Dangerous Knowledge : Georg Cantor

Inspiration for following few Dangerous knowledge posts is BBC doucumentry known as “DANGEROUS KNOWLEDGE” which is a must see and recommended.

“Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845 – January 6, 1918 ) was a German mathematician. He is best known as the creator of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are “more numerous” than the natural numbers. In fact, Cantor’s theorem implies the existence of an “infinity of infinities”. He defined the cardinal and ordinal numbers, and their arithmetic. Cantor’s work is of great philosophical interest, a fact of which he was well aware.The harsh criticism has been matched by international accolades. In 1904, the Royal Society awarded Cantor its Sylvester Medal, the highest honor it can confer.”

“Cantor was the first to formulate what later came to be known as the continuum hypothesis or CH: there exists no set whose power is greater than that of the naturals and less than that of the reals (or equivalently, the cardinality of the reals is exactly aleph-one, rather than just at least aleph-one). Cantor believed the continuum hypothesis to be true and tried for many years to prove it, in vain. His inability to prove the continuum hypothesis caused him considerable anxiety.”
“The difficulty Cantor had in proving the continuum hypothesis has been underscored by later developments in the field of mathematics: a 1940 result by Gödel and a 1963 one by Paul Cohen together imply that the continuum hypothesis can neither be proved nor disproved.”

Full Article at : http://en.wikipedia.org/wiki/Georg_Cantor

An ice-free Arctic this year?

“It seems our worst fears may come true. For the first time in human history, ice is on course to disappear entirely from the North Pole in 2008 itself, giving evidence to the process of global warming.

The disappearance of the Arctic Sea ice, making it possib

le to reach the Pole sailing in a boat through open water, would be one of the most dramatic — and worrying — examples of the impact of global warming on the planet. Scientists say the ice at 90 degrees north may well have melted away by the summer.”

Full Article at :

http://timesofindia.indiatimes.com/Earth/An_ice-free_Arctic_this_year/articleshow/3173764.cms

Dubai’s moving skyscraper

“Construction of the world’s first moving building, a 80-storey tower with revolving floors which give it an ever-shifting shape, is due to begin in Dubai.”

The Dynamic Tower, which will be built in Dubai, will feature 80 pre-fabricated apartments, spinning independently of one another.

 

Full Article and Videos at : http://news.bbc.co.uk/2/hi/middle_east/7472722.stm

Google:space race to the moon

“The race is part of the Google Lunar X Prize, which will put $20 million into the hands of the first privately funded team that can land a rover on the moon; have it travel on the surface for 500 meters or more; send back data, photos and video; and do it all by December 31, 2012.”

“The prize drops to $15 million after that date and goes away altogether after 2014.”

Full article at http://edition.cnn.com/2008/TECH/space/06/20/google.lunar.xprize/index.html

The secret of Bill Gates success

Nice article about the early days of Microsoft and Bill’s Business Approach.

here are the few Extracts:

“it wasn’t just what Microsoft did, but what his rivals didn’t do that let Microsoft get ahead”

“They did not understand how to bring in people with business experience and people with engineering experience and put them together. They did not understand how to go around the world.”

“Most of our competitors were one-product wonders. “

“They would do their one product, but never get their engineering sorted out.”

“They did not think about software in this broad way. They did not think about tools or efficiency. They would therefore do one product, but would not renew it to get it to the next generation.”

Full article and bill interview Video at http://news.bbc.co.uk/2/hi/business/7464074.stm 

There was once a civilization……

This is an extract from speech by CARLY FIORINA from HP Executive team.

There was once a civilization that was the greatest in the world.It was able to create a continental super-state that stretched from ocean to ocean, and from northern climes to tropics and deserts. Within its dominion lived hundreds of millions of people, of different creeds and ethnic origins.

One of its languages became the universal language of much of the world, the bridge between the peoples of a hundred lands. Its armies were made up of people of many nationalities, and its military protection allowed a degree of peace and prosperity that had never been known. The reach of this civilization’s commerce extended from Latin America to China, and everywhere in between.

And this civilization was driven more than anything, by invention. Its architects designed buildings that defied gravity. Its mathematicians created the algebra and algorithms that would enable the building of computers, and the creation of encryption. Its doctors examined the human body, and found new cures for disease. Its astronomers looked into the heavens, named the stars, and paved the way for space travel and exploration.

Its writers created thousands of stories. Stories of courage, romance and magic. Its poets wrote of love, when others before them were too steeped in fear to think of such things.

When other nations were afraid of ideas, this civilization thrived on them, and kept them alive. When censors threatened to wipe out knowledge from past civilizations, this civilization kept the knowledge alive, and passed it on to others.

While modern Western civilization shares many of these traits, the civilization I’m talking about was the Islamic world from the year 800 to 1600, which included the Ottoman Empire and the courts of Baghdad, Damascus and Cairo, and enlightened rulers like Suleiman the Magnificent.

Although we are often unaware of our indebtedness to this other civilization, its gifts are very much a part of our heritage. The technology industry would not exist without the contributions of Arab mathematicians. Sufi poet-philosophers like Rumi challenged our notions of self and truth. Leaders like Suleiman contributed to our notions of tolerance and civic leadership.

And perhaps we can learn a lesson from his example: It was leadership based on meritocracy, not inheritance. It was leadership that harnessed the full capabilities of a very diverse population–that included Christianity, Islamic, and Jewish traditions.

This kind of enlightened leadership — leadership that nurtured culture, sustainability, diversity and courage — led to 800 years of invention and prosperity.

In dark and serious times like this, we must affirm our commitment to building societies and institutions that aspire to this kind of greatness. More than ever, we must focus on the importance of leadership– bold acts of leadership and decidedly personal acts of leadership.

For Complete Speech visit  http://www.hp.com/hpinfo/execteam/speeches/fiorina/minnesota01.html.

Arctic may be ice-free in summer within five to 10 years

Read this article on bbcnews.

A few years ago, scientists were predicting ice-free Arctic summers by about 2080. Then computer models started projecting earlier dates, around 2030 to 2050. Then came the 2007 summer that saw Arctic sea ice shrink to the smallest extent ever recorded, down to 4.2 million sq km from 7.8 million sq km in 1980. By the end of last year, one research group was forecasting ice-free summers by 2013. “I think we’re going to beat last year’s record melt, though I’d love to be wrong,” said Dr Stroeve. “If we do, then I don’t think 2013 is far off anymore. If what we think is going to happen does happen, then it’ll be within a decade anyway.”

for Full Article visit : http://news.bbc.co.uk/2/hi/science/nature/7461707.stm