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##### General Relativity Loud and Clear

If you want to learn about general relativity, there are unfortunately few alternatives other than very complicated textbooks or vague dumbed-down popularization that explains nothing...

##### About numbers, episode 5 : Tensors

Updated (12/09/2016). The (foolish) purpose of this post is to tackle the concept of tensor, while trying to keep it accessible to the widest audience possible. For the layman (or specialist from another field of study) who just wants to know what this is about...

##### Tensors for the noob

If you are here, then it's because you don't like formulas and complicated calculations too much, but you're still curious about what is a tensor. So we will do a quick tour of the concept, in the easiest way possible....

##### About numbers, episode 4 : infinite numbers

« Eternity is really long, especially near the end. » Woody Allen (1935 - ) What is infinity ? How to grasp such a concept, by definition so immense that nothing can contain it ? As surprising as it may seem, the answer lies not...

##### About numbers, episode 3 : rational numbers

What is a fraction ? It seems easy to answer this question with the concept of proportion, but we will see that rational numbers possess some quite extraordinary properties....

##### The myth of Niels Bohr and the barometer question

In 1959 was published in the journal Pride of the American College Public Relations Association an essay entitled Angels on a Pin, by Alexander Calandra, professor of physics at Washington University in St. Louis, Missouri. The story is about a physics student who surprises his...

##### A mathematician’s lament

« The most desperate are the most beautiful lament » (Alfred de Musset, La nuit de Mai, 1835) A mathematician’s lament (2002) is an article from Paul Lockhart, a first-class research mathematician and teacher at Saint Ann’s School in Brooklyn, New York. Not only is it a...

##### About numbers, episode 2 : integers

A quantity of -2 objects, a marathon runner finishing -3rd, numbers smaller than nothing ?! What do negative numbers mean ? The answer to that question is easy only to those who are used to them. And for most of us, it doesn't matter what...

##### Icosian : A graph theory game

The Icosien game is a graph theory game. It was invented in 1857 by Sir W.R.Hamilton (1805-1865), a great mathematician to whom we owe - among other things - a reformulation of mechanics' formalism which now bears his name, and quaternions (which we'll tackle in...

##### What is time ?

« Put your hand on a stove for a minute and it will feel like an hour. Sit with a pretty girl for an hour and it will fly like a minute. That’s relativity. » This famous quote, attributed to Einstein 1 is a good description...

##### About numbers, episode 1 : Natural numbers

« God made the integers, all the rest is the work of man » Léopold Kronecker (1823-1891). There is no satisfying definition of the general concept of number. However, lots of particular numbers can be rigorously defined. Natural numbers, integers, imaginary, transcendent, algebraic, computable numbers,...

##### The father of relativity theory : Einstein vs Poincaré

« We are like dwarfs on the shoulders of giants. » This famous metaphor, attributed to Bernard de Chartres, a XIIth century philosopher, reused by Newton and Pascal among others, is a tribute to savant predecessors and an acknowledgment of the cumulative nature of scientific...

##### The group of special relativity

In its modern interpretation, the principle of relativity is profoundly linked to the group structure of Lorentz transformations. We will describe the equivalence relation between the two, and at the same time give a geometrical description of what is an inertial reference frame in special relativity....

##### Groups in everyday life

La structure de groupe est un concept fondamental, dont l’usage dépasse largement les mathématiques. Il est très utilisé en physique, et nous verrons dans un prochain article un exemple de groupe important dans la théorie de la relativité restreinte. Ici nous nous contenterons d’en donner la...

##### Seriously, what use is math ?

« Philosophy is written in this grand book - I mean the Universe - which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is...

##### What use is math ?

I suggest a little pseudo-scientific experiment which goal is to literally picture how useful the above mentioned study can be. In this so-called experiment, we will inquire about the daily activities of a human being. Let's consider an ordinary human being, from any ethnic origin or...