Sunday 17 October 2010

'Fractal' mathematician Benoit Mandelbrot dies aged 85

Benoit Mandelbrot

Mandelbrot saw that apparently random shapes followed patterns

Benoit Mandelbrot, who discovered mathematical shapes known as fractals, has died the age of 85.

Mandelbrot, who had joint French and US nationality, developed fractals as a mathematical way of understanding the infinite complexity of nature.

The concept has been used to measure coastlines, clouds and other natural phenomena and had far-reaching effects in physics, biology and astronomy.

Mandelbrot's family said he had died in a hospice in Cambridge, Massachusetts.

The visionary mathematician was born into a Jewish family in Poland but moved to Paris at the age of 11 to escape the Nazis.

He spent most of his life in the US, working for IBM computers and eventually became a professor of mathematical science at Yale University.

His seminal work, The Fractal Geometry of Nature, was published in 1982. In it, he argued that seemingly random mathematical shapes in fact followed a pattern if broken down into a single repeating shape.

The concept enabled scientists to measure previously immeasurable objects, including the coastline of the British Isles, the geometry of a lung or a cauliflower.

"If you cut one of the florets of a cauliflower, you see the whole cauliflower but smaller," he explained at the influential Technology Entertainment and Design (TED) conference earlier this year.

"Then you cut again, again, again, and you still get small cauliflowers. So there are some shapes which have this peculiar property, where each part is like the whole, but smaller."

'Powerful mind'

Fractal mathematics also led to technological developments in the fields of digital music and image compression.

It has also been influential in pop culture, with the patterns being used to create beautiful and intricate pieces of art. One such design is named in his honour.

Mandelbrot was also highly critical of the world banking system, arguing the economic model it used was unable to cope with its own complexity.

In a statement, French President Nicolas Sarkozy praised Mandelbrot for his "powerful, original mind that never shied away from innovation and battering preconceived ideas".

"His work, which was entirely developed outside the main research channels, led to a modern information theory," he said.


Saturday 14 August 2010

Definitions of Force

force

(fôrs, frs)
n.
1. The capacity to do work or cause physical change; energy, strength, or active power: the force of an explosion.
2.
a. Power made operative against resistance; exertion: use force in driving a nail.
b. The use of physical power or violence to compel or restrain: a confession obtained by force.
3.
a. Intellectual power or vigor, especially as conveyed in writing or speech.
b. Moral strength.
c. A capacity for affecting the mind or behavior; efficacy: the force of logical argumentation.
d. One that possesses such capacity: the forces of evil.
4.
a. A body of persons or other resources organized or available for a certain purpose: a large labor force.
b. A person or group capable of influential action: a retired senator who is still a force in national politics.
5.
a. Military strength.
b. The entire military strength, as of a nation. Often used in the plural.
c. A unit of a nation's military personnel, especially one deployed into combat: Our forces have at last engaged the enemy.
6. Law Legal validity.
7. Physics A vector quantity that tends to produce an acceleration of a body in the direction of its application.
8. Baseball A force play.
tr.v. forced, forc·ing, forc·es
1. To compel through pressure or necessity: I forced myself to practice daily. He was forced to take a second job.
2.
a. To gain by the use of force or coercion: force a confession.
b. To move or effect against resistance or inertia: forced my foot into the shoe.
c. To inflict or impose relentlessly: He forced his ideas upon the group.
3.
a. To put undue strain on: She forced her voice despite being hoarse.
b. To increase or accelerate (a pace, for example) to the maximum.
c. To produce with effort and against one's will: force a laugh in spite of pain.
d. To use (language) with obvious lack of ease and naturalness.
4.
a. To move, open, or clear by force: forced our way through the crowd.
b. To break down or open by force: force a lock.
5. To rape.
6. Botany To cause to grow or mature by artificially accelerating normal processes.
7. Baseball
a. To put (a runner) out on a force play.
b. To allow (a run) to be scored by walking a batter when the bases are loaded.
8. Games To cause an opponent to play (a particular card).
Idioms:
force (someone's) hand
To force to act or speak prematurely or unwillingly.
in force
1. In full strength; in large numbers: Demonstrators were out in force.
2. In effect; operative: a rule that is no longer in force.
[Middle English, from Old French, from Medieval Latin fortia, from neuter pl. of Latin fortis, strong; see bhergh-2 in Indo-European roots.]
force

