Proof without words

Today I came across William Dunham's awesome book titled The Mathematicial Universe with the following fascinating picture. It is a wordless proof.


This is silently proclaiming that 1+2+3+...n = (n)(n+1)/2! (Ok, that's not a factorial, but excitement!)

So the story is about the young Gauss who had a teacher that made him add 1+2+3+...100 so to keep the students busy all day. Gauss figured out that you can pair up the first and last number, 1 and 100, add them up so you have 101. The next pair, 2 and 99 also add up to 101. There are 50 such pairs so the answer is instantly 5050.

Let's decipher the picture.

Each white column is indicating 1,2,3... When you add them all up, it covers exactly half the area in the n by n+1 grid!

The author calls it immensely elegant. And I agree! Oh my I want to frame this!

Math is not always dry and boring.

Here is another one. It is saying adding odd numbers 1+3+5+7+9... you can always get a perfect square.



I noted that when I was a kid! One day I got so bored that I start counting tiles on the floor and noted the pattern.

So how do you prove it, in words?

Odd numbers can be represented by 2k+1, where k is an integer.
So 3 = 2(1)+1, 5=2(2)+1, 7 = 2(3)+1, and so on.

Let's add 1+3+5, we have 1+2(1)+1+2(2)+1, this is 2(1+2)+2+1
Let's add 1+3+5+7, we have 1+2(1)+1+2(2)+1+2(3)+1 = 2(1+2+3)+3+1.

See the pattern? Add n odd numbers, we get 2(1+2+3...n)+n+1.
Now apply the formula: 2(n)(n+1)/2 + n + 1, we have n(n+1)+n+1 = n²+2n+1. That is a perfect square.

Truck crashes into Chinatown Train Station

A truck slammed into the Chinatown Train Station during evening rush hour last Friday, killing 2 and injured a dozen.
See this Tribune article for details.

The weather was nice during the day before the accident. A heavy thunderstrom striked on that evening, as if heaven is weeping for the poor victims.

I got off at the same station just 1 day before. It can happen to ME.

The station is located at the T-intersection from the 90/94 exit and Cermak. Vehicles must turn left or right after exiting, or slam into the train station. In the ancient study of Feng Shui, that is a terrible spot, as it constantly seems like someone is coming toward you. Feng Shui specialists may advice you to put a mirror or something to reflect it somehow. While there is not really scientific basis of Feng Shui, the designer of the station should have used some precaution. A barricade like those surrounding government buildings should have been there to minimize potential damage.

I don't really blame the CTA for this. There IS plenty of space to turn left or right. Who would have thought that someone slam right into it?

After this incident, please, put barricades on any station that is in potentially dangerous T-intersection.

If the truck has smashed into the beam supporting the bridge to the other side of Cermak, it may kill just the reckless driver, or collapse the bridge, none of which are nice scenarios.

This is a terrible accident.

The Last Lecture

You may have heard about the life touching Last Lecture by the dying computer science professor Randy Pausch over the internet. Search for it in youtube if you like. Ok, here is the link. Today I saw the book form. This last lecture is not a computer science lecture, rather, it is a lecture of life. Over 6 million people has watched it! (That's about the population of the very crowded Hong Kong!)

The video lecture is full of witty charm. No wonder 6 million people viewed it.

In the last days of life, the professor's main concern are his kids. He need to jam pack what he would teach his kids for the next 20 years into a small book or lectures. In the lecture (book), he shared a lot about his life: childhood dreams and all that... he wanted to be in zero gravity and play for NFL, etc.

One page caught my attention: He "celebrated" the quadratic formula by painting it on a wall when he was young. I like the formula too, but didn't write it on my wall. However, I wrote about it in this article.

The lecture (and book) is jammed packed with life lessons: following childhood dreams and seizing and enjoying every moment of life. The positive attitude he had is such great impact on his viewers, especially his kids when they are old enough.

Here is his quote: "We cannot change the cards we are dealt, just how we play the hand."

* * *
If the professor lives to be 100+ years old, even if his researches rock the academic world, he probably would not have captured as much attention. Old saying: it is not how long you live, it is how you live that matters. Unfortunate folks with health issues are often comforted with that old saying.

How come we are more interested to hearing from people who are dying and not as interested to those who are not? Why did the Last Lecture capture so much attention?

