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regex - Vim search and replace, adding a constant - Stack Overflow
Thanks to str2float() a single addition is done on the whole number (in other words, 1.15 + 2.87 will give the expected result, 4.02, and not 3.102).
arithmetic  vim  howto  maths 
november 2018 by aries1988
How many dimensions are there, and what do they do to reality? – Margaret Wertheim | Aeon Essays

Yet the notion that we inhabit a space with any mathematical structure is a radical innovation of Western culture, necessitating an overthrow of long-held beliefs about the nature of reality. Although the birth of modern science is often discussed as a transition to a mechanistic account of nature, arguably more important – and certainly more enduring – is the transformation it entrained in our conception of space as a geometrical construct.

What is so extraordinary here is that, while philosophers and proto-scientists were cautiously challenging Aristotelian precepts about space, artists cut a radical swathe through this intellectual territory by appealing to the senses. In a very literal fashion, perspectival representation was a form of virtual reality that, like today’s VR games, aimed to give viewers the illusion that they had been transported into geometrically coherent and psychologically convincing other worlds.

In Newton’s world picture, matter moves through space in time under the influence of natural forces, particularly gravity. Space, time, matter and force are distinct categories of reality. With special relativity, Einstein demonstrated that space and time were unified, thus reducing the fundamental physical categories from four to three: spacetime, matter and force. General relativity takes a further step by enfolding the force of gravity into the structure of spacetime itself. Seen from a 4D perspective, gravity is just an artifact of the shape of space.

General relativity says that this warping is what a heavy object, such as the Sun, does to spacetime, and the aberration from Cartesian perfection of the space itself gives rise to the phenomenon we experience as gravity.

Whereas in Newton’s physics, gravity comes out of nowhere, in Einstein’s it arises naturally from the inherent geometry of a four-dimensional manifold; in places where the manifold stretches most, or deviates most from Cartesian regularity, gravity feels stronger. This is sometimes referred to as ‘rubber-sheet physics’. Here, the vast cosmic force holding planets in orbit around stars, and stars in orbit around galaxies, is nothing more than a side-effect of warped space. Gravity is literally geometry in action.

Aristotle was right – there are indeed logical problems with the notion of extended space. For all the extraordinary successes of relativity, we know that its description of space cannot be the final one because at the quantum level it breaks down. For the past half-century, physicists have been trying without success to unite their understanding of space at the cosmological scale with what they observe at the quantum scale, and increasingly it seems that such a synthesis could require radical new physics.

Like Newton’s world picture, Einstein’s makes space the primary grounding of being, the arena in which all things happen. Yet at very tiny scales, where quantum properties dominate, the laws of physics reveal that space, as we are used to thinking about it, might not exist.
physics  dimension  maths  future  science 
january 2018 by aries1988






2007年,陶哲轩写了一篇文章名为“Why global regularity for Navier-Stokes is hard”的博客。在这篇文章中,他认为求解类似NS方程这种的偏微分方程组就像寻找一个大尺度的定量的可以模化的特性,来对不可以预测的行为进行限定。


fluid  mechanics  explained  maths  research 
december 2017 by aries1988
Du bon sens en mathématiques
Vivant et pédagogique, Jordan Ellenberg explique comment éviter des pièges de la vie courante grâce aux statistiques et à la logique.
book  maths  life 
october 2017 by aries1988
Aerodynamics For Cognition |
By studying how birds fly and the structure of their wings, you can learn something important about aerodynamics. And what you learn about aerodynamics is equally relevant to then being able to make jet engines.                                 

The kind of work that I do is focused on trying to identify the equivalent of aerodynamics for cognition. What are the real abstract mathematical principles that constrain intelligence? What can we learn about those principles by studying human beings? 

We already do this to some extent. If you’ve ever used the strategy of gamification, where you’re using an app or something that gives you points for completing tasks, or if you make a to-do list and you get satisfaction from checking things off, what you’re doing is essentially using this external device as a mechanism for changing the environment that you’re in.

What machine-learning algorithms do when they're solving this problem is recognize that the thing you should be doing is exploring more when you first arrive in the city and exploiting more the longer you are in the city. The value of that new information decreases over time. You're less likely to find a place that is better than the places you've seen so far, and the number of opportunities that you're going to have to exploit that knowledge is decreasing.

My colleague Alison Gopnik, who has been pursuing this, has a hypothesis about cognitive development. When we look at children, that variability and randomness that we see is exactly a rational response to the structure of the problems they're trying to solve. If they're trying to figure out what are the things in their environment that they will most enjoy, then putting everything in their mouth is a pretty good strategy in terms of maximizing their exploration.