a·ble adj.
forc

er n.
Synonyms: force, compel, coerce, constrain, oblige, obligate
These verbs mean to cause a person or thing to follow a prescribed or dictated course. Force, the most general, usually implies the exertion of physical power or the operation of circumstances that permit no options: Tear gas forced the fugitives out of their hiding place.
Compel applies especially to an act dictated by one in authority: Say nothing unless you're compelled to.
Coerce invariably implies the use of strength or harsh measures in securing compliance: "The man of genius rules . . . by persuading an efficient minority to coerce an indifferent and self-indulgent majority" James Fitzjames Stephen.
Constrain suggests that one is bound to a course of action by physical or moral means or by the operation of compelling circumstances: "I will never be by violence constrained to do anything" Elizabeth I.
Oblige implies the operation of authority, necessity, or moral or ethical considerations: "Work consists of whatever a body is obliged to do" Mark Twain.
Obligate applies when compliance is enforced by a legal contract or by the dictates of one's conscience or sense of propriety: I am obligated to repay the loan. See Also Synonyms at strength.

force 1
Noun
1. strength or power: the force of the impact had thrown him into the fireplace
2. exertion or the use of exertion against a person or thing that resists: they used force and repression against those who opposed their policies
3. Physics an influence that changes a body from a state of rest to one of motion or changes its rate of motion Symbol: F
4.
a. intellectual or moral influence: the Superintendent acknowledged the force of the Chief Constable's argument
b. a person or thing with such influence: Hitler quickly became the decisive force behind German foreign policy
5. drive or intensity: he reacted with frightening speed and force
6. a group of people organized for particular duties or tasks: a UN peacekeeping force
7. in force
a. (of a law) having legal validity
b. in great strength or numbers
Verb
[forcing, forced]
1. to compel (a person, group, etc.) to do something through effort, superior strength, etc.: forced into an arranged marriage
2. to acquire or produce through effort, superior strength, etc.: he forced a smile
3. to propel or drive despite resistance
4. to break down or open (a lock, door, etc.)
5. to impose or inflict: a series of opposition strikes forced the appointment of a coalition government
6. to cause (plants or farm animals) to grow at an increased rate [Latin fortis strong]
force 2
Noun
(in N England) a waterfall [Old Norse fors]
force

(fôrs)
1. Any of various factors that cause a body to change its speed, direction, or shape. Force is a vector quantity, having both magnitude and direction. Contributions of force from different sources can be summed to give the net force at any given point.
2. Any of the four natural phenomena involving the interaction between particles of matter. From the strongest to the weakest, the four forces are the strong nuclear force, the electromagnetic force, the weak nuclear force, and gravity.

Force a body of men prepared for action, 1375; a body of police; policemen collectively, 1851. See also army, host, troop.

Thursday 12 August 2010

Albert Einstein

"Gravitation cannot be held responsible for people falling in love"

Henry Poincare'

"When one tries to depict the figure formed by these two curves and their infinity of intersections, each of which corresponds to a doubly asymptotic solution, these intersections form a kind of net, web or infinitely tight mesh . . . . One is struck by the complexity of this figure that I am not even attempting to draw."

Monday 3 May 2010

Monday 25 May 2009

The Mind Force Manifesto

Matter, mind, brain, body and society emerge from the same stream in the complexity of nature: we call this energy ‘Mind Force’.
Connections of genes and molecules, neurons and hormones, thinking and language, people and organizations form a continuous flow of synchronized interactions.
Interactions between networks across many scales, from molecular, to biological, to cognitive and social, sustain its scaling and cascading.
We recognize in this hyper network, the landscapes and fields of Mind Force.
The empowerment of individuals by Mind Force comes from integrating multiple perspectives and multiple complementary disciplines: simplicity and complexity are complimentary moments of our knowledge of each other, the world, and us.
Resources for research would follow the integrated path to a deeper knowledge based on multidisciplinary collaborations.
Science is lauded by societies beyond the circle of experts and recognized as a natural
mean of expanding lives, when it stays within the stream of Mind Force.
This flow sustains the inner strength and growth of individuals and communities



In September 2008, we organized a residential workshop in an ancient Charterhouse, at Pontignano, Siena, Italy. It was sponsored by the Department of Neurology and Behavioral Sciences, the Institute of Complex Systems Studies of the University of Siena and the Institute for Complexity Studies of Rome. During the conference, the panel produced the following Manifesto in order to sustain a shared public position.


The first and key contributors to the Mind Force Manifesto are:
Alfredo Ancora
Tito Arecchi
Harald Atmanspacher
Peter Fonagy
Walter J. Freeman
Alessandro Giuliani
Guelfo Margherita
Lamberto Maffei
Chiara Mocenni
Franco Orsucci
Mario Reda
Sergio Rinaldi
Andrea Seganti
Steven Suomi
Giuseppe Vitiello
Joe Zbilut
Riccardo Zerbetto
Alberto Zucconi
We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.

T.S. Eliot