People like and want inspiring stories, and don't mind spending about $15 to buy it as an gift item. Professor Pausch's ability to communicate his life lessons truly flourished. I am sure his impact would last, especially within the minds of his young children.

What do YOU have to say in your last lecture? We all must die some day.

Although it is very unfortunate that the very talented professor has terminal disease, he is also in some ways fortunate.

The professor at least knows his life will end in matter of months and had a chance to write the lectures. (I sure hope some breakthrough in medicine or a miracle somewhat would save him!) For far too many unfortunate people, death comes too soon too suddenly.

The professor has an audience (his students, family, etc). Unfortunately, not everyone has loyal audience. I hope you do.

You can also use your blog as your lecture hall. The entire web is your audience.

Rounding

"I won that double-digit victory that everybody on TV said I had to win, and the voters of Pennsylvania clearly made their views known -- that they think I would be the best president and the better candidate to go against Senator McCain," Clinton said Wednesday morning in a CNN interview.

So the numbers for Pennsylvania are as follows:
Obama: 1,042,297 45%
Clinton: 1,258,245 55%

But if you look (divide) closely, Clinton has 0.546934157 and Obama has 0.453065843.
Hmm, seems to be less than the 10% double digit victory.

Let's subtract: the answer is 0.093868315.

Let's round it to the nearest percent... ask an elementary school student. Will the student say 9% or 10%?

Another trick to deceive poorly math educated Americans?

About the "clearly made their views known" comment, even with a solid 55%, is it big enough a majority to be a really clear winner? 10% is THE smallest double digit victory and the winner is almost there.

Wanted: Political Wisdom

BBC article: http://news.bbc.co.uk/2/hi/americas/7359957.stm

As the candidates appeared on the US talk show circuit on Tuesday morning, Mrs Clinton was asked how she would respond if Iran launched a nuclear attack on Israel, and replied with a stark warning.

"If I'm the president, we will attack Iran... we would be able to totally obliterate them," she said.

"That's a terrible thing to say, but those people who run Iran need to understand that, because that perhaps will deter them from doing something that would be reckless, foolish and tragic," she told TV channel ABC.

In response, Mr Obama said: "Using words like 'obliterate' - it doesn't actually produce good results, and so I'm not interested in sabre-rattling."

He said only that Iran should know he would respond "forcefully" to an attack on any US ally.

That is a tough question to answer. I admit I have to look up obliterate to figure out the exact meaning of the word, but I can tell from context: total destruction.
Cold sweat come down as I imagine total annihilation taking place as nuclear bombs explode all over.

Isn't it horrible to wipe out the ENTIRE country to retailiate?

Political wisdom and patience are the requirements for a world leader. It is important to choose the right words. I like Obama's answer. He didn't give special status to Israel, and forcefully say he would respond if there is attack on any ally.

Let's wait a few more hours to see who wins in the Pennsylvania contest.

Interesting Sun Times cover

Today the Sun Times come up with a remarkable cover: a mirror image. Is it a first ever for Sun Times? This is a strong message indicating we can't turn our backs on gun violence.

Although I didn't actually buy a copy to read the details, I read it online. The END is near for newspapers? (Ok, that's another topic). The gun violence over the first warmer weekend of the year is troubling. When it gets warm, tensions heat up and people start shooting(!). We have streets of terror in Chicago! But just what we can do about it? Ban guns?! Time and time again we hear arguments like this: crooks will ALWAYS able to get guns. But look, at least make it harder, ok?

One cop says on TV, "why on earth are we allowing people to own AK47?" You've got a valid point, officer.

How do we curb the violence? More patrols on street of course... That seems to be best approach. Waita minute are we creating a Baghdad right here at home?

It is said to realize that we can't control violence over there in Baghdad and we can't control it here at home.

I do not agree with Virginia Tech students who want to bring a gun to classroom either. John Wayne and the Old West stay in black/white VHS tapes (or digitally re-mastered DVD)

Gun controls must be stronger. Unfortunately after case after case of violence still NO one is serious about it, until perhaps 500 die a day to get enough attention.

The next day the Sun Times is back to its nomal front page.

1+1=2

Today I came across some great math works at a local bookstore, I don't recall all the titles I browse through. I saw one book mentioned about a proof of 1+1=2 in a book called "Principia Mathematica" by Russell and Whitehead.
See this entry in wiki for details.

