tim

NBA 健身 汽車文化

[Juanlu_CabanillasGar @JuanluCaba_Unex]

📊 Multiple Linear Regression – A Complete Guide 👇

[Jonathan.S⚡️ @wenjie8964]

你没有敌人？

刘晓波在法庭上的最后陈述“我没有敌人”，已经成为中国当代政治史上最著名的文本之一。许多人将其视为一种崇高的道德宣言。

作为他曾经的学生。我理解这种赞赏，也尊重其中所体现出的宽恕精神。

然而，如果从政治学而非伦理学的角度审视，这句话却暴露出一个根本性的问题：它缺乏政治人物应有的自觉。

卡尔·施米特曾指出，政治的本质并不在于善恶、美丑或真伪，而在于朋友与敌人的区分。一个政治共同体之所以能够存在，正是因为它能够界定自身的边界，能够回答“我们是谁”以及“谁不是我们”。

政治首先不是关于爱与恨，而是关于权力、归属和决断。当一个共同体面临生存挑战时，敌我关系便不再是一种主观感受，而成为一种客观现实。

因此，从施米特的视角出发，“我没有敌人”首先面对一个无法回避的问题：如果你没有敌人，那么是谁将你判处十一年徒刑？如果答案是国家机器，那么敌我关系事实上已经存在。

它并不会因为当事人的否认而消失，更不会因为道德上的宽恕而解除。战争不会因为一方宣布自己没有敌人而结束，监狱也不会因为囚犯拒绝承认敌人的存在而自动打开大门。政治事实始终独立于个人意志而存在。

刘晓波的问题并不在于过于善良，而在于试图用伦理语言取代政治分析。宽恕是一种伦理行为，爱仇敌是一种宗教实践，但它们无法取消权力关系本身。

事实上，“我没有敌人”混淆了两个截然不同的命题。一个命题是“我拒绝仇恨任何人”，另一个命题是“我没有敌人”。前者是一种道德选择，后者却是一种政治判断。一个人完全可以拒绝仇恨自己的敌人，同时清醒地承认敌人的存在。两者并不矛盾。

历史上的政治人物大多明白这种区别：林肯在美国内战期间并不以个人仇恨看待南方，但他从未否认双方处于敌对状态；丘吉尔也不需要以私人情绪面对德国人民，但他必须承认纳粹德国是英国的敌人。

政治人物的首要责任不是表达自己的善意，而是准确认识现实，并据此作出判断与行动。

从这个意义上说，“我没有敌人”更像是一位道德见证者的宣言，而不是一位政治行动者的宣言。

刘晓波在其中展现出的宽恕精神无疑值得尊敬，但这种精神并不能代替对政治结构的认识。

一个拒绝界定敌我的政治运动，往往也难以形成真正的政治力量，因为它无法清晰说明压迫来自何处，责任由谁承担，也无法明确自身所要改变的对象究竟是什么。

当政治问题被完全转化为道德问题时，政治行动最终便容易退化为道德表达。它或许能够感动人，却未必能够改变现实。

当然，这并不意味着刘晓波的个人价值因此被否定。恰恰相反，在充满仇恨、斗争和报复叙事的中国政治传统中，他所表现出的宽恕与克制显得格外珍贵。

然而，政治学与伦理学终究属于不同的领域。作为一种道德宣言，“我没有敌人”具有令人敬佩的高度；作为一种政治判断，“我没有敌人”却难以成立。

因为在政治世界里，最危险的事情从来不是你是否承认敌人的存在，而是在你宣布自己没有敌人的时候，敌人早已把你视为敌人。

[The Math Mastery @naturevx0]

Logarithms Formulas Sheet

[朱韵和 @zhu0588]

傅斯年：苏联究竟是一个什么国家？
它是一个以意识形态为外衣、以专制统治为内核、以领土扩张为传统的帝国。世间总有许多人，把苏联当成一个理想国，以为他是人类前途的曙光。我觉得这是极大的错误，现在把我的观察写出来，以供国人参考。

第一，苏联不是共产主义国家，乃是国家资本主义加上新式专 制。所谓共产主义，是各尽所能、各取所需；苏联现在是严格的阶级制度，官僚高高在上，工人农民劳苦终日，生活程度极低，绝无平等可言。一切生产机关归国家所有，实则归党部官僚支配，这是最彻底的国家资本主义，而非共产。

