Mardy (Entratas super matematica)

The “idiotism” of software developers

Alberto Mardegan — Tue, 08 Nov 2022 17:11:55 GMT

Before you get angry at me for this title, please let me state that I count myself in the number of the “idiots” and, secondly, that what I mean by “idiotism” here is not to be intended as an offence, but as some traits of mindset which are typical of very logical brains.

Some months ago I finished reading Dostoevskiy's “The Idiot”, a book about an exceedingly good-hearted man, prince Lev Mishkin, whose behaviour was puzzling the people around him so much that they thought of him as an idiot. Sure, the fact that he was suffering from epilepsy didn't help, but it was far from being the primary reason for their thinking, since his epileptic seizures were very rare (if I remember correctly, only two occurred during the time of the story) and everybody's opinion had already formed well ahead of witnessing him in such a state.

He was an idiot because he was open, trustful, and especially because he could not “read between the lines” of what was been said to him: his social conduct was straight, and although he was following at his best the customs that he had been taught, he was supposedly awkward and unable to perceive and parse all the messages that are implicitly conveyed by social behaviours and human interactions. I added the word “supposedly” because, as a matter of fact, his behaviours were all perfectly normal for me: I only noticed their awkwardness when it was pointed out by the other characters, at which point I couldn't help smiling and acknowledging that, indeed, that thing he did was weird.

However, he was a good and caring person, and not without talents: he had an interest in calligraphy, and everybody liked to listen to him, as his speech was insightful and his thoughts were original. I wonder how many of my readers can identify themselves in such a character?

I definitely can. I won't get into the details, but I've felt many times on me the amused or puzzled glance of people (like that time in high school when I could not open a door in front of dozens of people, and I heard them say “So, that guy is the genius of mathematics?” — I'll never forget that!), often without understanding the reason for their reactions. Still, generally people seem to like my company and be genuinely interested in talking to me.

So, what's wrong with prince Lev Mishkin, me, and maybe with you too? Well, a few things, I would say. I'm not going to claim any scientific truth on what I'm going to say, these are just my own impressions and deductions, which seem to be shared by other people in the interwebs too, judging from a quick search I did; take them for what they are.

The first thing I notice is some common traits between us and autistic people: we tend to work better with things, rather than with people; we can focus on a certain thing (work, a mathematical problem, a game) and forget about the world around us; we have our unique hobbies, like solving puzzles, arguing about a specific and very narrow topic, learning artificial (both human and programming) languages; it's as if we needed to build a small, better world where we would feel safe and at ease.

The other thing, which I actually consider harmful and which I put efforts to change in my own life, is the fact that it's extremely easy to get us interested into a specific aspect of a problem, and make us forget (or just not notice) the big picture. That small part that we are looking at is stimulating and challenging, and we are led to think that it's core of the issue, and maybe of all the issues that affect our world. What is often missing is the ability to take one step back and try to look at the issue from a different angle, and especially the ability to listen for counter arguments; I mean, we do listen to them, but since we have, in a way, “gamified” the issue, even when we think that we are open to listen to the other side, we are in reality trying to win the counter-arguments, rather than genuinely trying to understand them.

Another thing which we have, is faith. Yes, you read it right: even though the IT world is probably the one with the highest percentage of atheists, men always need something to believe in. We just don't realize it, but we do hold a blind trust in certain persons and authorities. This does not mean that this trust lives forever and cannot be broken, but this generally does not occur because of a conscious realization of ours. Much more often than we'd like to admit, the reason why we lose faith in a certain person or authority is because the rest of the persons and authorities that we trust has told us so. In other words, even if there's undoubtedly a reasoning of our own, the full realisation and conviction occurs after having collected and compared the opinions (or statements) of those we trust. The net result is that the IT population is the one most trustful of the mainstream media, because it's the mainstream media who has more “voice”: that's where the most reputable journalists, scientists, activists are (and “reputable” is the key word here, since this reputation is recursively created by the mainstream media themselves or by their sponsors).

I might be biased by my own experience here, but it seems to me that there isn't a group of people more homogenous in their political (and generally, world) views than that of IT workers. When, in 2018, I saw the leaked video of Google's co-founder Sergei Brin and other executives' reaction at Trump's presidential victory, what I found most surprising was not the contents of the speech, as they were mostly mainstream opinions, but rather the fact that all this could be said in a company meeting. Something like this, I though, could never happen in an European company, as political matters are a conventional tabu in the work environment. But the point is that Brin and others could say those words only because they knew that the overwhelming majority of the audience shared the same opinion. I don't think you could find the same homogeneity of thought among shop assistants or philosophy professors.

