Two 12/12/12 12:12:12 moments frozen in time

Wednesday, 12 December, 2012

In case you miss these times last night and later today, I time-travelled to freeze the two 12/12/12 12:12:12 moments for your enjoyment.

The two 12/12/12 12:12:12 moments frozen in time

I call these twin 12/12/12 12:12:12 moments, the 12 x 6 moments. Mathematically,

12 x 6

= 72

42 (Answer to the Ultimate Question of Life, the Universe, and Everything)

+ 30 (the smallest Giuga number)

Q.E.D (or QED)

P.S. Hope you enjoyed reading the above as much in I in spending time to create them out of nothing! :)

Schneier’s Law

Saturday, 16 April, 2011

Something fun about cryptography. Enjoy.

“Schneier’s Law”

by Bruce Schneier on Friday, April 15, 2011 at 12:45pm

Back in 1998, I wrote:

Anyone, from the most clueless amateur to the best cryptographer, can create an algorithm that he himself can’t break.

In 2004, Cory Doctorow called this Schneier’s law:

…what I think of as Schneier’s Law: “any person can invent a security system so clever that she or he can’t think of how to break it.” Read the rest of this entry »

Sudoku bites first aid kit: Solver, Math Logic, Puzzle Generator

Sunday, 27 March, 2011

I was surprised to hear a good friend was recently bitten by the Sudoku bug and was battling against a tough puzzle. I have never caught the Sudoku bug. In order to satisfy my curiosity and help my friend, I did some research and looking around. I hope the following results can help.

*** Sudoku Bug First Aid Kit ***


After a few Goolge searches and testes/confirmations, I found an online 9×9 Sudoku Solver that seems to work very well and it comes with some helpful functions like hint, show candidates, and solve! The Solver can certainly be used to help train the mind to recognize patterns and thinking more logically when looking at a puzzle. Also check out the nice Sudoku background/Solving techniques.

Math Logic

Not satisfied by finding a solver, I discovered the wonderful 2010 preliminary paper “The Mathematics of Sudoku” by Tom Davis via the site. A must read for lover of Sudoku Puzzles.

Puzzle Generator

And as the icing on the cake, I found an interesting 2008 Harvard math students’ paper “hsolve: A Difficulty Metric and Puzzle Generator for Sudoku” A good read if you are interested in the challenges in measuring the “difficulty level” of a puzzle and how to generate a new random puzzle.

Concluding thoughts

Hopefully, the above three tools can help “Sudoku-bitten-victims” enjoy the puzzles more.

Additional readings:

Wikipedia Mathematics_of_Sudoku

* The Math behind Sudoku (from Cornell University) In particular, the bit about Sudoku being a NP-Complete problem.

The Man Who Saved Geometry – Donald Coxeter – TVO documentary

Friday, 22 October, 2010

The Man Who Saved Geometry (TVO 2009) (56:21 video)

By the middle of the 20th century, Geometry looked dead. The excitement in math had moved to computers and chaos theory. But one man – Donald Coxeter – kept the torch burning. Inspired by Siobhan Roberts book, King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry.

I had the honour to have one lecture by Prof. Donald Coxeter, it was a really cool class even I had little idea how important a person he was in math and in life.

[HT Erik Demaine who is in the documentary]

Benoît Mandelbrot (1924 – 2010)

Saturday, 16 October, 2010

Mandelbrot Exploration

Benoît Mandelbrot (1924 – 2010)

I am deeply saddened by the passing of Dr. Benoît Mandelbrot, in fact I didn’t want to believe the twitter “news” floating around last night until I see positive confirmation from a major news source (in this case, the NYT report talking to Dr. Mandelbrot’s wife Ailette).

Long time ago when I was taking an university Algebra class in the summer with an older and kind professor, I bought to the class a book with picture of a beautiful looking and mysterious object (I later learned, a Mandelbrot set) on the cover. The professor asked me why am I reading the book? I said the images were beautiful. He asked, “Why aren’t you reading the master himself directly?” As a result of this encounter, I have since tried to read original research papers or books when I can.

To me, Dr. Mandelbrot is the man that bought arts and beauty into mathematics for me. Before him, I didn’t quite appreciate the beauty in math. Beauty and the rigour of mathematics coexist beautifully in Mandelbrot set.

Thank you Dr. Mandelbrot, may you rest in peace. (I wished I had written you a fan letter before today. I hope you know you are well loved and respected.)

Fractal Zoom Mandelbrot Corner

Here is Dr. Mandelbrot in his own words in a TED2010 talk: Fractals and the art of roughness.

A fun animated video about Mandelbrot Set. [HT Wired]

For the record, the Oct 16th NYT article “Benoit Mandelbrot, Mathematician, Dies at 85” by Jascha Hoffman.

“Benoît B. Mandelbrot, a maverick mathematician who developed an innovative theory of roughness and applied it to physics, biology, finance and many other fields, died on Thursday in Cambridge, Mass. He was 85.

His death was caused by pancreatic cancer, his wife, Aliette, said. He had lived in Cambridge.

Dr. Mandelbrot coined the term “fractal” to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature.

“Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you blew them up with a microscope the more complexity you found,” said David Mumford, a professor of mathematics at Brown University. “He was one of the primary people who realized these were legitimate objects of study.”

In a seminal book, “The Fractal Geometry of Nature,” published in 1982, Dr. Mandelbrot defended mathematical objects that he said others had dismissed as “monstrous” and “pathological.” Read the rest of this entry »

Clarifying Harper government disinformation about census complaints

Tuesday, 5 October, 2010

The following two news reports and documents released via Access to Information Act clarifies some of Harper government’s disinformation about census complaints

– “Industry Canada queried Bernier census claims“, CBC News (emphasis added)

“An Industry Canada employee questioned Conservative MP Maxime Bernier’s claims in July that as minister he received about 1,000 complaints a day about the mandatory long-form census, internal documents obtained by CBC News show.

[…] Industry Canada’s “internal survey of correspondence did not show anything close to a thousand a day,” he wrote to Statistics Canada’s Connie Graziadei, adding in brackets “we got a standard 25-30 a year.”” [K comment: This, paradoxically, shows how important factual statistics collection is. Claim of 1,000 complaints a day with NO factual support of these complaints is another example of playing loose with facts at best and unethical behaviour at worst.]

– “Industry Canada’s query to StatsCan about Bernier claims on census complaints“, documents released to CBC News via the “Access to Information Act“.

– “Census change not about complaints: Bernier“, CBC News

Sharing incomplete ideas & giving proper credits

Saturday, 2 October, 2010

I am interested in seeing results and progresses, so I hope the mathematicians and computer theorists can figure some new ways to share ideas and give credits so they can get a few more cool open problems resolved in my lifetime.

Who Gets The Credit—Not Facebook Credits

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