In the first half of the 20th century, it was disreputable to try to study how the mind works because minds were things that you never saw or touched or intervened on. What you could see was behavior and the environment that induces that behavior, so the behaviorist psychologists said, "Let's get rid of the mind. Let's just focus on these mappings from environment to behavior." That's where a lot of behavioral data science is. If I show you this, then you click on this. If you've seen these webpages, then you're likely to go to this webpage. It's a very behaviorist conception of what underlies the way that people are acting.

In Australia, in the last year of high school, you have to make a decision about what you want to study at university. It was 1994, I was sixteen years old, and I had no idea what I wanted to do. I knew that I liked math, but I certainly didn't want to make a commitment to doing that for the rest of my life. I said, "Okay, I'll study the things that we don't know anything about—philosophy, psychology, anthropology." That was what I went to university to do.

One of the ways in which human beings still outperform computers is in being able to solve problems of reasoning about why you did the thing you did, what you're going to do next, what the underlying reasons were behind things that you did.

We as human beings are used to being surrounded by intelligent systems whose thoughts are opaque to us. It's just that normally those intelligent systems are human beings.
ai  thinking  research  human  interaction  communication  motivation  consciousness  brain  maths 
october 2017 by aries1988
Emprunts : mensualités, intérêt, taux, TEG, risque de taux - Images des mathématiques - CNRS
Ou comment impressionner son banquier

Comprenons le principe d’un tel prêt. Chaque mois vous versez une mensualité constante que l’on va chercher à déterminer, on la considère pour le moment comme une inconnue. Cette mensualité sert d’abord à vous « mettre à jour » avec la banque en lui versant la rétribution due ce mois-là pour la somme que vous restiez lui devoir depuis le mois précédent. Une fois « quitte » avec la rétribution de la banque, le reste de la mensualité sert à rembourser une partie du capital prêté (qui diminue ainsi progressivement, on parle de prêt à amortissement progressif). Tout cela est calculé pour que vous ayez remboursé la totalité à la mensualité N.

On est parfois surpris de constater, en recevant son « tableau d’amortissement », que l’on rembourse au début beaucoup d’intérêt et peu de principal. Vu le principe de ces prêts, c’est normal, puisque chaque mois, on paye l’intérêt sur la somme que l’on devait encore le mois précédent, très forte au début et faible à la fin.

Ceci explique sans doute que les prêts sur des durées supérieures à 20 ans, jusqu’à 30, ne soient vraiment apparus que ces 10 dernières années, avec la chute des taux de prêt.

Cette information doit être utilisée avec précaution et ne permet pas de comparer deux prêts s’ils ont des durées différentes. En effet cette information dit certes combien on va donner à la banque, mais pas à quel moment ! Or un banquier sait bien (c’est son cœur de métier) qu’à cause de l’inflation et des placements sûrs, une même somme en euros n’a pas vraiment la même valeur selon la date à laquelle on la reçoit.

les intérêts sont versés chaque année et portent à leur tour intérêt : ce sont les fameux intérêts composés

Donc attention, la donnée qui traduit vraiment l’effort de la banque, c’est le taux d’intérêt. C’est pour cela que c’est ce que l’on négocie âprement avec son banquier, ou que les informations données dans les sites Internet sur les prêts sont exprimées en taux.

Savez-vous que lorsqu’un commerçant vous propose un crédit gratuit supérieur à 3 mois, ceux qui payent comptant doivent se voir proposer un escompte ?

Comment comparer ces deux prêts de durée différente ? En calculant un taux d’intérêt assurance comprise, bien sûr.

Comment faire ? Pour chaque prêt vous calculez la mensualité à l’aide de 2, puis vous ajoutez le montant de l’assurance, et vous calculez comme on l’a vu plus haut le taux correspondant au total prêt + assurance.
learn  maths  home  finance  money  budget  immobilier  explained  law  moi 
september 2017 by aries1988
How Checkers Was Solved
“From the end of the Tinsley saga in ’94–’95 until 2007, I worked obsessively on building a perfect checkers program,” Schaeffer told me. “The reason was simple: I wanted to get rid of the ghost of Marion Tinsley. People said to me, ‘You could never have beaten Tinsley because he was perfect.’ Well, yes, we would have beaten Tinsley because he was only almost perfect. But my computer program is perfect.”

