心经

吾用心追求爱，小心呵护，却未见希望之成长，而跌至深渊。九九八十一难，终要历炼。

玄奘西行取经，历经千辛万苦，终成高僧，译众多佛家典籍，而以精炼的《心经》最为世人所知。

观自在菩萨，行深般若波罗蜜多时，照见五蕴皆空，度一切苦厄。舍利子，色不异空，空不异色，色即是空，空即是色，受想行识， 亦复如是。舍利子，是诸法空相，不生不灭， 不垢不净，不增不减。是故空中无色，无受想行识，无眼耳鼻舌身意，无色声香味触法， 无眼界，乃至无意识界，无无明，亦无无明尽，乃至无老死，亦无老死尽。无苦集灭道， 无智亦无得，以无所得故。菩提萨埵，依般若波罗蜜多故，心无挂碍，无挂碍故，无有恐怖，远离颠倒梦想，究竟涅槃。三世诸佛， 依般若波罗蜜多故，得阿耨多罗三藐三菩提。故知般若波罗蜜多是大神咒，是大明咒， 是无上咒，是无等等咒，能除一切苦，真实不虚。故说般若波罗蜜多咒，即说咒曰：揭谛揭谛，波罗揭谛，波罗僧揭谛，菩提娑婆诃。

最近读王守仁。其少时追求人生之终极意义，参悟“理”与“心”。经“格竹”等磨难，终顿悟心乃理之所以，理乃心之所存，实践知行合一，成就哲学圣人。 吾未曾用心，何来顿悟？ 烦恼终将过去，明日太阳会灿烂.

A Different Kind Of Nothingness

Photo Source: Evelyn Hockstein for The New York Times, Aug 24, 2008.

The sand of Namibia deserts shine in the sun light. The simple and pure colour, the strong contrast between bright and dark make the desert dazzlingly beautiful and attract many tourists to climb the dunes where the roads exist only temporarily. Well, it is certainly not a pleasant living place for many organisms which prefer chaos, organically-disordered chaos. Yes, pureness and simpleness is too good to be healthy to lives.

Love hurts...

It hurts so much.. esp when you thought you have touched the happiness of love and it is blown away.
Pressure amounts. How longer can I endure? Does true love exists?

山城重庆

八月湿热的夏天，3日到重庆逛逛。体会了古镇磁器口，逛了商业繁华之地观音桥、解放碑、三角碑，夜在朝天门看夜景。
垂直的高楼，上上下下的立体路面，浑浊的江水，雾蒙蒙的天气，繁华的街市是我对这一西部发展重镇的第一印象。
次日，雨。在重庆大学信步仙游，遭雨，在民主湖前避雨。湖中荷花虽已过旺季，依旧有娇艳的荷花伴同着即将成熟的饱满莲蓬。正面的湖中有紫色的莲花，我想是小时采过的“鸡头”吧。

两日来，山城之行未从给我带来喜悦开心之情。
夜行归，又想起Akon的Lonely很是贴切自己的心情。

Lonely by Akon

Lonely im so lonely,
I have nobody,
To call my owwnnn
Im so lonely, im mr. Lonely
I have nobody,
To call my owwnnn
Im so lonely,

Yo this one here goes out to all my playas out there ya kno got to have one good girl whose always been there like ya
Kno took all the bullshit then one day she cant take it no more and decides to leave

I wont up in the middle of the night and I noticed my girl wasn't by my side, coulda sworn I was dreamin, for her I was
Feenin, so I hadda take a little ride, back tracking ova these few years, tryna figure out wat I do to make it go bad, cuz
Ever since my girl left me, my whole left life came crashin

Im so lonely (so lonely),
Im mr. Lonely (mr. Lonely)
I have nobody (I have nobody)
To call my own (to call my own) girl

Im so lonely (so lonely)
Im mr. Lonely (mr. Lonely)
I have nobody (I have nobody)
To call my own (to call my own) girl

Cant belive I hadda girl like you and I just let you walk right outta my life, after all I put u thru u still stuck
Around and stayed by my side, what really hurt me is I broke ur heart, baby you were a good girl and I had no right, I
Really wanna make things right, cuz without u in my life girl

Im so lonely (so lonely)
Im mr. Lonely (mr. Lonely)
I have nobody (I have nobody to call my own)
To call my own (to call my own) girl

Im so lonely (so lonely)
Im mr. Lonely (mr. Lonely)
I have nobody (I have nobody)
To call my own (to call my own) girl

