In the hard sciences, which can often feel out of grasp for many lay readers, there are “great thinkers” who go far beyond the equations, formulas, and research. Minds such as Stephen Hawking philosophize about the functions and nature of the universe, the implications of our existence, and other impossibly fascinating, yet difficult questions. Stuart A. Kauffman is one of those great thinkers. He has dedicated his lifetime to researching “complex systems” at prestigious institutions and now writes his treatise on the most complex system of all: our universe.
A recent Scientific American article claims that “philosophy begins where physics ends, and physics begins where philosophy ends,” and perhaps no better quote sums up what Kauffman’s latest book offers. Grounded in his rigorous training and research background, Kauffman is inter-disciplinary in every sense of the word, sorting through the major questions and theories in biology, physics, and philosophy. Best known for his philosophy of evolutionary biology, Kauffman coined the term “prestatability” to call into question whether science can ever accurately and precisely predict the future development of biological features in organisms. As evidenced by the title’s mention of creativity, the book refreshingly argues that our preoccupation to explain all things with scientific law has deadened our creative natures. In this fascinating read, Kauffman concludes that the development of life on earth is not entirely predictable, because no theory could ever fully account for the limitless variations of evolution. Sure to cause a stir, this book will be discussed for years to come and may even set the tone for the next “great thinker.”
Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phenotypes, niches, ecosystems. We wish to argue that the evolution of life marks the end of a physics world view of law entailed dynamics. Our considerations depend upon discussing the variability of the very ”contexts of life”: the interactions between organisms, biological niches and ecosystems. These are ever changing, intrinsically indeterminate and even unprestatable: we do not know ahead of time the “niches” which constitute the boundary conditions on selection. More generally, by the mathematical unprestatability of the “phase space” (space of possibilities), no laws of motion can be formulated for evolution. We call this radical emergence, from life to life. The purpose of this paper is the integration of variation and diversity in a sound conceptual frame and situate unpredictability at a novel theoretical level, that of the very phase space.
Our argument will be carried on in close comparisons with physics and the mathematical constructions of phase spaces in that discipline. The role of (theoretical) symmetries as invariant preserving transformations will allow us to understand the nature of physical phase spaces and to stress the diﬀerences required for a sound biological theoretizing. In this frame, we discuss the novel notion of ”enablement”. Life lives in a web of enablement and radical emergence. This will restrict causal analyses to diﬀerential cases (a diﬀerence that causes a diﬀerence). Mutations or other causal diﬀerences will allow us to stress that ”non conservation principles” are at the core of evolution, in contrast to physical dynamics, largely based on conservation principles as symmetries. Critical transitions, the main locus of symmetry changes in physics, will be discussed, and lead to ”extended criticality” as a conceptual frame for a better understanding of the living state of matter.
From Jos Leys, Étienne Ghys and Aurélien Alvarez, the makers of Dimensions, comes CHAOS, a math movie with nine 13-minute chapters. It is a film about dynamical systems, the butterfly effect and chaos theory, intended for a wide audience. CHAOS is available in a large choice of languages and subtitles.
Our goal in the paper is to offer both an eulogy and a critique of the machine metaphor as a theoretical resource for understanding organic systems. We begin by presenting an abbreviated history of the machine metaphor, pointing out how it was instrumental in the development of modern biology, as it provided a conceptual basis for an analytical program in the sciences of life. Then we deal with what exactly makes the machine metaphor such a successful resource, pointing to what organisms and machines in fact share in common – based on the relational approaches advanced by Varela and Rosen, we suggest that both are ʻconstrained systemsʼ. In the third part, we present an alternative way of conceptualizing living systems, bringing now the disanalogies with machines to the foreground. Reviewing the independent work of different authors, we show that there is distinct organicist theoretical camp, where the organism is generally understood as an autonomous system. Finally, we observe that many authors from that camp are now reclaiming Kant’s treatment of organisms in the Critique of Judgment, in particular the concept of «natural purpose» – but those authors do that with a markedly anti-Kantian goal: to naturalize teleology. Our conclusion is that the view of organism as an autonomous system gives us the key to a naturalistic understanding that can finally overcome the mechanical view of nature so characteristic of modern thought. The machine metaphor, despite all its undeniable contributions to the advancement of biological research, shows itself ultimately insufficient for a complex view of the phenomena of life – and discarding it doesn’t need to mean any concession to vitalism: on the contrary, it may be exactly what we need to invigorate a robustly materialist project.
