Heinz von Foerster#Doomsday Equation

Von Foerster was born in 1911 in Vienna, Austria-Hungary, as Heinz von Förster. His paternal grandfather was the Austrian architect {{Ill|Emil von Förster|de}}. His maternal grandmother was Marie Lang, an Austrian feminist, theosophist, and publisher. He studied physics at the Technical University of Vienna and at the University of Breslau, where in 1944 he received a PhD in physics. His relatives included Ludwig Wittgenstein, Erwin Lang and Hugo von Hofmannsthal. Ludwig Förster was his great-grandfather.{{citation |last=Markoff |first=John |title=Heinz von Foerster, a Leading Information Theorist, Dies at 90 |newspaper=The New York Times |date=November 9, 2002 |url=https://www.nytimes.com/2002/11/09/obituaries/09FOER.html}} His Jewish roots did not cause him much trouble while he worked in radar laboratories during the Nazi era, as "he hid his ancestry with the help of an employer who chose not to press him for documents on his family."John Markoff, "[https://www.nytimes.com/2002/11/09/us/heinz-von-foerster-90-dies-was-information-theorist.html Heinz von Foerster, 90, Dies; Was Information Theorist]", November 9, 2002, The New York Times

He moved to the US in 1949 and worked at the University of Illinois at Urbana–Champaign, where he was a professor of electrical engineering from 1951 to 1975. He was also professor of biophysics (1962–1975) and director of the Biological Computer Laboratory (1958–1975). Additionally, in 1956–57 and 1963–64, he was a Guggenheim Fellow and also President of the [http://www.wennergren.org/ Wenner-Gren-Foundation] for anthropological research from 1963 to 1965.

He knew well and was in conversation with John von Neumann, Norbert Wiener, Humberto Maturana, Francisco Varela, Gordon Pask, Gregory Bateson, Lawrence J. Fogel and Margaret Mead, among many others. He influenced generations of students as a teacher and an inclusive, enthusiastic collaborator.

He died on October 2, 2002, in Pescadero, California.

Von Foerster was influenced by the Vienna Circle and Ludwig Wittgenstein. He worked in the field of cybernetics and is known as the inventor of second-order cybernetics. He made important contributions to constructivism.Segal, L. The Dream of Reality: Heinz Von Foerster's Constructivism, Springer, 2001. {{ISBN|0-387-95130-X}} He is also known for his interest in computer music and magic.

In 1949, von Foerster started work at the University of Illinois at Urbana–Champaign at the electron tube laboratory of the Electrical Engineering Department, where he succeeded Joseph Tykociński-Tykociner. With his students he developed many innovative devices, including ultra-high-frequency electronicsSee for example, in Review of Scientific Instruments 25: 640–653, 1954.

He also worked on mathematical models of population dynamics and in 1959 published a model now called the "von Foerster equation", which is derivable from the principles of constant aging and conservation of mass.

:$\backslash frac\{\backslash partial\; n\}\{\backslash partial\; t\}\; +\; \backslash frac\{\backslash partial\; n\}\{\backslash partial\; a\}\; =\; -\; m(a)n,$

where: n = n(t,a), t stands for time and a for age. m(a) is the death in function of the population age; n(t,a) is the population density in function of age.

When m(a) = 0, we have:Murray, J.D. Mathematical Biology: An Introduction. Third edition. Interdisciplinary Applied Mathematics. Mathematical Biology. Spring: 2002.

:$\backslash frac\{\backslash partial\; n\}\{\backslash partial\; t\}\; =\; -\; \backslash frac\{\backslash partial\; n\}\{\backslash partial\; a\}$

It relates that a population ages, and that fact is the only one that influences change in population density."Some Remarks on Changing Populations" in The Kinetics of Cellular Proliferation, F. Stohlman, Jr., ed., Grune & Stratton, New York, pp. 382–407 (1959); E. Trucco, Bulletin of Mathematical Biophysics 27: 285–304 and 449–471, 1965

It is therefore a continuity equation; it can be solved using the method of characteristics. Another way is by similarity solution; and a third is a numerical approach such as finite differences.

The gross birth rate is given by the following boundary condition:

:$n(t,0)=\; \backslash int\_0^\backslash infty\; b\; (a)n(t,a)\; \backslash ,\; dt\; ,$

The solution is only unique given the initial conditions

:$n(0,a)=\; f(a),\; \backslash ,$

which states that the initial population distribution must be given; then it will evolve according to the partial differential equation.

