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human consciousness, where instead of individual nerve cells or brain regions, a whole

new quality of existence and perception emerges.

Finally, in this chapter we would like to introduce five important representatives of

complex systems theory. We begin with Alan Turing, who thought in general terms about

the computer and its limits. This is followed by Rene Thom, who founded the general

theory about the behavior when crossing system boundaries. In addition, Benoit Mandelbrot

is introduced, who founded his own field with his fractals, to elucidate natural system

behavior and structures with simple principles, the fractals, as well as Leroy Hood, who is

an example as a highly recognized representative of the younger systems biology and its

application in medicine (there are many who could also be mentioned, not only in the

USA, but also from Europe. So he provides here only a strong example). Reinhart Heinrich

concludes the book, representing all non-US efforts in systems biology, which already

produced exciting initial results in the Soviet Union and the former GDR, for example on

phosphorylation cascades.

9.5

Pioneers of Systems Science

Alan Turing

Alan Turing has the merit (Hodges 2014) of having already mathematically thought out

what a computer would be capable of even before most computers were built. This makes

him at least one of the greatest computer scientists who ever lived. In his memory there has

been the “Turing Award” for the best computer scientist since 1966. Turing was English

and lived from June 1912 (London) to June 1954 (stigmatized for his homosexuality since

1952, died of a cyanide overdose, suicide/accident). With the help of the concept of the

Turing machine (Fig. 8.1) he was able to show clearly which problems computers and

formal systems can decide and which cannot (“On Computable Numbers, with an

Application to the Decision Problem”; 1936; Alonso Church’s lambda calculus showed

something similar earlier, but without this ingenious machine). In particular, it is impos­

sible to decide algorithmically when a Turing machine holds. Of his many other contribu­

tions to mathematics, logic and computers, it is worth mentioning that he deciphered the

code of the German cipher machine “Enigma” with the help of the first English large-scale

computer “Colossus” during the Second World War.

Rene Thom

Professor Rene Thom (02.09.1923–25.10.2002) was a mathematician. His “catastrophe

theory” attempts to describe specifically the discontinuous, erratic behavior of dynamical

systems (Poston and Stewart 1998). His theory studies the branching behavior of solutions

(bifurcations) as parameters vary as a mathematical treatment of chaos theory. His “theory

of singularities of differentiable mappings” means here the seven possibilities for mathe­

matical functions to change suddenly and abruptly its seven “normal types”.

9  Complex Systems Behave Fundamentally in a Similar Way