Sirius

苏轼有词《江城子·密州出猎》:会挽雕弓如满月,西北望,射天狼。这到底是什么弓,什么狼?

《晋书·天文志上》:狼为野将,主侵掠。又说:弧九星,在狼东南,天弓也,主备盗贼,常向於狼。原来天狼和弧矢是二十八宿之一的井宿中的两个星官。

1075年,苏轼时任密州知州。当时北宋与西北的西夏常年征战,北边的辽忙着宫廷政变。原来这是文青苏同学打了两只野兔后豪情万丈YY要杀西夏兵啊。

附:天狼星(Sirius)是夜空中最亮的恒星,处南天球(−16° 42′ 58“)。绝对亮度是太阳的25倍,离地球只有8.6光年,视星等-1.46。是大犬座(Canis Major)的主星,所以人称 Dog Star。天狼其实是双星,由一主序星和一白矮星组成。

How many protons in the universe

What is the probability to create a proton with two kinds of quarks (u and d)?

We know that
1. only protons are stable. Free neutrons (udd) will decay to protons (uud) in 15 minutes.
2. baryons (3-quark configurations) may have different angular momentum (J): 1/2 or 3/2. Protons and neutrons have their higher J companions, while uuu and ddd exist only in J=3/2 due to Pauli exclusion principle. All these four are called Delta particles.
3. anti-quarks form anti-matter, which has the same mass as particles of *ordinary* matter but opposite charge and quantum spin.
4. baryons contain virtual quark-antiquark pairs known as sea quarks, along the valence quarks.

To make life easier, let’s forget these complications for a moment and touch a simple 3-kid problem. What is the probability to find a family with 2 girls among all the families having three children?

You may think as follows. The configurations are {GGG, GGB, GBB, BBB}, where G=girl and B=boy. So the probability (P) = 1/4.

Unfortunately this does not sound right. From our everyday experience, 2-girl families are more common than 3-girl ones!

To correctly calculate the probability, we need to list every configuration with exactly the same possibility. “First girl, then boy, last girl” denotes as GBG, and so on. So the configurations are {GGG, GGB, GBG, BGG, BBG, BGB, GBB,BBB}. Counting{GGB,GBG, BGG} and P=3/8! This means there are 3 times chances for a 3-kid family to have 2 girls than 3 girls. Also notice that when a 2-girl family are expecting, the third kid is equally possible for girl or boy.

Back to the proton problem. The universe was a quark soup right after the big bang.  The *initial* particles were 3/8 protons, 3/8 neutrons, thanks to the insight from the 3-kid problem. The other 2/8 two Delta particles decayed in 10^(-24) seconds to protons. Therefore, the neutron-proton ratio was roughly 3/8:5/8=3:5.

Now comes the part that physics is more than math. When the universe was less than 1 second old, the temperature was so high that the protons and neutrons, with electrons and neutrinos, were in thermal equilibrium and could change one to other freely. The neutron-proton ratio was actually 1:1, before temperature dropped below the neutron-proton mass difference, and froze out at about 1:7. As a result, 7/8 of  the matter in the universe is proton!

Bonus: we can figure out that, based on the neutron-proton ratio, 75% quarks are in hydrogen (1 proton) and 25% helium (2 protons & 2 neutrons) when the big bang nucleosynthesis stopped in about 20 minutes.

Why the space is three dimensional

Because 4D space is not determinate.

Let’s construct a magic square. “In recreational mathematics, a magic square of order n is an arrangement of n^2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.”

For order 3, only one configuration exists. To sum up 3 rows, 3 columns, and 2 diagonals, we need 8 different combinations. And it is exactly what we can get!  Only 5 appears 4 times so it has to sit in the center. 2/4/6/8 appear 3 times so they are at the corners. 1/3/7/9 appear 2 times and they are at the edges. Then the square is totally determined.

8 3 4
1 5 9
6 7 2

We can always add an arbitrary number to all the numbers in the square, eg,

18 13 14
11 15 19
16 17 12

The story totally changes from 3D to 4D. We only need 10 combinations but there are 86 of them! You should imagine more features or restrictions can be imposed, eg, the sum 34 can be found in each of the quadrants, the center four squares, and the corner squares, and more, just like Albrecht Dürer did 500 years ago!

