Most of the Euclidean/Galileo/Newtonian days I struggle to keep focused on the proposition, I don´t know if it was because of the coffee I had previously drank or just because, but I was very aware of everything, very focused, and on task. While Isa was presenting Lemma 2, I wondered why was Galileo multiplying the rectangles and squares by four, and it wasn´t until the last step that we finally figured out why. Las week Kata presented proposition unequal parts, the rectangle composed of the unequal parts and the square made out of the half line or of the square made out of the line cut into equal parts, Here, Galileo uses this just unequal ones, he multiplies everything by 4 so that he can use the entire line, without to break and so, a beautiful butterfly came out. We were able to watch the entire process and we have had that butterfly since it was a worm. It was very representative of our beautiful moment of understanding and learning. We named her Galilemma in honor to Galileo and Lemma 2.
|Hey, I´m the square on the half|
After this we talked about the differences between Euclid and Galileo: in the enunciations of Galileo, he uses things that happen in the real world and he uses Euclidian geometry to prove it. But the things that he enunciates you can see happen in the real world. Euclid is much more philosophical in this sense and may I say more abstract. It is something that works perfectly in the mind and not necessarily in the real world. We also mentioned that we are logical beings, yeah, right, everyone knows that. But what this means is mucho more than what we usually think. Our knowledge is not only based on experience, but it also relies on logic. We don´t need to see some things or to prove them in order to believe that they are true. Euclid´s common notion 1 is a perfect example of this: “things which are equal to the same thing are also equal to one another” without doing an experiment or having a proof, we know this to be true. We know this by pure deduction. When we use a lot of examples that show the same result, we are inducting. The problem with this is that there is no way in which we can prove that the things which we have seen in the past will also hold truth for the future. There is no proof of them, the only thing we know about them is that until now we know this things to happen. This is what is called the problem of induction. I remember that I talked about this in an HIS seminar with a Norwegian guy who was reading Gödel, Escher, and Bach. He taught me about the problem of induction with the classical “white swan-grey swan” example that Andrew used today. This was a moment of serendipity. All of this talk took us into Stuart Mill and his claims of inductive generalization and into Kant´s hardwire logic system. Before this dialogue I would have said that we can only know what Mill says and that is the only method in which we achieve truth. After having this conversation I would say that I sympathize more with Kant´s theory. We are trapped in this sphere of human reasoning and knowledge, as Mises would say: it is our one and only truth. It doesn´t matter if there is anything outside of our sphere, because we can´t reach it or understand it. We are trapped in this human bodies and minds, it is what it is. Just like with the “self evident” propositions, there is no proof to many things that we think true, but still our logic permits us and makes us believe that it is.
Ways in which we learn and know
1) Self-evident, axiomatic, common notions, certainty.
2) Deductive inference from known facts.
3) Empirical knowledge: experience: induction (generalization from particulars).
After we had a dialogue on Human Action followed by a storm of acknowledgments I felt really good. We had such a productive day, full of learning and team work. Sadly we didn’t have such a long debrief because four of us were heading to the Business School for a conference called “Life in Silicon Valley”. Five young entreprenerus, with ages ranging from 16 to 25 came to the university and were to give what seemed a very interesting conference.
Followed by a run of about four minutes to get to the business school on time, Carla de Hess presented each of the speakers and the first hing that caught my attention was that the yonger girl mentioned that she had sent at least 200 mails to start her journey and that less than 20 got replied. The guy who opened the conversation was David (davidad.net) by saying that in Silicon Valley, people are more supportive of doing projects in general. Since he got a Phd from MIT at age 14, he mentioned that in Boston people would always ask him, after he told them about an idea that he had or a project: “why do you want to do this?” and in Silicon Valley the most popular response would be: “why are you not doing it yet?” or “how can I help you?”. David said that we should always be doing whatever we are excited about. These people were very excited about what they were saying. It is a shame that I am terrible at remembering names, I do remember that one of them is a Thiel Fellow working on making scientific knowledge more accessible to people. I could see that all of tem were extremely passionate human beings and they even offered to help us with anything that they could.
Pros of being in Silicon Valley (and their connections to our ideals at the MPC):
- Empowering environment
- Makes people happier
- Community of like-minded people
- Easy of failure
- Jumping at things you have never seen before and learning something out of them.
- Fast feedback
- Meritocracy: your degree doesn’t really matter, your past doesn’t really matter. What matters is what you are doing at the moment.
- Forgive and forget
- Environment of learning and curiosity
- Tolerance for risk
- Willingness to learn and listen
- Supportiveness of creation
- Peers intellectually engaged and interested in what you do.
- Incentive to produce as much as you can because other people are doing the same.
- Testing ideas
- Culture of innovation
- Group of people that genuinely believe that they can change the world, and they are doing so!
- Writing is important: not everyone can see you, but in nowadays everyone can read you.
- The general question is not why, but, “why not?”