摘录

“一个人在精神上足够成熟,能够正视和承受人生的苦难,同时心灵依然单纯,对世界仍然怀着儿童般的兴致,他就是一个智慧的人。”

我花了41年的时间明白了一个道理:
“决定孩子成功的最重要因素,不在于我们给孩子灌输了多少知识,而在于我们是否帮助孩子获得了以Grit为首的七项重要的性格特质。

Grit坚毅、Zest激情、Self-control自制力、Optimism乐观态度、Gratitude感恩精神、Social intelligence社交智力、Curiosity 好奇心。

不要在感觉糟糕的时刻结束。在遭遇挫折的那一刻就立即放弃,可能意味着你将错过最棒的时刻-比如最终打进了制胜一球或在演出结束后听到雷鸣般的掌声。”

“世界上只有一种英雄主义,

就是看清生活的真相之后,

依然热爱生活!”

“生活是否永远艰辛?

还是仅仅童年才如此?

里昂回答:总是如此。
生活如山,

有人岁月静好,

有人负重前行。
生活不止眼前的苟且,

还有诗和远方的田野。”

“所谓细节便是,你对达官显贵和保姆乞丐持一样的心,呈一样的笑。不以物喜,不以己悲。你拥有一颗悲悯的情怀于万事万物。你保持品行的高贵却又于高贵处平凡得一如脚下的泥土。”

“此生如若有你,何惧岁月老去?

只要我能时时看着你,

哪怕你的脚步,

如孩子般蹒跚,

我也会像,深海的鱼一样,

幸福、陶醉、沉迷……”

”他令我意识到爱并不是凝固不动的东西。正相反,爱是永无止境的探索和学习,两个人都应该尽力鼓励和引领对方见识更多更美的东西,成长为更加丰富与宽容的人。”

2016上班第一天9句话(ZT)

1.不为模糊不清的未来担忧,只为清清楚楚的现在努力。

2.只有先改变自己的态度,才能改变人生的高度。

3.在抱怨自己赚钱少之前,先努力,学着让自己值钱。

4.学历代表过去,学习能力才代表将来。

5.耐得住寂寞才能守得住繁华,该奋斗的年龄不要选择了安逸。

6.有些事情不是看到希望才去坚持,而是坚持了才看得到希望。

7.压力不是有人比你努力,而是比你牛几倍的人依然在努力。

8.你所做的事情,也许暂时看不到成功,但不要灰心,你不是没有成长,而是在扎根。

9.现实和理想之间,不变的是跋涉,暗淡与辉煌之间,不变的是开拓。

贵族精神(ZT)

告訴孩子,這就是「貴族精神」!

1、孩子,你一定要學會做飯。這與伺候人無關。在愛你的人都不在身邊的時候,使你能善待自己。(能獨立生存)

2、孩子,你一定要學會開車。這與身份地位無關。這樣在任何時候,你都可以拔腿去往任何你想去的地方,不求任何人。(自由)

3、孩子,你一定要上大學,正規的大學。這與學歷無關。人生中需要經歷這幾年,無拘無束又能染上書香的生活。(一旦走進社會,就進入了市場)

4、孩子,你知道嗎?足跡有多遠,心就有多寬。心寬,你才會快樂。萬一走不遠,讓書籍帶你走。(拓寬自己的視野,借助知識的視野)

5、如果世界上僅剩兩碗水,一碗用來喝,一碗要用來洗乾凈你的臉和內衣褲。(自尊與貧富無關)

6、天塌下來都不要哭,也不要抱怨。那樣只能讓愛你的人更心痛,恨你的人更得意。(平靜地承受命運,愛你的人自會關心)

7、就算吃醬油拌飯,也要鋪上幹凈的餐巾,優雅地坐著。把簡陋的生活過得很講究。(風度與境遇無關)

8、去遠方的時候,除了相機,記得帶上紙筆。風景是相同的,看風景的心情永不重復。(畫面和情感的記憶是不同的)

9、一定要有屬於自己的空間,哪怕只有5坪。它可以讓你在和愛人吵架賭氣出走的時候,不至於流落街頭,遇到壞人。更重要的是,在你浮躁的時候,有個地方讓你靜下來,給自己的心一個安放的角落。(獨立人格)

10、小孩的時候要有見識,長大的時候要有經歷,你才會有個精緻的人生!(讀別人的經歷,找自己的經歷)

11、無論什麽時候,都要做一個善良的人。請記住,擁有善良,會讓你成為最受上天眷顧的人。(這種眷顧未必是財富與權勢。善有善報,所報者,愛也)