In 1958, he formed the Biological Computer Lab, studying similarities in cybernetic systems in biology and electronics.{{Cite web |url=http://bcl.ece.uiuc.edu/ |title=Biological Computer Laboratory |access-date=2007-07-02 |archive-url=https://web.archive.org/web/20070510142442/http://bcl.ece.uiuc.edu/ |archive-date=2007-05-10 |url-status=dead }}

He was the youngest member of the core group of the Macy conferences on Cybernetics and editor of the five volumes of Cybernetics (1949–1953), a series of conference transcripts that represent important foundational conversations in the field. It was von Foerster who suggested that Wiener's coinage "Cybernetics" be applied to this conference series, which had previously been called "Circular Causal and Feedback Mechanisms in Biological and Social Systems".

{{Redirect-distinguish|Doomsday equation|Doomsday rule}}

A 1960 issue of Science magazine included an article by von Foerster and his colleagues, P. M. Mora and L. W. Amiot, proposing an equation representing the best fit to the historical data on the Earth's population available in 1958:

Fifty years ago, Science published a study with the provocative title “[https://www.researchgate.net/publication/233822850_Doomsday_friday_13_November_AD_2026 Doomsday: Friday, 13 November, A.D. 2026]”. It fitted world population during the previous two millennia with P = 179 × 10⁹/(2026.9 − t)^0.99. This “quasi-hyperbolic” equation (hyperbolic having exponent 1.00 in the denominator) projected to infinite population in 2026—and to an imaginary one thereafter.

:—Taagepera, Rein. [https://www.sciencedirect.com/science/article/abs/pii/S0040162513001613 A world population growth model: Interaction with Earth's carrying capacity and technology in limited space] Technological Forecasting and Social Change, vol. 82, February 2014, pp. 34–41

File:World population since 10,000 BCE (OurWorldInData series), OWID.svg as t approaches 2026.9. On 13 November 2026, t surpasses 2026.9, and the number of people living on the planet Earth suddenly becomes negative or imaginary.]]

In 1975, von Hoerner suggested that von Foerster's doomsday equation can be written, without a significant loss of accuracy, in a simplified hyperbolic form (i.e. with the exponent in the denominator assumed to be 1.00):

:$\backslash text\{Global\; population\}=\backslash frac\{179000000000\}\{2026.9\; -\; t\},$

where

• 2026.9 is 13 November 2026 AD—the date of the so-called "demographic singularity"Korotayev, Andrey. [https://jbh.journals.villanova.edu/article/view/2329/2251 The 21st Century Singularity and its Big History Implications: A re-analysis] Journal of Big History, II(3), June 2018, pp. 73–119 and von Foerster's 115th anniversary;
• t is the number of a year of the Gregorian calendar.Korotayev, Andrey. [https://jbh.journals.villanova.edu/article/view/2329/2251 The 21st Century Singularity and its Big History Implications: A re-analysis] Journal of Big History, II(3), June 2018, pp. 73–119. "We have already mentioned that, as was the case with equations (8) and (9) above, in von Foerster’s Eq. (13) the denominator’s exponent (0.99) turns out to be only negligibly different from 1, and as was already suggested by von Hoerner (1975) and Kapitza (1992, 1999), it can be written more succinctly as N_t = C/(t^* − t)."

Despite its simplicity, von Foerster's equation is very accurate in the range from 4,000,000 BPKorotayev, Andrey. [https://jbh.journals.villanova.edu/article/view/2329/2251 The 21st Century Singularity and its Big History Implications: A re-analysis] Journal of Big History, II(3), June 2018, pp. 73–119. "Note that von Foerster and his colleagues detected the hyperbolic pattern of world population growth for 1 CE –1958 CE; later it was shown that this pattern continued for a few years after 1958, and also that it can be traced for many millennia BCE (Kapitza 1996a, 1996b, 1999; Kremer 1993; Tsirel 2004; Podlazov 2000, 2001, 2002; Korotayev, Malkov, Khaltourina 2006a, 2006b). In fact Kremer (1993) claims that this pattern is traced since 1,000,000 BP, whereas Kapitza (1996a, 1996b, 2003, 2006, 2010) even insists that it can be found since 4,000,000 BP." to 1997 AD. For example, the doomsday equation (developed in 1958, when the Earth's population was 2,911,249,671[https://www.worldometers.info/world-population/world-population-by-year/ World Population by Year] Worldometer) predicts a population of 5,986,622,074 for the beginning of the year 1997:

:$\backslash frac\{179000000000\}\{2026.9\; -\; 1997\}=5986622074.$

The actual figure was 5,924,787,816.

