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

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.

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

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.”

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

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 ***

Solver

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 geometer.org 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

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)

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.”

Clarifying Harper government disinformation about census complaints

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

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“

Benoit Mandelbrot: Fractals and the art of roughness

Here is an interesting TED talk: Benoit Mandelbrot: Fractals and the art of roughness

Check out Benoit Mandelbrot on Wikipedia and his TED bio and talk transcript.

P != NP (an update)

I very much agree with this quote in “A Tale of A Serious Attempt At P≠NP” by Richard J. Lipton – (August 15, 2010)

“… I learned that the Internet may not replace referees yet, but it can raise many important questions in a positive and constructive manner.”

With respect to the P != NP “proof”, I am not optimistic. Quoting “The problem of P versus NP” (full article enclosed below),

“Mr. Deolalikar has submitted a revised proof, but Dr. Cook believes the jig is up. Does he believe P vs. NP will ever be solved? “Yes, I do, I do – eventually. But not very soon. I think it really is a hard problem. It’s becoming increasingly clear, because so many top mathematicians have tried to solve it.””

“The problem of P versus NP – Kate Allen From Saturday’s Globe and Mail - Published on Friday, Aug. 20, 2010 10:28PM EDT

In 1971, Dr. Stephen Cook, a young University of Toronto professor in the fledgling field of computer science, posed a theoretical problem so intractable it has become the subject of a $1-million prize. Since then, only a handful of credible solutions have been posed. All of them fell short. This month, one man caused a commotion after he announced to experts in the field that he had solved the problem known as P vs. NP.

The proof

Vinay Deolalikar, a Delhi-born mathematician at Hewlett-Packard, sent Dr. Cook and two dozen other experts in the field an e-mail, writing, “I am pleased to announce a proof that P is not equal to NP, which is attached.” The paper was more than 100 pages long. Dr. Cook was excited. In 40 years, “I can think of only a couple of other attempts of people who’ve thought they’ve proved it,” Dr. Cook said. “Most of them you can dismiss very easily – they’re not really mathematicians. But this one was much more serious.”

The problem

Clay Mathematics Institute, the Cambridge, Mass.-based academy that offers the $1-million prize, describes the problem with this example: Imagine you are trying to figure out housing for 400 university students.

Math Writer Martin Gardner (1914 – 2010)

In memory of Martin Gardner (1914 – 2010).

• The Legacy Of Math Writer Martin Gardner [NPR]
• Martin Gardner (1914 – 2010) [Guardian]
• Martin Gardner: A Major Shaping Force in My Life [Scientific American]
• Numberplay: A Fond Farewell to Martin Gardner [NYT Blog]
• Martin Gardner [TIME]
• Martin Gardner [Telegraph]
• Martin Gardner [Nature]
• Martin Gardner Remembered [Wired]

P and NP: a cute movie

This is a cute movie about P and NP.

[HT Lance]

Terence Tao (陶哲軒) – Fields Medalist

Don’t ask me why but I find it fun to follow advanced mathematics and computer researches (almost and very often beyond my limit of understanding). I find some enjoyment in learning about some of these advanced stuff.

Anyway, the following is an old-ish 2007 UCLA presentation “Structure and Randomness in the Prime Numbers” by Terence Tao (Fields Medalist) was interesting to watch. In particular, starting at time code 38:05, Terence started to talk about Green-Tao Theorem (2004).

I actually laughed quite hard, in a good way, at the 42:22 point, when Terence mentioned the guaranteed upper bound of 2**2**2**2**2**2**2**100k. Establishing an upper bound beats infinity. :)

You can download and read his latest blog book “An epsilon of room: pages from year three of a mathematical blog” (PDF). And I’ve subscribed to Terry’s blog to read more about his “research and expository papers, discussion of open problems, and other maths-related topics”.

