Area 1

Note: The following information are referenced to my previous knowledge and are not entirely my independent research.

We think we are quite familiar with the concept of area, or the 2 dimensional "size" of a shape cover over a plane (say it is the surface of the earth, or the table, or paper, or R X R plane).

But what is area? How do we REALLY measure area? Why are formulas for areas so, weird looking? Some of the questions will be solved below, but not all. To do this we have to DEFINE what the heck IS area.

First, we have to define shapes. We say by shape we mean the set of ALL, "closed", 2 dimensional graphs. I cannot establish a clear concept of "closed", we can consider closed as meaning there is a finite region within the graph.

Now, we define a square, a square is a shape with 4 identical sides, and the angle between any two adjacent sides is pi/2 radian. Why we use radian? We will see in later sections. Further, we call a square with side 1 a unit square.

Now we DEFINE the area of a UNIT SQUARE as 1 square unit. You can think of it as its side times side, but that's not it----- the area is defined for it.

Then we say the area of a shape is the total number of UNIT SQUARES that fits in the closed region (as the concept of closed is not perfect, you can assume we are dealing with common shapes).

We will work step by step on some example to show this definition works really well in the next section.

N/A

It is yet again another year. Again and again, life filled with joy, sadness, excitement and pain has gone by.When I look up at the sky I thought of a question: Do I deserve my friends, the people I love, I care about probably the most?

Then my brain, which I brutally ignored (not really) for the past decade spoken yet again its wise words.

"We all have what we treasure, and what we do not. It is not always so important those we treasure is also treasure to everyone else. Dreams, believes and love, everyone have different opinions, interpretation. What is important is YOU, yes what you believe is the most important.

"What you believe is important, your friendship your loved ones, even though they might not even care the same about you. But should those change your feelings towards them? Let me answer with a story.

"There once was a person, gender unknown, Mathematical Skill unknown as neither of those matters. Let's use 'he' for convenience sake. He was on a quest, to look for what it takes to be a hero. He found this old guy, sitting a a rock beside the road. He asks 'do you know need what one need to be a hero?' The old man asked him back instead, 'what is a hero?'

"The person thinks, in his mind he flashes images of warriors slaying dragons, elfs saving lives, and that is what he told the old man. The old man says, 'so why does hero do those?' 'To help the weak of course.'

"Old man smiles, and he asks 'do you think heroes wants or expects to get something in return?' 'Of course, they expect...' then the traveler stops, and thought. The old man finishes for him 'a hero helps people regardless of what they receive young one. A hero are expecting to be able to make a difference in people's life and see the joy and peace in society. A hero loves others whether the other like him (or her) or not. A hero might never be heard but still continue his deeds.' The old man paused, and continued, 'There was once a clan under attack from another powerful clan. Every clan member joined the fray. One of the soldiers fled the frontline. What do you think he is?'

"The traveler replied 'a coward, or a weakling, free rider.' 'Or is he? You never considered other possibilities hey? Well, can't blame young people. Well, he realized there is a back door to his clan's village. Only a few knows, so no one bothers. He believed that it is entirely possible the enemies sneak up, but no one listens. He, out of love and care and strong belief, fled the frontline to check. Yes, an army of enemy is coming. There is no time to call for reinforcement, so this person stood there for 10 days all by himself without sleep, drink of water or anything, single handily defended the village. Now do you still think he is a coward?' The traveller was silent.

"'That warrior died and the only tale about him that's been passed on is that 'he is a coward who fled from the frontlin'. He probably knows this, but out of his belief, his love, he take that name to protect his village. Now that is a hero. You can be a hero, too. There are, or at least will be people you care and love. Protect them, trust them and continue that love and care regardless of what they might think of you, then you will be a hero.'

"As a light flashes through the travelers eye, he realizes that what he was looking for was right there. When he look up to thank the old man, the old man was gone.

"Now you want to be a hero right? I know you do fat person (namely Alfred), then you should not let your love and care for others fade no matter how they treat you. Love them, protect them and believe in them, you will be a hero."

That ends my thought.

So, my friends, for this Feb. 14, be my Valentine. Whoever you might be, I will love you.

Remark: Love doesn't necessarily need to be romantic.

P.S.Story is a abbreviated story from FF VII

Time Travel Paradox

The famous paradox about time travel is "if I change something if I go back in time, what would happen in the future when I get back". Stephen Hawkin's one is more interesting --- if I go back in time and kill my parents, then I will never be born, then I can't kill my parents...

These all seem to be paradoxes, but it can be solved if the MANY WORLD Theory is true. Many world theory suggest that the possibility wave function doesn't collapse into a straight line, but rather separate into multiple lines that co-exists ---- each possibility create a separate and parallel universe.

So, I will use a diagram:

So let's use it to solve the paradox. Suppose the reality now is reality 1 on the very left, now you go back in time. If time is a single line, it is much easier, but it's a web, you go back to an intersection of a web. When we time travel, we go back to where event A is. We know to get to our reality, Event B1 must happen, so suppose you changed something, so that Event B1 didn't happen. Since there are infinitely many other possibilities, for simplicity, and without loss of generality, we assume Event B2 happened. Well, that leads to another universe for that time. So what ever happened that caused reality 1 will not be changed at all, nothing happend in YOUR future, but rather a parallel future.

Using Hawkin's example, suppose I went back and, since I am not very violent, kidnapped one of my parent so they never met. Then if I were to travel "back" to the future, I would still exist ---- but with no identity because I came from a different universe. I can still "kidnap" my parents before I was born because they are not REALLY my parents until I am born. Hence, the paradox is not so paradox after all.

Now, another question comes up ---- when you travel "back" to the future, which future are you in? I assumed you will be in the future where Event B1 fails, but is it really?

Hacking

Like it or not, more and more people are getting hacked. Not just regular people now, even the mighty GOVERNMENT are getting hacked. Hacker is everywhere, can our personal information really be kept safe anymore?

While striving to improving internet security, computer companies and anti-virus programs can only do so much to protect our confidential information. There is always flaws, and guess what, good hackers only need a tiny flaw to get pass the security ---- whether it is through a new type of virus (which is more complex) or some thing as simple as sending out fake warnings/emails. If you see warnings on the internet like "Your computer is under attack from the viruses!" Don't trust them, they are virus links themselves, close that page and move on. Search with more trusted anti-virus programs such as AVG, McAfee etc.

But like I mentioned before, good luck protecting your personal information, you will need it.

Paradox

Einstein says that everything in this Universe is relative, there is nothing that is absolute. But this statement is quite absolute, it is a paradox of life, or is it?