el trastero

so, what if instead of being asked to implement solutions, you were instead asked to solve problems?

a bad boss is that who thinks (s)he knows or is capable enough to take certain types of decisions by his/her own, hiding the actual problem from his employees, who have then to deal with a solution (that of his/her choice).

thing is, but more often than not bosses are not there for thinking. in fact, bosses probably became bosses exactly cause they cannot solve these sort of problems (anymore, perhaps). they do solve other types of problems, but not these. they fact the might think they can is often a problem (or leads to a non optimal solution).

so, a good boss is that who exposes the raw problem to his people and trusts their judgement and creative problem solving skills. that boss might even believe in people’s self-management. i think the formula is very simple – trust on your people’s experience, skills and intelligence and delegate on them. you as a boss take the other decisions, which you probably like better. then you have good ingredients for success.

it’s always a good exercise to remember people to tell you in raw words what has actually to be solved in the first place, not just what they thought it had to be done.

… am one of the most systematically happy thing on earth!

and i get this realization about every other day.

…or may be not?

the fact that in the previous game we got 4 different graphs is of course a consequence of using a decimal positional system to write our numbers. what if we were using hexadecimal system? or if we decided to work in base 13 instead? how many distinct graphs would there be for each base? how long would the transient states be before the graphs start to repeat, if they were actually guaranteed to repeat?

damn, see?, there’s always new questions to answer. that’s the (beautiful) problem with playing around with maths – once you start, you can’t stop, cause there is always a new game to be played as soon as you finish with the current one.

of course i couldn’t resist answering these questions. so, here we go, i computed all the graphs for all bases from base 2 (binary) to base 31. and indeed, for a given base, the sequence of graphs seems to get periodic. these are the results:

observation: for bases with simple factorization, the number of graphs and period seem to equal the biggest factor minus one. it also seems that those bases don’t have transient phase. for the bases with multiplicity in their factors (bases 4, 8, 9, 12, 16, 18, 20, 24, 25, 27 and 28), i cannot explain the numbers yet.

seems like i have not been the first human being in this territory, the sequence is apparently known as the Carmichael function, and is referenced to as A002322 in OEIS. still, it’s amazing how far you can go in the depths of maths in a matter of minutes by making a couple of simple questions to youself!

i was having a closer look to the other day’s observation about 13² and 31², and i could quickly demonstrate that indeed, for two digit numbers, the only possibilities are 11, 12 and 13. basically, the demo it boils down to the behavior of the last digit when the numbers 0 to 9 get squared.

now this, rather than putting my mind to rest, brought some new questions. see, when doing this squaring number experiment, you can indeed know with which digit your result will end based on the original number. for example, any number ending in 4 will produce a number finished in 6 when squaring. when finished in 3, you’ll get a 9. for 7, a 9 too. for 6, a 6. you can draw a graph that shows how the units of your numbers flow: { 0->0, 1->1, 2->4, 4->6, 5->5, 6->6, 7->9, 8->4, 9->1 }, which has four fixed points. now, the natural question that arises is, what if rather than squaring we start rising the numbers to the third power, or forth, and so on? what kind of patterns/graph will we get? or, how many different graphs will we get?

i couldn’t resist trying out and seeing for myself. this is the experiment:

so, we see than when rising to the cubic power, we get an interesting set of six fixed points and two cycles!! when rising to the forth power, you get something similar to squaring where 1 and 6 become sinks. when fifth powers are computed, however, all the dynamics collapse to 10 fixed points! so it seems we get a rich set of graphs and behaviors. fixed points, sinks, cycles… how many different graphs/dynamics do exist as we increase powers? in theory there are up to 7 source digits landing in 8 destination digits, so that’s at maximum of 2 million potential graphs. do all of them get exist really?

in fact the excitement fades away as soon as we try power 6, which produces the same dynamics as squaring. perhaps just an unfortunate coincidence? not really. seems like power 7 produces the same graph than power 3, and that power 11 and 15 for the matter.

apparently, there are only four different graphs that emerge for all possible power exponents, which are distributed sequentially. how boring…

no me importa desvelarme, o despertarme en medio de la noche,
y pensar que seguramente estoy soñando cuando te creo a mi lado,
y entonces sentir tu calor, escuchar tu respiración, sentirte y estirar la mano para tocarte y asegurarme de que no deliro,
y darme cuenta de que estás aquí realmente.

y de las dos posibilidades para lo que continua, la segunda es pegarme a tu espalda, sonreir, y dormirme de nuevo. no me importa despertarme, tantas veces como sean posibles.

