Mathematical shapes can affect our lives and the decisions we make.
hockey stick graph describing the earths average temperature over the last millennia has been the subject of a controversial debate over reliability of methods of statistical analysis.
From this to this …
The long tail is another new icon, described in a new book, developed in the Blogosphere, by Chris Anderson called “The Long Tail”:
Forget squeezing millions from a few megahits at the top of the charts. The future of entertainment is in the millions of niche markets at the shallow end of the bit stream. Chris Anderson explains all in a book called “The Long Tail”. Follow his continuing coverage of the subject on The Long Tail blog.
As explained in Wikipedia:
The long tail is the colloquial name for a long-known feature of statistical distributions (Zipf, Power laws, Pareto distributions and/or general LÃ©vy distributions ). The feature is also known as “heavy tails”, “power-law tails” or “Pareto tails”. Such distributions resemble the accompanying graph.
In these distributions a low frequency or low-amplitude population that gradually â€œtails offâ€ follows a high frequency or high-amplitude population. In many cases the infrequent or low-amplitude eventsâ€”the long tail, represented here by the yellow portion of the graphâ€”can cumulatively outnumber or outweigh the initial portion of the graph, such that in aggregate they comprise the majority.
A niche is a concept that at minimum is the tendency of a species to prefer a particular set or range of values. To express this with a function requires a â€˜humpâ€™ or â€˜inverted Uâ€™ shape centered on values optimal to the species growth and reproduction. Below are three ways to do this is with functions: step function, a truncated quadratic, and exponential.
Other examples of mathematical shapes in action can be found in the climate science journal GRL Naturally Trendy and Long term persistence in climate and the detection problem. Long term persistence or LTP refers to the tendency for the effect of random fluctuations to persist over very long time scales, giving the appearance of trends.
Readers of this blog will be familiar with the many articles written about LTP, red noise, and random series with LTP inspired by the extensive work of Koutsoyiannis in hydrology. Niche markets are important for small businesses, as they can find it profitable to serve markets too small for mainstream businesses. Anderson argues that products with low sales volume can collectively exceed the relatively few current bestsellers.
Statistical analyses collectively called ‘niche modelling’ can be applied in many areas of life. Currently I am actively developing a business delivering the analytics of niche modeling to business. More can be read about this at the site NicheShape.