH

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 ≥ 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.

8:07 AM #

1.  Chris says:  
   
   To me the inverse is the more relevant question. At what age should someone be having their x-life crisis? When should I start feeling like I'm 50?
   

   10:18 AM, January 30, 2008

2.  Anonymous says:  
   
   If we extend Bill's function, it can also explain the phenomenon of so many young adults moving back in with their parents rather than setting off on their own. After all, now 40 is the new 28, and 30 is the new 16.
   
   And the implications for college campuses of 20 being the new 4 are staggering. :-)
   

   10:55 AM, January 30, 2008

3.  Anonymous says:  
   
   Well, here's some data, from:
   http://www.infoplease.com/ipa/A0005140.html
   
   If you define : "x is the new y if
   g1(x) = g2(y)" then, by doing interpolation, we get:
   
   10 is the new 0
   20 is the new 13
   30 is the new 22
   40 is the new 32
   50 is the new 42
   60 is the new 53
   70 is the new 63
   80 is the new 74
   90 is the new 88
   
   
   Of course this is only a first-order approximation since
   by the time you move from 50 to 60,
   60 becomes even younger.
   So life-expectancy has greatly
   increased, unless you're pretty old - if we want to keep this trend, we must fight aging:
   http://www.fightaging.org/
   

   1:49 PM, January 30, 2008

4.  John Sidles says:  
   
   The average age of a first-award NIH R01 award has risen to 42 (!)
   
   Sscientifically speaking, this means "42 is the new 25". :(
   

   3:39 PM, January 30, 2008

5.  Fred Green says:  
   
   Hi, Bill.
   
   70 is not the new 60, if we view it democratically. 70 is the new 50 (3170 hits and, as I recall, the caption of a great New Yorker cartoon).
   
   Perhaps your function should be multivalued.
   

   11:19 AM, January 31, 2008

6.  Anonymous says:  
   
   The function is more complex at the low end too.
   
   I read that girls are beginning puberty in the US at 7-8.
   
   So that means 8 is the new 14.
   
   Only gets 3 results though and those are talking about the size of women's clothing(thats using the search sentence as a single string in quotes)
   

   10:23 PM, January 31, 2008

7.  cdnlopull says:  
   
   So typical of Yahoo: accuracy be damned. The ACTUAL PHRASE IS :*40* IS THE NEW *50* (remove the caps and asterisks, and THAT phrase returns *OVER 86 MILLION HITS*). It originated in CANADA, due to a proposed change in retirement age, and refers to people over 40 being discriminated against in hiring as badly as people over 50 were a few years ago, as a result of that change. Yahoo is heading downhill SO fast, Microsoft will probably end up buying y'all out, or something.
   

   11:32 PM, February 02, 2008

8.  bob says:  
   
   I am 70, dateing a woman who is
   45=30 year difference.
   Will this "50 is the new 40"
   improve my bedroonm performance?
   

   10:59 AM, February 05, 2008

9.  Mark Sissons says:  
   
   Well, all I can say is, my website is FiftyIsTheNewForty.net, so I'm not sure HOW I feel about the numbers you put up there!!
   

   8:35 PM, February 25, 2008