Waita minute, I thought Principia was the great Newton work? (I saw a handwritten copy of that at a museum! Um, I dare to complain, excuse me, Issac Newton Sir, can you please write a bit more legibly please) But this is not Newton's work of course. Even if I can see what Newton wrote I still can't understand, because it is in Latin. Even if it is in English I can't understand because it is some tough reading(!)

Check that scan out in the middle of that wiki entry of the Whitehead and Russell's work. An unintelligentable looking proof (ok, to me) showing... "From this proposition it will follow, when addition has been defined, that 1+1=2". I have no idea what those asterisks and stuff are, perhaps refering to some other section of this thing.
I can't validate this proof, but isn't it strange trying to prove 1+1=2?

Toddlers know 1+1=2. You don't need such proof.

Look, numbers are NAMES for quantities. You teach a toddler like this: See that ball over there? Bring it to me... Good boy. You have one ball. Can you repeat? One ball.
Look, can you find another ball? Bring it to me... Good! You start with 1 ball, now you give me another one, we say you have TWO balls.

1+1 means you start with 1, add another one, how many do you have now?

1+1=2 by definition, you don't need such unintelligentable proof.

An idea to streamline election

Obama and Clinton clashes continue as they stab each other every day on various issues. Both are determined to win, but both can't get enough delegates, and the suspense continue as we wait for more state primaries. The Super Tuesday was super because it involves many states. How about more states switch the primary date to the same day so the race ends more quickly? It is dragging on wasting time and money.
After the 2008 election, I hope the states sync up their primary dates.

Also, how come the candidates need 2025 delegates to win? How about changing to a simple rule: you win if you get most votes. That regular and super delegates way to elect seem a bit odd. Be fair, no need to divide into regular and irregular delegates.

Ideas to Save the Planet

It is a saddening to read this Time Magazine cover story on the Clean Energy Scam. It is ironic that biofuels actually damage the earth faster by clearing of forests to grow corn and driving prices of everything up. As the author put it, "it's dramatically accelerating global warming, imperiling the planet in the name of saving it".

Look folks, if that is heading the wrong direction, go back! As monks in kung fu dramas typically say, "turn around, the shore is right behind you", telling the big bad guys that it is STILL possible to repent (as if swimming off the shore). Some bad guys do actually repent and follow the master monk, but some don't. Too late, people already invested lots of money on this biofuel scam. It isn't likely to slow down, until it is too late.

So fossil fuels is bad, biofuels is bad. Ok, just what to do?

One thing that definitely helps is the hybrid electric car! At least that slows down consumption of gas, isn't it? Still not a very long term solution but at least it delays the problem. But a hybrid car is so expensive! The price must come down for it to become popular alternative. A tax reduction is a great way to encourage people buying one. What about full electric cars? How do I charge it? Instead of gas station we will have charge stations? How long does it take to charge? What about hydrogen fuel things? Is it around the corner? Is it going to be a green scam like the biofuel? A lot of things to sort out before we can significantly help the planet with non-gasoline cars.

The energy-saving lightbulb may also be a scam of some sort. Yea it lasts long, but costs much more than a regular bulb. But that mercury stuff in it pollute the environment! For the environments sake I do have energy-saving bulbs instead of regular bulbs, I'll toss them out with care when it runs out, theoretically in a few years.

Plastic bags and water bottles are the #1 enemy of environmentalists. I do agree with an extra fee for bottled water. I also would agree with a 10 cents a plastic bag fee: to encourage you to use your own reusable bags. Sometimes smarter legislations can help the environment.

Bureaucratic non-smart IT departments: how about require less useless meetings to discuss big colorful packs of powerpoint files already on screen? Just have people read the electronic copy, ok? Code reviews: (I haven't seen one in a while). It is ok to tell me just read the new code, don't need to print a DIFF report of what you changed.

When proposing solutions, one must assess the long term feasibility. Do they know the drastic effect of biofuels before they clear out the forests in Amazon? Is it really ok to use that energy saving lightbulb?

Shutting down power for an hour (while is an admirable way to increase awareness) is too minimal an effort that I didn't bother to participate.

Interactive Chinese Chess Guide

Chinese Chess Tutorial with video(!)
http://www.kfjhs.hlc.edu.tw/chess-speak/chess-speak.htm

Javascripts that lets you visually view move sequences and common tactics
http://www.kfjhs.hlc.edu.tw/chess-k/index.htm

I hope he put some full games played by masters.