An attempt is made to model the structure of science and art discovery processes in the light of currently defined ideas on the societal flow of knowledge and conservation of information, using the versatile physical concept of toroidal geometry. This should be seen as a heuristic model that is open for further development and evolution. The scientific process, has been often described as a iterative and/or recurrent process. Current models explain the generation of new knowledge on the basis of a number of sequential steps (activities) operating in a circular mode. This model intrinsically assumes this process to be congruent for all individual scientific efforts. Yet, such a model is obviously inadequate to fully describe the whole integral process of scientific discovery as an ongoing interactive process, performed in a cumulative fashion. This implies that any new cycle starts from a different perspective or, optimistically seen, is initiated from a higher level, in a spiral mode, that takes into account the ongoing rise of scientific perspectives. Also, any model that attempts to picture the scientific process, should include potential interactions of concepts or hypotheses, in the sense that concurrently developed concepts may (mutually) influence each other and even may be mixed or superposed or, alternatively, may even result in concept extinction. Science and art progression, both seen as an individual effort and as a historically-based flow of events, is inherently a non-linear or even sometimes a chaotic process, where quite suddenly arising visions can cast a very different light on main-stream scientific thought and/or seem to remove existing barriers in more traditional “habits of the mind”. In contrast to the rather gradual evolution of science, the history of art sometimes even shows complete rejection of preceding conceptualizations and styles. The dynamics of cognition and perception are fruitfully suggested by the rotational dynamics of a torus as a basis for its “self-reflexive” property. Also, the torus exhibits contraction/relaxation loops, in which the torus turns inside out in a vibrating mode, implying strange loop trajectories. This suggests that the toroidal geometry embodies a cognitive twist, relating the “inside” to “outside” of knowledge as with a Möbius strip, a phenomenon that can be seen as the basis for self-consciousness. The torus geometry may also be applied to the art process on the basis of personal experience, intuitive vision, intention, imagination, and technical realization of the becoming piece of art. The finalization of the art concept can be conceived as a sort of knotting of the spiral information process: By literally connecting both ends of the toroidal information trajectory, the spiral is closed and a final product is created. Importantly, both scientists and artists may be inspired by intuition and serendipity, possibly through contact with an underlying knowledge field, as identified in modern physics. Unfortunately, science that often claims objectivity, sometimes seems dominated by a range of subjective human attitudes, not different from any other field in society. One factor is the deficient science-philosophical education of our students in the current curricula and loss of academic worldviews in university careers, in which “time is short” and necessary moments for reflection scarce.
God’s dice liberates us from the prison of determinism, the hopeless tedium of the cosmic clock and the inevitable death of entropy. We have instead an intelligent Universe, where ever new and evolving life forms thrive on Chaos, where negentropy creates higher order from decaying forms. The clock is not winding down as the second law of thermodynamics had thought, it is ever being created anew. God is back in the picture, not just as the creator of the machine who then left — the ghost in the machine — but as the Strange Attractor, the origin of inexplicable and unpredictable order from chance.
We consider the fabric of spacetime from a wide perspective: from mathematics, quantum physics, far from equilibrium thermodynamics, biology and neurobiology. It appears likely that spacetime is fractal and quantum coherent in the golden mean. Mathematically, our fractal universe is non-differentiable and discontinuous, yet dense in the infinite dimensional spacetime. Physically, it appears to be a quantum coherent universe consisting of an infinite diversity of autonomous agents all participating in co-creating organic, fractal spacetime by their multitudinous coupled cycles of activities. Biologically, this fractal coherent spacetime is also the fabric of conscious awareness mirrored in the quantum coherent golden mean brain states.
Whitehead’s philosophy, discontinuous nondifferentiable spacetime, fractals, coupled activity cycles, deterministic chaos, quantum coherence and fractals, golden mean.
It is shown how both the principles of extremum of entropy production, which are often used in the study of complex systems, follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant. A brief discussion on the validity of the application of the mEP and MEP principles in several cases, and in particular to the Earth’s climate is also presented.
In a recent paper  Reis showed that both the principles of extremum of entropy production rate, which are often used in the study of complex systems, are corollaries of the Constructal Law. In fact, both follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant.
In this paper it is shown how the so-called principle of “minimum energy expenditure” which is often used as the basis for explaining many morphologic features in biologic systems, and also in inanimate systems, is also a corollary of Bejan’s Constructal Law .
Following the general proof some cases namely, the scaling laws of human vascular systems and river basins are discussed as illustrations from the side of life, and inanimate systems, respectively.
The principles which underpin physical law are at the heart of science. New ideas and new concepts are examined and evaluated in terms of how they lead to new insight into present paradigms. The lectures discuss methodology, important mathematical structures and various aspects of symmetry, how they lead to consistency, or otherwise, with present understanding, and how also they can facilitate quantitative analysis. Read More
Reproduced from: https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/ FUNDAMENTAL PHYSICS The Peculiar Math That Could Underlie the Laws of Nature New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.” Natalie Wolchover Senior Writer/Editor July 20, 2018 DOWNLOAD AS PDF In 2014, a graduate student at the University of Waterloo, Canada,… Read More