Today was Kata's morning meeting. She brought us some paper and made us draw. But not the conventional way of drawing!
First it was not watching and knowing...
Secondly, it was not knowing and watching.

It was quite fun. And I find quite interesting, how scientific work needs that awareness, of the senses and of the knowledge in order to grasp the discovery in its more precise explanation...

This was the first dialogue I enjoyed with the MPC talking about Words and Rules. Definitely, this experience was really cool.
We decided to understand the theories that were introduced in chapter IV "In Single Combat".

Pablito commented something that is really relevant in this chapter: It is not just a matter of understanding verbs, language or grammar. It goes beyond: it is a study of the mind, of the methods of thinking. Are we fully rational? Are we fully empiricists?

The dialogue evolved beautifully, and I was able to understand many things I didn't see before in the chapter. Those are written in my reflections of the chapter.

This chapter talks about the different methods of thinking that are introduced in the preface. Is the mental process in which our language conjunctions happen associative or pure memory?

Pinker describes the two different theories: Chomsky and Halle's, and Rumelhart and McClelland's. Chomsky and Halle talk about how our mind is full of memorized rules, while Rumelhart and McClelland talk about how our mind is a network of associations. This is a debate that brings the matter to a more profound field: philosophy. The two schools of thinking: empiricism and rationalism. Chomsky and Halle's theory would be the rational, therefore, etc. (As my friend Euclid would say.)

Pinker mentions that the way language works, is a combination these two methods of thinking:

"Prince and I have proposed a hybrid in which Chomsky and Halle are basically right about regular inflection and Rumelhart and McClelland are basically right about irregular inflection. Our proposal is simply the traditional words-and-rules theory with a twist. Regular verbs are computed by a rule that combines a symbol for a verb stem with a symbol for the suffix. Irregular verbs are pairs of words retrieve from the mental dictionary, a part of memory. Here is the twist: Memory is not a list of unrelated slots, like RAM in a computer, but is associative, a bit like the Rumelhart-McClelland pattern associator memory. Not only are words linked to words, but bits of words are linked to bits of words."

Pablito presented Proposition 7 today. His presentation was beautiful, I got more excited with Euclid! Again, Euclid is conquering my heart.

Given two straight lines constructed on a straight line (from its extremities) and meeting in a point, there cannot be constructed on the same straight line (from its extremities), and on the same side of it, two other straight lines meeting in another point and equal to the former two respectively, namely each to that which has the same extremity with it.

This is the proposition. One of the cases (the one we worked) is like this:

I got some "Aha moments", and understood Euclid perfectly. Now, this is what social cooperation means! It would've been even more fruitful if absolutely everyone had said their thoughts.

Amazing. Thanks Pablito.

We presented today Proposition 11 through 16.
The class was divided in two: those who didn't understand the first propositions and the others that were on track.
It was productive for both of the sides, and we made a great progress. 

We had a dialogue on the fourth chapter of the book Taming the Infinite, in which Ian Stewart talks about  Algebra.
The beauty of Algebra is something that a lot of people have observed in the dimension to be actually aware that Algebra is a meta-cognition of the rules of mathematics. It actually begins the language, and recalls the possibilities. 
Carmen made an excellent connection to Consilience. I made a connection with Euclid. 

"In advanced mathematics, the use of letters to represent numbers is only one tiny aspect of the subject, the context in which it got started. Algebra is about the properties of symbolic expressions in their own right; it is about the structure and form, not just number. This more general view of algebra developed when mathematicians started asking general questions about school-level algebra. Instead of trying to solve specific equations, they looked at the deeper structure of the solution process itself."

On the last chapters we got to explore new terms like WYSIATI. (What You See Is All There Is). This is used to explain that overconfidence that we humans suffer. That illusion of knowledge we tend to have. A lazy System 2 would recall to the known, instead of doubting the known. 

Another term learnt was Mental Shotgun, it means that one is predisposed to compute more than the things we actually want to compute. For this, I might give the credit to the unconscious computations that Wilson speaks about in Consilience.