si un pez grande es lo que hay al final de la teta,
entonces una anaconda grande es… un… ¿preservativo para culos? ¿comor?

we are walking down polk street. it’s sunny, we have nothing to do for the rest of the day but do nothing, and we feel really good, comfortable in our simple t-shirt and jeans. i am pretty sure hers looks nicer than mines by the way, but still, whoever is walking behind us seems to have his doubts:

- hey guys, i don’t know who of you two has a nicer ass – he says to us

he’s a man, in his 35s, and i’m sure he’s being honest on that he feels attracted to hers as much as he likes mine. this is how this city is after all. and i love it. we laugh, thank him for the double compliment, and wish him a great day.

i always found it intriguing that 13² = 169 while 31² = 961, and that 12² = 144 while 21² = 441

and of course, same applies to 11² = 121 (and perhaps to 10² = 100 with 01² = 001 too)

although pretty self-consistent for the most part, seems that i am one of those rare people that occasionally change their mind about certain topics, ideologies, positions and believes. it can hurt your pride, but it can help to readjust little things. give it a try, feels good.

i can hear the bell of the cable car from my bed, as it passes by my block. in fact, i just woke up 5 seconds ago, and this is the very first sound i hear today. i smile. then i yawn, stretch out, and sit on my bed. it’s sunny outside, i can see the blue sky through the window. i take a moment to deliberately not think of anything, but listen to my senses instead. comfort, warm, light, colors, sounds, calm. i wait in silence a little bit more, waiting for that magic step to happen, when all these primitive feelings get melted together into one single and higher feeling. happiness. yes, happiness has to be cooked, built and listened to. i learnt to cook happiness long time ago. you just need to allocate time for it. the cable car rings its bell again. i think that i’m lucky that what for most people is just the iconic symbol of a great city, it’s nothing but a simple, ephemeral and anecdotal event in my day. the feeling becomes an idea now. i am so lucky. the cable car rings again. okey, gotta go to work, my day starts here.

alternative titles:
- cooking little moments of happiness
- on how sensations lead to feelings, and feelings to ideas, all the way up in a staricase of consciousness

For a given a parametric parabola of the form

which could well represent a blade of grass growing in direction b and bending down to gravity in direction c, which of course has derivative

the length between its base defined at t=0 and its tip at t=T, is, as we know (after applying the binomial expansion),

where

which has happens to have the not-so-simple solution

Probably T=1, but still, seems that when defined through a velocity and an acceleration, the length of a parabolic shape of a blade of grass is indeed surprisingly complex – it involves a logarithm and a couple of square roots, the point being here that i can’t find an intuitive interpretation to it really. However, we should be grateful there actually exists an analytic solution for it.

Again, we know so little beyond second degree polynomials!

i’m walking home late in the dark and lovely night of the city, only interrupted by a few lamps that through some light in the streets. just a few feet in front of me there’s this homeless who is pushing a trolley and comes my way. “nice hat there”. my hat has always been an effective conversation starter, no matter the context. “thx”, i answer. i pay some attention to the guy. he’s in his 50s, has white beard, wears a red cap and i think he has blue eyes. “sorry to disturb. how’s going. can i tell you a joke?”. unlike many homeless, this guy seems to be present and aware, really talking to me. his sight is sharp and focused on me. “sure, go ahead!”. he tells me three variations of the classic “how many XXX does it take to replace a light bulb”. i understand two out of three of the jokes, which is a very unusual score for me, especially given the context (although, again, this guy speaks very clearly). this makes me really happy. he proceeds to explain me that his father is a great joke teller, and that he can remember every single joke he was ever told, even many years after. “i bet you are the same”, i respond, and add a “what’s your name?”. his names is Dave. he asks for my name and he learns my name is Indigo, with d. “okey Dave, i gotta turn right here”. “i’m sorry i am asking this Indigo, but would you by any chance have 75 cents to spare?”. “sure, i have one dollar if that works”. he nods, i give him one dollar, and turn right. “have a good night”, “same for you”.

this random man that i’ll never see again in my life just helped improve my self esteem regarding my english listening skills. and it only costed me a bit of an open attitude, patience and attention. and one dollar. not bad!

- wow, you have two cavities! bad, bad. so tell me inigo, is there anything sweet that you regularly eat???

- hm, other than the 16 spoons of sugar for my cereals every morning, then heavy loaded 6 strawberry jelly toasts of the evening, and the one condensed mil can i have for desert every night for dinner, no, not really. i don’t like chocolate, candies, cookies, cakes or anything like that – i generally don’t like sweet.

