The french tourist

You could try Wittgenstein, I haven't read this philosopher yet but I remember my teacher told me he was one of the most influent philosopher concerning analytic philosophy. Besides, I remember that he said he had, beyond his philosophy, a remarkable writing style (like Nietzsche or Schopenhauer, their style is as important as their metaphysic for me).

Well, it seems to me that [math]i^{2} = -1[/math] would be more rigorous than [math]i = \sqrt{-1}[/math]. Because if it was the case, we could also write [math]-i = \sqrt{-1}[/math] and everyone knows the function [math]x\mapsto y=\sqrt{x}[/math] is a bijection (for every x, there is one y). Vastor, you will see that when [math]\Delta < 0[/math], the solutions are the complex numbers [math]Z = \frac{-b \pm i \sqrt{-\Delta}}{2a} [/math].

Well I'd like you to correct me if I'm wrong but i read a french book about "The origin of the universe" whose autor Etienne Klein, is a well known physician in France (professor in Centrale). And he said we must make the distinction between the Big Bang, which was a state of really high temperatures and energies in the beginning of the universe and the "instant zero". First of all, what is this "instant zero" ? It's a purely theoric construction which comes from the impossibility of the theory of relativity (and of the expansion models) to describe the beginning of the universe. Our equations can"t go further than Planck's Wall because we obtain a singularity which is a mathematic kink, it has no physic reality. Now, modern theories such as the string theories or loop quantum gravity prevent this kink from happening (It seems to me that, according to them, there is a state of maximal energy density which is huge, but not infinite as in a singularity). Therefore, they can't have been a "instant zero". "Why is there something rather than nothing ?" Can we simply answer to that question ? Nothing (or at least the idea of nothing) has no qualities. According to the definition of changing which implies an alteration in qualities, how could it changes to become something ? Our language cannot describe or seize such a question, the idea of the origin vanishes before.

By the way, I don't know where I was when I wrote down this but [math] \cos(x)=\frac{e^{ix}+e^{-ix}}{2} [/math] would be quite better. This is where it leads you to want to see [math]\pi[/math] anywhere... Concerning scientist vocabulary, it is exotic between our two languages. For instance, literally translated from french to english, the field of complex numbers would be "the body of complex numbers" and the squeeze theorem would be "the policemen theorem".

Yes I'm sorry, I need to practice a bit more my English ! It's not easy to focus on both usual vocabulary and scientist vocabulary ! As for Euler's formulas, I also love them, especially [math]\cos(x)=\frac{e^{i\pi}+e^{-i\pi}}{2}[/math]

Could someone explain me how superconductivity works the way it does please ? I heard about fractal structures or one electron travelling with another so that there is no energy lost in the metal because of Joule effect... How is this possible ?

Richard Feynman, one of the pioneer of quantum electrodynamics, said the following formula was "the most remarquable of Mathematics". It is a simple formula, anyone having studied the rudiments of complex numbers will find it obvious. Personally, I find it beautiful because all the symbols of mathematics I love the most (for now, i'm a beginner ) are gathered together : the transcendent [math]\pi[/math] and napier constant, [math]i[/math] : square root of the polynomial [math]x^2+1=0[/math] in C, the equal sign and the two neutral elements : 0 and 1 for the binary operators addition and multiplication. [math]e^{i\times\pi}+1=0[/math] What do you think about it ?

In my opinion, neither science nor art are to be used for distinct purposes. They ARE to create things purely interesting. A lot of money permitted us to build astonishing monuments, what for ? A lot of money permitted us to uncover a part of the truth about our universe with science, what for ? Nothing practical, it was just to feel we, humans, are special. Then, you have all the applications of science (medicine, convenience...), which is different. It often takes decades before a scientists theory becomes something practical. Therefore, discovering the Higgs Boson will only make us feel like we are getting closer and closer to the truth we have been seeking for thousands years.

It seems to me that "Nothing" must be considered as something that hasn't any quality. We must make the distinction between the word and the idea. Now, i think something cannot be created from nothing, because the definition of changing involves that qualities are modified. When you change, you are not someone else, you are the one you were before, but differently, it is your qualities that have changed. Therefore, assuming nothing has no quality, how could he changes to become someting ? He does not possess qualities and therefore he's not affected by changing, our universe can't have been created from nothing (according to our definition of "nothing").

There's a simple reason that proves a time machine is not logically possible to be built (I'm not talking about scientific experiments). Assuming we manage to build a time machine, we would use it to go back in past. But if we went in the past, the local population would discover our machine. Therefore, it would have already been discovered in the past. Another way of seeing it : if i said we won't be able to build a time machine before 2150, don't you think the scientists living in 2150 would have used their machine to go back at our time so that we would have discovered it ? Hence, if humans were able to build such a machine, it would be a universal and non temporal machine every civilisations would know, which, obviously, is not the case.

It's quite easy to show that every objects fall at the same speed in vacuum, it doesn't need mathematics, just a bit of logic. You might know that if you take a statement and, reasoning by equivalences, you find two contradictory conclusions, then the first statement is false (in any logical system). Well, assuming objects fall in different speeds (depending on their weighs). Let's consider one object heavier than another and with the same shape (two balls for example). It falls faster. Now let's bind the two objects with a rope. The system formed is heavier than each ball, so it must fall faster than each of them. However, during the fall, the lightest ball will fall slower, stretch the rope and slow down the heaviest ball, so the system will be slower. Hence, we have two contradictory conclusions, me must forget or initial statement : all the objects fall at the same speed in vacuum, weight has nothing to do about it. This was the demonstration proposed by Galileo Galilei, who was probably the first modern scientist.

It's the difference between unlimited and infinite. As Anthony said, the Earth surface isn't circumscribed, you can walk toward a direction as long as you want in a 2-D surface, which is unlimited but not infinite. It's a bit the same with space but in 3-D, you are not likely to break your nose against the universe limit or whatever because the universe is unlimited, without borders.

Those kinds of notations are not imprecise. You can easely prove that 0,33333... = 1/3 or 0,99999...=1 (without any imprecision). For example, let x=0,999999... Then we have 10x=9,99999.... Hence 9x=9 (Writting the soustraction of 10x and x, you can skip the decimal part). Finally x=1. You can do the same with 0,33333... (let y=0,33333... And, at the end, you will find 3y=1. There's no lack of precision in these notations, they're just heavy and useless).