Monthly Archives: December 2010


only after two weeks of regularly wearing this sweater i realize that it actually has pockets. the sad part is that i remember to have already looked for them a couple of times.

cuánto tiempo lleva darse cuenta de que efectivamente un jersey tiene bolsillos? dos semanas. lo peor es que recuerdo haberlos buscado en al menos un par de ocasiones.

“the universe is infinite, thus, everyting exist”


infinite means countless or without limits, not exhaustive: the set of integer numbers is infinite, but it doesn’t contain 1/3, sqrt(2) or PI.

besides, the universe might be infinite in size, but that has little to do with the variety of its content. i’m sure the universe doesn’t contain any Homer Simpson – shaped galaxy made of cylindrical stars and planets made of paper.

i might, at best, define the universe to be everything that exists.

it´s $400. or is it $40?

I already spoke about the line of embarrassement. The other day I found myself putting the line at random, at my convenience.

I was proudly saying that one should be morally offended to buy some pants that are $400. I was trying to make the point that even if you could afford it, it is sort of an aberration thinking that a whole small family can in fact be fed for a month with that amount of money.

Now, I realized that apparently I allow myself not to be morally self offended when I buy my $40 pants in h&m. But it’s interesting, cause I’m sure I can feed almost as many families in this planet with $40 a month as I can with $400. I sometimes forget how poor the world is.

So, why did I put my line somewhere between $40 and $400? Cause that’s convenient to me and my global weak morality. In the end, it’s like when you donate some money once a year – it’s not about the help you provide, it’s all about you feeling well, and nothing more.

tonight is so cold

it’s so freaking cold. isn’t it. that’s why i run tonight. also, because i don’t have the courage to walk by these people and look to them, sleeping here in the streets barefoot, with nothing but an old blanket, knowing that tonight some are gonna die, or get injured forever. cause, it’s so freaking cold. isn’t it.

about crosses

you should already know, by now, what i think about crosses (and religions) and other similar symbols:

#ifdef GL_ES
precision highp float;
uniform vec2 resolution;

float u( float x ) { return 0.5+0.5*sign(x); }
void main(void)
    vec2 p = (2.0*gl_FragCoord.xy-resolution)/resolution.y;
    float r = length(p);

    vec3 col = vec3(1.0,1.0,1.0); 
    col = mix(col,vec3(0.0,0.0,0.0), u(2.0*u(1.0-abs(5.0*p.y-1.0))+1.0-5.0*abs(p.x)-u(abs(p.y)-.8))   );
    col = mix( col, vec3(1.0,0.0,0.0), u(1.0-r)*u(r-0.9*u(abs(p.x+p.y)-.1) ));
    col *= u(1.0-r) + 0.5+2.0*max(sqrt(r)-1.0,0.0);

    gl_FragColor = vec4(col,1.0);

tres no es suficiente

como ya comenté en una o dos ocasiones, me quedé bastante impresionado cuando leí los 13 libros de Euclides (con densidad exponencial, es decir, detenidamente al principio, y más en diagonal según avanzaba). sobre todo porque los antiguos griegos no necesitaban números para comprender matemáticas (vamos, geometría), y demostraron cosas tan complicadas como cómo resolver ecuaciones cuadráticas sin ellos. del mismo modo, tampoco tenían divisiones, sino proporciones, y no necesitaban de raíces cuadrados sino que pensaban en lados de cuadrados.

sin embargo, a pesar de lo potente de sus intuiciones, también estaban llenos de limitaciones. y no sólo limitaciones prácticas, como la falta de lenguage simbólico, que provocaba que un simple enunciado matemático requiriese de decenas de lineas de texto. sino que además, estaban limitados a cálculos que, en lenguage de hoy en día, implicaban una, dos o tres multiplicaciones, y no más. pues al estar limitados en su imaginación a las tres dimensiones, no concebían el concepto de contenido para rectángulos extruídos más de tres veces. así que, tan claro como era para ellos algo como un binomio elevado al cuadrado (“if a straight line be cut at random, the square on the whole is equal to the square on the segments and twice the rectangle contained by the segments”) o al cubo (ver dibujo de abajo), jamás demostraron ni siquiera entendieron el conceto de un binomio a la cuarta potencia.


a primera vista, los chavales de las generaciones nuevas parecen retrasados mentales. pero yo tengo confianza en ellos, estoy seguro de que la nuestra les parecía lo mismo a nuestros mayores.

at first sight, teenagers in the new generations seem all retarded. but i have faith on them cause, i’m sure, my generation looked didn´t look very different than that too to our elders.