The doomsday equation is called so because it predicts that the number of people living on the planet Earth will become maximally positive by 13 November 2026, and on the next moment will become negative or imaginary.Taagepera, Rein. [https://www.sciencedirect.com/science/article/abs/pii/S0040162513001613 A world population growth model: Interaction with Earth's carrying capacity and technology in limited space] Technological Forecasting and Social Change, vol. 82, February 2014, pp. 34–41.

"This ‘quasi-hyperbolic’ equation (hyperbolic having exponent 1.00 in the denominator) projected to infinite population in 2026—and to an imaginary one thereafter."

{{Portal|Systems science}}

• Macy conferences
• Power law: The equation that he derived for the date calculated is one that nowadays is called a power law.{{citation needed|date=April 2014}}
• List of dates predicted for apocalyptic events
• The Dream of Reality by Lynn Segal, 1986. A book summarizing von Foerster's constructivist epistemology.
• Malthusian growth model
• Jakob von Uexküll

Von Foerster authored more than 100 publications.The [http://www.univie.ac.at/constructivism/HvF/bib.htm Bibliography of Heinz von Foerster 1943–2003], from Alexander Riegler, dec 2003 gives an overview of all his publications. Books, a selection:

• 1949, Cybernetics: Transactions of the Sixth Conference, (editor), Josiah Macy Jr. Foundation: New York, 220 pp.
• 2002, Understanding understanding, a volume of von Foerster's papers, published by Springer-Verlag, 2002.
• 2010, with Monika Broecker: Part of the World. Fractals of Ethics – A Drama in Three Acts. Heinz von Foerster's most extensive biography. First published in German in 2002: with Monika Broecker. Teil der Welt. Fraktale einer Ethik – ein Drama in drei Akten.

Articles, a selection:

• 1958, "Basic Concepts of Homeostasis." In: Homeostatic Mechanisms, Upton, New York, pp. 216–242, 1958.
• 1960, "Doomsday: Friday, November 13, AD 2026," with P. M. Mora und L. W. Amiot, Science 132, pp. 1291–1295, 1960.
• 1961, "A Predictive Model for Self-Organizing Systems," Part I: Cybernetica 3, pp. 258–300; Part II: Cybernetica 4, pp. 20–55, with Gordon Pask, 1961.
• 1964, "Biological Computers," with W. Ross Ashby, In: Bioastronautics, K. E. Schaefer, Macmillan Co., New York, pp. 333– 360, 1964.
• 1969, "What is Memory that it may have Hindsight and Foresight"
• 1971, "Computing in the Semantic Domain"
• 1971, "Technology. What Will It Mean to Librarians?"

{{Reflist}}

• Asaro, Peter M. (2007). [http://cybersophe.org/writing/Asaro%20HVF%26BCL.pdf "Heinz von Foerster and the Bio-Computing Movements of the 1960s,"] {{Webarchive|url=https://web.archive.org/web/20110725214225/http://cybersophe.org/writing/Asaro%20HVF%26BCL.pdf |date=2011-07-25 }} in Albert Müller and Karl H. Müller (eds.) [http://www.echoraum.at/edition/wisdomechoraum3.htm An Unfinished Revolution? Heinz von Foerster and the Biological Computer Laboratory | BCL 1958–1976.] Vienna, Austria: Edition Echoraum.

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• [http://www.stanford.edu/group/SHR/4-2/text/interviewvonf.html Humanities Review Interview] {{Webarchive|url=https://web.archive.org/web/20140527034248/http://www.stanford.edu/group/SHR/4-2/text/interviewvonf.html |date=2014-05-27 }} at Stanford University
• [https://web.archive.org/web/20040803132733/http://www.univie.ac.at/constructivism/HvF.htm The Heinz von Foerster Page]
• [https://web.archive.org/web/20070510142442/http://bcl.ece.uiuc.edu/ Biological Computer Laboratory web site, University of Illinois]
• [http://www.cybsoc.org/heinz.htm An anthology of Circularity Principles] from the Heinz von Foerster entry at [http://www.cybsoc.org/ The Cybernetics Society]
• Gooch, Sherwin, & Nordin, Hud, {{YouTube|tPV_oGJFBmA|"High Tech Heroes television interview, episode 10, part 1," Heinz von Foerster discusses the founding of Cybernetics, and the possibility of achieving immortality through prosthetic brains, Foothill College, California, August 22, 1989.}}
• {{YouTube|4Er2llrFgww|"High Tech Heroes, episode 10, part 2."}}
• [http://archives.library.illinois.edu/archon/index.php?p=collections/controlcard&id=1020 "Heinz Von Foerster Papers at the University of Illinois Archives"]

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