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I Ching and math

My mom arrived in US. And brought me 3 books.
One of them is about I Ching and using hexagrams to solve xMO level math problems.
The hexagrams' Yin and Yang parts maps to 0 and 1, or -1 and 1 respectively.
It's quite easy to use the 0,1 to form a Boolean Algebra and then using that to solve Olympiad problems. Also it was shown to solve the game Nim and a few classic coloring problems.
1 and -1 can form a Abelian group(-1,1), solve another set of math problem.
A Boolean vector can represent graphs, solves yet another kind of math problem.
It also consist of some discrete probability things...
and more...

It's just using the I Ching terminology as a isomorphism to modern mathematics.
Quite interesting. It's not useful, but it proves a point. That I Ching's hexagrams' structure has many mathematical ideas that's considered quite modern.

This graph limited the mind of ancient Chinese mathematician. Sad.
If they have done mathematics just for the sake of it instead of using it for real application only, then maybe, we can have a lot more useful theorems.

In most dynasties, mathematicians have very low social status. But people who does I Ching have high status due to common people and philosophers believe I Ching is the answer to everything(like 42.) So Chinese mathematicians start to do math that related to I Ching, and rarely let themselves to do math outside the I Ching framework.

I hope I get a decent job doing math.

A word deserves it's own post

RadiAsian

Get it? sounds the same as radiation. Puns!

Rarely one can meet something better than sperm donation

in

Post advocated by an ad on Facebook.

Three reasons to donate sperm.

1. Giving back to the community:
Allowing the world to change for the better/worse by allowing lesbians and single women can have kids too. It feels great to help people.(puns not intended)

2. Earn some money.
See, $75 to $150 per donation, if one donates once per day and say, getting $100. And donations on Sundays and Saturdays receives over shift pay. A total of say, $800 per week!
jkjk, there is no way one can earn enough money by just donating sperm. It's physically impossible to generate that much sperm consistently every week. Unless you are on something that helps with sperm production, and I doubt those sperm will be healthy sperms.


Making a living! Pun!

3. Ok ok now, seriously, this is the reason I started to talk about this.
I saw this in a biological perspective and personal perspective.
I think the meaning of all organism is to pass down it's genes. Sperm donation really does help no matter if one already has a family or not. It increase the rate of your gene's survive in the entire gene pool. Be proud of that.

My mom wants me to have kids. But I don't like kids(Puff... Ancient Chinese way of thinking). I don't want to have responsibility of taking care a child, and children are generally, too ignorant to have a conversation with me, unless I have the patients to bring them up to at least 16 years old.
I also don't want to get married, so I am free and don't have to listen to anyone or consider about anyone's feeling. Oh yeah!
Since my mom wants me to have kids(with my genes), I can get her some by donating sperm, which will impregnate someone I don't know and produce a offspring I don't know either. I have no responsibility at all, and I fulfilled my mom's requirement about my adult life. Isn't it nice, helping people while help myself. Win-win situation for everyone.

Not everything is transitive, bitch

On the lunch table, there were a conversation going on. Where Matt and Peter mentioned something about bitch and transitive relation.


It's over 9000!

I don't believe it!
I feel it's like saying:
"I'm filled with lead because I eat rice imported from China. So I have natural shielding against Gamma radiation."
You are doing it wrong!
Bitch is a binary relation, let's use "A\to B" to detonate A is B's bitch. This binary relations says B will do what A asks.
They theory:
A\to B
B\to C
then
A\to C
I don't believe in it.
Record of the conversation, paraphrased for clarity, P(Peter), S(Matt) and M(Mgccl).

M: (to S) If you are my bitch, and P is your bitch, how does that makes P my bitch?
S: If I'm your bitch, you can order me to do something so I can order P to do something.
M: How can you be sure that P will listen to me?
S: There is an level between two bitches, you can command me then I command P to do your job.
M: Doesn't that allows a cycle? What if I'm P's bitch? Then it forms a cycle and everyone becomes everyone's bitch. Like six degree of separation, there must be a six degree of bitchness.(clear phrase would be six degree of bitch separation)
P: How about let's test your theory, you go to the security guard and let you go in (w/e place I forgot)...
M: Then I have to find whom he belong to.
P: It's like six degree of Kevin Bacon.
M: OMG I love bacon, it's so tasty, it's $2.99 per pound in Wal-mart.

Distracted...
But I should stop when I saw this

There is an level between two bitches, you can command me then I command P to do your job.

Then it is not transitive property anymore.
Unless bitch is a relation says if A can order B direct or indirectly. But that would form a cycle for sure, there is no way the entire human population isn't connected though bitch-bitchmaster connection. It will certainly cause everyone to be my bitch, and I'm everyone's bitch.(A directed cyclic graph)
Which makes the binary relation bitch not useful at all, making it can't explain anything, it has no mathematical value.
Bitch have to be a binary relation that doesn't include indirect control.
Just my 2 cents.
The Hillary picture have nothing to do with this article.
So is this picture, but instead of Hillary, it's a very cute Japanese girl.
Ok what is with me and Asians these days...

