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Homepage of Jan Karman Middelburg (Neth)

Design & Copyright Jan Karman Last revised: January 2023

The B-Toe

How it started One of my most favorite melodies of Bach, that I play on my flute, is his Alto Aria from
Cantate BWV 170, "Vergnügte Ruh, beliebte Seelenlust".
Transcribed for his Oboe Concerto, it is written in D major, with this passage, going down
to B.

How would I ever be able to play this on my flute, i.e. one with just a C-foot?
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Mortality tables are usually graduated for either practical or scientific purposes. The formulae, in which the mortality is expressed as a function of x (= age) are often of the type (Makeham's law):
m_{x} = A + B.c^{x} (force of mortality)
with A, B and c as parameters. Finding the values of those parameters from the crude material is the hard part.
King-Hardy's method is a suitable way to transform this power function into a linear equation system; it is solved here by way of a least square K-runtime function.
See also E.Zwinggi - Versicherungsmathematik
When invoked, one will find four controls in the bottom part. The first two controls act like a spinbox, the two right most controls simulate the Windows-locator. The challenge is to find as large as possible ranges for making the "law" valid.
Later, famous methods came from Thorvald N. Thiele, published posthumously in 1910, and more recent approaches and remarks can be found at W.J. Willemse.

Recommended for Africa: G.M.K. Kpedekpo - Essentials of Demographic Analysis for Africa

Jan Karman LinkedIn Middelburg (Neth), November 2006