12、笑容、優雅、自信,是最大的精神財富。擁有了他們,你就擁有了全部。
這就是「貴族」精神。

 

 

Holy Night 12-24-2015 (ZT)

  
凡事皆有定期,万物皆有定时。

生有时,死有时;

栽种有时,拔出有时;

杀戮有时,医治有时;

拆毁有时,建造有时;

哭有时,笑有时;

哀恸有时,跳舞有时;

抛掷石子有时,堆砌石子有时;

怀抱有时,放弃有时;

寻找有时,失落有时;

保守有时,舍弃有时;

撕裂有时,缝补有时;

默默有时,言语有时;

喜爱有时,恨恶有时;

争战有时,和好有时,

万事万物皆有其时。
——《圣经·传道书》

  
爱是恒久忍耐,又有恩慈;爱是不嫉妒,爱是不自夸,不张狂,不作害羞的事,不求自己的益处,不轻易发怒,不计算人的恶,不喜欢不义,只喜欢真理;凡事包容,凡事相信,凡事盼望,凡事忍耐;爱是永不止息。
——《新约·哥林多前书》

  
已有的事,后必再有;已行的事,后必再行;日光之下,并无新事。
——《旧约·传道书》

  
一代过去,一代又来。地却永远长存。
——《旧约·传道书》

  
已过的世代,无人记念,将来的世代,后来的人也不记念。
——《旧约·传道书》

  
忿怒害死愚妄人,嫉妒杀死痴迷人。
——《旧约·约伯记》

  
心所憎恶的共有七样,就是:高傲的眼,撒谎的舌,流无辜人血的手,图谋恶计的心,飞跑行恶的脚,吐谎言的假见证,并弟兄中布散分争的人。
——《旧约·箴言》

  
人有见识,就不轻易发怒;宽恕人的过失,便是自己的荣耀。
——《旧约·箴言》

  

我喜欢春夏秋冬和每天的你(ZT)

   
“我喜欢夏天的雨

雨后的光

和任何时候的你”

——青慕《青慕 三行情诗集》

 
“谁说现在是冬天呢?

当你在我身旁时

我感到百花齐放,鸟唱蝉鸣。”

——夏洛蒂勃朗特《简爱》

   
我想要和你一起看春天最美的花

坐在夏天的树下看星星

一起走在秋天的黄昏里

让冬天的阳光温暖你

因为

我喜欢春夏秋冬和每天的你

    
    
    
 

Are Singularities Real? (ZT)

Are Singularities Real?

It’s hard to imagine infinity: something that is, by definition, larger than everything you can imagine. Physicists have to deal with the unimaginable every day, and have the tools to do so. But does their math describe reality?

Mathematicians have found a way to pack infinity into manageable equations and theorems as part of a class of mathematical oddities called “singularities.” To a mathematician, a singularity is simply a point where a function breaks down, as 1/x does when x gets close to zero. The defining property of a singular point is that it’s impossible to predict what happens beyond it. But are the singularities in mathematicians’ equations just an abstract concept? Or do they occur in nature?

spiral_620

Flickr user slightly-less-random, adapted under a Creative Commons license.

The word “singularity” was popularized in a 2005 book by Ray Kurzweil, who uses it to refer to an impending revolution in artificial intelligence (AI). According to Kurzweil, once artificial intelligences become smart enough to improve their own kin, a feedback loop will lead to a runaway process. After that, all bets are off: nobody knows what will happen. But Kurzweil’s technological singularity, if it comes to pass, is not a true singularity. There is no law of nature that limits our ability to predict what might happen once AI evolves past the “singularity” point; we’re confined instead by the limits of the human mind.

Though they sound exotic, mathematical singularities are actually common in solutions to all but the simplest equations in physics. The formation of shock waves and cracks, and even the motion of a billiard ball bouncing off a hard wall, can contain singularities. While these singularities fulfill the mathematical definition, they aren’t physically real either: they arise from idealized assumptions that physicists make to force the messy world of reality into the neat one of mathematics. In reality, no crack is perfectly sharp, no wall is perfectly hard, no shock wave is perfectly localized.

Here is another example: Turn down the water on your kitchen tap until it starts dripping. The hydrodynamical equation describing the surface of the drops has a singularity at the pinching point: you cannot from one drop predict where the next will be. But this singularity, too, can be avoided by applying a more suitable theory. Using atomic physics, you could, in principle, calculate exactly how the water stream breaks apart on the level of single atoms. All these singularities are thus artifacts of using a theory outside its range of applicability, on distances so short that a more precise theory would be needed.