第二，苏联的政治，是极端的寡头专制。表面上有苏维埃，实际上一切权力集中于少数人之手，最后集中于一人。人民没有言论自由，没有出版自由，没有集会自由，没有迁徙自由。全国布满特务机关，人人被监视，稍有异见，便遭放逐、监禁、流放西伯利亚，甚至处决。这样的政治，绝不是近代文明政治，乃是近代最严密的专制。

第三，苏联的民族政策，是大俄罗斯主义的变相侵略。口头上提倡民族自决，实际上压制各少数民族，强制俄化，兼并土地，控制经济。继承沙皇俄国的扩张传统，只是换了一个主义的外衣，野心丝毫未减。

第四，苏联的国际作风，是以世界革命为名，行国家扩张之实。他在各国培植共产党，不是为了解放当地人民，而是为了做苏联的外围、做苏联的棋子。凡是有利于苏联地缘扩张的，就鼓动动乱；不利于他的，便随时出卖别国革命。外交毫无信义，只讲利害，不讲道义。

总而言之：苏联不是理想国，乃是集近代政治罪恶、经济压迫、思想禁锢、领土扩张之大成的一个强国国家。

我们中国人对苏联，不必盲目崇拜，也不必无端仇视，只当认清他的本质：他是一个以意识形态为外衣、以专制统治为内核、以领土扩张为传统的帝国。

认清这一点，然后可以定我们对苏的国策，不被空想迷惑，不被宣传裹挟。

（1933年9月3日，《独立评论》第66号）
注：此文发表于1933年，当时斯大林统治下的苏联正进行第一个五年计划与农业集体化。傅斯年根据其在欧洲的观察，写下这篇极具前瞻性的批判文章。后来收入《傅斯年全集》。

图：1932年，斯大林在他的办公室里。

[ScieVision @scievision369]

Polar Coordinates ✍️

Most people learn to describe locations using horizontal and vertical distances from a reference point. You go this far right and this far up, and you reach your destination. But imagine you are a lighthouse keeper describing the position of ships at sea. You would naturally say the ship is three miles away in the northeast direction. You would not break it into separate horizontal and vertical components. This natural way of describing locations using a distance and a direction is exactly what polar coordinates do. Every point in a plane is described by two numbers: how far it is from a central origin point called r, and what angle it makes from the rightward horizontal direction called theta. All points at the same distance from the origin form a perfect circle, and all points at the same angle form a straight line radiating outward from the center.

This system becomes very powerful for problems that have circular or radial symmetry. The gravitational pull around a planet, the electric field around a charged particle, the heat spreading through a circular disk, the ripples expanding from a stone dropped in water, and the quantum structure of atoms all radiate outward from a central point. Describing these phenomena using the horizontal-vertical system makes you fight against the natural symmetry of the problem. Describing them in polar coordinates allows you to work with the symmetry, often turning a complicated problem into a simple one.

In polar coordinates, there are two natural perpendicular directions that are different from the fixed horizontal and vertical directions of the ordinary system. The radial direction points directly away from the origin through your current location and changes as you move around the plane. If you are to the upper right of the origin, the radial direction points upper-right. If you are directly below the origin, the radial direction points downward. The angular direction is always perpendicular to the radial direction and points counterclockwise, tangent to the circle passing through your current location. Both directions rotate and shift as you move from point to point, making calculus in polar coordinates geometrically richer than in the ordinary system where the directions stay fixed.

The gradient is a mathematical operation that takes a function describing a physical quantity like temperature or electric potential and produces an arrow at each point showing the direction of steepest increase and how steep that increase is. In polar coordinates, this arrow has two contributions. The first comes from how quickly the function changes as you move directly outward or inward from the origin. The second comes from how quickly it changes as you rotate around the origin at a fixed distance. This second contribution needs to be divided by the radius because at large distances from the origin, a small rotation sweeps through a large physical arc, while at small distances the same rotation sweeps through a tiny arc. The gradient must measure change per unit actual physical distance rather than per unit angle, so this geometric correction is important.

