Fundamental Theorems

At work I worked an summer intern. I am not too impressed with his programming skills. I expect nicely documented, neat codes. I TOLD him, don't add a lot of Strings in Java, use a StringBuffer. He didn't listen. I haven't seen him come up with anything other than putting together in a rather slopppy way what his collegues told him.

One day calculus was the topic. So it was a couple years ago that this college intern took calculus. I decided to quiz him: so, do you recall the Fundamental Theorem of Calculus?

He doesn't know.

This is like asking "have you heard of 'To be or not to be'" to someone who says who has read Hamlet.

I am not asking for a proof. I didn't ask the intern to do an outrageous difficult asterisk problem, nor recall some little known obscure theorem. It was the fundamental theorem. I am not so impressed. Students take classes and they forget right away. What is the purpose of education?

Speaking of fundamental theorems. There are many (and I only know 3).

Elementary school students (including YOU) know the Fundamental Theorem of Arithmetic: all numbers can be factored uniquely into primes. Take 100 for example, we have one way to factor it: 2²5². (Ok, you got a super child prodigy if you find an elementary student who can prove it)

High school students may have heard of the Fundamental Theorem of Algebra: all polynomials of degree n have n roots, where they may be complex. Can't factor a quardratic? The quardratic formula gives you two complex solutions. The proof is easy to state but difficult to prove and it is Gauss's triumph accomplishment. This really is the gateway from real numbers to complex numbers.

I don't see a Fundamental Theorem of Geometry. My vote goes to the Pythagorean Theorem. This is the gateway from rational numbers to irrational numbers.

Saw someone studying ODE on CTA

Typical college students have seen some Ordinary Differential Equations (ODE) in their calculus class, perhaps just briefly because the curriculum is already jam packed. Typically a student is considered "had calculus" if he or she can take a derivative of a function and do some integration. How much of that knowledge is retained after a few years may perhaps be modeled using an exponential decay. (Now that's an application of a differential equation!)

I admit I forgot all my diff equations. These are simply not used often enough nor basic enough to retain in my memory. No, I am not going to put much effort in recalling this lost memory either, because I don't find much use of it now.

One day I was challenged: tell me ONE use of calculus, tell me ONE use of trigonometry. My answer: how do you think current technology is possible if everyone only know how to do 4 basic operations, (although I can't pinpoint exactly where that integral or derivative is needed)

On CTA, one day I saw a lady in 30s or 40s reading a photo-copied LaTex-written packet about differential equations. This looks like a professor-written unpublished book.

It's got a lot of matrices and perhaps involving some eigenvalues.

Not sure what class from what school is that lady taking. She definitely does not look like the age of a typical college student who are forced to take some requirement classes.

Yes, you can still continue to learn any subject (including math) even if your age is beyond the interval of [18..22]!

Debate 1

I watched all 90 minutes of the first McCain-Obama debate. This is the first time ever that I watched a full presidential debate. I am glad there were no commercials. America deserves full attention in moments like these.

It IS a remarkable moment in American history. That 700 billion rescue is really a huge challenge for the country. Yet we see there are so many disagreements to be worked on.... And I think the discussion is NECESSARY. We need prudent wisdom here. I don't have a good solution for the financial crisis, but yikes, it doesn't seem the candidates have a very clear solution either?! America longs for prudent leadership especially at this moment. Am I going to find it in either candidates?

Both candidates say Washington is a mess. Is one of these two candidates able to fix it?

McCain didn't even LOOK at Obama at all in full 90 minutes. He of course, won't talk to Iran... He definitely demonstrated his maverick style.

I think both candidates have well rehearsed and done well. McCain did better than I expected. But I think there was no real clear winner.

The host can't keep the gentlemen within the time limits. The candidates don't answer questions directly. I think there is some red-green lights reminding the candidates how much time is left. Suggestion: how about show that on TV. Even though they are most powerful men in politics, they also need to respect time-limit rules set.