The one type of singularity that might be real—that physicists don’t know how to resolve—is the one that appears in Einstein’s theory of General Relativity when matter collapses under the gravitational pull of its own weight. There is nothing in General Relativity that then stands in the way of this collapse. It will continue until all the matter is located at a single point of infinite matter density and infinite space-time curvature: a singularity.

The singularities that appear inside black holes pose a big problem for physicists. Crossing a black hole’s event horizon is like jumping into a river upstream of a waterfall, at a place where the water flows faster than you can swim. Whatever you do, you’ll end up being pulled down the waterfall. Likewise, whatever falls into a black hole is pulled down into the singularity. And once there, it reaches its end.

At the black hole singularity every particle’s path seems to dead-end. Space-time stops at the singularity, and nobody knows what happens at this point.  Yet we cannot imagine how something can just end. The black hole space-time is for this reason referred to as “incomplete,” but in General Relativity there is no way to complete it. This is the origin of the black hole information loss problem: It is the horizon that makes the information irretrievable, but it is the singularity that ultimately annihilates it. This is a big headache for physicists because such annihilation of information is incompatible with quantum mechanics.

The Big Bang is a singularity, too. If you run the expansion of the universe which we observe today backwards, then the density of matter must have been larger the younger the universe was, all the way back to an initial moment where the density must have been infinitely high: it must have been singular.

Are these singularities real, or just vestiges of the gap between math and reality? Based on their experience with other systems, physicists suspect that the singularities in General Relativity are a warning, a tip-off that we need another theory to describe the physics in the extreme situations when gravity is very strong and its quantum effects are very large. Physicists still don’t know how to describe the quantum effects of gravity, but we hope that by doing so we will one day resolve the singularities.

None of our measuring devices can show an infinite value. Not only have we never observed it, we don’t know how to observe it—we don’t know how to even give meaning to such an observation. Physicists therefore treat singularities as symptoms of an ill theory in need of a cure. It would be possible to mathematically deal with the singularities. But based on past experience and intuition, for all we know so far, nature doesn’t like sudden ends. Does nature make an exception for black holes? Right now, we just don’t know.

Why Is Our Universe Filled With Spirals? (ZT)

Why Is Our Universe Filled With Spirals?

spiral-galaxy

The spiral galaxy M81 as seen through a combination of X-ray, optical, ultraviolet and infrared imaging techniques. 

Can you tell me why a spiral design seems omnipresent in our natural world and in the universe? I see this pattern in plant tendrils, flowers and leaves, pinecones, the unfurling of needles, as well as in astronomy. 

— Dorothea Fox Jakob, Toronto

The short answer is, sadly, we don’t really know. Nature does seem to have quite the affinity for spirals, though. In hurricanes and galaxies, the body rotation spawns spiral shapes: When the center turns faster than the periphery, waves within these phenomena get spun around into spirals.

The florets in a sunflower head also form two spirals, but there’s no rotation here — it’s simply an efficient packing solution for the plant. With 55 florets running clockwise and 34 counterclockwise, the sunflower is an example of a pattern of numbers called the Fibonacci sequence, named after the medieval mathematician who popularized it. It’s a simple pattern with complex results, and it is often found in nature.

The Fibonacci sequence starts with 0 and 1 and increases based on the sum of the previous two numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21 and so on. You’ll notice that both groups of florets in a sunflower match Fibonacci numbers — as do the number of rows in a pinecone, the arrangement of leaves on a stem and many other natural formations. In fact, the spiral shape itself is built upon the rapidly increasing pattern of the Fibonacci sequence.

But since nature’s swirly patterns result from a few different mechanisms, the phenomenon is likely coincidence more than some underlying physical property of the universe. Nevertheless, it is striking that many natural examples follow this number sequence, either broadly in their curling shape or with their actual numerical values.

[This article originally appeared in print as “Ask Discover.”]

Snowcrystal

Snow flakes
 About the author

Kenneth G. Libbrecht is a professor of physics at the California Institute of Technology (Caltech). A North Dakota native, Ken studies the molecular dynamics of crystal growth, including how ice crystals grow from water vapor, which is essentially the physics of snowflakes. He has authored several books on this topic, including The Snowflake: Winter’s Frozen Artistry, The Secret Life of a Snowflake, The Art of the Snowflake, and Ken Libbrecht’s Field Guide to Snowflakes. He can be reached at kgl@caltech.edu.