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."

So, for programming Marce, Carmen and I will be making a mini project which will inform the user about the percentage in which people have been absent.

For this, there will be needed an input of the amount of days people haven't attended the MPC, and the program will print out the percentage you've been out.

Edward O. Wilson emphasizes on how important the science is to humanity. How objective truth is so important, and how pseudosciences are dangerous and keep us living in an illusion. A dangerous illusion.

Humans have developed tools in order to attain a better understanding of the world. Or to live better. The discoveries and the tools have been innovated and recreated, perfected and have let us understand things that we thought gods were able to do in the past.

It amazed me how unexplainable it is, yet, that math is present in our universe, like if it was articulated in a logical structure. Is it? Probably.

Scientists are trying to understand the ultimate. To achieve objective laws, by trial and error. But consilience is attainable when something is proved as truthful. And this chapter is of deep meaning to me, and of great importance to the core of the chapter:

"Science, to put is warrant as concisely as possible, is the organized, systematic enterprise that gathers knowledge about the world and condenses the knowledge into testable laws and principles. The diagnostic features of science that distinguish it from pseudoscience are first, repeatability: The same phenomenon is sought again, preferably by independent investigation, and the interpretation given to it is conformed or discarded by means of novel analysis and experimentation. Second, economy: Scientists attempt to abstract the information into the form that is both simplest and aesthetically most pleasing - the combination called elegance - while yielding the largest amount of information with the least amount of effort. Third, mensuration: If something can be properly measured, using universally accepted scales, generalizations about it are rendered unambiguous. Fourth, heuristics: The best science stimulates further discovery, often in unpredictable new directions; and the new knowledge provides an additional test of the original principles that led to its discovery. Fifth, and finally, consilience: The explanations of different phenomena most likely to survive are those that can be connected an proved consistent with one another."

Diego's morning meeting was great! I had so much fun, we saw so many different things. We had a little bit of everything.
First of all, he gave us some mathematical problems to deal with like doubling numbers or dododoubling them. (Yes, it's 3 times doubling a number). We received a prize if we actually did the problem and it was complex, I have to admit. At least I received one prize. Also, I notice my pupils where dilated. Haha, kidding, but I notice that some people gave up easily.

After this, we watched a little Hayek vs. Keynes. Rap. AMAZING. I love these videos, I would watch them again and again. (Notice the Bible joke)

After this, Dieguito was on fire! He brought us MPC cupcakes :) (but, we had to eat them like educated people)

So I've been advancing in Ruby so far. I've learned about Strings, about controlling flow, comparisons and operators.

You find a lot of logic here.
Long live Codecademy.

Kyle told us that he would arrive late, so the last group presented their Project Euler's problem: number 10. That problem is sick, insane! Haha,
This is what it prescribes: 

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.


So, first I came to the idea that if we found a common sense in all prime numbers the formula could be done. But, there was an issue: Pablito mentioned that there's no formula to this beauty.

But still, I recognized that there are some numbers that if they were divided with primes, the remainder wouldn't be zero. These are the numbers we came up with:

2, 3, 7...

But, the theory was wrong. There are exceptions. So, we're still figuring out. 

Today Carmen and Pablito worked in their problem out of Project Euler. They decided to do number 20. After several trials and errors, they did it.

Here's the problem:


n! means n  (n  1)  ...  3  2  1

For example, 10! = 10  9  ...  3  2  1 = 3628800,
and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.

Find the sum of the digits in the number 100!


After that we discussed on how important libraries are in Guatemala and Kyle shared his "Sopa de Piedra" project with us. This project consists in a library for children who want to learn by themselves go and have fun and learn lots of stuff! There is were real things happen! 

I love Walt Disney for making these kind of terms that were sometime so complex and divine for mathematicians and turning them into a language so comprehensible that it just amazes you. 

We take so many things for granted. So many things. And they have this complexity, this story that can turn to be so interesting. The world is full of wonders, of doors waiting to be opened. 

Where our number symbols come from.

The evolution of our nature is so amazing. There's a theory that we took a standard to counting till ten because our fingers are ten. I have also a theory that is related of the previous chapter: that Pythagoreans saw the number 10 as something really important because of 10 = 1+2+3+4. So, probably there's a cultural evolution in this standard and the meaningful part of our natural resources as 10 fingers. (Is that a numerical representation of our universe? this is a joke.). There's a really good quote related with what I just said:

"Only recently did humanity settle on the current methods for writing numbers, and their use became established through a mixture of tradition and convenience. Mathematics is about concepts, not symbols - but a good choice of symbol can be very helpful."


Numbers weren't found all at once: we had models that counted till 10, till 20, till 8! And eventually we adapted to one that was more efficient. The number 0 was found by the Babylonians and it was ignored. Still, it reappeared centuries after with the Hindus. It also reappeared with an isolated culture: Mayans. I can't help to see that incredible knock of something that is TRUE, the existence of a number that doesn't represent nothing at all! The ZERO! 


The use of certain numbers for calculation started spreading thanks to markets, and this was through Italy. Stewart mentions "There was metaphorical trade in ideas as well as literal trade in goods." And there is where Fibonacci (Leonardo di Pisa) shows up. He wrote the first book which became really famous using the Arabic numbers. He was like the Cervantes or Dante for numbers! 


Also, the market promoted the usage of negative numbers. (Hindus were the ones who approved them, because some cultures rejected the idea). But you know, debts are a fact and the way to successfully document and talk of them is through negative numbers!  

Geometry is the beautiful and visual way of mathematics. Because of pictures are less formal than symbols, (they're more easy to understand), the beginnings of geometry are reflected in that approach to this "easy" but really important form of calculation.

The logic of geometry is almost surreal (as ironic as it may sound). Pythagoras saw in music a mathematical presence. That makes me wonder whether the universe is a really logical thing, instead of a chaotic set of even. Is this chaos numerical? 

Still, reminding the fact that music is merely perceived by humans only it makes me think the complexity of our brains to understand the universe through that symmetry and beauty of sound. I mean, we have this idea of whole steps, octaves and fourths in music! Is it a matter of culture that we became accustomed to certain sounds?

Also, triangles and symmetry is so beautiful and has this sense of perfection that cultures even considered them sacred because they were so rational! (fatal conceit anyone?)... Then, Hippasus of Metapontum discovering that the diagonal that divides a square is irrational made people really angry that they killed him. (idem. Haha).

My beloved Euclid comes to the scene, (300-250ish B.C.). The language for the book Elements is simply unique. He gets you through the second dimension through tons of connections (even if it's mainly conceptual). The logic of Euclid is simply amazing: he sets the rules of the game and throughout the reading you play with those. 

"Rational thinking, logical argument, is equally vital. Our world is to complex, potentially too dangerous, for us to base decisions on what we want to believe, rather than on what is actually the case. The scientific method is deliberately constructed to overcome a deep seated human wish to assume that what we want to be true -- what we claim to "know" -- really is true. In science, emphasis is placed on trying to prove that what you deeply believe to be the case is wrong. Ideas that survive stringent attempts to disprove them are more likely to be correct."