Whoever the ultimate winner is: there is a lot of work ahead. United States is in a critical moment.

Great Depression?

You may have seen this (classic) picture from your history lessons. (Also found in Wiki)



There are lots of talks about is America going into another Great Depression.

Many ill-educated lazy American students may not even heard of the Great Depression. That Wiki article featured very good information there.

It was horrible and lasted many years. People out of work all over and poverty all over.

America did not get out of the Great Depression until World War II. It is unthinkable to see America go into another one and getting out the same way.

Pumping 700 BILLIONS. Yikes, how much did the Iraq War cost so far? It is perhaps even more costly than the war. And just how many billions we need to rob American tax money?
Ok, will pumping that 700 billions SOLVE this issue? Or just patch it temporary?

Does the very subject of economics ever progressed since the Great Depression?
I expected all those Nobel Price guys learned from experiences and able to manage the financial world. If not, give that million dollar prize BACK.

China needs much tighter quality control

The olympics put China in spotlight in a good way. Everyone was proud of China's progress (although that cute girl was only just lip-synching in the opening ceremony). Well China is in the spotlight again, in a negative way, with that kidney stone causing milk powder.

We have already seen lead paint toys and tainted dog food from China in their exports.

Tainted milk is actually not new. I have heard similar incidents a couple years ago, but not as widespread as this time.

I think the story is this: evildoers farmers add stuff to their milk to increase protein count in order to sell it to the milk company. Unfortunately the milk company only count protein. I am not sure if that stuff is detectable, but people MUST test their product safety.

How selfish are those evildoers, profit at expense of poor innocent babies. Punishment? They'll probably get shot after some meaningless trials. I would make those guys drink that stuff and have their kidney failed. However, shooting them may actually be more humane.

Just how much other stuff in China are tainted?

We should not just worry about milk powder: chocolate, cookies and many other stuff contains milk powder.

Common Sense in Finance

Recently Hurriance Ike strikes but the finance world is striked by another kind of storm: Lehman Brothers go bankrupt and AIG is rescued by the Federal Reserve. Yes, you hear about those in news too.

Whoah, stocks can fall 90+% in one day!

Of course, the question is WHY?

The answer that I am given through radio talks and news is this: mortgage problems. So it was too easy to get loans. You can even buy a house without proof of income. Lose job? no longer can pay? Foreclosure. but no one buys that house now. So a ripple effect occurs and can bring down giants like Lehman Brothers and AIG.

Of course, any bad news come and people sell their stocks in panic. Snowball effect occurs.

Bad unemployment numbers? stocks tumble.

Bad relation with foreign country? stocks tumble.

People are so sensitive to news.

This game is too volatile to play. But everyone is playing it. Your 401k is at work.
Your retirement depends on this game.

Ok, why are all those supposed-to-be-smart business executives in expensive suits are so DUMB to let people to easily get loans? Should they know better? Perhaps we should simply use common sense in finance.

The underlying problem is people can't pay. Jobs are not here. Things are not produced here. How do you suppose to make those payments? "Well it is cheaper from China and India" Although this is true. but this is so short-sighted, Mr. Expensive-Suit-and-tie-Executive. Let's see when you get bankrupt next.

yIKEs

Texans beware, Ike is coming, YIKES.



Note that pun in the headline... Ok folks, it is no laughing matter that hurricane is going to destroy some houses and business (and your insurance may refuse to pay).

I found it fairly interesting that hurricanes get names. Originally all women, now alternate between man and woman with that starts with ascending letters in the alphabet. Think they create names on the fly? No, the names are all planned out. Let's see if your name is found here.

Storms are getting more devastating... Mother Earth's wrath on global warming?
Whether you agree or not, violent weather are coming.

Unfortunately, wacking old lightbulbs and change them to "twisted yet brilliant" bulbs isn't going to stop Ike now.

Puns are fun. But a headline like "The End is Near, My Dear" is not too much fun.