And then there is his most quotable line: “Chess is like looking out over a vast open ocean; checkers is like looking into a bottomless well.”
ai  competition  duel  engineering  game  genius  human  maths  story 
august 2017 by aries1988
Maryam Mirzakhani’s Pioneering Mathematical Legacy
Siobhan Roberts speaks with colleagues of the late Maryam Mirzakhani, the only woman ever to win the Fields Medal, the highest honor given to mathematicians.
maths  female  iran  research  talent 
july 2017 by aries1988
Le mathématicien Yves Meyer reçoit le prix Abel
La « théorie des ondelettes » du Français a révolutionné la compression des données audiovisuelles.
march 2017 by aries1988
A history of nothing: how zero went from nil to something | Aeon Videos
From ancient trade to modern theoretical physics and computer programming, the history of mathematics closely mirrors the history of zero – first as a concept, and then ultimately as a number. Narrated by the UK mathematician Hannah Fry, this short animation explores how the evolution of the understanding of zero has helped shape our minds and our world.
maths  video  india  arab 
may 2016 by aries1988
Eugenia Cheng Makes Math a Piece of Cake
CHICAGO — We had just finished the mathematician Eugenia Cheng’s splendid demonstration of nonassociativity where the order of operations counts — as it does…
story  maths  uk  usa  dessert  cuisine  book  female 
may 2016 by aries1988
New Biggest Prime Number = 2 to the 74 Mil ... Uh, It’s Big
Prime numbers are crucial to fields like cryptography, but this one is so big that it has no practical use, at least not anytime soon. (The Gimps software does have a practical use, playing a key role in uncovering a flaw in Intel’s latest Skylake processors.)
maths  discovery 
february 2016 by aries1988
How to get rich with maths
Exponential growth can make or break you. Get your head around it early enough and you could retire as a millionaire
january 2016 by aries1988
How maths can help you create the perfect Christmas Day | New Scientist
But what if you want to guarantee a larger number of friends or strangers? Over the years mathematicians have tried to calculate the Ramsey numbers, R(m,n), which tell you the number of people, R, needed to ensure m friends or n strangers, but it’s tricky. The number of possibilities grows so rapidly as the size of your party increases that while R(4,4) is known to be 18, mathematicians have only pinned R(5,5) down to between 43 and 49. Hungarian mathematician Paul Erdős once said that if aliens demanded an accurate calculation of R(5,5) within a year to deter an invasion, we could probably just about do it – but if they demanded R(6,6), we would be better off launching a pre-emptive attack.
fun  christmas  maths  instapaper_favs 
december 2015 by aries1988
typography - Should subscripts in math mode be upright? - TeX - LaTeX Stack Exchange
Using "all italics" is unfortunately an often committed sin. You should italicize only variables.

Everything else should be upright. For example:

function names (sin, cos, log, ln etc...)
dimensionless numbers (Re, Pr, Ra...)
exact infinitesimal increments (dx, dy et... in BOTH integrals and differentials)
descriptive text
all descriptive variable indices (unless they are also variables)
Exceptions to this rule may still apply, i.e. the Euler-number $e$ is no variable, but still traditionally written in italics.
best  practice  latex  maths 
september 2015 by aries1988
The Singular Mind of Terry Tao
in the process, he will have also solved the Navier-­Stokes global regularity problem, which has become, since it emerged more than a century ago, one of the most important in all of mathematics.

‘‘A very central part of any mathematician’s life is this sense of connection to other minds, alive today and going back to Pythagoras,’’ said Steven Strogatz, a professor of mathematics at Cornell University. ‘‘We are having this conversation with each other going over the millennia.’’

Long ago, mathematicians invented a number that when multiplied by itself equals negative 1, an idea that seemed to break the basic rules of multiplication. It was so far outside what mathematicians were doing at the time that they called it ‘‘imaginary.’’ Yet imaginary numbers proved a powerful invention, and modern physics and engineering could not function without them.
maths  idea  fluid 
august 2015 by aries1988
Embedding a Torus (John Nash) - Numberphile
This videos features James Grime with a little bit of Edward Crane. Ed's full discussion of Nash and embedding: Nash shared both...
video  maths 
june 2015 by aries1988
Bamboo Mathematicians
In the late 1960s, a species of bamboo called Phyllostachys bambusoides--commonly known as the Chinese Mainland Bamboo or Japanese Timber Bamboo--burst into flower. The species originated in China,...
biology  evolution  model  maths 
may 2015 by aries1988
Michio Kaku: Is God a Mathematician?
Don't miss new Big Think videos! Subscribe by clicking here: Michio Kaku says that God could be a mathematician: "The mind of God we…
physics  maths 
may 2015 by aries1988
Slime Mold Grows Network Just Like Tokyo Rail System | WIRED
The researchers then borrowed simple properties from the slime mold’s behavior to create a biology-inspired mathematical description of the network formation. Like the slime mold, the model first creates a fine mesh network that goes everywhere, and then continuously refines the network so that the tubes carrying the most cargo grow more robust and redundant tubes are pruned.