- wow. you have ONLY two cavities!

hablar élfico, que léfico

i’ll be waiting for you tonight in my dream

it rains heavily in downtown, the water slides fast downhill. the reflection of the neon lights in the wet pavement, the smoke coming out the drains, the ultimate urban environment cliche ever. and the silence of a city that has gone to sleep a while ago, a dark cat hides behind a box in the corner of the alley, the smell of the humid environment. i heading home. but i want to arrive wet today. so i close my umbrella and let the rain drops hit me. i slow down. i’ll take my time.

ok, guys. this is actually very simple. there is no way you can fix aliasing in postprocess. not geometric aliasing, for sure. and you perfectly know it. so, stop wasting your time inventing new hacky techniques and devoting more shading power to them. please do face the real challenge: use the silicon to implement massive supersampling (we can start with 8x, no need to go the standard 121x of the film industry), and make it transparent to the user. until you have that, stop bothering us. seriously. thanks a lot from the deepest of my heart!

remember, TV was 600 px wide and it always looked far more real than any 1920 videogame – it’s not about pixel shading power, it’s about geometry supersampling.

i just discovered while listening to music, that if you shake your head fast enough in front of the speakers, to and away from them, you can totally experience the Doppler effect. aaaand, yes my friends, that’s how i spend my time in front of the computer…

“automathemagically”

that’s how certain things happen sometimes!

so, from silent ripping to shameless copying, passing through pretended inspiration or innocent replication, the work i give for free on my website has been reused (i’m avoiding the word plagiarized) quite a few times in many different places and forms.

indeed, i always claimed it was there for free, and the only thing i asked for was some recognition and proper credit. but i never stated it explicitly, as i counted in the fairness of the people, who come to the website to learn or get inspired (education should be for free). but of course we don’t all share the same standard of honesty, and despite i regularly found dishonest moves and offensive and actions, it never has bothered me that much.

things are getting much better lately – i believe people start to feel increasingly more exposed when they cheat on my work, so they’re changing their attitude, sadly motivated by fear rather than by uprightness. in any case, now i get emails asking me what kind of software license i distribute my work under… since i never explicitly state anything in my site about legal terms cause i felt it was unnecessary, but of course i understand that some people feel insecure about this “code of honor” way of thinking and unspoken rule of fairness that i assume everybody should naturally follow, and that they want to protect themselves against potential problems when they get to use my work/code in an event or product.

so, it seems i’ll now have to go through all the crap of licensing literature and shitty open source GPL, BSD, LGPL, CC and MIT fucking terms and learn, take an stupid official decision and publish it crystal clear somewhere in my site, in order to protect them from their own behaviour.

i know, the real world is not a fairy tale. but you know what, sometimes, only sometimes, i wish it was less fucked up and it was a little bit more like one. specially when I have pay the prize – who said i don’t have the right to be selfish too?

this one always made my cry, “el 7 de septiembre”, by the spanish band Mecano (1991). i always thought it was the saddest thing ever. i’m for the first time in my life thinking that, perhaps, it can be read differently.

who would say that
after such a long time
after we broke our bounds
we keep looking forward to our anniversary

the 7th of september
it’s our anniversary
and we don’t know if we should kiss in the chick or in the lips

in either case, tear!

- how fast is it?
- i think it’s around 340 meters per second
- … how fast is that?
- well, it’s like it takes only 3 miliseconds for you to hear what i’m saying right now, right?
- i… suppose. but i’m still not sure how fast it really is…
- ok, let me put it this way: it’s like you fart, but you run away before we can actually hear it.
- got it!
- ¬¬

can you recommend me some dream for tonight?

¿me puedes recomendar un sueño para esta noche?

i was looking at this hanging lamp and i realized that it was trying to mimic an old candelabra, with it’s bulbs faking flames, and attached to white candlesticks with fake melted wax. i thought it was funny that more than almost two centuries after the invention of the light bulb, not only we still keep designing lamps after the ancient way of illuminating houses, perhaps looking for inspiration in shapes or design, but that we actually mimic the full candle thing.

