some people claim they can take control over their dreams and drive them to their pleasure.

i wouldn’t totally discard that possibility, but still their assertiveness makes me smell they are being fooled by their own dream. for example, what if they just had dreamed they were under control. or even better, what if random things might have been waved normally in their dream without any control from their part whatsoever, and that only a posteriori when they think of what they dreamed they construct the delusional sense of control they never had?

i have two reasons and facts for me to be skeptical: first, it is of humans nature (and evolutionary interest) to detected and see causality everywhere, even where there isn’t (prove – we have religions). second, we still think too high of ourselves and our abilities to act consciously.

over here there seems there’s a tendency to not measure things with units but by comparisons to other objects. crazy, i know! but yeah, the truth is that hearing things like “the crater was big like two football stadiums” or “elephants are as heavy as trucks” is pretty common.

i wonder if this strategy of replacing measures with comparisons is the result of some people’s inability to use units comfortably. could it be they never developed an intuition for measures and sizes and units? that would render them measure-illiterate, and that’s why they would be resorting to comparisons, just like in ancient civilizations? i’m just trying to make sense of the facts. but in any case, i am tempted to claim that this (joke of a) measurement system they have in place here is part of the problem.

now, today i found the gem of the gems in this regard, written somewhere in the internet: “it was as heavy as a sixteen-pound bowling ball”. which blows my mind. because, apparently, the “it was as heavy as sixteen pound” wasn’t concise and intuitive enough…

for some reason it reminded me of that quiz adults back home do to mock young kids or “Captain Obvious” sort of people , that reads “which color was the white horse of Santiago?”. Only that this time it’s not really a quiz to mock anybody, but part of how things actually work here. i’m still confused about it all.

When you take any shape (say, a sphere) and you apply a transformation to it, and you fold/branch it, and then keep doing it (in theory forever), chances are you get fractal. You know this if you played with IFS fractals and Julia sets back when they were popular in the 90s. The recipe works in almost all forms, including a rotation and translation (transformation) followed by an absolute value mapping (folding/branching):

I made this one last night, relatively quickly, for I faked almost everything that has to do with lighting: there are no shadow rays, occlusion or indirect lighting going on. Orbit traps are used instead for surface coloring and occlusion darkening.

Hm, after some simplification, the cubic power of a quaternion becomes:

q^3 = q·(4·q_x² – {3,1,1,1}·|q|²)

(where the 4-way products here are component wise multiplications), or in other words,

vec4 quaternionCube( in vec4 q ) { return q * ( 4.*q.x*q.x - vec4(3.,1.,1.,1.)*dot(q,q) ); }

which is surprisingly compact, and not as asymmetrical as one would expect perhaps.

Also, it seems to be generalizable to complex numbers, z^3 = z·(4·z_x² – {3,1}·|z|²), and to reals as well.

Seems people need to fulfill a lot of needs before they can be happy

However, they need only one excuse to claim they are unhappy

los niños del mundo desayunan Nesquick. nosotros desayunamos ColaCao
los niños del mundo juegan con Lego. nosotros jugamos con Tente
los niños del mundo meriendan con Nutella. nosotros merendamos con Nocilla
los niños del mundo tienen M&M. nosotros tenemos Lacasitos

plagios absolutos. creo que lo único original que hemos inventado nosotros es el chupachups?

Being in the airport waiting for an almost 3 hours delayed flight is a great opportunity to go to the store and read for free magazines with articles that you’d never, never ever, read otherwise.

On other news, why can you Americans keep endlessly doing jokes about the arms of the tyrannosaurus rex? I find it really amusing. Also, in a similar geeky note, just so you know and stop doing culturally artifacted math puns, you are pronouncing both Uranus and Pi incorrectly. You didn’t know? Boomer, huh?

I love the random conversations of the people waiting by the gate after all the smartphone batteries have gone below 50% charge and people switch them off and start interacting with one another. Indeed, Americans do engage in random interaction, just like that, as if nothing. I’m still not used to it, but I like it, and I like them for that!

Lastly, I feel like having some strawberry yogurt. Gonna grab one.