Fricker points out that such a malleable system may be useful for creating networks that need to change over time, such as short-range wireless systems of sensors that would provide early warnings of fire or flood. Because these sensors are destroyed when disaster strikes, the network needs to efficiently re-route information quickly. Decentralized, adaptable networks would also be important for soldiers in battlefields or swarms of robots exploring hazardous environments, Fricker says.
maths  transport  metro  tokyo  biology 
february 2015 by aries1988
Femmes, échecs et maths
En France comme dans la plupart des pays, les filles sont les grandes absentes des filières scientifiques, au lycée comme dans l'enseignement supérieur. En 2012, elles ne représentaient que 38 % des effectifs des terminales S spécialité mathématiques, 29,7 % des effectifs des classes préparatoires scientifiques aux grandes écoles, 28 % des élèves diplômés d'une école d'ingénieur, et 27 % des titulaires d'une licence professionnelle en sciences. Le déséquilibre est tel que, depuis 2000, la mixité des formations est l'un des chantiers prioritaires des conventions interministérielles sur l'égalité.

Quand une fille échoue en maths, ses parents se désolent pour ses études en général, pour le bac à obtenir... Alors que si c'est un garçon, il semble que leur narcissisme de parents soit atteint : l'image idéale du garçon qui devrait être fort en maths est touchée. Ce préjugé est moins explicite aujourd'hui qu'il y a vingt ans, mais il continue cependant à exercer ses effets de manière sournoise.
today  maths  debate  france  education  children  parenting  female 
november 2014 by aries1988
Mathématiques françaises : une excellence à préserver
Plusieurs médaillés français possèdent la double nationalité : franco-russe pour Maxime Kontsevitch (2006), franco-vietnamienne pour Ngô Bao Chaû (2010) et franco-brésilienne pour Artur Avila (2014). Témoins de la vitalité des mathématiques françaises, ces résultats sont d'autant plus remarquables qu'ils s'inscrivent dans un contexte international de plus en plus concurrentiel. Ils résultent d'un travail de très longue haleine de structuration de la communauté mathématique française.

En 2010, ce prix a été remis à Yves Meyer, professeur émérite à l’Ecole normale supérieure de Cachan et membre de l’Académie des Sciences pour ses travaux sur les ondelettes, qui ont révolutionné le traitement du signal utilisé notamment dans le traitement de l’image et de la vidéo. Pour ce mathématicien « l’avenir des mathématiques réside dans une sorte de respiration avec toutes les sciences et toutes les technologies » et il donne l’exemple de l’apport des mathématiques dans le domaine des neurosciences où pour lui « la compréhension du cerveau progresse et progressera grâce à la modélisation mathématique, seule à même d’envisager et de structurer des mécanismes dont la description ...

Développer l'attractivité française de la discipline, susciter des vocations auprès des plus jeunes, mettre cette excellence au service de l'innovation, renforcer la place des femmes, sont autant de défis qu'il faudra relever pour continuer à faire de la France, une des championnes mondiales des mathématiques.
maths  france  today  excellence 
september 2014 by aries1988
How to crack improbability and win the lottery – David Hand – Aeon
This distinction – between the chance that you (or, indeed, any other particular person) will win the lottery and that someone will win – is a manifestation of what I call the law of truly large numbers. If a large enough number of people each buy a lottery ticket, then the probability that someone will win becomes substantial. It grows so large, indeed, that someone wins almost every week.

If you win the lottery one week with a one-in-14-million chance per ticket, then your chances of winning it the next week are unaltered. Statisticians say that the two events are independent, but another way to put it is that the lottery numbers don’t remember who has won previously: the outcome of one draw doesn’t affect the following one.

The same does not hold for the Titanic. For if one compartment is damaged so that it floods, what does that say about the probability that a neighbouring compartment might also be damaged? Well, clearly our answer depends how the damage occurs. As it happens, the Titanic’s maiden voyage was through iceberg-infested waters. If an iceberg were to strike the side of the ship penetrating the double hull, isn’t there a good chance that it would also damage neighbouring compartments?