Since the impact of first impressions are great, one of the habits we want to improve is the habit of being amazed with the ordinary. That is what constitutes an extraordinary man.

Besides, I was really amazed in our matching skills with sounds. For this, I am asking myself the question: why do we react in certain forms toward a kind of musical scale or chord? Is there a language behind this? 

Dylan told us something about how the frequencies are a tool for us to have a perception of this matter, this was really interesting: Primitive men designed their caves in a certain way that the waves perceived by the brain are below the 20Hz our ears perceive. For this, the cavemen just felt weird vibes, these were infrasonic vibes!!

We make questions because of System 2. The questions are biased in unfamiliarity and of course, it requires effort to wonder, to proof our instinctual possibilities. Because first impressions, as I said in the latter chapter, are really influential; we tend to jump into conclusions and we are lazy often to ask questions. It's hard to accept our ignorance.  

So we have a learnt and an instinctual income in our judgements. Also, we put prototypes in our minds according to the situation. Kahneman puts a perfect example: the birds in the oil. There was a fund raising in which different big amounts of birds were about to be saved. When the number of birds is nearly impossible for us to visualize we tend to respond likewise: it doesn't matter if there's 2000 or 200 000 birds, people had a similar response. 

"the awful image of a helpless bird drowning, its feathers soaked in thick oil. The almost complete neglect of quantity in such emotional contexts has been confirmed many times."

We connect different emotions to different types of things. For example loud noises and crimes. 

"If you heard two notes, one for the crime and one for the
punishment, you would feel a sense of injustice if one tone was much louder than the other."

Also, we don't just call one computational workout when we want to find out something. The way I see it, is like a quantum unconscious selection of scenarios and formulas. For this I would also recall the illusion Consilience keeps telling us about. 

This chapter is all about irregular verbs and plurals. It is amazing how we memorize these, and we think that maybe these words were created just like that. Past tense is brought, present tense is bring, etc. Well, no. That's not "just" it.

Language is an evolving system of words. And the tense of many irregulars were at some time, years ago, rules. 

"Words rise and fall in popularity as the needs of daily life change, and also as the hip try to sound different from the dweebs and graybeards. Speakers swallow or warp some sounds to save effort and to enunciate or shift others to make themselves understood. Immigrants  or conquerors with regional or foreign accents may swamp the locals and change the pool of speech available to children."


Ah, beautiful words. In this paragraph I can see the cultural, economical and political income of the changes in language. Isn't this extremely beautiful and complex? So many cultures meeting and making mixtures being translated in words. Words that we use so casually.

We tend to jump into conclusions. This is our System 1 screaming, because our System 2 is lazy. It is fine to make some intuitive movements, but sometimes System 2 acts simultaneously in unfamiliar situations. In this, it jumps into conclusions. 

"System 1 bets on an answer, and the bets are guided by
experience. The rules of the betting are intelligent: recent events and the current context have the most weight in determining an interpretation. When no recent event comes to mind, more distant memories govern."

Doubting and reconsidering is the job of System 2. It makes us "unbelieve" certain things. I think that is one of the reasons why people tend to just say yes when their teacher tells them the "right" answer.

"System 1 is gullible and biased to believe, System 2 is in charge of doubting and unbelieving, but System 2 is sometimes busy, and often lazy."

Also, we tend to jump to conclusions in occasions which are he president’s politics, you probably like his voice and his
appearance as well. Even height! Hello Barack Obama! Well, that's the reason why the new impressions which are the more superficial tend to be the more influential.

On this, I think that System 1 retrieves to all of that unconscious neurons we have. And there the competitions of scenarios happens.

"The combination of a coherence-seeking System 1 with a lazy System 2 implies that System 2 will endorse many intuitive beliefs, which closely reflect the impressions generated by System 1. Of course, System 2 also is capable of a more systematic and careful approach to evidence, and of following a list of boxes that must be checked before making a decision-- think of buying a home, when you deliberately seek information that you don’t have. However, System 1 is expected to influence even the more careful decisions. Its input never ceases."