Say you want to intersect a ray with a planar coordinate system (a regular plane with a center point and two perpendicular vectors defining a 2D coordinate system). You are interesting in getting the distance to the intersection point along the ray (t), and the 2D coordinates of the intersection point in the coordinates system of the plane (s,t). So, given you ray with origin o and direction d, and your plane with center c and generating vectors u and v, you can proceed in two ways:

[1] The traditional way: computing the intersection with the plane (t), then project its relative position with respect to the center of the plane into the two coordinates axes (s,t).

[2] The elegant way: solving the 3×3 linear system of equations for (r,s,t) all at once, at a single step. You can do this by using Cramer’s law.

The second solution, despite more expensive, turns out a lot more elegant (more symmetric and regular, that is)

vec3 intersect( vec3 o, vec3 d, 
                vec3 c, vec3 u, vec3 v )
    vec3  q = o - c;
    vec3  n = cross(u,v);
    float t = -dot(n,q)/dot(n,d);
    float r =  dot(u,q+d*t);
    float s =  dot(v,q+d*t);
    return vec3( t, s, r );
vec3 intersect( vec3 o, vec3 d, 
                vec3 c, vec3 u, vec3 v )
    vec3 q = o - c;
    return vec3(
        dot( cross(u,v), q ),
        dot( cross(q,u), d ),
        dot( cross(v,q), d ) ) / 
        dot( cross(v,u), d );

This is one example of how you can use the function in order to draw oriented planar patterns:


visiting a work colleague in her office for coffee break, and spending more than one hour playing piano and singing classic disney movie songs.

you know, all those guys trying to unify quantum mechanics and general relativity by means of a universe of a higher dimensionality than 3+1, face the frustrating but very necessary need for a scientific a prove of their model in the form of a repeatable experiment. of course, finding traces of the existence of such 5th or 6th dimensions for example is way too indirect and elusive, and chances are they are not real but only existent in this mathematical model that desperately tries to unify the four forces, and the big and the small.

now, here in my nightly train commute from the office to the city, i often have the impression i actually must be making use of the dimensions 5, 6 and 7 every time i have to leave the train car…

usually the car is really packed with people, to the point that passenger have little to no space and margin of movement at all. the situation gets really complicated for me, because i have my bike surrounded by people who have been pushing and finding gaps between it and other passengers, quite like in a tetris game. so almost every night, when we leave Montgomery station and i realize i have to get off at the next stop, i freak out. i never see how i and my bike are going to make it out of the car. then i say “excuse me”, and magic happens – as if this a magic password for the opening of a stargate to higher dimension where i somehow was able to maneuver my bike freely just in time to return to our regular 3 dimensional world right before the door opens at Powell station. i’m normally unaware of the process, i only know i say “excuse me” and then i’m automagically and instantly at the door quitting the car, not aware of what have possibly happened between those two moments of space-time.

this happens to me in the train almost every night, it seems to be a very repeatable experiment indeed. maybe i should contact the guys at Cern.

i am in my bike heading home. it’s not that late really, still in the one digit PM-s, but the city has already turned its face into its night face, the more decadent one.

i’m waiting here for the red traffic light to turn green, at that weird corner in SF where a fancy trendy restaurant shares the cross street and address with the market of cheap sex. to my left, a group of people in elegant dresses and suits just left the restaurant. to my right, a prostitute starts walking the zebra crossing. when she passes by me and my bike she fires her hook in form of a smile and a “hi baby…”. i look at her, smile, shake my head, and break the eye contact rapidly and look to the infinity. that seems to be the protocol, or at least, one way to do it safely through the situation. finally the traffic light turns green and i resume my pedaling for one more block of sketchiness before i reach more transparent waters.

this little encounter starts a new thread of thought that keeps my head busy until i finish my ride home. this time i don’t think of these women themselves, of how conflicting for their lives it must be to do that, or what needs and dramas pushes them to do it in the first place. this time my thoughts go to the counterpart of the business – those who pay for sex and the very idea of paying for sex in itself. bear with me for a bit, i hope not to offend anybody (and if i do, you probably don’t enjoy reading this blog in general anyway). because i’ve seen many, may people paying for sex in form of expensive ticket to music festivals or expensive clubs, perfume, alcohol and invitations to drink, fantastic sexy dresses, cab rides, love hotels, breakfasts, and “good bye, see you soon”s. for the most part there’s a lot more going on than just the desire of a sexual encounter, granted. however, can anybody categorically assert there’s only one way of paying for sex?

of course these are not all the same. ideas like “courtship” or “socialization” come to my mind while i keep biking home. but still, to me, if i put all social context, accepted morals and established behaviors aside, the question phrased the way still sort of holds in some ways.

