Heinz von Foerster

Heinz von Foerster

Born November 13, 1911
Vienna, Austria
Died October 2, 2002 (aged 90)
Pescadero, California
Citizenship United States
Nationality Austria
United States
Fields Cybernetics
Institutions University of Illinois at Urbana–Champaign
Alma mater Technical University of Vienna
University of Breslau
Known for von Foerster Equation
Second-order cybernetics
Computer science
Artificial intelligence
Influences Ludwig Wittgenstein
Influenced William Ross Ashby, Gordon Pask, Gotthard Günther, Humberto Maturana, Francisco Varela, Ernst von Glasersfeld, Stafford Beer, John C. Lilly
Notable awards Wiener Gold Medal (1983)

Heinz von Foerster (German spelling: Heinz von Förster; November 13, 1911, Vienna – October 2, 2002, Pescadero, California) was an Austrian American scientist combining physics and philosophy, and widely attributed as the originator of Second-order cybernetics. He was twice a Guggenheim fellow (1956–57 and 1963–64) and also was a fellow of the American Association for the Advancement of Science, 1980. He is well known for his 1960 Doomsday equation formula published in Science predicting future population growth.[1]

As a polymath, he wrote nearly two hundred professional papers, gaining renown in fields from computer science and artificial intelligence to epistemology, and researched high-speed electronics and electro-optics switching devices as a physicist, and in biophysics, the study of memory and knowledge. He worked on cognition based on neurophysiology, mathematics, and philosophy and was called "one of the most consequential thinkers in the history of cybernetics".[2] He came to the United States, and stayed after meeting with Warren Sturgis McCulloch, where he received funding from The Pentagon to established the Biological Computer Laboratory, which built the first parallel computer, the Numa-Rete.[3] Working with William Ross Ashby, one of the original Ratio Club members, and together with Warren McCulloch, Norbert Wiener, John von Neumann and Lawrence J. Fogel, Heinz von Foerster was an architect of cybernetics and one of the members of the Macy conferences,[4] eventually becoming editor of its early proceedings alongside Hans-Lukas Teuber and Margaret Mead.[5]


Von Foerster was born in 1911 in Vienna, Austria-Hungary, as Heinz von Förster. He was the grandson of Austrian architect Emil Ritter von Foerster. He studied physics at the Technical University of Vienna and at the University of Breslau, where in 1944 he received a Ph.D. in physics. His relatives included Ludwig Wittgenstein, Erwin Lang and Hugo von Hofmannsthal. Ludwig Förster was his great-grandfather.[6]

He moved to the USA in 1949, and worked at the University of Illinois at Urbana-Champaign, where he was a professor of electrical engineering from 1951–1975. He also was 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 Wenner-Gren-Foundation for anthropological research from 1963–1965.[4]

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 inclusive, enthusiastic collaborator.


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.[2] He made important contributions to constructivism.[7] He is also known for his interest in computer music and magic.

The electron tube laboratory

In 1949 von Foerster started work at the University of Illinois 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[8]

He also worked on mathematical models of population dynamics and developed a general model now called the "von Foerster Equation"

The mathematical formula can be derived from first principles and reads:

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:[9]

It relates that a population ages, and that fact is the only one that influences change in population density; the negative sign shows that time flows in just one direction, that there is no birth and the population is going to die out.[10]

It is therefore a transport equation; it can be solved using a characteristics method.[9] Another way is by similarity solution; and a third is a numerical approach such as finite differences.

To get the solution, the following boundary conditions should be added:

which states that the initial births should be conserved (see Sharpe–Lotka–McKendrick’s equation for otherwise), and that

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

Biological Computer Laboratory

In 1958 he formed the Biological Computer Lab, studying similarities in cybernetic systems in biology and electronics.[11]

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

A 1960 issue of Science magazine included an article by von Foerster and his colleagues P. M. Mora and L. W. Amiot proposing a formula representing a best fit to available historical data on world population; the authors then predicted future population growth on the basis of this formula.[12] The formula gave 2.7 billion as the 1960 world population and predicted that population growth would become infinite by Friday, November 13, 2026 – von Foerster's 115th birthday anniversary – a prediction that earned it the name "the Doomsday Equation."

Based on population data obtained from various sources, von Foerster and his students concluded that world population growth over the centuries was faster than an exponential. In such a situation, doubling-time decreases over time. Von Foerster's tongue-in-cheek prediction of Doomsday on November 13, 2026, was based on an extrapolation into the future of doubling-time, with the finding that doubling-time would decrease to zero on that date.

Responders to his Doomsday prediction objected on the grounds of the finite human gestation time of 9 months, and the transparent fact that biological systems rarely persist in exponential growth for any substantial length of time. Those who knew von Foerster could see in his rejoinders an evident sense of humor.

Doomsday Equation: recent research

The hyperbolic growth of the world population observed until the 1970s has recently been correlated to a non-linear second order positive feedback between demographic growth and technological development that can be spelled out as follows:[13]

See also


Von Foerster authored more than 100 publications.[14] Books, a selection:

Articles, a selection:


  1. Heinz von Foerster, P. M. Mora and L. W. Amiot (November 1960). "Doomsday: Friday, 13 November, A.D. 2026. At this date human population will approach infinity if it grows as it has grown in the last two millenia". Science. 132 (3436): 12911295. Bibcode:1960Sci...132.1291V. doi:10.1126/science.132.3436.1291. PMID 13782058.
  2. 1 2 Foerster, Heinz V; Müller, Albert; Müller, Karl H.; Rooks, Elinor; Kasenbacher, Michael (2013). The Beginning of Heaven and Earth Has No Name: Seven Days with Second-Order Cybernetics. Fordham University Press. ISBN 978-0823255610.
  3. Jamie Hutchinson. Von Foerster made Illinois a cybernetics "nerve center" Ingenuity newsletter, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, May 2004
  4. 1 2 The Heinz von Foerster Page
  5. Biography of Heinz von Foerster 2002
  6. Markoff, John (November 9, 2002), "Heinz von Foerster, a Leading Information Theorist, Dies at 90", The New York Times
  7. Segal, L. The Dream of Reality: Heinz Von Foerster's Constructivism, Springer, 2001. ISBN 0-387-95130-X
  8. See for example, in Review of Scientific Instruments 25: 640–653, 1954.
  9. 1 2 Murray, J.D. Mathematical Biology: an introduction. third edition. Interdisciplinary Applied Mathematics. Mathematical Biology. Spring: 2002.
  10. "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
  11. Biological Computer Laboratory
  12. Heinz von Foerster, P. M. Mora and L. W. Amiot (November 1960). "Doomsday: Friday, 13 November, A.D. 2026. At this date human population will approach infinity if it grows as it has grown in the last two millenia". Science. 132 (3436): 12911295. Bibcode:1960Sci...132.1291V. doi:10.1126/science.132.3436.1291. PMID 13782058.
  13. see, e.g., Introduction to Social Macrodynamics by Andrey Korotayev et al.
  14. The Bibliography of Heinz von Foerster 1943–2003, from Alexander Riegler, dec 2003 gives an overview of all his publications.

Further reading

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