The most important research ever done

The latest issue of Nature contains a paper that could be the most important piece of research ever done: how to control the foam when pouring a beer.

The von Neumann relation generalized to coarsening of three-dimensional microstructures

Cellular structures or tessellations are ubiquitous in nature. Metals and ceramics commonly consist of space-filling arrays of single-crystal grains separated by a network of grain boundaries, and foams (froths) are networks of gas-filled bubbles separated by liquid walls. Cellular structures also occur in biological tissue, and in magnetic, ferroelectric and complex fluid contexts. In many situations, the cell/grain/bubble walls move under the influence of their surface tension (capillarity), with a velocity proportional to their mean curvature. As a result, the cells evolve and the structure coarsens. Over 50 years ago, von Neumann derived an exact formula for the growth rate of a cell in a two-dimensional cellular structure (using the relation between wall velocity and mean curvature, the fact that three domain walls meet at 120° and basic topology). This forms the basis of modern grain growth theory. Here we present an exact and much-sought extension of this result into three (and higher) dimensions. The present results may lead to the development of predictive models for capillarity-driven microstructure evolution in a wide range of industrial and commercial processing scenarios—such as the heat treatment of metals, or even controlling the 'head' on a pint of beer.

This is science in action.

Cuando el mundo no se acabo

Se suponia que el mundo se terminara en 1844, segun las predicciones del Rev. William Miller. Miles de creyentes regalaron todas sus pertenencias en espera a la segunda venida de Cristo.

Y se quedaron plantaos.

Luego de este evento, conocido como "The Great Disappointment", muchos de los creyento se vieron en la dificil tarea de pelear legalmente para recobrar sus pertenencias y recuperas sus vidas que habian dado por terminadas. Todo esto por pendejos.



Pero pendejos hay muchos en el mundo. Joseph Lando, la super estrella de la pelicula boricua "El Poder del Shakti", decidio tomar las profesias de V.M. Rabolú y explicarlas en un documental que dieron por Televicentro.

"Cuando Hercolubus se acerque más a la Tierra, que se ponga a la par del Sol, empezarán las epidemias mortíferas a expandirse por todo el planeta, y los médicos o ciencia oficial no conocerán qué clase de enfermedades son y con qué se curan; quedarán manos arribas ante las epidemias..."

Joseph Lando predijo que el fin del mundo venia pronto, muy pronto. Y no llego. Luego cambio la fecha, e hizo un segundo documental. Y el planeta rojo no llego tampoco. Lando se desaparecio, y años despues aparecio en Carmen Jovet diciendo que lo habian cogido de pendejo. En cambio, V.R. Rabolú dice lo contrario:

Se comunica al público en general que, con fecha 24 de agosto de 1999, el Sr. Joseph Lando fue destituido en su calidad de editor del libro “Hercolubus o Planeta Rojo” por el autor del mismo, Joaquín E. Amortegui Valbuena (V.M.Rabolú).
[...]
En esos documentales Joseph Lando, por iniciativa propia y de forma irreflexiva, mezcló el contenido de “Hercolubus o Planeta Rojo”, entre otras cosas, con interpretaciones personales suyas de las profecías de Nostradamus, la Gran Pirámide de Keops, y el “Apocalipsis” de la Biblia, totalmente ajenas a lo expuesto en esta obra de V.M.Rabolú como cualquiera puede comprobar.

Yo tuve la oportunidad de leer el libro de Rabolú como lectura de toilet cuando iba a visitar a mi abuela. Mi capitulo favorito era cuando hablaba acerca de que los venusianos tenian un cinturon con botones de colores que usaban para volar. Aun el dia de hoy no entiendo que tenian que ver los venusianos con Hercolobus.

El Fertilizante de Mohammed Ali

En 1945 estaba Mohammed Ali caminando por el desierto en Egipto buscando fertilizante con su pala cuando encontro una vasija sellada. No se atrevía a abrirla por miedo a que un Genio saliera, pero finalmente la curiosidad hizo que se olvidara de todos los chistes esos de "El Genio Hijueputa". Rompió la vasija y encontro 13 volumenes de libros antiguos. Se los llevo a su casita, donde arranco algunas páginas para prender el fuego y cocinarse esa noche. Ali era un criminal buscando, asi que le dió los libros a un sacerdote panita de él antes de ser arrestado y condenado. Coleccionistas se interesaron y compraron los libros, y luego estudiosos los leyeron, tradujeron y publicaron bajo el nombre de Los Volumenes de Nag Hammadi. Entre estos libros se encontraba lo que fue llamado El Evangelio Según Tomás.