Big Bang Machine

The Big Bang Machine - Large Hadron Collider is here... to create the big bang conditions to study particle physics! This big thing costed billions and created some fears that it would create a black hole to devour the earth.

Well particle accelerator is nothing too new. The Fermi lab is right here around Chicago (but I never visited, I SHOULD!) Besides studying the big bang, this Big Bang Machine will also try to detect the theoretical "Higgs boson", which explains a basic question: why do things have mass?

Ok, where does "mass" come from. Such basic question, yet nobody knows the answer now. And many people who don't know much about science think current science can explain everything.

There are plenty of basic questions that scientists don't have answers.

One more related topic: you may have heard of matter and anti-matter. Electrons have negative charge, and protons have positive charge. Anti-matter is reversed, and they do exist (not just in science fiction). Scientist can create anti-matter in those labs and they annihilate with matter (violently). The question is this: why does regular matter win and anti-matter loses?

Another unexplained observations are the dark matters... There is still a lot to study in physics. But not everyone can handle the ultra difficult mathematics involved.

Yan can cook, but the Thai PM can't

This piece of news is rather interesting. The Thai PM got kicked out of office for hosting a cooking show.

Ok, it was more than the cooking show. Thousands of people have been protesting him for a long time, camping outside of the Government House, making him declared a state of emergency.

I have no clue about Thai politics.

However unpopular President Bush gets, if he shows up in a cooking show I don't think Bush will get impeached. The Thai folks should probably come up with a better reason?

Unthinkable if something like this happens in America: people caming outside the white house demanding a president to leave office... Even more unthinkable if people do that in China. Yikes that reminds me of Tinanenmen Square...

Fireman's sacrifice

In HongKong, a huge fire killed 2 brave firemen who let the victims use their precious oxygen tank. One of them is only 25 year old. He received maximum honor and respect in the funeral, as reported by headlines*.

Yes, everyone is proud of the fire fighters.

However, what is not reported in the headlines is the cause of the fire... what cause these brave individuals die?

There are MANY old, ill-maintained buildings in Hong Kong, and most people living in that area can't afford better housing and couldn't care less about fire safety. Stairs are jammed packed with junks. The buildings probably don't have sprinklers and fire extinguishers. Poor maintained buildings and dense population is disaster bound to happen.

As we pay respect to the brave fire fighters, these old buildings need some remodeling!

But yikes, where is the funding? If you ask the poor residents who live in these areas, they close their doors.

*取義 comes from the following from 《孟子》
魚，我所欲也，熊掌，亦我所欲也；二者不可得兼，舍魚而取熊掌者也。
生，亦我所欲也，義，亦我所欲也；二者不可得兼，舍生而取義者也

Title bar out of style?

New programs hate the title bar. They take it OFF.
Google's new Chrome browser does not have the title bar.
Music programs such as Windows Media Player, Real Player, ITune and all that don't show the title bar (but some allow you to turn it on).

Why does the world not like title bars? Look folks, Windows is better than DOS because things have a consistent interface. Title bar, menu bars, window resize and all that.

I prefer the Title bar.

I played with Chrome. It is fast and tracks your browsing history very visually...
Where is the title bar and the status bar? The status bar is HALF width in Chrome.

I like the status bar in the bottom, and the Windows menu at the bottom. I NEED a bottom line. I've head some say the Start menu bar in bottom has root from video games, such as Star Raiders!

Ooh, Microsoft is going to release IE8 soon.

But what do you do with a browser: you type a URL and go. Don't need to be super fancy.

Firefox works for me... I am not dumping it yet.

New player in browser: Chrome

Google will soon release a new browser, known as Chrome. Before they release it, they released a comic book. Now that's innovative.

I am sure it will have many innovations. I *hate* IE7 and Office 2007... Those menus drive me nuts (if I can find them).

I use IE6 at work, I think it is fairly decent.
When I install AT&T Yahoo DSL, it ADDS tabs ability to my IE6, causing it to crash crash crash. I use Firefox at home. I like it much.

Let's see how much new excitement it will bring...