Been all about the world ain't neva met a girl that can take the things that you been through
Never thought the day would come where you would get up and run and I would be out chasing u
Cuz aint nowhere in the globe id rather be, aint noone in the globe id rather see then the girl of my dreams that made me
Be so happy but now so lonely

So lonely (so lonely)
Im mr. Lonely (mr. Lonely)
I have nobody (I have nobody)
To call my own (to call my own)

Im so lonely (so lonely)
Im mr. Lonely (mr. Lonely)
I have nobody (I have nobody)
To call my own (to call my own) girrll

Never thought that id be alone, I didnt hope you'd be gone this long, I jus want u to come home, so stop playing girl and
Come on home (come on home), baby girl I didn't mean to shout, I want me and you to work it out, I never wished Id ever
Hurt my baby, and its drivin me crazy cuz...

Im so lonely (so lonely)
Im mr. Lonely (mr. Lonely)
I have nobody (I have nobody)
To call my own (to call my own)

Im so lonely (so lonely)
Im mr. Lonely (mr. Lonely)
I have nobody (I have nobody)
To call my own (to call my own) girll

Lonely, so lonely
So lonely, (so lonely),
Mr. Lonely, so lonely
So lonely, so lonely, (so lonely), Mr. Lonely

Neptune - The Blue Planet

Neptune, which was named after the Roman god of the sea, is a planet of blue. Its atmosphere consists of methane, hydrogen, helium, and water. It has very strong wind. The wind velocity could reach to 2100 kilometers per hour, which is almost supersonic. Though the name is ironically correct, the planet is as blue as sapphire. However, scientisits still do not understand completely why it is so blue!

No man is island

But how to connect to the continent? Is there any island shared by two?

On Aug 8, I just found the origin of 'No man is island'.
This is a quotation from John Donne (1572-1631). It appears in Devotions Upon Emergent Occasions, Meditation XVII:

All mankind is of one author, and is one volume; when one man dies, one chapter is not torn out of the book, but translated into a better language; and every chapter must be so translated...As therefore the bell that rings to a sermon, calls not upon the preacher only, but upon the congregation to come: so this bell calls us all: but how much more me, who am brought so near the door by this sickness....No man is an island, entire of itself...any man's death diminishes me, because I am involved in mankind; and therefore never send to know for whom the bell tolls; it tolls for thee.

Penrose Tiling

In one of the previous posts, I mentioned the surprise connection of Penrose rhombi tiling from 2-D to 3-D. In fact, the seemingly weird idea may review deeper meaning of Penrose tiling. Actually, de Bruijn, a Netherlands mathematican, found the Penrose tiling can be constructed from the projection of the Voronoi hypercubes of a plane in 5-D space onto the plane itself. The plane has to be the golden-ratio plane. Furthermore, at different dimensions, one obtains various kinds of colorful tilings. If we choose the 3-D space that is orthogonal to the 2-D golden plane in the 5-D space, we could obtain the 3-D Penrose rhombi tiling by projecting out the Voronoi hypercubes onto the 3-D space. The 3-D Penrose rhombi tiling is intimately connected with the semi-periodic crystal packing patterns which shows local 5-fold rotation symmetry. That is an interesting topoic itself in chemistry and physics. Penrose mused that the tiling is a reflection of the electron correlation effect at the quantum mechanics level.



Well how to understand the idea? Here is an example of one-dimensional tiling. On a 2-D space, we first draw a straight line with a slope of golden-ratio. The blue grid is with a gap of 1 and can be seen as a Z^2 space. The blocks in light green are the Voronoi square cells that enclose the straight line. If we project the Vornoi square sides onto the golden-ratio straight line, we will get a series on long and short segements that cover the whole line. And the ratio of the long and short lengths is again the gold-ratio. The tiling pattern is given by the Fibbonacci sequence. It is so called Fibbonacci tiling of reals.

The Voronoi cubes of a plane in 3-D space.


The following Penrose tilings are generated with a sub-division (deflation) algorthims found by de Bruijn and Han. In this algorthim, a half rhombi is divided into two or three smaller half rhombus scaled-down by golden-ratio.The division can go on infinitely and get more and more complex structures. The following pictures show the same tiling region but to different depths.

Depth = 3


Depth = 5


Depth = 8


I have not figured out the details on how to get the tiling from projection in 5-D space to 2-D plane or 3-D solid.