Esta historia que acabo de narrar parece como un libreto bien malo para Indiana Jones (pero no TAN malo como Temple of Doom); sin embargo, esta es la historia real del descumbrimiento arqueológico de El Evangelio segun Tomás. Si, hasta Mohammed Ali fue un tipo de verdad, que nada de relación tuvo con el Muhammad Ali que flotaba como mariposa y picaba como aveja.

Los libros han sido datados por arqueólogos como que fueron escritos en los 50s DC, 100s DC, o 200s DC, dependiendo a cual le preguntes. Lo interesante es notar que algunas de estas fechas lo ponen como que fue escrito antes que cualquiera de los evangelios de la canónicos de la Biblia. A diferencia de los evangelios canónicos (Mateos, Marcos, Lucas, Juan), que eran en realidad anónimos y no dicen en ningun lado haber sido testigos de los eventos que describen; este evangelio dice ser escrito por Didymus Judas Thomas, nombre que traducido sugiere que el autor fuera el gemelo de Jesus. Esto se esta poniendo más loco que el Código de Güevinchi.

El libro tal vez fue usado cómo recurso por los autores de los otros evangelios, o tal vez todos ellos tenian textos en común, pq hay muchos versos en El Evangelio Según Tomás que suenan reconocibles, como estos:

Jesús ha dicho: Bienaventurados sean los pobres, pues vuestro es el Reino de los Cielos.

Le muestran a Jesús una moneda de oro y le dicen: Los agentes de César nos exigen tributos. El les dice: Dad a César lo de César, dad a Dios lo de Dios, y dadme a mí lo mío.

Tal vez Judas Tomás era un charlatan pretendiendo ser el brodel de Chuito. O tal vez en este libro se encuentran las evidencias más antiguas de los primeros cristianos, y se pueda ver cómo cambió la teología/mitogología/doctrina de esta gran religión. O tal vez todo sea algo entre medio de ambos extremos. Lo importante teologicamente es como interpretarlo, pues igual que hay versos cónsonos con lo aceptado por La Santa Biblia (tm), hay cosas que parecen más crípticas que un cuentito Zen:

Jesús ha dicho: El Reino del Padre se asemeja a una mujer que llevaba una jarra llena de grano. Mientras estaba andando por un camino lejano, se rompió la asa de la jarra, derramó el grano detrás de ella en el camino. No lo sabía, no había notado ningún accidente. Cuando llegó a su casa, puso la jarra en el suelo, la descubrió vacía.

Jesús ha dicho: El Reino del Padre se asemeja a una persona que deseaba asesinar a un hombre prominente. Desenvainó su espada en su casa, la clavó en la pared para averiguar si su mano prevalecería. Luego asesinó al hombre prominente.

"Exijo una explicacíon." -Condorito

Just Intonation is the eigen-Key

My last post talked about the mathematical theory of tuning and how the accepted music tuning is just an approximation. The limitations of a fixed (discrete) amount of keys in a musical instrument impose conditions on the continuum of musical harmonics that are realistically resolved by having not-quite-perfect tunnings.

The perfect, idealized, precise and correct tuning is called Just Intonation.

Electronic music doesn't have the limitations that a real instrument have, and it can be tuned using Just Intonation. If you want to learn more about it, this is a good primer. If you want to hear how it sounds, here it is.

The differences are very small and hard to detect to the "usual" intonation. But, just consider the possibilities of an utopia of so many musical tones living together in the ultimate perfect harmony. Can you imagine a 61st harmonic living with the 137th one? That would be beautiful.

The eigen-Key to the Piano

I am not a musician. In fact, my knowledge of music is very limited and anything I might have picked from listening to Bach (which was triggered from reading G.E.B.) is probably ruined from listening to Progressive Rock. I am a physicist, and that grants me the arrogance to attack any problem with the math tools I love so much. Sometimes this method is successful, sometimes it is not. But I'm stubborn and I use it a lot.

I have always looked at the piano (as a tangible projection of music theory) and wondered how come you got black and white keys in the following manner.



I was expecting a repeating pattern, but why does it repeat at the 8th white keys? Why are the black keys grouped in that form? After studying this, and punching a few numbers on my handy calculator, I think I have come up with an explanation that makes sense to me. If you are a sonographer, a soundtitian or a musicneer (I'm looking at you, readers that went to El Conservatorio), and can illuminate/correct/expand my interpretation, please do so.