Assuming that you have followed me this far into my rambling, and that you recognize that there might be some truth in what I wrote, you might now be wondering if there's a way to counterbalance our “idiotic” traits. Unfortunately I don't have a full answer, as myself am only halfway there (but maybe I'm too optimistic here? and does this road even ever end?), but there are a few things that I think are absolutely worth trying:

Talk with people. Better if face to face, or at least in a video call; just 1-on-1, avoid groups, or you'll get on the defensive and try to defend your position for the sake of not losing the argument in front of an audience. But it's not a fight. Your goal when talking should not be that of convincing or getting convinced, but rather just to understand the other points of view.
Read both sides of the narrative. Try to see the other party's argument as they themselves present it, and not how it is presented in the media you usually read. Media often use this trick, to either invite “clown representatives” of the other point of view just to ridicule it, or they give them too little time, or extrapolate their answer out of context, just to make them appear unsensible.
Always assume that other people are smart, and that no one is bad.
Whatever the argument, try to answer the key question: “Cui bono?” (who profits?) to be at least aware of all the hidden interests behind this and that. They don't necessarily invalidate a position, but they must be considered.
Lose faith. The only faith you are allowed to keep is the faith in God (or Gods), if you have it: but men, theories, institutions, authorities (including religious ones!), these must always be assumed to be imperfect and not blindly trusted. People serve their interests or can be manipulated. Try always to start from a clean table and an empty mind, and see if they have enough arguments to convince you.
Do never assume “They can not all be wrong” or “If this were wrong, at least some media would report it”. It just doesn't work this way, this is again a matter of having faith in the majority. Think of how many times in (recent) history you were presented an unambiguous truth, which later came out to be a scam (Iraq war being a famous one).
Defocus. You might be spending a lot of energy into something that's not worth it. I mean, feel free to pursue whatever hobbies you like, as long as they make you feel better. But if you think you have a mission, think twice about it. Think about the world you'd like to live in, and whether/how this mission contributes to it.¹
Ask questions. Be curious. Be challenging. For any topic, there are questions that have not been answered in mainstream media². Find the answer, then find explanations, never stopping at the first satisfactory one, but always get at least two competing answers. From here, ask more questions, rinse and repeat. And at every step ask yourself this: why didn't I know about this? Is someone trying to hide the truth from me?
Aim at improving. Whenever you read something or talk to people, keep a humble attitude and try to be challenged. Your goal should be that every reading and every dialog should make you wiser, even if what you initially read and heard sounded like garbage. There are always reasons for all these thoughts you disagree with.
Reach out to the people nearby. Try not just to be sympathetic to the needs of some population living far away from you, which the media has singled out as being those needing your compassion, and try instead (or in addition to that) to be sympathetic and helpful to the people around you. To your neighbours, to those you see in the public transport and, first and foremost, to your relatives.

Summing up, what I want you to realize is that we IT workers are easily exploitable. All those thought manipulation techniques represent a problem to everyone, but it's particularly with us that they tend to be especially effective; as a matter of fact, I've found that awareness of how the power controls us is higher among uneducated people, because they are more distrustful of the media and just tend to consume less of it. We, on the other hand, are not only well educated to respect the authority (see Noam Chomsky on education), but our logical, detail-focused mind can be easily externally controlled by continuously stimulating it to focus on specific things and not others.

How would Dostoevskiy call us?

I was recently surprised when I read people in a forum who were discussing avoiding doing business with Saudi Arabia because of their human rights record. Seriously? We are talking about a government who has indirectly caused the death of more than 300 thousands people in Yemen, and your main reason to criticize them is human rights? It's like asking the police to arrest a killer because before the assassination he misgendered his victim! Yet the elephant in the room continues to go unseen. ↩
My favourite one is: which country hosts more refugees from Ukraine? ↩

Cammino quindi penso - 2018-09-06 - Le difficoltà della matematica

Alberto Mardegan — Thu, 06 Sep 2018 17:53:00 GMT

Per riuscire in matematica è necessario essere più intelligenti della media?

