We've seen, in "The Camel Problem", that one motivation of NUMALGEBRA is that >ratio apportionments (according to a will may be known but [possible apportionments are unknown
So one must WORK BACKWARD FROM THE AMOUNT INHERITED TO DETERMINE THE ACTUAL APPORTIONMENTS, USING THE RATIO APPORTIONMENTS AS "COEFFICIENTS" OR "PARAMETERS".
This is analogous to the algebraic (Ü) problem,
6x3 — 23x2 — 6x — 8 = 0,
which has the solution-set,
x = {4, 1/2, ¯2/3}, obtained by working
back from 0 to the unknown x, using the coefficient-set {6, ¯23,
¯6, ¯8}.
I hope you can now understand "algebra from inheritance motivations".
Happily, INHERITANCE conditions have improved remarkably from Babylonian-Egyptian or Islanic times, thanks to "The Welfare State".
Yes, this term is used perjoratively; by those without compassion; and those ignorant of its meaning. Briefly, The Welfare State began with Social Security. So, either
- You depend on Social Security now,
- or you're planning to do so in the future,
- or, if you're rich enough to speak perjoratively about it, you should be happy that its surplus helps out with The National Budget each year, cutting down on the amount the Government must borrow, so the banks have money you can borrow at a "satisfactory" rate.
The Welfare State is usually attributed to Britisher, Sir William Beveridge. But he is a late comer. We owe most to a disparate trio of individuals, whom I call "The Odd Triple":
- Abraham De Moive,
- Florence Nightingale,
- Prince Otto von Bismark.
Abraham De Moivre (1667-1754) was born in France, a Huguenot (like our own Paul Revere),
differing religiously from the Roman Catholic majority. In 1685, King Louis XIV revoked The
Edict of Nantes which had granted civil rights to Protestants. 400,000 Huguenots emigrated to
England, to The American Colonies, and elsewhere. Young De Moivre was briefly imprisoned, then
allowed to escape to England, where he lived the rest of his life.In 1718, De Moivre published a momentous treatise on probability theory: The Book of Chances. (This included the first appearance of the "bell" curve sometimes attributed to Gauss, but should be credited to De Moivre.) This book contained a paper showing that an effective formula for an annuity (collecting for a "pension") could be approximated by a simple linear equation. This was improved later, and the annuity became a "stock-in-trade" of the burgeoning insurance industry.
Moivre, himself, enjoyed no such a benefit. Efforts of Sir Isaac Newton and astronomer William Halley to find a teaching job for this French mathematician were of no avail. So, until age 80, De Moivre supported himself by sitting in a London tavern, tutoring in mathematics, calculating odds for gamblers, and compiling tables for insurance companies.
This, or any other annuity formula, is ARITHMETIC BACKWARDS.
- KNOWN: Desired accumulation.
- KNOWN: Years of investment before "reaping".
- KNOWN: average interest on investment.
- UNKNOWN: Amount to invest each period to achieve desired accumulation.
Amortization is annuity translated from individual math (or insurance math into business math). Instead of borrowing money from the bank for new quipment or some other NEED, a manager can "lay away" money for this purpose. Again, ARITHMETIC BACKWARDS: ALGEBRA.
FINANCIAL ARITHMETIC is replete with other versions of this PATTERN. But the part of the subject which WORKS BACKWARD should be subsumed under "Financial Algebra" -- another instance of "the puzzlement of Algebra".
As a teen-ager, Florence Nightingale (1820-1910) was tutored in mathematics by the great British
mathematician, Joseph Sylvester (1814-1897), who later said she was the best student he'd ever
taught.While initiating military nursing during the Crimean War (1854-56), Nightingale also initiated the military alottment system. Nightingale asked married soldiers in the hospital to put aside for their families a little of the money they might waste in drinking and gambling or spending on other women. Late at night, after her ardurous duties (nursing, supervising, doing paperwork), Nightingale wrote explanatory letters to the families, including the funds. The top military became ashamed at this extra duty left to a courageous overworked woman. So they created the military alottment system.
After retirement to England, Nightingale worked in seclusion, furthering the nursing profession (establishing several schools) and developing statistical methods for gathering data, while sketching fundamentals of a Welfare State. So, Florence Nightingale, not Sir William Beverduge, was resonsible for initiating the Welfare State in Gt. Britain.
Otto Eduard Leopold, Prince von Bismarck, was a Prussian statesman who in
1871 founded the German Empire and served as its first chancellor for 19 years. In doing so,
Bismark provoked the Franco-Prussian War of 1870-71 as an opportunity to bring the South German
states into unity with the Prussian-led North German Confederation and build a strong German
Empire.This resulted in a crushing defeat for France, overthrowing French Emperor Napoleon III and the "Third Empire". The German Empire was proclaimed at Versailles on Jan. 18, 1871, a triumph of Prussian militarism and imperialism.
France was forced to pay a huge indemnity and to give up most of Alsace and Lorraine. But Paris resisted, and revolutionaries established THE COMMUNE OF PARIS, an insurrection against the French government from March 18 to May 28, 1871. This was the first great threat of Socialism and Communism in Europe. Karl Marx's support of THE COMMUNE and his writing about it established Marx as the leader of The First International (of Socialism) and Marx became synonymous throughout Europe with the revolutionary spirit symbolized by the Paris Commune.
These developments gravely disturbed Bismark, and he began laying counter-plans. The first compulsory social insurance programs on a national scale were established in Germany under Chancellor Otto von Bismarck: health insurance in 1883, workmen's compensation in 1884, and old-age and invalidity pensions in 1889.
Armies of soldiers were replaced by armies of bureaucrats and clerks to implement this system. Germany's example was soon followed by Austria and Hungary. Thus, a crusty old Prussian militarist initiated "The Welfare State" in Europe -- as a "safety valve".
These results -- instigated by this "Odd Triple" -- grew into an immense part of our economy, which goes by the name, fiduciary ("held in trust", from Latin, fiducia, meaning "in trust").
The American economist, John Kenneth Galbraith speaks of our "fiduciary economy" (rather than "Welfare State"!), because more is invested in pension plans of the Federal Government, of labor unions, of corporations, etc., than in any other part of our economy.
Thus, the dominant part of our economy is engaged in ALGEBRA!