The Laplacian is a more complex operation that measures at any point whether the function value there is higher or lower than the average of its immediate surroundings. If the Laplacian is positive, the point sits in a local valley, cooler or lower than its neighbors. If negative, it sits on a local peak, hotter or higher than its neighbors. If zero, it exactly matches the average of its surroundings. This simple idea of local averaging has significant physical consequences. Temperature at equilibrium has zero Laplacian everywhere because no point can be persistently hotter or cooler than its neighbors once equilibrium is reached. Electric potential in areas without charges has zero Laplacian.

[SolvingForZ @SolvingForZ]

👏👏👏

[中美对标 @new_voa]

我以前一直以为，《红色轮盘》最大的价值，是曝光了温家宝家族财富。
后来发现，我可能读错了。
我一直想不通一件事。
如果沈栋只是想救段伟红，为什么偏偏在她仍然被控制的时候出版《红色轮盘》？
直到把整本书按时间线重新排列，我才发现：
出版时间、宣传路径、财富地图、四年茶叙……这些看似毫无关系的内容，其实都在完成同一件事。
这本书真正挑战的，也许从来不是某一个人，而是整个中南海。
沈栋真正公开的，不是财富，而是财富怎样变成了一件政治武器。
当我把王岐山四年的茶叙、《纽约时报》的报道，以及段伟红掌握的财富地图放到同一条时间线上，一个以前从没人认真讨论过的问题突然浮现出来：
这本书真正想告诉中南海的，到底是什么？
这期节目，就是我的答案。
https://t.co/59JFZe7iVH

[心灵书舫 | SoulSloop @SoulSloop99]

告诉你一个冰冷的现实：“有研究表明，人活到50岁的概率为92%，活到60岁的概率为83%，能活到70岁的概率是44%，活到80岁的概率是18%，活到90岁是1%，活到100岁的概率是0.6%。

也就是说，有一半左右的人是活不过70岁的，所以说人这辈子很快会过去，珍惜当下，活好人生中的每一天非常重要。”

一组冰冷又真实的数据，瞬间撕碎了人们对“来日方长”的美好幻想。我们总以为人生漫漫、岁月悠长，总觉得还有无数时间可以挥霍、无数机会可以重来，总习惯性把遗憾留给明天、把期许寄于未来。可冰冷的概率告诉我们，人生从无永恒，岁月极其有限，大半人的一生，不过短短七十余载。生命是一场不可逆的单程旅途，没有彩排、没有重来，转瞬即逝便是常态。

莎士比亚曾说：“在时间的大钟上，只有两个字——现在。”过往是无法改写的旧章，未来是难以笃定的期许，唯有当下的每一分、每一秒，是我们真正能够掌控、切实拥有的人生财富。很多人终其一生，都在为过往懊悔、为未来焦虑，终日深陷精神内耗，却唯独忽略了触手可及的当下。纠结曾经的得失、忧虑未知的风雨，白白耗费了有限的光阴，等到岁月老去、韶华不再，才惊觉一生匆匆，从未认真活过属于自己的每一天。

杨绛先生曾坦言：“人生就是一场体验，请你尽兴就好。”生命的本质，从来不是追逐无尽的长度，而是沉淀丰盈的厚度。不必执着长命百岁的执念，不必畏惧岁月老去的常态。七十载光阴，已是人间圆满；平安顺遂一生，便是最大的福气。那些纠结名利得失、困于人情纷扰、沉迷攀比内耗的执念，在生命概率面前，都显得微不足道、毫无意义。

丰子恺有句通透的人生箴言：“不乱于心，不困于情，不畏将来，不念过往，如此，安好。”人生最大的智慧，就是接纳生命的无常，看清岁月的有限，与生活温柔和解。人这一生，风雨起落皆是常态，得失聚散皆是寻常。很多时候，我们的疲惫与痛苦，并非生活太过艰难，而是我们想要的太多、释怀的太少。总盯着未得到的，总遗憾已失去的，却看不见当下拥有的平安、健康与温暖。

梭罗曾说：“过去的已经过去，未来的还未到来，我们唯一能把握的，就是现在。”五十岁之前，我们为生活奔波、为责任奔波，忙着学业、忙着事业、忙着养家糊口，常常身不由己、身疲心累。总想着等有空了再陪伴家人、等安稳了再享受生活、等合适了再奔赴热爱。可生命从不等人人，意外从不打招呼，太多“下次”“以后”，最后都变成了“再也没有”。

