House of CardsCentral Limit Theorem Proof:

1. Depends on Taylor's Theorem.

1. Taylor's Theorem depends on Calculus

1. Calculus depends on a function being  differentiable.

1. Differentiable functions exist if the function is smooth at the tangent.

1. Derivative is not defined at discontinuities. 

Dilemma: What in Nature is Smooth ?

Statistical Assumptions: (http://en.wikipedia.org/wiki/Statistical_assumption)

1. In practice more than 31 items are necessary before any statistic can be calculated.
2. Random variables are IID - Independent, Identically distributed.
3. Central Limit Theorem - in larger sample populations tend to be a Normal distribution.
4. ... see Wikipedia and it's associated references

This means that the pictures of the items on the previous page are "undefined".

The dilemma is that humans can easily recognize these objects.

TruthOrStatistics-InNature

Truth or Statistics

In nature we call truth: 

               earth, wind, fire, air

               leaves, trees, forests

               rain, streams, rivers, oceans

               sun, fog, rain, snow, antartica 

               dust, sand, desert, sahara

                

In mathematics we have:

               x, y, f(x)

               functions - linear, non-linear,  logistic, differential, transcendental 

               

In financial analysis they call it Alpha.  

                http://seekingalpha.com/

                http://www.investopedia.com/articles/financial-theory/08/deeper-look-at-alpha.asp

Truth

Leaf, Twig, Branch, Tree, Forest...

Rain Drop, Rain, Stream, River, Ocean