01 January 2012

The Welfare State and the exponential function

The greatest shortcoming of the human race is our inability to understand the exponential function. (Professor Albert Bartlett)
I do not know that I would agree that unawareness of the exponential function is the greatest shortcoming of the human race, but certainly this unawareness (real or apparent) facilitates legislation which is designed to reduce the advantages of one section of the population while increasing those of another. This may be represented as ‘fair’, but it should not be overlooked that it may produce drastic shifts in the balance of the population quite rapidly.
If an initial quantity A increases by n%, and the result is again increased by n%, and so on, the resulting growth is shown by the graph of
y = A(1 + n/100)x.
To illustrate how this may apply to groups in the population which are increasing continuously, here are the charts of a hypothetical population group which numbered one million in 1945 (at the onset of the Welfare State) and increased by 1%, 2%, 3% and 4% respectively until the present day, i.e. 66 years later.
Characteristically, the exponential graph remains close to the lower axis at first, but the gradient gradually increases until it is more vertical than horizontal and tends asymptotically to infinity (i.e. it approaches infinity ever more closely and rapidly, but without ever reaching it).
On the timescale being considered, the increase in the population supposed to increase by 4% per annum is already acquiring the characteristically exponential appearance, aiming upwards rather than merely along the lower axis.
The unsophisticated are unlikely to imagine how great the changes may be which ultimately result from relatively small percentage changes in taxation or benefits, which may be applied, initially, only to small populations.

I appeal for financial and moral support in improving my position. I need people to provide moral support both for fundraising, and as temporary or possibly long-term workers. Those interested should read my post on interns.