数据昭示着残酷真相：能安稳走过古稀之年的人不足半数，高龄长寿更是寥寥无几。这世间最奢侈的幸福，从不是家财万贯、功成名就，而是三餐温饱、身心康健、家人安好。清晨的朝阳、傍晚的晚风、家人的陪伴、平淡的烟火，这些看似寻常的日常，其实都是生命馈赠的稀缺温柔。

稻盛和夫说：“活在当下，行在今日，才是对生命最好的馈赠。”真正的活在当下，不是躺平懈怠、虚度光阴，而是不纠结过往遗憾、不焦虑未来迷茫，全心全意活好眼前的每一刻。认真吃好每一餐、踏实过好每一天，珍惜身边的每一个人，做好当下的每一件事。不浪费光阴在无谓的攀比内耗中，不辜负岁月在无端的纠结焦虑里。

人生最珍贵的从来不是遥不可及的未来，而是转瞬即逝的现在。昨日之日不可留，明日之日未可知，唯有今日最真切。不必叹岁月匆匆，不必忧人生无常，生命的长度无法掌控，但生命的温度与厚度，永远由自己定义。

看过生命的概率，更该读懂生活的真谛：人生短短数十载，不过三万余天，转瞬即逝。往后余生，放下执念、释怀过往、看淡得失。以温柔之心待生活，以从容之态渡岁月。珍惜每一个当下，善待每一次遇见，用心体验生活的烟火，认真奔赴生活的美好，不辜负时光，不亏欠自己，便是此生最好的圆满。

[ScieVision @scievision369]

Hyperbola ✍️

It is one of the four conic sections. These curves form when you slice a double cone with a flat plane at different angles. A horizontal slice produces a circle. A tilted slice yields an ellipse. A slice parallel to the side creates a parabola. A steep slice that cuts through both halves of the double cone produces a hyperbola. This is why a hyperbola consists of two separate curved pieces, called branches. Each branch comes from one half of the cone, and they open away from each other in opposite directions, like two mirror-image curves facing away from a common center.

The key property that identifies a hyperbola is the difference of distances. Take any point on either branch and measure its distance to each of two special anchor points called foci. The difference between those two distances remains the same constant, no matter which point on the curve you choose. This contrasts with an ellipse, where the sum of those distances stays constant. The sum creates a closed oval, while the difference results in two open branches that extend outward indefinitely.

Every hyperbola is centered around a geometric heart known as the center. The center is positioned exactly halfway between the two branches and between all the symmetric pairs of special points. The center is not on the curve itself but serves as the reference point for the geometry, represented as the large blue dot in the diagram. From the center, the key distance called a extends horizontally to the vertices, which are the tips of the two branches and the closest points each branch reaches to the center. Another important distance called b extends vertically to the co-vertices. These auxiliary points lie directly above and below the center but do not fall on the hyperbola itself. They are crucial for understanding its shape. The foci are located farther out from the center than the vertices along the same horizontal axis, always beyond the vertices, unlike in an ellipse.

The two dashed diagonal lines that intersect at the center are the asymptotes. These lines are one of the most visually striking features of a hyperbola. They are straight lines that the branches approach as they extend toward infinity but never actually cross or reach. As you follow either branch farther from the center, it gets closer to one of these diagonal lines, becoming nearly indistinguishable at great distances while always remaining just a bit away. The steepness of the asymptotes affects the shape of the hyperbola. Steep asymptotes create narrow, tightly pinched branches, while shallow asymptotes produce wide, broadly spreading ones. Conveniently, the asymptotes are exactly the diagonal lines drawn through the corners of an invisible central rectangle. This rectangle's horizontal half-width is a, and its vertical half-width is b.

The three key distances—from center to vertex, from center to co-vertex, and from center to focus—are related by the Pythagorean theorem. The focal distance serves as the hypotenuse of the right triangle formed by the center, a vertex, and a co-vertex. This means the focal distance is always longer than either of the other two distances. Hyperbolas appear in nature and technology, from the paths of comets and interstellar objects flying past the Sun too quickly to get captured in orbit, to spacecraft gravity-assist maneuvers around planets, to radio navigation systems that determine positions using the constant difference in signal arrival times from two transmitters, to the uniquely curved cooling towers of power plants designed this way for structural strength while using less material.