the second thought that crossed my mind was that, in fact, many kids have probably never had to use a candle in their lives, nor seen one other than in birthday cakes, so what does the actual candle-shaped electric lamps look to them? like some arbitrary design? are they conscious about what that shape actually is/was? the third though went to the smart phone next to me, which is digital and tactile (funny thing that “digital” actually means “with the finger” already in roman languages!), which has this phone symbol to trigger a calls. now, that symbol is designed after the old phone hook device, which most kids today have never seen or heard of. so, how the hell do they understand that that symbol means “call”? it’s not by association as the symbol means nothing to them, but memorization, making this symbol pretty arbitrary as a choice for the function it represents. so, how many other symbols are out there which have meanings i learnt by heart without me ever knowing they actually represent?

here i go today to get my weekly supply of condensed milk. i’m grabbing few other things too, but the main point of coming here is to grab 6 cans of condensed milk. that should suffice for this week.

the shop is the family grocery-and-random-stuff business of this old asian couple. it’s right below my apartment and i visit it often. usually the woman tries to initiate a conversation with me, and i always try to do my best to smile and not seem very antisocial. this time, she opens the conversation with something new.

indeed they recently closed the grocery store where i usually do my main shopping. because of that, i buy my condensed milk here now, as she has noticed. so she asks me about what it is for and how i cook it. to her surprise, i explain that i don’t use it for anything fancy cooking but first dinner (i usually have two dinners, or three) and that i don’t cook it, but drink it directly. i explain the infamous technique of the two holes and the flow of milk (no dirty joke or porn reference intended here). she nods, and then starts talking about the two ways she used to eat it when she was a kid, and how they usually cook it at her home country. so delicious! she takes a break (and gives me one) and finishes putting all the stuff in the bag. but then she goes on explaining how they prepare it in mexico. finally she gives me price of my purchases, and i pay.

if i was a good socially acceptable and grateful person, i’d probably try some of her advices and give her some feedback next week on how good it was cooking it the way she took so much care and time to explain about. but, you know me, i probably won’t. or, will i? i always surprise myself!

today i (involuntarily) read a news claiming that “the average person has been in 17 cities during his/her life”. i think this sentence, although we all can sense what it really tries to say, is wrong. the sentence should probably have been “people have been in an average of 17 cities during their lives” instead.

of course the thing is that one cannot average people really. you can only average things that can be defined somehow by a number, meaning stuff that you can count or measure. so you can indeed average certain qualities of people, but not people themselves. and even if you defined a person to be a set of qualities, still, how would then the aggregate of the average of the qualities represent the qualities of some sort of average person? i don’t think people are linear, nor ergodic.

besides, if your intuition is not that strong with maths anyway, think about it this way: seems tempting to simplify and pretend there exists something like an “average Joe”, but, and be honest here, is anybody around you “average” in all ways? did you actually ever meet Joe?

bypass, mass, trespass, pass, bass, grass, surpass, compass, embarrass, class, glass

I’m grocery shopping, I need some stuff. Most people are still working at this time of the day, meaning the supermarket is pretty empty. Indeed it’s so silent today that the background music can be actually be heard.

I know this one very well, I used to “sing” it a lot when I was a boy, and it’s recorded in some deep sector of my brain. It brings me so many memories. Memories from different moments of my life, both early childhood and my premature adulthood. In fact, the more I grew, the better I liked and related to this song. Of course, I immediately start singing to it, aloud:

I’m walking along the corridor with the milk. Seems I’m not alone in this, the woman coming the other way is singing too. We look at each other, smile, and keep singing:

It’s funny that by the time I sang this for the same time of course I didn’t speak a word of English and therefore I had no clue what this meant. But even after I actually learnt some English, it would still take me quite a few years to grasp the real meaning of it – only after having experienced the brutal solitude that brought me into tears and desperate cry and made me stronger I could really understand these lyrics. Anyway, lets keep going and grab the two other couple of things I still need from this supermarket.

Done, time to pay. The cashier looks at me and grins as I sing while waiting for her to pass all the articles through the scanning machine.

I leave the supermarket, I walk home, happy to be here. I’am very tempted to call this place home, but even if I couldn’t, I’m happy nevertheless.

if you don’t do anything bad today, at least dream about it

let’s define a rotonym to be a word for which a rotation (or a cyclic shift) of its words produces another legal word. these are a few such rotonym words that i have found in english:

a vellll, que me aclare… ¿las pistolas están permitidas, pero no los pezones? ¿comorllll, qué les pasa a éstos? menuda aberración moral.

aparte que, que yo sepa, nadie ha muerto aún de un chorrazo de leche, ¿no?

so, let me get this right… guns are allowed, but nipples are not? w.t.f. is wrong with you, people? coming from the old continent, this is such a moral aberration.

besides, please let me know when was the last time somebody died from a milk shot