We live in a complex world, and the different components of a system are often locked in a web of interconnections that are difficult to tease apart. When trying to make sense of them, it is common to assume independence as a first approximation. But this can lead to major miscalculations. The Yale sociologist Charles Perrow has developed an entire theory of what he calls ‘normal accidents’, based on the observation that complex systems should be expected to have complex, undetected, interactions. A frightening thought.
probability  maths  science  explained  disaster 
june 2014 by aries1988
 在北大混了四年,一事无成;在未名上也呆了快一年了,制造了几千篇的垃圾。要毕业的人想法总是奇怪的,譬如说竟然真的要正经的写几篇文章了。最初写成这些东西的时候,我发给了几个朋友,一个学数学的师弟说他很感动,一个非数学系的mm说他后悔当初没有选数学系,无论怎样,他们能这样子讲,我很感动,这是发自内心的那种。现在的打算是每天贴2-3个故事,一直到欧毕业那天。很多事情难免有些too old,这个我也没有办法,激动人心的事情毕竟只有那么多。   不多说了,真心的希望大家会喜欢,哪怕只有一点点的喜欢。这些文字偶给了一个名字,叫做“偶心目中的英雄---Heroes in My Heart”
maths  scientist  story 
november 2012 by aries1988
這就是所謂的大數法則:在二項分布的機率模型假定之下,只要實驗的次數 n 夠大,則事件發生的次數比 ,從機率的觀點來看,就會很接近 p 值。這是機率論萌芽初期的一個重要定理,它由 Jakob Bernoulli(1654~1705年)首先證得完整,而在他死後發表於1713年。可注意者,Chebyshev(1824~1894年)是十九世紀的數學家,生在 Bernoulli 之後,我們用他的不等式反推 Bernoulli 的大數法則是有違歷史順序的。不過 Chebyshev 不等式非常簡單,而且很容易推廣到其他的機率分布,正足以說明大數法則的基本所在。
maths  explained 
november 2012 by aries1988
 ----------------------------------------   给那些喜欢数学和不喜欢数学的人们   给那些了解数学家和不了解数学家的人们。   ----------------------------------------
story  maths  scientist 
october 2012 by aries1988
Skepticblog » The Colorado Massacre, Gun Control, and the Law of Large Numbers
A large-numbers analysis allows us to understand on a societal-level scale why such events happen randomly and without any specific cause common to all (drugs, gangs, bullying, depression, psychopathy, psychosis, violent video games, and the like). History and population demographics for rates of mass murder show that Aurora-size events are going to happen again and again and again, and there is no way to predict who is going to do it, where, or when.

When the Second Amendment was written stating that citizens have a right to “keep and bear arms,” rifles took over a minute to load one bullet at a time. The most crazed 18th century American could not possibly commit mass murder because no WMMs existed at the time.
googlereader  guns  violence  usa  maths  numbers  psychology  opinion  debate 
august 2012 by aries1988
game  life  family  maths 
august 2012 by aries1988
august 2012 by aries1988
Why should I be using TeX for graphics?
By this time I hope it is clear that so much is possible, thanks to the excellent work of so many people. We are capable of producing little gems of graphics ourselves, thereby enrichting our already beautiful typography using TeX. This is a revolution that has been ongoing for the last couple of years, rendering everything accessible to the public. And I hope you are convinced to try some of it yourself for your next paper, course notes, thesis or book.
maths  review  drawing  graphics  overview  text 
june 2012 by aries1988
很多中国人是从徐迟的一篇报告文学中知道哥德巴赫这个名字的。在这篇文章里,徐迟讲述了数学家陈景润刻苦钻研,终于在哥德巴赫猜想研究上取得重大突破的真实故事。文章最初刊登在《人民文学》杂志 1978 年第 1 期上,标题就是“哥德巴赫猜想”,《人民日报》和《光明日报》随即转载,一时间传遍全国。
november 2011 by aries1988
war  maths  modelisation 
august 2011 by aries1988
“想象一个小球,仅受重力,从点 A 出发沿着一条没有摩擦的斜坡滚至点 B。怎样设计这条斜坡,才能让小球在最短的时间内到达点 B?”
maths  physics 
april 2011 by aries1988
我不是一个数学家。我甚至连数学专业的人都不是。我是一个纯粹打酱油的数学爱好者,只是比一般的爱好者更加执着,更加疯狂罢了。初中、高中一路保送,大学不在数学专业,这让我可以不以考试为目的地学习自己感兴趣的数学知识,让我对数学有如此浓厚的兴趣。从 05 年建立这个 Blog 以来,每看到一个惊人的结论或者美妙的证明,我再忙都会花时间把它记录下来,生怕自己忘掉。不过,我深知,这些令人拍案叫绝的雕虫小技其实根本谈不上数学之美,数学真正博大精深的思想我恐怕还不曾有半点体会。
education  learn  maths  explained 
april 2011 by aries1988
maths  turbulence  moi 
january 2011 by aries1988
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