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
Why quantum physics is believed to be so weird? Can we understand it without reading tons of scientific formalism? The answer depends on the incentive behind the question;
What people mean by saying that quantum physics is weird? Let’s see some possible reasons;
Is it because you cannot understand the formalism? The formalism itself is not weird; maybe it is hard besause you are not so familiar with the mathematics behind it.
Is it because you cannot get the physical insight behind it? Then welcome to physics; the hardest part in any physics discipline is not to use the mathematics, but to develop an intuitive understanding by grasping the insight of the theory. This ability is very hard to be taught.
Is it because you cannot accept the philosophical implications of quantum physics? Then we have you have to clarify a little more; What do you mean by philosophical implications? Is it that you are worried that the famous cat cannot be both dead and alive in the same time¹? Which means that you don’t like the innate uncertainty that quantum physics is introducing? In this case you assume that classical physics does not lead to any cats that they are dead and alive in the same time. But is this really true?
Classical physics is a study of how things, like stellar objects and planets, can move relative to one another in a regular fashion. In the language of classical physics, in order that we can have a theory about a certain subject matter we must presuppose that we already have two things in place;
a) We must have a kinematical framework in which we can define how the things to be studied might be distributed in space and time
b) We must have a dynamical understanding of the powers and properties that might successively occupy specific places in space.
The first framework is provided by the Cartesian analytic geometry. The second framework is provided by Newtonian laws, which they describe the evolution of things in space and time.
Classical physics offers a very important promise; if we know the initial state parameters of a system, theoretically, we can solve the equations that describe the dynamics of the system and know the full behavior of the system in the past and the future. In simple worlds it means that if your cat is missing then if you put all the parameters of the system in a super computer that solves the dynamics of the world that you live in, you can find out with 100% certainty if your cat is dead or alive. The cat cannot be both dead and alive in the same time.
But there are some objections there;
1. Chaos: Even if a system is deterministic it cannot be 100% predictable, and that is because you can not measure the initial state parameters with infinite accuracy.
2. Complexity: Let’s assume that we don’t care about chaos, because we have found a way to measure with infinite accuracy. Then we face some problems that they derive form computer science; How long will it take for this super computer to decide if the cat is dead or alive? If it takes more that a cat’s life time then we don’t need to perform the calculation because the cat is 100% dead. The problems is now transformed from pure physics to pure computational complexity.
3. Let’s assume now that we are lucky and the complexity of the calculations is not a problem (we have a super computer, and the equations of the dynamics of the world is an easy problem). Even in the situation that we can we really solve the equations for the whole universe and find out the position and speed of every single elementary particle of the world at any given time, can we really sort this kind of information? Imagine that we are talking about all the elementary particles of the world, even for a single snapshot you have a problem of storage; since the unit of storage cannot be smaller than one elementary particle! You cannot even describe a single snapshot of the universe , which means that there are points in the universe that you are uncertain of their properties. Maybe you can calculate if the cat is alive but then you cannot know what is the situation of all the cats in the universe!
So uncertainty can’t be the reason that quantum physics is considered weird.