Le problema del numeros allegre - solution post 21 annos

Alberto Mardegan — Fri, 16 Mar 2018 20:10:00 GMT

In 1997, io participava a un competition mathematic appellate, originalmente, "Gare di matematica". Le test consisteva de octo questiones, e un de illos me colpava particularmente, perque io habeva absolutemente nulle idea super como solver lo. Alicun annos postea, io monstrava iste problema a mi amicos qui studiava mathematica con me al universitate, e mesmo illes non poteva solver lo. A ancora 5 o 6 annos retro io retrovava le texto del question e provava a solver lo, ma sempre sin successo.

Ben, alicun dies retro io casualmente me recordava de iste question e decideva de facer un altere tentativa: io recercava le texto del question in internet e, non sin fatiga, lo trovava. Io lo presenta a vos, traducite a interlingua:

Un numero n es appellate “allegre” si per alicun selection de x, y integre resulta n = 2x² + 3y² (exemplos : 11 = 2 · 2² + 3 · 1², 12 = 2 · 0² + 3 · 2²). Demonstra que si n es un numero allegre, alora anque 7n lo es.

Iste vice io esseva plus fortunate, e solveva le problema in alicun minutas. Io va presentar vos le solution plus in basso, post un longe sequentia de punctos, pro assecurar que vos non lo lege accidentalmente, si vos non vole saper lo, pro probar a solver le question:

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Infortunatemente io debe dicer que mi solution non es multo elegante, ma anque le solution offerite in le sito del organisation non es multo melior.

Io initia per scriber le expression pro 7n:

7n = 7 · (2x² + 3y²) = 14x² + 21y²

Como continuar? Mi solution parte del observation que isto non pote esser un problema troppo difficile, post que illo es dedicate a studentes que deberea solver lo in alicun decena de minutas. Isto significa que on debe initiar a cercar un solution breve, e forsa non troppo sophisticate. In practica isto significa que, quando nos cerca de scriber le expression de 7n in le forma 7n = 2a² + 3b² (lo que nos debe facer, pro demonstrar que 7n es allegre), nos debe initiar a cercar un solution que non require de decomponer le numeros x e y, ma al contrario nos debe sperar que a e b es exprimibile como expressiones "simple" de x e y — ubi con "simple" io intende expressiones con productos e additiones, ma sin fractiones, radices o altere operationes plus difficile).

Alora, on debe trovar un maniera de decomponer le numeros 14 e 21 in un forma 2a², plus un resto del forma 3b² (isto es lo que io appella "allegrisation" in le tabula):

summa	decomposition	"allegrisation"
14	0 + 14	2 · 0² + 14
	2 + 12	2 · 1² + 3 · 2²
	8 + 6	2 · 2² + 3 · 2¹
	18 - 4	2 · 3² - 4

Io ha usate le color rubie pro evidentiar quando le decomposition es incompatibile con le forma de un numero allegre: in le prime linea, 14 non es un multiplo de 3; in le tertie linea le exponente pro le parte remanente es 1, ma nos necessita 2; e in le ultime linea, le resto es negative, alora illo non es exprimibile in le forma 3b², viste que b² es sempre positive. Le ultime consideration porta nos a excluder omne altere decomposition ubi nostre a es plus grande que 2.
Alora, le unic decomposition favorabile es lo del secunde linea: 14 = 2 · 1² + 3 · 2². Si nos pote trovar un tal decomposition anque pro 21, alora nos pote progreder!

summa	decomposition	"allegrisation"
21	0 + 21	2 · 0² + 3 · 7
	2 + 19	2 · 1² + 19
	8 + 13	2 · 2² + 13
	18 + 3	2 · 3² + 3 · 1²
	32 - 11	2 · 4² - 11

Le decomposition 21 = 2 · 3² + 3 · 1² nos lassa sperar que le problema ha un solution facile. Nota ben: in le eventualitate que nos non succedeva a trovar iste decompositiones pro 14 e 21, nos non poteva affirmar que le theorema del numeros allegre non valeva; nos simplemente debeva constatar que nostre procedimento pro demonstrar lo falliva, e haberea debite cercar un altere via pro demonstrar lo. Fortunatemente nos ha trovate iste decompositiones, e nos pote continuar a sperar: io dice "sperar", perque de facto nos ha ancora nulle garantia super le facto que nos succedera a trovar un formulation de 7n que satisface le conditiones de "allegressa". Nos ha solmente trovate que nos pote scriber lo como

7n	= 14x² + 21y²
	= (2 · 1² + 3 · 2²) · x² + (2 · 3² + 3 · 1²) · y²
	= 2 · x² + 3 · (2x)² + 2 · (3y)² + 3 · y²
	regruppa secundo le coefficientes 2 e 3:
	= 2 · (x² + (3y)²) + 3 · ((2x)² + y²)
	= 2 · (x² + 9y²) + 3 · (4x² + y²)