oh, olvidé / i forgot

que también veo el parpadeo de los monitores o lámparas fluorescentes en muchos casos que el resto de la gente no parece ver nada. muy molesto, de verdad.

that i also happen to see the flickering in screen monitors and fluorescent lamps in many cases that other people seem to not notice anything wrong. very annoying, i tell you.


yo no sé a qué frecuencia sale ese pitido de las televisiones y algunos otros aparatos electrónicos, que al encenderse los oigo incluso desde el otro lado de la casa. una vez soplé un silbato de perro y no escuché nada, así que supongo que no tengo superpderes (¡cachis!), pero alto debo de tener el umbral porque parece que casi nadie es capaz de escuchar el pitido dichoso. ¿o sí?

i don’t know what’s the frequency of those tones that tv sets and other electronic devices produce when you switch them on, cause i can hear them even from the very other side of the house. once i blowed one of those whistle they have for dogs and i heard nothing, so i’m sure that i don’t reach ultrasounds or have superpowers (meh…), but i must have a high frequency threshold cause it seems almost nobody out there can hear the damn sound. or, ¿do you?

aún me pasa – it still happens

a veces me despierto llorando
otras, palpitando de emoción
pero en cualquiero caso,
siempre me sorprendo
de que aún sueñe contigo

sometimes i wake up crying
other times, i wake up and my heart beats of excitement
in anycase,
i can’t believe i still dream of you

formal proofs

the way math grow, in the big scale of things, is an additive process (locally it can be a big mess of intuitions, fights, and faith. anyway). so, it’s a process on which new theorems are proved by using previously proved theorems, and so on all the way down to the basic axioms of mathematics, which you cannot prove anymore, but accept as true (axioms can be changed such that new mathematics can be created, but that’s another story, for now we just accept those that produce maths that make sense to our perceptible world). this has worked fine so far.

however, this process of building mathematics means that, of course, one must be familiar with the theorems that are gonna provide help on proving the new ones. as we continue developing maths, and we escalates in knowledge, as we invent new branches and theories, and define new fields, things get both more abstract and more of course more numerous. perhaps, up to a point beyond which no human can keep all the necessary information in his brain or simply follow the level of abstraction involved. then, humans will need some help.

in fact, i think that day is already now. computers assist mathematicians into proving their theorems, by formally checking that every theorem, lemma, proof, law and corollary involved in every single step is indeed formally correct. note than i’m not speaking of computational checking (as if maths where about numbers), but really going down to the basics of symbolic logic in every step.

in the other hand, even if we obviate the issue of the volume of a forma prove, as things get more abstract and complex, i guess humans are not that reliable anymore for formal proving and we shouldn’t count on them for formal discussions. then, i suppose, it will be the computer’s job to proof the theorems, and humans job to only propose new ones. cause for creating new theories and propose theorems, you only need some basic understanding and lot of intuition. and at that, we humans are good. so, ¿shall we let the computer do the mechanical part?

so, to give you an idea, think it like this: in these computer programs, even things like 1 + 1 = 2 are formally proved from the properties of arithmetic. now, i read that even the simple definition of the number “1” requires an expansion of four trillion symbols when expressed formally in such computer systems. not that you need to go that down every time, building maths is like modular design, but still.

in this place…

…one gets used to expect the unexpected. which doesn’t mean you don’t get surprised anymore. it just means that a day you don’t see anything particularly extraordinary, you get disappointed.

aquí uno se acostumbra a esperar lo inesperado. lo que no quiere decir que no te sorprendas ya más. simplemente significa que si un día no ves nada particularmente extraordinario, te vuelves a casa decepcionado.

one beautiful morning

one beautiful morning in the city. sunny and cold. yellow light and blue shadows – as usual, here. it reminds me that it’s not the case in the places i have been living before, not like this. nowhere else i’ve seen this strong tinting of complementary colors. only in movies. coincidentally, most movies i have watched were produced here. it must be the air, the temperature, the polution, the latitude, something.

una mañana preciosa. soleada y fría. luz amarilla y sombras azules; lo habitual en esta zona. verlo me recuerda que no es tan habitual en los sitios en los que he vivido antes. no así de fuerte. nunca he visto antes un contraste tan intenso de colores complementarios. sólo en las películas. será casualudad que la mayoría de las películas que he visto se hicieran aquí. debe ser el aire, la temperatura, la contaminación, la latitud; algo.

San Francisco, one beatuful morning of December