Archive - Aug 2008

Date

Complexity of remember physics equations

I did some physics problem and now I see something non-desirable with physics:
Too many equations to remember.
Physicist creates so many words and letters to detonate trivial combination. Those increase the amount of stuff to be remembered.
Why do they still do it? Because it help one remember them easier.(Seems like a paradox but not...)

But I still don't like to remember stuff.

From now on
m=mass, t=time, l=length
Pressure. What a useless word.
What if I replace the word pressure with \frac{m}{lt^2}. For example the following questions.

In a system, an object with the area of 14m^2 are under 19pascal pressure, what is the force excreted on this object.

Express elementary way I like.

In a system, an object with the l^2 of 14m^2 are under 19 kg/(m·s^2) \frac{m}{lt^2}, what is the \frac{ml}{t^2} excreted on this object.

I found this much easier.

I don't know how many formulas I have to remember, but I think it's O(n^2)(maybe lower) if there are n physics terms.
I know it improves the speed of computation. It's hash table speed... O(1) for finding relationship between all those placeholders...

I like to reduce it to exactly n formulas. (Lower bound? maybe can be improved, for a lot more computation)
Convert w/e physics term into the 5 basic units. mass, time, length, charge and temperature. Remember that.
The computation is bad...
One have to know should one term multiply or divide another term, which will be consist of a few subtraction and addition because it's purely about cancellation.
This has to be done by trial and error. bring it to O(2^n) computation time. when there is only k terms involved in an equation, the worst number of trials are 2^(n-1).
an simple algorithm
List the exponents in for each basic unit present in the equation on lines. the last line is what we want in the result.

sign m l t
1 -3 1
2 2 1
1 0 1
2 -1 1

add signs so the sum of the rows will result the last row. from trial and error, a few simple techniques can be used to find the answer faster.

sign m l t
+ 1 -3 1
+ 2 2 1
- 1 0 1
2 -1 1

The formula is found, plug in the numbers!

Yes, it is in fact a hand based version of this computer science problem

Given: vectors v_1 to v_n
The solution is unique and exists.

Create an algorithm that can find c_1 to c_{n-1} that are either 1, 0 or -1 so
v_n = \sum _{k=1}^{n-1} c_kv_k

I think there is some improvement to the algorithm. If I can prove the following.

Suppose v_k(x) is the xth element in the vector1.
If the solution of the c's for v_n = \sum _{k=1}^{n-1} c_kv_k is unique.
Then the solution for the c's for v_n(x) = \sum _{k=1}^{n-1} c_kv_k(x) is also unique, for arbitrary x.
If [v_k] is the dimension of a vector2.
Then we expect to reduce to 1/[v_k] of the original running time..


Disproved. Counter example
given<1,a>,<1,b>, want <1,a>

Physics is not my thing. Don't like trivial applied math with experiments.

  1. 1. Is there a specific mathematical notation for that?
  2. 2. Again, any standard notation for that?

Upgrade and migration is never easy

My site is still running Drupal 5 for few obvious reasons:
1. Some of my modules don't have stable Drupal 6 version yet
2. Update cost a lot of time and might not success the first time due to the amount of module I'm currently working on.
3. These days wordpress become better and better, and wordpress become almost 100% automatic. Really want to move to wordpress, but a migration will cause so much problems requires hours and hours of time to solve.(mostly, URL redirection and specific tags used in Drupal)
4. Oh I wish I'm rich so someone else manage my site and I just make demands and those things will be done.
5. Watched snakes on a plane today. badass movie

Standard Standard Standard.
If only all of these CMS and Blog stuff using a standard so they can be converted easily.
Everyone uses their own way to do the same stuff. Putting the pressure on people who want to convert between different formats. What am I going to do with all my 1

  1. 1. tags?
    I'm stuck in Drupal 5, hopefully only a few more weeks.

Canceled the ticket

I'm not going to China anymore.
What I'm doing will tear the family apart.
My biological parents in China told me they wish I would change my mind and not come home because my mom and dad are fighting over this issue constantly.
They are right.
I can't be that selfish.
Non-refundable ticket. Laid to waste. First time in my life I spend that large amount of money. Bravo.
Thx Ahana.
I shall do whatever makes me most happy.

Either way it's not going to be happy. I should pick the one make most people happy.

I wonder, if I have stereotypical white parents, maybe I get to do what I like instead of what they like.

