The French and American nationality, Mandelbrot, named and developed the fractal theory as a mathematical way to capture the infinite complexity of nature.
Fractals are used for measuring natural phenomena, that were regarded as non-measurable, such as clouds or coastlines. These discoveries have applications in many fields such as geology, medicine, astronomy, mechanical engineering, but also economics and anatomy.
According to his family, Benoît Mandelbrot died in Cambridge, Massachusetts from pancreatic cancer.
French President Nicolas Sarkozy in a statement paid tribute to the great mathematician, “a strong spirit, authentic, never hesitated to make innovations and to fight against established views.
Benoît Mandelbrot was born in Warsaw on November 20, 1924, in a Jewish family of Lithuanian origin. To escape the Nazi threat fled to France with his family, and then moved to the United States after the Second World War.
A very good video about fractals and Mandelbrot
Mandelbrot set Tools
This is an old paper by Luigi Foschini about the problem of interpretation of quantum physics which has raised a discussion about the effectiveness of science and its limits;
The unexpected discoveries at the beginning of the century, particularly thanks to Heisenberg, Bohr, and Godel, has driven the science to drastic changes, opening new, extraordinary, and infinite research fields. After this, many scientists saw, and still today see, a crisis, with dreadful meaning, in the science. However, this crisis is only present in that type of science, driven by determinism, which is strictly linked to the common sense.
In this paper the author answers the question of the title negatively; Science and specifically physics is not in crisis,what happens is that for the first time quantum physics forces us to face the “hypotheses of effectiveness” of every theory in physics that consists of excluding factors of the problem in order to make it simpler and thus available to study;
How many times one has supposed it ideal (rigid bodies, geometrical bodies, material points). How many times one supposes that the resistance of an electric device is negligible? How many times is friction considered negligible? And taking into consideration the two-bodies problem, one forgets the interactions among the bodies of the universe, isn’t it? Physics and engineering are permeated with hypothesis of this kind, without which we could not adventure in building models or formulating theories. The more or less indirect consequences for engineering are constituted by the introduction of the safety factor, by the concept of reliability of devices; in physics we speak about the experimental errors, the domain of validity of a theory and so on.With all these hypotheses, how could one say what is the nature? This is nota mere philosophical speculation, a sophism, a formal problem.
What is in crisis is the old deterministic view that we can complete science in the way that it can describe everything. That is has not happened in physics (” the unified theory of everything”) but -most important- cannot happen with the formal language of physics; mathematics.
However, one is not allowed to think that mathematics is the last hope for Determinism. As a matter of fact the analogous of the principles of indeterminacy for mathematics was expressed by Kurt G ̈del in 1931 . In his article, he stated the impossibility to realize the hilbertian program: in 1900, during the Second International Congress of Mathematicians in Paris, David Hilbert introduced a list of 23 problems which covered the most different fields of mathematics . Among these, point 2, relative to the demonstration of non-contradiction of arithmetics, deserves a particular attention. From Hilbert’s viewpoint all mathematical theories should have been reduced to formal systems: then this would have been enough to demonstrate the non-contradiction. In 1930, G ̈del wrote an article, which was published one year later where he demonstrated that this was not possible. As a matter of facts, within a sytem like that expressed by Bertrand Russell and Alfred N. Whitehead in the Principia Mathematica it is possible to express propositions which are not decidable within the system’s axioms. One can view this as the impossibility of defining each concept through a unique and defined linguistic universe.
Crisis is not something to fear of -as the title of the blog you are reading suggests also;
Using the term ‘crisis’ they suggest something dreadful, that will lead to the very end of science. Some scientists think that this crisis is already operating and it is the result of the principles up to now discussed, others think it will come along with the Great Unified Theory. Nevertheless, the word ‘crisis’ shows no dreadful meanings: it derives from the Greek κρισις, which in turn is linked to κρινω, which means ‘to divide’ and metaphorically ‘to decide’ 2 . It were the Greeks the first to introduce the process of analysis as a division of a thesis in propositions, leading more easily to truth. If, within a theory, we separate or, better, underline, some essential laws we could then consider them as principles for a new theory.
