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^[9]

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.

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

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:^[10]

${\displaystyle {\frac {\partial n}{\partial t}}=-{\frac {\partial n}{\partial a}}}$

It relates that a population ages, and that fact is the only one that influences change in population density.^[11]

It is therefore a continuity equation; it can be solved using the method of characteristics.^[10] 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:

${\displaystyle n(t,0)=\int _{0}^{\infty }b(a)n(t,a)\,dt,}$

The solution is only unique given the initial conditions

${\displaystyle n(0,a)=f(a),\,}$

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 Lab, studying similarities in cybernetic systems in biology and electronics.^[12]

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.^[13] 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.