This week’s doodling happened during coffee break, in about 30 minutes. I used 16 inversions of the z plane (1/z) moving origins, followed by a twists. Every point/pixel gets transformed with these 16 maps and the distance to the origin is mapped to a color through a cosine with three different phases. Will see what I end up doing next week. For now, homework is done.

this is a funny group of people that the gods have decided to crowd together tonight, here by this door of this car of this late metro train. it’s the wednesday night of an anonymous week of the year. we are all participating, some more shyly, others more vibrantly, in this spontaneous concert that we have here.

next by where my and a girls bikes are resting there’s a young man with a hat who has started playing guitar as soon as he has entered the train in West Oakland. i immediately do the eye contact, smile, and decide to support him into building his audience. others join rapidly, happily, with huge grins in their faces, almost as if they had been desperately waiting for an excuse for leaving their smartphones.

one of the first ones to join in is a punk blond girl who has a puppy, which moves at the feet of the musician and looks up to her owner, me, and the musician alternatively. behind the punk girl, by the other door, there’s a gothic young redhair teenager. sitting in front of me a blond curly haired boy with a skateboard, to his left an asian office employee young lady. then there’s me and the other biker girl. there’s plenty exchange of eye contacts and smiles between all of us. and that makes me thing of how different all this would have been, what of an sterile space this would have been, if it wasn’t for the musician and his music.

in fact, now it’s the third song the plays already. this one is quite fast paced and happy. now, a super young cute black about-5-years-old girl stands up from her seat a couple of rows back and comes our way while her mum follows her while smiling. the little girl joins in the middle of the concert space, in front of the musician, and with the help of her mum who’s holing the by the arms, starts dancing. everybody looks at her, including the puppy. the scene is pretty cute and somehow magical. some of us laugh, some grin, some. there’s clearly a lot of happiness here right now. it’s clearly a celebration. a celebration of the small things probably.

yeah, a wednesday night in the metro is just as good as any other place, or what am i saying – it’s perhaps the best place, to to celebrate such things.


(grrraaaaawwwwwwww!) okey, time to wake up! i did nothing but relax last night, and same this morning. (diving in thoughts) to make things even better, i’ve got three days ahead fully packed of no-plans-whatsoever. (huge grin). ok, end of transmission (happy, and one foot on the floor)

due to entering the credit card number in a multitude of online websites over and over again for many years, people end up knowing their credit card number by heart eventually.

i am clearly not one of those people.

i’ve been doing mathimages for almost 20 years now. back in the beginning most of my drawings were purely geometrical. because doing geometry in the computer is just easy: lines, cubes, spheres… these are all geometrical objects with simple mathematical descriptions and therefore easy to compute. since computers are made exactly for that, compute, creating images (or sounds) in the computer with such shapes is by far the easiest.

of course, the challenge of moving away from such simple geometrical shapes and producing organic imagery instead (ie, rich in shapes, textures and movement, yet not random but with rhythm) is indeed a fight against the machine, and also the ultimate goal (from a technical point of view) of creating mathimges. that’s way i enjoy it better trying to create such natural/organic images than doing easier geometrical work.

however, for this week’s mathematical image i decided to do all my regular improvised jam coding session strictly in geometry-land. no attempts to break regularity or silhouettes, no diving in memories in search of the shapes of nature. instead, i played only with one of the most regular and euclidean of all structures: an infinite grid of cubes.

as usual, a jam session is a jam session, improvisation drives it all. so sure, the image could be better, but the exercise turned out fun once again:

when i pay a check with credit card and i stamp my signature, i often draw a smiley face as well next to the signature.

because in my innocent and inaccurate version of the world, there’s a poor banking intern assigned the task of manually double checking all the signatures for approving all the transactions that happen every day. and i want to make that intern smile.

i know none of this is true, that there’s no intern checking anything. but i still have the funny though, and laugh at myself for thinking about it while putting my signature.

and then, before finishing,… just in case… i draw the smiley face.