[VAN MUTOKA @vanmutoka1]

« On peut éviter la réalité, mais on ne peut pas éviter les conséquences du fait d'éviter la réalité. »Ayn Rand -

[Cosmos Archive @cosmosarcive]

What is gravity?

Newton explained gravity as a force that attracts objects toward one another. His ideas accurately describe everything from falling objects to the motion of planets and remain essential in science today.

Einstein later introduced a deeper perspective. Instead of treating gravity as a force, he showed that mass and energy reshape the fabric of spacetime, causing objects to move along its natural curves.

Newton's theory is remarkably accurate for everyday life. But Einstein's explains the universe on its grandest scales, revealing why light bends around massive objects, why time passes more slowly in strong gravitational fields, and how black holes can exist.

[Physics In History @PhysInHistory]

" If you want to Learn something, teach it !"

[KHALID @H0H0v]

Vivani's Theorem.

It reveals a simple but beautiful truth hidden inside an equilateral triangle by treating distances like pieces of a perfectly balanced puzzle. Imagine picking any point inside the triangle and dropping straight lines (perpendiculars) to each of the three sides. Each of these distances may look different on their own, some short, some long, but together they follow a surprising rule.

No matter where the point moves inside the triangle, the sum of these three distances never changes. It always equals the height (altitude) of the triangle itself. Even though the point shifts around, making one distance grow and another shrink, everything stays in balance, like a constant total being redistributed.

This steady sum acts as a hidden measurement tool. It tells us that the geometry of an equilateral triangle has a built-in harmony, where all internal positions are connected through a single, unchanging value.

[Mathematica @mathemetica]

Functions often approach a steady output as the input nears a particular value without the need to evaluate at that exact spot.

This graphic explains the general definition of the limit for such a function f near point a.
Its graph depicts the curve moving toward height L with x approaching a, paired with the notation lim_{x→a} f(x) = L.

It is used to calculate instantaneous rates of change like velocity in real-world motion problems.

[Sam Mathverse @Sam_Axiom]

🚀 Vector Calculus Series — Part 1

Every expert once started with a single vector.

Today, we build the foundation that makes Gradient, Divergence & Curl finally make sense.

Master the basics now. Thank yourself later.

🧠 Part 1: Vector Calculus Basics
🔁 Repost to help someone learning mathematics.
💬 Drop your questions below!

[Math is Sacred @mathissacred]

Understanding! The Numbers.

[Sam Mathverse @Sam_Axiom]

🧠📚 Mathematics Formula Series – Basics
Differentiation Formulas | Part 1

Differentiation becomes much easier when you remember the core formulas.

Follow us for More.

This cheat sheet brings together the most important basic differentiation formulas in one place, making revision faster and problem-solving more confident.

📌 Save this post for quick revision before your next test or exam.

[Бианка @BiankaB12]

One of my longest-standing arguments is that we are not living in Orwell’s 1984, where truth is centrally suppressed and censored by force (that’s former communist societies, modern-day China, Russia, North Korea).

We are living in something much closer to Huxley’s Brave New World.

The truth is not hidden - it is almost always readily available. But it is buried beneath an industrial quantity of noise: propaganda, outrage, half-truths, conspiracy theories, influencer theatre, algorithmic rage bait and an endless stream of content designed not to inform us, but to keep us emotionally stimulated.

The modern information system does not need to censor the truth when it can simply drown it in noise.

A fact no longer has to be disproven - it only has to be surrounded by a hundred competing claims, stripped of context and nuance, turned into partisan ammunition and pushed into the same feed as celebrity gossip, memes and 15 second videos engineered to deliver the fastest possible dopamine hit. By the time the truth reaches us, it appears as just another piece of content competing for our attention.

That is the more sophisticated form of control: not preventing people from knowing, but exhausting their capacity to care.

Orwell feared a world in which people would be deprived of information. Huxley feared a world in which they would be given so much distraction, stimulation and triviality that they would lose the desire to seek it.

The defining struggle of our age is therefore not simply between truth and censorship, but between truth and indifference.