Too Fabulous to Last

Too Fabulous to Last ForeverDavid Harvey, in his always entertaining and frequently excellent, though always [un]consciously anti-socialist, talks, proposes compound growth, which is merely the expression of capital itself, as one of the most alarming of his 17 contradictions of capital.¹There must be dozens of graphs of compound growth on the web, but I computed my own using Wolfram Alpha, the primary mathematical tool of the web.The inspiration is Capital, Volume 3, Chapter 24, where Marx discusses an entire British administration, under Pitt, falling for a certain Dr Price’s scheme of borrowing at simple interest but charging [the nation] at compound interest, and thereby solving the British national debt once and for all.  Such are:  “the fabulous fancies of Dr Price, which outdo by far the fantasies of the alchemists;  fancies, in which Pitt believed in all earnest, and which he used as pillars of his financial administration”. Dr Price’s Paradigm ExampleDr Price’s epitome of capitalist desire is:  “A shilling put out to 6% compound interest at our Saviours birth” (presumably in the Temple of Jerusalem) “would… have increased to a greater sum than the whole solar system could hold, supposing it a sphere equal in diameter to the diameter of Saturn’s orbit.”Marx’s discussion is worth reading for the litany of fantasies that arise naturally out of the institution of banking.²With regard to fixing the national debt, Marx proceeds: “With Dr. Price’s aid, Pitt thus converts Smith’s theory of accumulation into enrichment of a nation by means of accumulating debts, and thus arrives at the pleasant progression of an infinity of loans — loans to pay loans. “[Dr Price] regarded capital as a self-regulating automaton, as a mere number that increases itself (just as Malthus did with respect to population in his geometrical progression), [and] he was struck by the thought that he had found the law of its growth in the formula        s = c (1 + i)ⁿ ,       [1]in which s = the sum of capital + compound interest, c = advanced capital, i = rate of interest, n = the number of years in which this process takes place.”[Capital, Vol. 3, Ch. 24.] New Shillings for OldHere is the graph of Dr Price’s formula for c = 1 shilling, invested to mature after n = 2014 years.The horizontal scale from 0 to 10, represents the fixed rate of interest i (%).Thus 1 represents a fixed rate of interest of 1%, …, and 10 represents a fixed rate of interest of 10%.The vertical axis from 0 to 80, represents the yield s, as the number of shilling coins, amassed over 2014 years, in powers of ten.  This is a logarithmic scale.³Thus, 3 represents 1000 shillings [one thousand, or 10³],6 represents 1,000,000 shillings [one million, or 10⁶],9 represents 1,000,000,000 shillings [one billion, or 10⁹], …,80 represents one followed by 80 zeroes of shillings [10⁸⁰].  How to Read the Graph  i  s  1% 10⁸  2% 10¹⁷  3% 10²⁵  4% 10³³  5% 10⁴²  6% 10⁵⁰  7% 10₅⁸  8% 10⁶⁷  9% 10⁷⁵ 10% 10⁸⁵Reading from the graph, Dr Price’s 1 shilling, invested at 6% per annum compound interest, after 2014 years, would yield 10⁵⁰ shillings, or100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Visualizing ThisIf each shilling stacks 1 mm high, a column of them would reach:the Moon when the yield was 10¹¹ shillings [~400 AD]Pluto when the yield was 10¹⁵ shillings [~600 AD]Proxima Centauri when the yield was 10¹⁹ shillings [~750 AD]the Andromeda Galaxy when the yield was 10²⁵ shillings [~1000 AD]the edge of the Observable Universe when the yield was 10³⁰ shillings [~1200 AD]And we still haven’t got to Dr Price’s 10⁵⁰ shillings.⁴ Notes¹ http://www.thersa.org/events/audio-and-past-events/2014/the-contradictions-of-capitalism ↩ [Back]² Marx passes the [to me] fascinating observation that: “romanticism in all walks of life … is made up of current prejudices, skimmed from the most superficial semblance of things.  This incorrect and trite content should then be “exalted” and rendered sublime through a mystifying mode of expression.”Yet young Marx and Engels dabbled in romantic poetry, while mature Marx admired Shelley and Byron, William Morris is our socialist pioneer, Rosa Luxembourg loved German romantic Lieder, etc. ↩ [Back]³ Similar logarithmic scales in powers of ten are used to measure earthquakes [Richter], sound [decibel], acidity [pH].  A logarithmic scale in powers of two is used for camera apertures [F-stop], etc. ↩ [Back]⁴ If a shilling weighs 10 grams then a pile of them would weigh as much as the Universe when the yield is 10⁵⁸.  At a higher fixed interest rate of 10%, Dr Price’s shillings are destined to overflow the Universe’s volume before our current century is out. ↩ [Back]