it’s interesting to realize that i never had to think of race issues until i moved to this place. furthermore, i never before knew there were still “issues” with race, to begin with. not so extended as i have come to understand recently.

just to put things in context and give you an idea of what i’m talking about – i was grown up in a quarter of a million inhabitant city and studied in a city populated by one million people. hence, both were reasonably sophisticated urban areas. yet, i had never seen a latinamerican, arabic, african or asian person other than in the movies and TV until the age of 23 when i moved to the capital of europe. even there things didn’t get much better. for example, i can say that the amount of asians i saw during those 7 years can be counted with the fingers of a single hand.

this means that my only contact with race conflicts had been little to none, and i was only aware of them through the conflicts portrayed in documentaries, movies and news (which i never trust for you are never sure how much of what you see in those media is real and how much is just there as hyperbole serving the narrative). of course i had been exposed to some degree of racism in one form or another, for in such lack of prominent race or cultural diversity back there back there in the old continent, language and cultural localisms have often been used as excuses to create conflict. also, the recent massive immigration from latin america, euroasia and africa to europe are starting to rise conflicts and hence awareness. but in any case, it is undeniable that the magnitude and intricacy of the issue of racism that americans have to live with every day are unheard to me (and probably to the average european immigrant in americam).

in fact, being grown so unexposed to a multicultural and multiethnic reality, the average european feels too optimistic, probably too confident and surely too naive regarding race issues in america, the first country on the planet to celebrate diversity for more than a century. “way, wasn’t this already solved?”. however one learns with disappointment that we these hairy monkeys called humans have not solved the issue yet, and that the topic is fact pretty vivid issue and continuous topic of debate. i am still very tangentially exposed to it. i am however often find myself reading about race or talking about it in casual conversations with friends. which is something new to me. new and sometimes difficult for me and most eurokids, simply because we the lack the life experiences in a multicultural and multiracial reality that allows us to have developed an opinion and taken a position.

however we might enjoy some advantages. for example, we do join such discussions with some sort of tabula rasa mindset, free of preconditioned opinions nor real cultural artifacts. i’m thinking that perhaps we can see things a bit clearer, free of pre-established believes or indoctrinated “truths” blocking our view. we’ve never been educated in any particular point of view regarding the topic.

one such thing that i clearly see is the mistake of assuming that the average (liberal) white person feels (or should feel) guilty for all the atrocities done by white people during the centuries. i’ve seen this idea expressed multiple times. i’d like to inform them that i feel no connected or related whatsoever to the fucking bastard spaniards who killed the native americans, nor i feel responsible for the slavery white americans practiced. if anybody thinks i should feel guilty for what other people from which i only share skin color or blood did, then they are being racist. because race is not something transcendental that carries identity with it. culture is the mechanism to transfer identity. race isn’t. or not even – perhaps my very strong sense of individuality and the fact that i always have problems feeling blame or pride for what a group of people i am told i belonged to do or achieve, doesn’t help me here.

another cultural artifact i personally am free from (i think!) is famous whole american idea of the “white default” – that the US mostly agrees that americans are “white” by default. and that therefore black, yellow and brown people are out of the norm and must in fact be labeled as such. this is something carved so strongly in the very language that it is unconsciously accepted by all americans regardless of their race. for example, the news in the TV will talk about “a man” if the subject of the news is a so called “regular” white man, but will specifically talk about “a man of color” if he subject was a black man. indeed, analyzing the use language is a good way to measure one society’s idiosyncrasy, morality and standards. and it seems clear that being any color buy white is considered the exception to the rule in the american collective consciousness.

i do think i am still in my naive euroflowepower view of things, and relatively free of these preconditioned opinions and artifacts. i wonder if this will always be so, or if being now exposed to this new culture will, over the years, change and shape the way i subconsciously think and feel about these issues.

i had this silly joke idea in my head, and i needed to put it out there. i am sorry.

because it’s a visual joke, and because i cannot draw with my hands (well, obviously nobody can, what i mean is i can’t draw with a pencil or tablet), i asked my friend to execute it for me. thanks!!!!

for me, clearly, the one place you absolutely don’t want to put the “watch your step” warning sign in, is the step itself.

anywhere but in the step, for Aristotle’s sake. what’s wrong with you, people? why am i alone in this one again?