Editing Heinz von Foerster (section)

==Work==
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]].<ref name=FUP/>  He made important contributions to [[Constructivist epistemology|constructivism]].<ref>Segal, L. ''The Dream of Reality: Heinz Von Foerster's Constructivism'', Springer, 2001. {{ISBN|0-387-95130-X}}</ref> He is also known for his interest in computer music and [[Magic (illusion)|magic]].

===The electron tube laboratory===
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 electronics<ref>See for example, in ''Review of Scientific Instruments'' '''25''': 640–653, 1954.</ref>

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.

:<math>\frac{\partial n}{\partial t} + \frac{\partial n}{\partial a}  = - m(a)n, </math>

where: ''n''&nbsp;=&nbsp;''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'')&nbsp;=&nbsp;0, we have:<ref name="ref1">Murray, J.D. ''Mathematical Biology: An Introduction''. Third edition. Interdisciplinary Applied Mathematics. Mathematical Biology. Spring: 2002.</ref>

:<math>\frac{\partial n}{\partial t} = - \frac{\partial n}{\partial a} </math>

It relates that a population ages, and that fact is the only one that influences change in population density.<ref>"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</ref>

It is therefore a [[continuity equation]]; it can be solved using the [[method of characteristics]].<ref name="ref1" /> 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:

:<math> n(t,0)= \int_0^\infty b (a)n(t,a) \, dt ,</math>

The solution is only unique given the initial conditions

:<math> n(0,a)= f(a), \, </math>

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

===Biological Computer Laboratory===
In 1958, he formed the ''[[Biological Computer Laboratory|Biological Computer Lab]]'', studying similarities in cybernetic systems in [[biology]] and [[electronics]].<ref>{{Cite web |url=http://bcl.ece.uiuc.edu/ |title=Biological Computer Laboratory<!-- Bot generated title --> |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 }}</ref>

===Macy conferences===
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".

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

A 1960 issue of ''[[Science (magazine)|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:
<blockquote>
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 × 10<sup>9</sup>/(2026.9 − ''t'')<sup>0.99</sup>. 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
</blockquote>
[[File:World population since 10,000 BCE (OurWorldInData series), OWID.svg|thumb|The global population is equal to <math>\tfrac{179000000000}{2026.9 - t}</math> and [[Hyperbolic growth|hyperbolically grows]] 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 number|imaginary]].<ref name=Taagepera/>]]
In 1975, [[Sebastian von Hoerner|von Hoerner]] suggested that von Foerster's doomsday equation can be written, without a significant loss of accuracy, in a simplified [[Hyperbolic growth|hyperbolic]] form (''i.e.'' with the exponent in the denominator assumed to be 1.00):
:<math>\text{Global population}=\frac{179000000000}{2026.9 - t},</math>
where
* 2026.9 is 13 November 2026 AD—the date of the so-called "demographic singularity"<ref>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</ref> and von Foerster's 115th anniversary;
* ''t'' is the number of a year of the [[Gregorian calendar]].<ref>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<sub>t</sub>'' = ''C''/(''t<sup>*</sup>'' − ''t'')."</ref>

Despite its simplicity, von Foerster's equation is very accurate in the range from 4,000,000 BP<ref>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. "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."</ref> to 1997 AD. For example, the doomsday equation (developed in 1958, when the Earth's population was 2,911,249,671<ref name=Worldometer>[https://www.worldometers.info/world-population/world-population-by-year/ World Population by Year] Worldometer</ref>) predicts a population of 5,986,622,074 for the beginning of the year 1997:
:<math>\frac{179000000000}{2026.9 - 1997}=5986622074.</math>

The actual figure was 5,924,787,816.<ref name=Worldometer/>

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 number|imaginary]].<ref name=Taagepera>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 number|imaginary]] one thereafter."</ref>