Friday, June 26, 2015

Claude Shannon: Centennial and Machines

Claude Shannon and his electromechanical mouse Theseus. Retrieved from http://www.kerryr.net/pioneers/gallery/ns_shannon5.htm

Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was a distinguished American electrical engineer and mathematician who founded the field of Information Theory when he published his landmark paper "A Mathematical Theory of Communication" in 1948. He worked on anti-aircraft and cryptography systems during World War II, and later on had a career at the AT&T Bell Labs and as a Professor at MIT. The MIT Technology Review Magazine ran an article on this Reluntant Father of the Digital Age shortly after his death.


In fact, while Shannon was still a student at MIT, he wrote what has been touted as the Most Important Master's Thesis of the Twentieth Century (putting forward the idea that Boolean algebra can be used for computing). Many technological fields that we know of now (such as the digital revolution, secrecy and cryptography, artificial intelligence, wearable computing) can all be traced back to Shannon's pioneering ideas and work.


Despite all these achievements, Shannon is surprisingly little known. Next year 2016 is Shannon's centenary. To get the public know more about Shannon, the Information Theory Society is on a drive to make a movie about this scientific genius of the twentieth century. Incidentally, Shannon did appear in a movie once - back in 1961 - in a MIT Centennial Film called The Thinking Machine. At 50:09 mins of the film, he shared his vision of a future machine capable of learning by experience. The Information Theory Society also aims to organize events worldwide to celebrate the Shannon's centenary. 


I wonder: What little bits of things can we prepare or do to celebrate Shannon's centenary?

Perhaps, particularly endearing is Shannon's fun-loving and unconventional side: To amuse himself, Shannon created very clever mechanical and electrical toys -- a juggling robot, a maze-solving mouse, a chess-playing machine, a mind-reading machine, a manipulator to solve the Rubik's cube game etc. The Ultimate Machine is another such curiously uncanny toy -- we have one built from a small motor, off-the-shelf electronics and recyclable. See video below.




In a 1987 interview, the Omni Magazine asked Shannon: Do you find it depressing that chess computers are getting so strong? 


Shannon replied: I am not depressed by it. I am rooting for the machines! I have always been on the machines' side. Ha-ha! 



Tuesday, June 16, 2015

Googling Arithmetic Limerick


While using Google to scour the Internet for poems on arithmetic and algebra, I came across the following three limericks. The first is similar in spirit to the Carroll's poem and the next two are similar to Diophantus puzzle in my earlier posts. 

Leigh Mercer, a noted British wordplay, wrote the following (excerpt from Word Ways, 1980, pp. 36):



A dozen, a gross, and a score 
Plus three times the square root of four 
Divided by seven 
Plus five times eleven 
Is nine squared and not a bit more.

Interestingly, Google's omnipotent search engine can "solve" this limerick automatically by entering the following slightly modified verse into the Google search bar:

(a dozen, and a gross, and a score plus three times the square root of four) divided by seven plus five times eleven



The following two are by David Pleacher, a retired mathematician:

Said a certain young lady named Gwen 
of her tally of smitten young men, 
"One less and three more 
Divided by four 
Together give one more than ten." 

How many boyfriends had she? Answer here.

Some freshmen from Trinity Hall 
Played hockey with a wonderful ball; 
They found that two times its weight, 
Plus weight squared, minus eight, 
Gave "nothing" in ounces at all. 

What was the weight of the ball? Answer here.

Friday, June 12, 2015

Learning and Testing


In many Asian countries, standardized testing is the hallmark of primary and secondary school education. Outside of regular schools, numerous after-school coaching activities, preparation schools and commercial tuition centers thrive in training young students to excel in standardized testing. This is big business - involving enormous education spending in the hope of getting a good enough grade for these pressure-cooker standardized tests.

In Hong Kong and Singapore, the sense of anxiety and dread lingers among primary and secondary school children in the lead-up to sitting en masse for UK-style standardized exams (primary school leaving exams, O-level, A-level). And in the hot summer month of June, in mainland China, massive number of students travel across the country to sit for the national higher education entrance examination - a high-stakes game - that requires gadgets like multi-rotor drones as invigilators.

I recently came across an Edweek article "Rethinking the Emphasis on Standardized Testing" on the traditional standardized testing in Asia and how it affected mathematics proficiency and even the lifetime success of a student. The article's author started a First-in-Math venture to host math tournaments in the United States to play 24 Game - in fact a card game that originates from China in the 1960's. Have a go at the 24 Game to test your reflex and sharpen your mind (The game at http://www.4nums.com is free)! This is big business indeed - going by the 17 billions (and still counting) of problems solved as advertised on the First-in-Math's website.

One interesting takeaway from the Edweek article is that:
Testing has its place as long as it doesn’t push kids away from a sense of wonder and fascination for the world around them....  A far more worthy goal would be to create a system wherein the whole individual is addressed, developed, and encouraged to thrive in the pursuit of a better life. 

I think this pretty much sums up personalized learning as the next frontier in education. What truly amazing technological innovations can we envision in this quest to advance personalized learning? Will that be an ecosystem of mobile digital tutors, an Internet of peer learning, automated software to individualize learning, learning analytics at scale, smarter interactive computer tests driven by computational neuroscience, AI, cloud computing and machine learning? Or will it be more powerful surveillance drones?

Monday, June 1, 2015

Diophantus Puzzle

Diophantus was a Greek mathematician whose work laid down important foundation for the development of algebra. Listed on Wikipedia is an interesting puzzle to guess the age of Diophantus:


'Here lies Diophantus,' the wonder behold.
Through art algebraic, the stone tells how old:
'God gave him his boyhood one-sixth of his life,

One twelfth more as youth while whiskers grew rife;
And then yet one-seventh ere marriage begun;
In five years there came a bouncing new son.

Alas, the dear child of master and sage
After attaining half the measure of his father's life chill fate took him. 
After consoling his fate by the science of numbers for four years, he ended his life.'

This Diophantus puzzle has a similar flavor to the Carroll's puzzle in my previous post. Here, however, a finite sequence of moves (in fact, events in the timeline) is applied to an unknown - Diophantus's age. 
How long did Diophantus live?