Science

Take a coin and toss it a number \(N\) of times in a time interval of duration \(T\). Suppose that every time you get head you win \(a\) euros and that you lose the same amount of money when you get tail. Then your capital is a random process with ups and dows like this:  This process is a stochastic process usually called “Random Walk” and its properties depend on the parameters $N, a $ and \(T\). ...

When tea is poured in a cup of hot water, we observe a phenomenon called diffusion: in the end particles of tea spread evenly throughout the mass of water and we enjoy our cup of tea. Diffusion occurs as a result of the second law of thermodynamics (increase of entropy) and can be modeled quantitatively using the diffusion equation (or heat equation). This is a funny equation, since it establishes that the velocity of spreading is infinite while the mean root square fluctuations of the position of the particles grows in time as ...

Or… Correlation implies causality. This is a logical fallacy. Keep this in mind when analyzing data. There are numerous cases of how people use this logical fallacy nowadays (most typically in newspapers). For example, the following graph shows a correlation between global warming and the number of remaining pirates. But this does not imply (of course), any causality between them. By the way, this graph appears in a Bobby Henderson’s clever parody of the type of arguments in Intelligent Design. ...

I have been on holidays during the last two weeks visiting Argentina. The picture above was taken on top of the Perito Moreno glacier, which is amazing. Most glaciers we found where blueish, including the icebergs found floating in the rivers. The reason for that is that the thicker the ice or snow layer is, the better red colors are absorbed by the layer and only the blue colors are reflected (see a more detailed explanation here). ...

You can’t fold a paper more than seven or eight times. Don’t believe me? Then try it. Thinner paper? Longer paper? It doesn’t matter; you just can’t do it. I used to play this game with my friends which were always amazed and asked for an explanation. Is there any physical or mathematical constrain to do it? Nope: it is simply a matter of scale. If you have a paper of length L and you fold it, the length now is L/2. ...

In a recent Nature article, Albert-Lászlo Barabási and João Gama Oliveira, have found the perfect excuse for lazy people not answering some emails in their inbox: they analyzed the time response of emails and found that they follow a power law probability distribution of the form P(t) = 1/t. In particular this implies that not even the mean response time is finite. Hey! why should you then expect me to answer your emails within my lifetime period! ...