Hands on experience with Wii

I finally got a chance to play on the innovative Nintendo Wii.
Originally every store was out of it. You simply can't buy one. Well I wasn't one of those getting in line to buy one, console games are not priorities of life now.

Video games have came a LONG way in recent years. Graphics are better than ever. Yet game play has not been so innovative. When people were shooting aliens on Space Invaders in 1970s, a different type of game play: Pac-man simply energized the video gaming industry. The gaming arcade later was filled with shooters with powerups, 2D sprite adventures and all that in the 80s.
The innovative 6 button fighting saga of the Street Fighters were a true knockout to usual 2D scrolling brawl games in the 90s. First person adventures such as Lara Croft and Half-Life were a blast in the PC games. The arcades die as PCs become more powerful so games are played at home. Then there were the innovative music games: dance dance revolution, and some guitar/drum games. Since the early 2000s, I have not seen real revolutionary innovations until the Nintendo Wii because of the unique controller.

At first I thought it only adds swinging ability to play sport games such as tennis and bowling, there are actually MUCH more you can play with. I played with a few games that requires shaking it up down, swirl it, or shoot on screen like Time Crisis! Now that's fun and innovative.

Gaming hardware: before the Wii almost all games were played on a joystick/joypad and buttons. Trackball, light guns merely do the same thing, except you move faster. There really hasn't been anything new since the dawn of gaming.

The Wii really adds new tweaks to the standard joystick. BTW, I have a minor complain of the joypad. For home games, ONLY Atari makes joysticks, every system make joypads that can add pain to your thumb. Yes I have heard of professional joysticks for MAME.

While everyone works on making graphics even more realistic and beautiful the innovative Nintendo guys work on the controller. Way to go Nintendo.

Another plus for the Nintendo: the games I saw have cute characters. Games CAN be fun without violence.

Although the Wii is fun I am still not buying one, I have spent too much time in front of the TV and the computer already!

Jin Yong's essays 金庸散文

I have a copy of collected short writings of the legendary martial-art novelist Jin Yong. This is collected from a column of newspapers from the 1950s.

I have not read a lot of Jin Yong myself, although I KNOW they are good as I love most TV series and comics based on the novels. I am a visual person: I can't focus on reading pages of pages of text, however beautifully written. Kung fu is best presented with actual action! (TV producers: don't over use that CG please). I enjoy reading (and writing) short chunks of text.

In this collection Jin Yong covered a lot of topics: history, travel log, and thoughts from movies and operas, and thoughts from the classic, including western literature such as Shakespeare. He even included a talk about Chinese discovery of π. You can this page here. I am glad I already know most of what he had to say about π.

Jin Yong writes in no-nonsense, sometimes more educational than entertaining manner, demonstrating his immense knowledge on a wide varity of topics. I wish he included more thoughts on Chinese literature.

A big section of the book is on Shakespeare as he shared his thoughts on Julius Caeser, Taming of the Shrew, Othello, Hamlet, and much more. Jin Yong gave big two thumbs up with Shakespeare's works, pinpointing what is great with them, how beautifully written are the conflicts among the characters etc. I am almost illiterate with Shakespeare, absolutely hated some of the endless dialogues.

I am certain that every Chinese love Jin Yong's works. He has achieved the greatness of a true master. Yet he enjoys Shakespeare so much. Perhaps I am just not an truly educated person.

Afraid the world is not at unrest

Top story today: Pelosi calls on Bush to boycott Olympic opening ceremonies.
See here for details.

But she says U.S. athletes should not boycott Games. Now is that double standard?

Ok, just what is the purpose of the olympics? It is a PEACEFUL world event. Though it is a competition, a show off of power, nevetheless the world comes together every 4 years in a friendly diplomatic setting.

It is the first time China ever hosted the Olympics: it is a very significant historic event.

The Tibet folks: they are rioting all over. Buddhists are SUPPOSED to be quietly meditating Budda; they are not supposed to even hurt an animal. I suppose rioting is more violent than eating a hamburger? How would other nations handle riots?

How did the United States handle a bunch of renegate states trying to secede from the Union? Human Right records: does the fraction 3/5 remind anyone?

The Speaker of the House should focus on domestic matters, and get US as quickly out of Iraq as possible. Peace is what you should seek, not unrest.

Bush should GO to Beijing for Olympics. Don't make another diplomatic disaster.