16  3  2 13
5 10 11  8
9  6  7 12
4 15 14  1

助攻王的热血得分

在这个10w人的镇子,有3k华人;我来了一年,大概认识了300;其中有20人,一起打篮球。

在周五,在9pm。

对方是HR,DP,ZB,我方有AG,LS,LF和我。

是的,4vs3,我方完全没有篮板。

但是,我们有AG的抛射和跑位,LS的停跳和传球,LF的勾手和卡位。

夜未央,最后一局。

我们落后5球。我决定挺身而出,热血奋战。

突破上篮,急停跳投,怎么打怎么有,10投8中。

很快就追平到9vs9。决胜球!

面对盖帽王ZB的严密防守,我当然可以硬拔,或者强突。

但是流着助攻王血液的我,看到AG在罚球线无人防守,球就传出去了!

跳起,出手!

=========

两周后,掌握了几项自由泳的要点后在桑拿房高歌东方之珠,穿透力极强的声波打的水蒸气纷纷凝结。忽然门被撞开,传达室的大爷上前几步激动地拉着我的手说"我有32场演唱会。。。"

time management

今天Iowa的Susan R. Johnson 来讲Thriving Amidst Chaos。回头找我自己以前写的
https://sukye.wordpress.com/2011/06/23/pomodoro-technique-2/
不禁泪流满面。

嘛都知道,嘛都不做。

从今天起:
每天伊始都要列计划。
指明每个活动的期待结果。
早睡<11PM早起~6AM。
每天一小时阅读、半小时写作,半小时听讲座。
每周四次健身。
工作六天娱乐一天。

读书:
The Now Habit, by Neil Fiore, 2007

replace “I have to” by “I choose to”
replace “I must finish” by “when can I start”
replace “this is so big” by “I can take one small step”
replace “I must be perfect” by “I can be human”
replace “I dont have time to play” by “I must take time to play”
altogether: I choose to start on one small imperfect step knowing I have plenty of time for play.

guilt-free play gives quality work.

plans, action, and solutions are required to direct the energy and complete the work of worrying.

before deciding to go to a recreational activity, take time out for just 30min of work.

发现神数9801

1/9801 = 0.00(010203040506070809101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979900)(repeat)

这是为什么呢?

原来,1/99 = sum_{n=1}^{n=inf} (1/100)^n,
而 1/9801 = (1/99)^2 = (1/100) sum_{n=1}^{n=inf} n (1/100)^n

ps1,其实我是看到有人提到1/998001想到的。

ps2,wolframalpha.com 还算错了,漏掉了98。

超光速汽车

澳洲现在最大的土著就是袋鼠了。

其大型动物的灭绝恰和3w5k年前人类坐船来澳洲重合。

人性本恶,物性本善。土人见外人不以为意,等明白过来却无处可逃。

反应速度小于外物速度是很没安全感的。

就好比我们过马路,坐看看,右看看,走走再看看。

可是要是有车每秒能跑一迈,咱还来得及看到它吗?

能造的出也不能让Y上路啊。

--读《Guns, Germs and Steel 》有感

漏网

家里的无线老断,我也就重启一下router,得过且过。

年中到朋友家玩,才知道802.11,还有啥abgn。

我家的是Linksys wireless-b,11 Mbps。

本来想感恩节顺个便宜的,后来打算买Apple TV2,便索性也弄个他们家的router。(入手42″ LCD HDTV,壁炉上的“神龛”就48″ 大。)

特点是,贵,还不打折。

一咬牙在ebay上买了Apple AirPort Express,802.11n,号称150Mbps。

其实,速度瓶颈在接入cable上。现在我家用的是Charter Internet Express,
也就12Mbps。

这还不算。我刚发现我的cable modem, Motorola SBG900,其实是有无线的。
802.11g, 54 Mbps。完全够用了!

通过在不同网站的测试,我的11n还是比11g快15%-40%的。不过都没超过11Mbps!

如果

如果前面有5辆车在等红灯,就觉得遇到了traffic。

如果计算距离用时间而不是里程。

如果去个隔壁州就觉得是去度假。

如果你们那酒吧和教堂一样多。

如果全城的加油站都一个价。

如果经常在walmart遇到熟人。

你就知道你住在了一个小镇。

如果你认识很多人都撞过鹿。

如果你觉得大家都知道twin city是指哪。

如果你说往南就是去iowa。

如果你周末去wisconsin就是为了买烟火或啤酒。

如果你认为喜剧片grumpy old men是纪录片。

如果你认识四季:almost winter, winter, still winter, and road construction.

如果所有人家都有车库,所有车库同时也是冰箱。

你就知道你住在了minnesota。