johan gielis

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First part of my career was in plant biotechnology and botany. In 1997 I discovered what was originally introduced as the Superformula, but is now known as Gielis Transformation GT (or Gielis Curves and Surfaces), a generalization of Gabriel Lamé's curves. These curves can be found everywhere in nature. We have also developed a variety of technological products, ranging from modelling and computational software to antenna technology.Our current research is applying

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B. Harun Küçük

University of Pennsylvania

Alexander C . T . Geppert

New York University

David Seamon

Kansas State University

Armando Marques-Guedes

UNL - New University of Lisbon

Kathryn LaFevers Evans, Three Eagles

Pacifica Graduate Institute

Marco Sgarbi

Università Ca' Foscari Venezia

Mariafelicia De Laurentis

Università degli Studi di Napoli "Federico II"

Abhas Mitra

Homi Bhabha National Institute (HBNI, BARC, MUMBAI)

Viacheslav Kuleshov

Stockholm University

Harijono Djojodihardjo

Institut Teknologi Bandung

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Conquering Mount Improbable

Entropy is originally a concept from thermodynamics that distinguishes between useful and useless... more Entropy is originally a concept from thermodynamics that distinguishes between useful and useless energy 1. This led to the Second Law of Thermodynamics, which states that entropy always increases. The Hamiltonian principle states that the differential equation for the Second Law is equivalent to the integral equation for Least Action. In the information age, entropy has been found to be related to complexity. There are two main approaches, one of which is based on C. Shannon (1916-2001) and the other on A.N. Kolmogorov (1903-1987). The former is communication theory, while the latter is the basis of Algorithmic Information Theory (AIT), which studies the shortest algorithm for encoding a message that yields the "best possible compression". This is of course also usage-based and refers to 'optimal' methods of data processing. The commonly used example is a particular sequence of binary digits, symbols or characters. Each of these sequences is called a message. Two sequences (or strings) are: 1 "Useful energy" is somewhat anthropocentric, in the sense of "usefulness for humans". Our scientific and technological worldviews are largely dominated by the concepts of entropy and complexity. Originating in 19th-century thermodynamics, the concept of entropy merged with information in the last century, leading to definitions of entropy and complexity by Kolmogorov, Shannon and others. In its simplest form, this worldview is an application of the normal rules of arithmetic. In this worldview, when tossing a coin, a million heads or tails in a row is theoretically possible, but impossible in practice and in real life. On this basis, the impossible (in the binary case, the outermost entries of Pascal's triangle and for large values of) can be safely neglected, and one can concentrate fully on what is common and what conforms to the law of large numbers, in fields ranging from physics to sociology and everything in between. However, in recent decades it has been shown that what is most improbable tends to be the rule in nature. Indeed, if one combines the outermost entries and with the normal rules of arithmetic, either addition or multiplication, one obtains Lamé curves and power laws respectively. In this article, some of these correspondences are highlighted, leading to a double conclusion. First, Gabriel Lamé's geometric footprint in mathematics and the sciences is enormous. Second, conic sections are at the core once more. Whereas mathematics so far has been exclusively the language of patterns in the sciences, the door is opened for mathematics to also become the language of the individual. The probabilistic worldview and Lamé's footprint can be seen as dual methods. In this context, it is to be expected that the notions of information, complexity, simplicity and redundancy benefit from this different viewpoint.

johan gielis

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