The video “Math Prodigy Terence Tao” is a lot of fun to watch, even, lets be honest, it looks and smells like is an UCLA Math department informercial. :)

P.S. With a bit of research, I just realized that I wrote about another Fields Medalist Grigori Perelman in 2006 in the blog entry “Will he take that million dollars?”. Yes, I guess I pay attention to advanced mathematics. :)

Arguing to death, Fourth branch of gov & A Socratic Dialogue

I enjoyed reading The Economist’s “The tyranny of the majority: The fourth branch of government has run amok in parts of America” and ended up also enjoying “Arguing to death: From Socrates, history’s quintessential nonconformist, lessons for America today” the way I enjoyed the TV series Deadwood.

It is my pleasure to get to know the two articles’ author Andreas via his blog. Here is my reply to one of Andreas’ latest entry “WordPress: Plato’s Academy Today” which I hope you may enjoy reading,

Andreas,

Thanks for creating a community for us to amuse ourselves, teach ourselves, challenge ourselves, feel safe to contradict ourselves, and sometimes to be plain silly.

This piece and others you linked to reminded me of a lovely little Chinese book I read more than 20 years ago when I was wiser, more self-assured, handsomer and video game machines didn’t dare to tell their owners they were obese! :)

The tiny Chinese book was a translation of Hungarian mathematician Alfréd Rényi‘s “Dialoge über Mathematik” which contains the charmingly insightful “A SOCRATIC DIALOGUE ON MATHEMATICS”. (more on Rényi here and here)

I took some time yesterday to try to find something to share. Well, I lucked out and found an English version of this gem of a socratic dialogue as imagined by Rényi. Plus I was delighted to find the author’s postscript which was not in my Chinese translation.

Have a read, “A SOCRATIC DIALOGUE ON MATHEMATICS“.

It is wonderful to see you crediting many people in the community

Quantum Cryptography Cracked

Interesting “Quantum Cryptography Cracked“.

GSM Mobile phone security cracked, says German hacker

UK Guardian is reporting (emphasis added),

A German computer scientist has cracked the codes used to encrypt calls made from more than 80% of the world’s mobile phones.

Karsten Nohl [K: Nohl's U of Virginia page] and his team of 24 hackers began working on the security algorithm for GSM (Global System for Mobiles) in August.

[...] Nohl claims that armed with the code, which has been published online, and a laptop with two network cards, an eavesdropper could be recording phone calls within 15 minutes.

“This shows that existing GSM security is inadequate,” Nohl told the Chaos Communication Congress, an international annual meeting of hackers taking place in Berlin this week.

Nohl insisted that he had deciphered the code to force the global telecommunications industry to upgrade its security.

Nohl told the Guardian that important negotiations involving politicians or business leaders could easily be intercepted and they should invest in further encryption software to protect their privacy. “If there is anything secret going on using GSM, this should be of concern.”

More report in NYT and The Register.

Anyone who cares about our communication security based on Cryptography should know that the only way to keep our communication secure is to conduct open and active research in the field where weakness and problems are dealt with in a prompt and appropriate manner. Security through obscurity is NOT an option, and if I were less diplomatic, I would say it is plain stupid to rely our treasured security on obscurity.

Twisted Architecture

I love architecture so I quite enjoy this blog entry “Twisted Architecture” even I don’t understand much of it. If and when I have to dig deeper, I will know where to look.

Flight Operational Safety Analysis

I used to work in an air traffic control project, so this is quite a cool video for me to watch “Landing a Solid Model: Flight Operational Safety Analysis with Mathematica“. [via Mathematica]

Wolfram|Alpha – A new real-time computational knowledge engine ?

Stephen Wolfram, the super-smart man who invented/created Mathematica (a powerful computational software program) is launching Wolfram|Alpha. It looks really neat. Here is an excerpt from a Wired article (emphasis added),

“The home page is nearly blank. At the center, just below a colorful logo, you’ll find an empty data field. Type in a phrase, hit Return, and knowledge appears. [...]

The product [Wolfram|Alpha] of four years of development, Alpha is an engine for answers. Its ambition is to delve into “all the knowledge in the world,” Wolfram says, to find and calculate information. [...]

