the notes of X

Permanent Confusion


Church and Turing / Being stupid

We leave the room and turn walk in the direction opposite to the one from which I came, going through a big corridor which resembles the one from my school where the classrooms are. I hear all kinds of sounds coming from the direction where we are headed - footsteps, music, and also numerous different voices, all shouting and having conversations. I panic as I realize that I am about to make my first “public appearance” to the people in the facility. I try to calm myself by saying to myself with a smug voice (which is, for some reason, the way I usually talk to myself) that I most likely surpass those people in any respect conceivable, and so all I have to do to make a good impression is to act natural, only to realize that I don’t even know what does it mean to act natural in this facility, and that I hardly got any clues for it from my encounter with Alex. I try glancing at him, and trying to see the expression he would adopt before entering, only to realize that he is already a few steps in front of me and going so fast that I almost have to run just to keep up with his pace, and observing the difference between the way we move reminds me of the even bigger difference between the way we are seen by the others makes it apparent that sticking with him is not a good strategy. So what, should I act to the people here in the same way as I act to my classmates? The question reminds me that the way in which classmates usually act towards each other is much different from the way they do it at my school - the spirit that dictates our actions is that of competitiveness - it is all about who knows more and who can do more in a framework that is almost as rigorously-defined as the subject matter which it puts to the test. In other words, my behavior was always based on a precise set of goals, something which I am sure I won’t see here, except if just “getting better” counted as a goal, and it most definitely could not (if I had time I would have spent a few seconds just to appreciate the irony of the fact that letting myself slip for just a few hours from the norms very strict environment that I inhabited all my life has at my school has put me into an environment that, as far as I could see, contained no rules whatsoever. But maybe it was just me being too quick to judge.)

As we get closer to the door I start seeing the people in the hallway. The way they act resembles the one in a school, but it definitely is unlike my school, where everyone just sits there and rest on their shoulders because they are tired, and talk, if not to about the things we study, about computer games or problems that are probably formally equivalent to the things we study. I continue talking, considering the different ways in which I can act. Should I try to make my best to find unlikely friendships with Alex’s circle, which was what I was set out to do originally, or should I take some time to wander through the hallway to look around and be like “Sorry, I just want to hang around for a sec, it’s OK, if you don’t wish to wait for me then, maybe we can meet after”. Or should I quickly find my crowd (or the one that resembles it most) and ditch everyone else, or should.

Without me noticing, (as these things always seem to happen without us noticing) this dilemma has become like a leitmotif of my life. It was the dichotomy that is best exemplified by comparing the approaches of two great computer pioneers - the well-known Allan Turing and the (perhaps slightly less known) Alonzo Church. The dichotomy was apparent in this account by Solomon Feferman.

Kleene and Rosser had received their Ph.D.’s by the time Turing arrived and had left to take positions elsewhere. So he was reduced to attending Church’s lectures, which he found ponderous and excessively precise; by contrast, Turing’s native style was rough-and-ready and prone to minor errors, and it is a question whether Church’s example was of any benefit in this respect.

So, should I be more like Allan Turing - passionate, giving a voice to my ideas, as weird as they can be, and live a life with a lot of ups and downs, or like Alonzo Church - pragmatic and disciplined and always following a strict plan. You could observe how both approaches worked for both of those people by studying their biographies, but for me, it is much more important to consider how they influenced their work, In fact this is why I picked exactly those two people who, if you don’t know, where the first to devise formal models capturing the concepts of an “alghorithm” and “computation” (there was also a third guy who did at the same time as them but no one remembers him). Look into the Turing Machine - a weird, you might say convoluted model, and try to compare them with the Alonzo’s solution which is as simple and elegant as the symbol, (the only symbol!) that contains its gist - the Greek letter lambda. True, Alonzo was much more spot on, nailing the concept of computation without any kind of ceremony, but Turing Machines - in addition to answering the question they are set out to answer, raise so many other questions that they changed the direction that the whole field took. But although I am always eager to apply it, that whole Church/Turing dichotomy was never of much use for my life - beside the fact that I cannot decide who’s side I am on (Turing machines are cooler, but at the same time I lean towards Church simply, because his life was more stress-free) I always seem to be put in situations where neither approach seems feasible, or it is hard to differentiate which is which, like for example right now following Alex would be Turingy (I invented the word), because I would be meeting people who I wouldn’t normally meet, but at the same time abandoning Alex would be Turingy, as well, him being the only (friendly) person I know. In short, I often realize that I am thinking in a given way just for the sake of thinking in this way - maybe it is not the choice I make between Church and Turing, but the dichotomy between them itself, that defines my life. It (the dichotomy) certainly defined the way I acted as we reached the room and the first impressions that I made to the people there - a few moments after we entered the hallway I realized that there some people are staring at me, while I was still contemplating how should I behave, based on the comparison between Church and Turing, while gazing at the ceiling like a complete idiot.

Still, at that moment I wasn’t certain that I looked stupid i.e. I was like any other person who sees everyone being stupid and ridiculous all the time and has the sneaking suspicion that they too, are sometimes stupid, but are never really sure of it, although the data no doubt shows it to be the case. As if me being stupid was something that is highly unlikely, like those events in American movies where they always say “Impossible!” or “I checked the calculations three times!”, before they realize what we, the spectators already know from the trailer (meteors, zombies, aliens etc.) And even in those situations nobody really believes they are stupid, except if they think that the way that they are being stupid is not stupid to them. It seems to me that we, people, are defined by our imperfections - although they make us self-appauled, we insist on them in the same way as we insist to be heard when we speak even if we don’t have anything substantial to say.

Like, even if I knew how should I behave in this situation, even if I have some “oracle” in my brain, that was capable of devising the most well-received way to act in a given social situation, I would probably never use it, or use it very rarely, as I assume that the social strategies, the ways of acting that it would output for me would be so different from the way I act usually, that using them would mean, for me becoming its puppet (I won’t be using it, instead it would use me.) Thinking about this, makes me happy for being so socially awkward or, more precisely, socially clueless (I think this expression should exist) i.e. not knowing how to act, as actually knowing how to act in a given situation would mean that I would be able to be seduced by the potential social success to ditch my whole personality. to which I most probably would give in, given my usual levels of anxiety. So probably I am better off where I am now - stuck in the undecidable (note my clever use of computer science terminology) dichotomy between Church and Turing.

Meeting my roommate Alex / Picking friends / Who am I / How switching places would solve both of our issues

Hallway Church and Turing / Being stupid

X Nerd stereotypes / How I got my nickname / Establishing connection with my younger self

Fence Outside / Not being punished / Discreet and continuous models

Outside This or nothing / The moon / Fractals / Me and Alex / Explanations / Is the world mathematical

The sleepover Anna's childish behavior / Critics / Boring robots / Adoring Anna

The sleepover contd Irony / Heroes and deserters / Retreat to where? / Real and ideal / Choices

Sex Anna's fantasy / What makes us weird / The establishment and being normal

Cigarettes Alex's good night sleep / About me and Alex again / Sex and love / The proof that P does not equal NP