## The father of fractals, Benoit Mandelbrot, is dead

The mathematician **Benoît Mandelbrot** who developed the geometrical shapes, fractal, died at the age of 85 years.

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.

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A very good video about fractals and Mandelbrot

http://video.google.com/googleplayer.swf?docid=8570098277666323857&hl=en&fs=true

↔

**Life**

### http://en.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot

### “He Gave Us Order Out of Chaos” — R.I.P. Benoît Mandelbrot, 1924-2010

### http://en.wikivisual.com/index.php/Mandelbrot_set

### Benoit Mandelbrot on Risk, Efficient Markets, and Bachelier

**Interviews**

### Benoit Mandelbrot: Fractals and the art of roughness

**Mandelbrot Set**

### Introduction to the Mandelbrot Set

### Mandelbrot Set

### Mandelbrot Set Zoom

### The Mandelbrot Set

### Mu-Ency – The Encyclopedia of the Mandelbrot Set

### 3D Mandelbrot fractal

**Mandelbrot set** Tools

### Julia and **Mandelbrot Set** Explorer

### Mandelbrot Applet

### The Mandelbrot Set

### Zoomable Mandelbrot Fractal

### Mandelbrot Explorer

### Mandelbrot

### Mandelbrot

### Studying Mandelbrot Fractals

### iFractal

**Books**

**DVDs on Mandelbrot set**

## Deceiving God and free circulation of knoweledge

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

## Heisenberg’s uncertainty principle and quantum memories;

There is a very good post here that tries to explain a paper that was published by scientists from LMU and the ETH in Zurich, in which they argue that **we can do** measurements in quantum physics systems that “violate” the uncertainty principle that Heisenberg has introduced.

## Heisenberg’s uncertainty principle

About the uncertainty principle I will give an example which is wrong as an explanation of the principle¹, but I hope you will understand what uncertainty means;

Assume that we have a dark room and in the room there is one ball of unknown color. We want to learn where excactly the ball² is located in the room and what color it is. For this purpose we have only two choices; there are two agents that we can use to measure, one agent (“cat”), can tell you only about the position of the ball but in order to find the position it needs to change the color of the ball. The second agent (“dog”), it can tell you about the color of the ball but in-order to do that it relocates the ball.

This way you cannot know the position and the color of the ball in a specific point of time; If you use the cat and the cat returns saying, that the ball is under the center of the table then you know that most possible the ball color has changed. If you use the dog and the dog returns saying, that the ball is blue then you know that the position of the ball has changed.

Two points that you need to know here;

First, you can use the dog after the cat (or the other way around) and after the last measurement you know exactly were the ball is and what is the color. The problem of the uncertainty is that **you don’t know what the initial position and color of the ball was. **Using one of the two agents you introduce “uncertainty” in either the position or the color of the ball, depending what you use first. Of course you cannot use the two agents together (cat and dogs don’t work together :-)) so you cannot know where the ball is and what color it has in the same point of time.

Second, let’s “quantify” our example; When you ask the cat to measure the position of the ball, the cat will ask you; “how accurate you want the results?” if you respond that you want the exact position of the ball then the cat will say that it can repaint the ball to any possible color. That means that after the exact measurement of the position of the ball the uncertainty of the color is huge; you do not have any clue about the color! If you respond to the cat that you want to know the position within an error of 1 meter, let’s say, then the cat (because it does not have to do much work!) will respond; “OK, then I will repaint the ball in a tone of red”. This way you know at least after the measurement that the color of the ball is a tone of red, you do not know the exact color but you have a clue at least, so the uncertainty in this case is smaller.** That means that position and color in our example are somehow competitive; After one measurement, the more you know about the one the less you know about the other, that is the core meaning of the uncertainty principle.**

## quantum *entanglement*

Now there is another “feature” in quantum theory that seems to make things really strange; entanglement.

Assume that in the previous example of the ball before you ask of any agent to do a measurement, you know that there is another ball (“ball1”) that has interacted briefly with our ball and they shared colors. If both balls were the normal (“classical”) balls that we know we would know that both of the balls have the same color. So after the cat would have measured the position of the ball, most definitely ball1 would have different color from ball (remember that the cat agent change the color). In quantum theory simple things like that don’t happen;

the property of quantum entanglement says that ball1 would change its color to be the same color with our ball after the cat measurement!!! Confused? **Quantum entanglement says that if two particles (the balls) are entangled then, the specific property that they are entangled with, it will have the same value for both particles despite how far the two particles are!** You can understand that by supposing that when you measure the first particles spin and you find it to be up, then at the same time the second particle’s spin is changing to up! So in our case whenever you measure the color of ball1 then you know what the color of ball is!

## Violation of the uncertainty principle

The idea is actually very old, since the first steps of quantum theory, and actually it was a

direct outcome of the famous EPR experiment that was the last act of the famous **Bohr-Einstein debate** about the completeness of quantum theory. Nobody back then has payed attention that in the EPR experiment we can circumvent the uncertainty principle.

In the example of the entangled balls above, entanglement gives a great opportunity to measure both qualities in the same time; Assume that after the entanglement we use the dog to measure the exact color of ball1 and the dog returns with the answer red. Then we ask the cat to do an exact measurement of the position of the ball (not ball1), and the cat returns with the ball’s position. We know now that the exact position of the ball (the cat cannot change its position). What about the color? After the cat did the measurement we know that the color can be anything, but we want to know the color before the cat interfered! We have it! It is the color of ball1; red! Since the two balls are entangled we know that when the dog was measuring the color of ball1 it was also measuring the color of ball without changing balls position (since it was doing a measurement on ball1 not ball)

This way quantum entanglement help us to get more information from a quantum system than we could normally get!

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¹ In quantum physics theory the uncertainty does not happen because the equipment that we use to measure is imperfect and it disturbs the fragile subatomic particles when they measure them. Uncertainty is a very important part of the theory itself and it has nothing to do with the technology of the measurement.

² We are talking about not a normal ball, but about an imaginary “quantum” ball.

** **

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