A dilemma, not two lemmas

It has to be the largest dilemma I have faced in my life.
I could either go to China, do my math, come back without a place to live and getting student loan for college, or
stay in US, and do my best at math, then have a place to live and get most of my college tuition covered by my parents


Cretan Labyrinth. School of Finiguerra

Nice work getting me to this point, Chao.

It all started with my plan to go to China study math intensively so I can get myself into USAMO, so I have a good college application. At least this is what I told my parents about.

My dad, opposed. He says I have too much to do in US. Intel Science Talent Search(STS) might be the better option, since I have a great mentor and he can help me with the research report a lot. that is, if I am in US while I'm writing it. The college essays should be done in US, so I can get my English teacher to correct my grammar and can personal ask teachers to write recommendation letters.
He also knows USAMO is in April, way too late for first year college application.
So he told me, if I aboard the plane next week, he will not welcome me in his house and I better find somewhere else to live.

Fair enough. He is a reasonable man. Because if he is paying so I can live in the house. It's perfectly ok to do this. I perfectly understand and I don't blame him at all.
I do even agree with what he said. It's true, maybe I have a better chance at STS and it might be easier to get into a better college if I just stay in US.

My mom, agreed, but she has no power and no money. She also want me to get into a good college, USAMO sounds nice to her.

Now it is up to me.

I lied.
I didn't lie about USAMO can help me with getting into good colleges.
I did lie about the motive for USAMO, which will lead me to study in China. It's not because USAMO helps with me getting into a good college, maybe even my dream one, MIT.
I want to take USAMO because I want to take it.

What I would like better? Getting into MIT or getting into USAMO?
I chose the latter.
I don't care about how suck my application will be and how I can never make into STS semi-final due to my absence from my mentor. It's not important. I don't like science anyway.
Why would I lie about my motivation?
My parents, biological ones and legal ones, only cares about what college I goes to, what I want to do isn't really important.

In the beginning, I did everything for MIT, until I later found the goal was not MIT, but USAMO.

I started my life many years ago, there is always an feeling of emptiness, I felt I'm worthless in every aspect. I thought that's because I'm not in an environment that can bring out my worth.
I'm inferior to people in many subjects, all humanities subjects and even science subjects. I don't see myself capable to create an artistic drawing, moving novel or start a scientific project. Those are not my things.
As I grow up, I still know what I'm good at. I'm bad at everything.
Until I joined Mathlete in 10th grade.
I'm actually good at something.
But even if I perform at top of the school in math, there are still other schools in Suffolk County can send out students that can beat me.
I still have doubt of how good I actually am. Again, I believe it's because of my environment constrained me. I have to go to MIT to finally grow freely.

I have been selected into Suffolk County All-Star Team and participate in ARML, I finally understand what I am suppose to do--math.
My performance at the AP test, considering never studied some of those subjects, are nice. Lead me to understand it isn't my environment. It is myself.

I need to know, who I'm I and what I'm capable of. When I first heard there are people out there take time to "search for who they are", I loled, I found it funny. "Only white people do that" was my comment. Fate is ironic. USAMO suddenly is above MIT. USAMO will prove how good I am in math. I can finally know I am valuable. USAMO will complete me.
If I tell this to my parents, they will lol.
"WTF? Search for your own worth? You want to know who you are? You taking USAMO just for the sake of taking it? Haha, you are joking right?"

I was meant to do mathematics, it's the best thing I can do. If I fail at that, what's the point of even going to good colleges. I don't deserve anything better than Stony Brook if 4 months of intensive study can't place me in top 500 in US.

The dilemma is placed in front of me. I have 5 days left.

I remember making jokes about dilemma. it's two lemmas. Math pun.
Irony.

The decision is hard...
Homeless is not the worst could happen to me. I fear the following if I did make to China.

Few weeks later, I'm crying in my bed silently about how I didn't improve enough to take on the preliminaries confidently. All my effort rated "Fail" because my overvaluation of my ability. Waking up the next day like nothing ever happened. Smiling while tell my parents that "I will make it" when the hope already died out.

USAMTS question is not that hard to me compare to 1 year before.

Homeless is the way to be.

Ticket to China and return

in

In case anyone was asking...


If you try to assassinate me and fails, it would be great for my essay for MIT.

Essay A Tell us about an experience which, at the time, really felt like "the end of the world" -- but had it not happened, you would not be who you are today. Describe the process through which you discovered value in the negative.

Honey Pot that kill bots