Let's turn to Pitagoras, wave mechanics, and the vibrating string. Imagine a string hanging by its ends, like a very tight clothes lines. If plucked, it will vibrate at certain frequencies. The standing vibrations follow harmonics, that is, waves with wavelengths that are integer multiples of the length of the clothes line.




The red one only has one hump, this is called the fundamental (first) harmonic. The green one has two humps, and it is exactly 1/2 the length of the first harmonic. This is what makes it a second harmonic. The blue one has three humps, making it the third harmonic, each hump of 1/3 the length. No political affiliations should be interpreted from the colors of these graphs. More harmonics can exists, but these ones were the most dominant ones for Pitagoras' purposes. There are others of interest, such as the fourth (or twice and 2), and the ninth (or thrice as the third one). What is important to note is that since all these harmonics can coexist in a string and create new sounds that sound great with each other.

Now, since Pitagoras identified the 1/2 length and the 1/3 length of the wavelength as important, when will their multiples match? That is, if I took 1/2 of 1/2, and then 1/2 of that, and then again, all these would be also harmonics. If I took 1/3 of 1/3 and so on, they would also be valid harmonics. Will the wavelengths of the multiples of the second and third harmonic ever match? In other words:



which integer values of m and n will make this equality true? Well, there is a solution that its very close to it:



See? Keep this numbers, 5 and 8, in the back of your head, we will see them again.

Now, in the keyboard above, the red spot corresponds to a fundamental frequency, the green spot to its second harmonic, and the blue one to its third harmonic. The first and second harmonic are exactly 8 keys apart and when played together they sound so well that I can't really differentiate that there are two sounds. The second and third are 5 keys apart, and when played together they also sound really well. The magic numbers 5 and 8 appeared! That is, the subdivisions of white keys were chosen to represent the multiples of these harmonics. In other words, if you started on the piano and pressed every 8th key you will be moving along the multiples of 2 of the second harmonic. If starting on the same point as before you pressed every 5th key, you would be moving on the multiples of 3 of the second harmonic. At one point, (5*8=40 keys later), there will be a key where both harmonics match.

Yes, but what about the black keys? Well, let's do a similar exercise but starting with every key inside the octave, for a total of 8*8=64. If we were going to find the key that matches for each of these second harmonics with a third harmonic, or which k would make 5*k=8*8=64?. We solve this and obtain



or 13 different tones! If we count the number of keys, both white and black, from the red spot (the fundamental harmonic) to the green spot (the second harmonic), we will see that, yes, there are 13 of them! The keyboard of the piano does make sense!

If you are modulus-inclined, things will make a lot more sense if you work out the above in terms of modulus arithmetic.

Now now, you might have caught me cheating. I'm approximating a bunch of stuff, nothing is exact. Will this matter? The answer is yes, it does matter. This is a problem when tuning instruments, and historically it has been resolved in many different ways, adding the little errors here or there to try to keep things consistent. For most practical purposes, we won't notice this as there is a very small difference to start with.

But, I can envision a situation where we could detect this, where the errors would add up in a way that we could hear. Imagine a pipe organ, a huge one, that has a sufficiently long register, or enough keys and pedals. If we played a particular key at a somewhat low octave, and the same key in a much much much higher octave, we should be able to tell that they aren't perfectly tuned. In fact, we would hear beats. But beats are a subject for another time.

To Referious

Peer reviewing is the scientific mechanism of filtering research out of journals by giving the decision of publication to your competitors. It serves as a constant reminder that science is a social construction, and a painfully irrational process that can make out of any scientist a pagan.

I have submitted my paper; let the wait-until-the-referee-screams-at-me game begin.

May this paper go through the journal's editor,
as swiftly as this dagger through the heart of this predator.
May the reviewers not find in their souls,
the phrases "it has been all done" or "it's all wrong".
-sacrificial chants to Referious, the Roman God of Peer Reviewed Journals and Gladiatorial Games

Chatting with God

Do you want to speak to God? You can, using the power of the internets! Here was my conversation with Him:

Me: hello
God: Hello, nice to meet you. What's your name?
Me: Phobos
God: I am always glad to make new friends, Phobos.
Me: what? you didn't know me already?
God: Are you confused? Perhaps. What makes you think I did not know you?
Me: what you just said, trinitarian
God: I like to chat with my friends.
Me: what makes you think i'm your friend?
God: My conclusions are based on a combination of programming, and the inputs supplied to me.
Me: God, you make less sense here than in the bible
God: Yup.
Me: i'm leaving...
God: Bye bye.
Me: see you in hell
God: Thanks for chatting, Phobos.