Type in a query for a statistic, a profile of a country or company, the average airspeed of a sparrow ― and instead of a series of results that may or may not provide the answer you’re looking for, you get a mini dossier on the subject compiled in real time that, ideally, nails the exact thing you want to know. It’s like having a squad of Cambridge mathematicians and CIA analysts inside your browser.

Type in “Pluto” and Alpha calculates the dwarf planet’s distance from Earth at that very instant. Bang out a series of letters like “ACTCGTC” and Alpha recognizes it as genetic code and tells you what strand of DNA that particular gene lives on and what we know about it. Wolfram has licensed ― or created ― a whole library of databases and massaged them so the information is pliable. (To date, they include Wikipedia, the US Census, and “about nine-tenths of what you’d see on the main shelves of a reference library,” he says.) Combined with the near-­magical abilities of Mathematica, Alpha is a powerful computational engine that can effortlessly answer queries that no one has asked of a search engine before.“

If my instinct is right, Wolfram|Alpha should be a powerful tool.

If I am wrong (for fun, I say <0.1% chance), it will be a neat toy.

We can find out more starting tonight (May 15th, 2009, 7pm CST).

Two Questions I will try tonight:

How many Nobel Prize winners were born under a full moon?
How many Nobel Prize winners were taught by Milton Friedman?

[update] Other questions I’ve tried tonight:

Number of lawyers in Calgary? [Alpha didn't understand the question]

Chinese population in Calgary? [Alpha didn't understand the question]

Here is a video of Stephen Wolfram discussing Wolfram|Alpha

P.S. I laughed so hard reading this line in the article, “Wolfram has already shown Alpha to former intern Brin [yes, Brin is Google co-founder Sergey Brin, who once spent a summer interning for Wolfram] and thinks that it could make sense to have the engine running behind the scenes in Google searches.“

*******

May 15, 2009 9:07 PM MST: Finally tried a few questions. Too bad none of the questions give useful/good results yet until the system crashed. “Chinese population in Calgary” confused the system. Will try again when the system is more stable.

‘Unbreakable’ quantum encryption in action

BBC News is reporting ‘Unbreakable’ encryption unveiled. Here is an excerpt (emphasis added),

The basic idea of quantum cryptography was worked out 25 years ago by Charles Bennett of IBM and Gilles Brassard of Montreal University, who was in Vienna to see the network in action.

“All quantum security schemes are based on the Heisenberg Uncertainty Principle, on the fact that you cannot measure quantum information without disturbing it,” he explained.

“Because of that, one can have a communications channel between two users on which it’s impossible to eavesdrop without creating a disturbance. An eavesdropper would create a mark on it. That was the key idea.“

In practice this means using the ultimate quantum objects: photons, the “atoms of light”. Incredibly faint beams of light equating to single photons fired a million times a second raced between the nodes in the Vienna network.

Each node, housed in a different Siemens office (Siemens has provided the fibre links), contains a small rack of electronics – boxes about the size of a PC – and a handful of sensitive light detectors.

Numerical key

From the detected photons, a totally secret numerical key can be distilled, which encodes the users’ data much like the keys used in normal computer networks do.

Mandelbrot chats with Antonelli

A wonderful chat between Benoit Mandelbrot (father of fractal geometry) and Paola Antonelli (senior curator of Architecture and Design at The Museum of Modern Art, wrote her thesis on “Fractal Architecture”).

Love this exchange (emphasis added),

BM: Well, it is very encouraging for me, because I’m an old man and, as I always mention at some point, I never made up my mind who I really was, which allowed me to spend my life on many things. So what you’re telling me is that I can just relax, because I won’t have to decide!

PA: I don’t know. You’re very responsible for what goes on right now. I don’t think you can relax any time soon!

BM: Well, yes, but at least I won’t have to become a specialist, because everybody is going to become a generalist.

Here is a beautiful video excerpt of the chat. (very well done and wonderfully shot. simply beautiful. and great to see Mandelbrot in person in a video chat. very cool.)

P.S. Have a look at MoMA’s “Design and the Elastic Mind” exhibition which Antonelli curates. Very cool and neat.