Save money in BNL cafeteria

When I first entered BNL summer research program, I was told the cafeteria offers 20% discount to research students.
After some investigation, it is in fact, not correct. I feel like BNL lied to me, cheated on me. I don't feel safe at BNL anymore.

Suppose function f(x) = amount I pay for food that normally cost $x. The definition of f(x) is:

f(x) = \normalsize \left{
\begin{eqnarray}
x &&(x<3.5)\\
x-0.75 &&(3.5 \le x < 5)\\
x-1 &&(5 \le x < 8)\\
x-1.5 &&(8 \le x < 12)\\
x-2.25 &&(12 \le x < 15)\\
x-3 &&(15 \le x )\\
\end{eqnarray}
Graph of f(x) compare to x and 0.8x

d(x) = \frac{f(x)}{x}
Graph of d(x) compare to 0.8

Graph of f(x) using d(x) with some transformation as gradient. darker = less percent discount.

Function s(x) is the average discount from 0 to x. Defined as
s(n) = \frac{\normalsize\int\limits_{0}^n d(x)\mathrm{d}x}{n}
s(15) = 0.85
s(x) is a monotonic increasing function for x>15.
So on average, if one spend $15 or more, one has less than 15% discount!

After analyze the entire system, how can we take advantage of it and get as much discount as possible?
You can break the order into pieces so it fit into some range, or combine order with someone else to get maximum profit.
For example, a $7(with tax) order composed of 2 $3.5 lasagna. Normally you pay $6, but split it into two orders, you pay$5.5. Doing it everyday can save up to $15 when the research program ends!
I don't have enough skills on problems like this, my guess is there is no simple analytical formula to find how exactly buy stuff to get the best result, it's best to use computer to find a numerical answer.

Without out a computer, you have to do a little calculations, bring a table of values would be nice, here is one from $3.5 to $15, every 10 cents gap. With amount of money before savings and discount expected. Orange = 20+% discount, Yellow = 18.75+% discount.(remember to add tax while looking at the menu)

$ % $ % $ % $ %
3.5 0.2143 6.4 0.1562 9.3 0.1613 12.2 0.1844
3.6 0.2083 6.5 0.1538 9.4 0.1596 12.3 0.1829
3.7 0.2027 6.6 0.1515 9.5 0.1579 12.4 0.1815
3.8 0.1974 6.7 0.1493 9.6 0.1562 12.5 0.1800
3.9 0.1923 6.8 0.1471 9.7 0.1546 12.6 0.1786
4.0 0.1875 6.9 0.1449 9.8 0.1531 12.7 0.1772
4.1 0.1829 7.0 0.1429 9.9 0.1515 12.8 0.1758
4.2 0.1786 7.1 0.1408 10.0 0.1500 12.9 0.1744
4.3 0.1744 7.2 0.1389 10.1 0.1485 13.0 0.1731
4.4 0.1705 7.3 0.1370 10.2 0.1471 13.1 0.1718
4.5 0.1667 7.4 0.1351 10.3 0.1456 13.2 0.1705
4.6 0.1630 7.5 0.1333 10.4 0.1442 13.3 0.1692
4.7 0.1596 7.6 0.1316 10.5 0.1429 13.4 0.1679
4.8 0.1562 7.7 0.1299 10.6 0.1415 13.5 0.1667
4.9 0.1531 7.8 0.1282 10.7 0.1402 13.6 0.1654
5.0 0.2000 7.9 0.1266 10.8 0.1389 13.7 0.1642
5.1 0.1961 8.0 0.1875 10.9 0.1376 13.8 0.1630
5.2 0.1923 8.1 0.1852 11.0 0.1364 13.9 0.1619
5.3 0.1887 8.2 0.1829 11.1 0.1351 14.0 0.1607
5.4 0.1852 8.3 0.1807 11.2 0.1339 14.1 0.1596
5.5 0.1818 8.4 0.1786 11.3 0.1327 14.2 0.1585
5.6 0.1786 8.5 0.1765 11.4 0.1316 14.3 0.1573
5.7 0.1754 8.6 0.1744 11.5 0.1304 14.4 0.1562
5.8 0.1724 8.7 0.1724 11.6 0.1293 14.5 0.1552
5.9 0.1695 8.8 0.1705 11.7 0.1282 14.6 0.1541
6.0 0.1667 8.9 0.1685 11.8 0.1271 14.7 0.1531
6.1 0.1639 9.0 0.1667 11.9 0.1261 14.8 0.1520
6.2 0.1613 9.1 0.1648 12.0 0.1875 14.9 0.1510
6.3 0.1587 9.2 0.1630 12.1 0.1860 15.0 0.2000

Someone can design a program so it's possible to calculate the most optimal solution if at most x order splits is possible for n individual food with each of the food's price p_n.

P.S. The summer science program(Research Program:Science Program::Gentoo:Ubuntu) started today. So many Asian girls!(at least 8) it's unbelievable! It's like MIT! Haha, I was wondering where's the Asian when I entered the research program(only me + 1 more person).

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