Slavoj Zizek is one of the most popular contemporary philosophers, BBC considered him as the ‘Elvis Presley’ of Philosophy. He is considered to continue the tradition of the philosophy of Marx, Hegel and Lacan.
Žižek identifies the modern Cartesian Deceiving God in the face of Capitalism;
Slavoj Zizek has determined that late-modern capitalism has engendered a whole range of alternative seductions to keep the eye and brain off of the Real. The Real only exists as a fragment, fast receding on the horizon as fantasy and often phantasm intercede. These dreams and nightmares are systemic, structural neuroses, and they are part of the coordinates of the hegemonic. The hegemony – the prevailing set of coordinates – always seeks to ‘take over’ the Real, and, therefore, this contaminated Real must be periodically purged. (http://www.egs.edu/faculty/slavoj-zizek/biography/)
NewScientist recently published an interview with the “most dangerous philosopher in the west” Slavoj Žižek. In the interview he is suggesting that we should be critical of Science since it is entangled with capitalism and looses its objectivity. We should question it, because Science is also our only weapon to defend our existence against the threats of Nature.
Science is completely entangled with capital and capitalism. It is simultaneously the source of some threats (such as the ecological consequences of our industries or the uncontrolled use of genetic engineering), and our best hope of understanding those threats and finding a way to cope with them.
He believes that we are naive believing, that we are a threat to Nature, because that means that we underestimate our fragility; “in fact Mother Nature is not good – it’s a crazy bitch.” That of course does not mean that we should continue destroying the environment, in the contrary we should understand that what is on stake here is our own existence as a whole. We do not want to see that we do not control Nature; changing just our behavior is not going to save us because there is a point of no return.
I’m against the ecologists’ anti-technology stance, the one that says, “we are alienated by manipulating nature, we should rediscover ourselves as natural beings”
This is indeed a very interesting view for someone influenced by Marxists’ views, since he continues with;
We should alienate ourselves more from nature to be aware of our fragility
But following his thinking we can understand that, in the core, there is the argument of the ‘threatened’ Science; We cannot just denounce Science and its technological achievements just because Science is in crisis due to its entanglement to capitalism. We have to defend Science from being abused (identify what is “bad Science”, whose only purpose is profit at any cost) purify it and use it to really empower ourselves in all possible ways. Since capitalism is the “deceiving Deity” we should be very critical of the purposes of the scientific achievements, we need to read behind the lines… According to Zizek there is a guideline to this quest of good Science; the use of commons, knowledge is a common we collectively own it, and the more it circulates the more powerful it becomes. We should defend our right to open knowledge;
The problem for companies is how to prevent the free circulation of knowledge
Researchers (Henrich, Heine and Norenzayan) surveyed the literature in the field of behavioral science. The authors point out that, based on the population samples in the studies they surveyed, a western undergraduate college student is 4,000 times more likely to be a participant in a behavioral sciences study than anyone other person on the planet. They created an acronym to describe this population: Western, educated, industrialized, rich and democratic (WEIRD), which, according to the survey, actually does describe the population samples upon which most of the world’s investigations into human behaviors are based.
The issue is that -according to the authors- WEIRDs are potentially different from the rest of the world, which makes them a bad sample; The WEIRDer you are, the more you perceive a world full of separate objects, rather than relationships, and the more you use an analytical thinking style, focusing on categories and laws, rather than a holistic style, focusing on patterns and contexts.
“Our findings suggest that members of WEIRD societies are among the least representative populations one could find for generalizing about humans. Overall, these empirical patterns suggest that we need to be less cavalier in addressing questions of human nature, on the basis of data drawn from this particularly thin and rather unusual slice of humanity.”
If WEIRD people are indeed weird, the authors hypothesize that growing up in an industrial-era environment with plenty of 90-degree lines and carpentered edges led to WEIRD people’s sense of vision being susceptible to the deception.
“We live in this world with police and institutions and pre-packaged food, TV, the Internet, watches and clocks and calendars. Our heads are loaded with all this information for navigating those environments. So we should expect our brains to be distorted,” Dr. Henrich says.
Some psychologists doubt whether privileged Westerners actually are the odd people out. They note a human tendency, throughout history and across cultures, to regard one’s own group as unique, and they doubt whether a more wide subject pool will sustain the idea that WEIRD people are finally “weird”.