Esque nos ha finite? Certemente non! De facto, nos ha obtenite un formulation simile a illo del numeros allegre, ma le expressiones inter parentheses non es quadratos perfecte: illos es solmente le summas de quo quadratos, ma nos manca de un termino. Le formula pro le quadrato de un summa, nos rememora, es (a + b)² = a² + 2ab + b²; nos ha a² + b², ma le duple producto 2ab manca. Hic nos debe ancora tentar le fortuna: forsan le duple productos que nos manca in ambe le expressiones pote esser addite sin alterar le valor del expression?

Que nos considera qual es le duple productos que manca: in le prime parte del expression, nos volerea haber un 6xy, e in le secunde parte un 4xy; ma le prime parte es multiplicate per 2 e le secunde per 3, alora nos vide que le productos que manca es le mesme, in cata parte: 2 · 6xy = 3 · 4xy = 12xy. Si vos non ha comprendite lo que io ha scribite in iste ultime duo paragraphos, non dispera: toto essera plus clar in le formula in basso, si tosto que vos vide como io continua le equation precedente:

= 2 · (x² + 9y²) + 3 · (4x² + y²)

= 2 · (x² + 9y²) + 3 · (4x² + y²) + 12xy - 12xy

= 2 · (x² + 9y²) + 3 · (4x² + y²) + 2 · 6xy - 3 · 4xy

= 2 · (x² + 6xy + 9y²) + 3 · (4x² - 4xy + y²)

= 2 · (x + 3y)² + 3 · (2x - y)²

e isto es definitivemente un numero allegre!

Nota que le longor del demonstration es causate solmente de mi desiro de monstrar non solmente le passages del demonstration (lo que poteva esser facite in alicun lineas de expressiones) ma anque le procedura mental que me portava a trovar iste demonstration. Como io scribeva, io non esseva multo satisfacite, quando io trovava iste demonstration; al contrario, io provava un certe senso de delusion, perque io me expectava un solution genial, intuitive, e non un serie de tentativas tanto empiric. Ma toto es ben, lo que fini ben, nonne?

Cammino quindi penso - 2017-06-13 - Il paradosso di Zenone

Alberto Mardegan — Wed, 14 Jun 2017 13:24:00 GMT

Il paradosso di Zenone, o di Achille contro la tartaruga, mi offre uno spunto per parlare di infinito.

Cammino quindi penso - 2017-06-13 - La dimensione impercettibile

Alberto Mardegan — Tue, 13 Jun 2017 07:53:00 GMT

L'esistenza di una quarta dimensione geometrica è compatibile con le teorie dei matematici, che la trattano come una naturale estensione di concetti e proprietà ben noti. Tuttavia la nostra mente non riesce a raffigurarsi entità a quattro dimensioni, limitata com'è dalla nostra esperienza.

Ma come potrebbe una creatura in quattro dimensioni interagire col nostro mondo? In quali forme potrebbe rilevarsi, e come sarebbe capace di operare su di noi?

Cammino quindi penso - 2017-05-19 - Astrazione, qual è il limite?

Alberto Mardegan — Fri, 19 May 2017 18:03:00 GMT

Utilizzo l'esempio dei numeri immaginari per mostrare come non ci sia un limite per il pensiero astratto.

Cammino quindi penso - 2017-05-15 - Zero, numeri negativi e tempi storici

Alberto Mardegan — Mon, 15 May 2017 16:42:00 GMT

La realtà in cui viviamo ha una grande influenza sulla nostra "forma mentis", sulla nostra capacità di pensare a determinati concetti. Lo zero e i numeri negativi ne sono due semplici esempi: oggigiorno sono concetti compresi da chiunque, ma è stato sempre così?

Cammino quindi penso - 2017-04-28 - Matematica e verità

Alberto Mardegan — Fri, 28 Apr 2017 06:13:00 GMT

Le verità della matematica sono assolute, ma risiedono solo nella nostra mente.

Cammino quindi penso - 2017-04-24 - Matematica, in anticipo sui tempi

Alberto Mardegan — Mon, 24 Apr 2017 07:41:00 GMT

Forse il principale motivo per cui a molti non piace la matematica è la sua astrattezza e inutilità pratica. Senza negare questo, provo a dare uno spunto di riflessione.