[Sussex] On the Other hand

[Geoff Teale]

Nike wrote:
-----------
> > Have a beer... it'll all look much better then ;)
> The beer or the problem ?

The problem of course. 

Beer, it could be argued, always looks good, and a second one is always more
attractive than the first.  However proof for the increasing attractiveness
of beer as one consumes it is fundementally flawed.

In this case lets take `b to represent the function "beer".

`b   = 1
  1 

OK, so we have established that the first beer has a constant level of
attractiveness (1).  
As we have proven that one beer has an attractiveness quotient of one, and 0
beers obviously have no level of attraction we can summarise that a second
beer's attractiveness as being the effective summation of these beers, thus:

`b  =    `b + `b    
  2        0    1


This theorum is indeed supported by all available evidence.  The
mathematicians amongst you will be way ahead here.  The temptation is to
shout, "Aha!  Beer conforms to a series" and jump to the logical assumption
that :

`b   = { `b  + `b + ... `b   + `b     }
  n  	     0     1        n-2    n-1


However we hit a flaw when we try to put this rule into practice. 

`b   = 128
  9

This is fine, but, by induction we should see beer 10 = 256, but in reality
we get:

`b   = 25.6
  10

The tenth beer has only 1/10 it's expected level of attractiveness.  

`b	 = 2.56
  10.5

.. half way through the tenth beer we find that it now has only 1/100 of
it's expected attractiveness.

           2   -2750
`b	= (`b  )
  11       9

Here we have the net result of the decline, by the time we reach the 11th
beer the attractiveness is equivalent to the square of the ninth beers
attractiveness to the -2750.  This constant (1.27447352890596E-570)is known
as the Whitbread Razor but has been reexpressed in recent experiments at
both Imperial College, London and the Massachussets Institute of Technology
as "Absolute Diaphramitery Contraction Force 1".

Finding a fundemental algorithm to handle this problem remains one of the
great unsolved mysteries of modern mathematics.

-- 
GJT
geoff.teale at claybrook.co.uk




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