[MUSIC] We are now halfway of this course. We already cover a lot of topics. But maybe it's good to make a kind of recap, because the topic is quite, it's quite difficult. It's all about thinking, so, just to have this recap let's make a little exercise. You see a list of 40 words from mathematics. Look at the words. Now I ask you to organize it and you feel when we are facing the world, we want to organize it. So what comes in your mind? As a possibility to organize. Probably the first one is to use existing categories like numbers, and then you could put zero and you could put 23 and, and others. Maybe you can use light operations and you put addition and subtraction etc,. That's a way. What do you do? You use existing concepts. You use existing simplifications. But you can be more creative. You can organize the 40 words in a different way. For example, imagine you are a teacher and you teach French. Probably you have another ID to organize. Yet, this is strange, some of those words are the same in French, both in French and in English like zero, equation Surface, et cetera. And certainly, you have another way to organize. But of course, this is more creative. It is creative, but it is objective. You, no discussion. Surface is the same in French and English. Imagine you are interested in poetry. And you love poems. Maybe in, you're interested by words with the same end like, I don't know, angle and triangle and things like that, because you want to write poems. And again, this is creative, a bit surprising, but objective. And then you have a third way to organize, completely subjective, words you find difficult and others you find easy. But, of course, that's your point of view and people won't agree. So you see, even if we share this. Desire to organize many different way. Classic with existing concepts or more creative and then you have two options. Objective and subjective. And this is a good exercise to recap, you remember lecture number two? It was highly sophisticated, highly sophisticated with the, this is simplification of the sys, simplification. But it's good just to remember, how does it work between the world and ourself? Does this probably the most simple possibility, you have the world, you simplify the world and you use the simplification. Using a simplification is called deduction, not too challenging. Simplifying is induction, is when you build the category, the concept, you conceptualize. And that's where everything happens. We will see the next lecture where big mistakes and great ideas suddenly come. It's why we induce. Probably a good analogy is mathematics. Induction is more like arithmetic. You see one restaurant and then another restaurant and then another place where you can eat, and suddenly [SOUND] you add them like in arithmetic and you build, you create a concept, a restaurant, a restaurant. Probably deduction is much more like algebra. You use x, the variable x restaurant and you go down to the world. And you can test whether it's a good concept or not. So you see, and this is a good wake up. Thinking is like an interaction between the world and yourself with some rules. We need to go a little bit deeper in rigor because you have noticed I don't use any numbers. I don't use any figures. But philosophy is also about good definition. Like Descartes said, clear and distinct ideas. So, the next four slides are definition. Definition. Maybe a bit dry, but we cannot skip them and we going to use them a lot. So, let's move to the first definition. A model. I've talked about, a lot about models in the last lecture and still now. We need a definition and now you have time to read it. A definition is really important we're going to use this word so much, we need to avoid any kind of confusion. So, a model is a simplification. You have see I have called a model a box and that comes from the thinking new box concept that we will see in the next. lecture. But from the very start, you, you know that creativity is my passion. And the whole story, the whole course is organized in such a way that we will finish with creativity and innovation. That's why I use box as a synonym for, for model. So, we need also, good definitions of the two arrow so let's talk about deduction, you won't be surprised to read what you read because that's what I said to many, many times. Deduction is the easy stroke of the thinking, you move from the simplification and you go down the world. You go to the market, etc. To me, one day on computers. I told you. The other definition, is more important, because that's where everything can happen. When we, when we induce something not really rational happens. You don't control completely an induction. You just see little piece of the world and suddenly you craft a concept. It's a process which is not 100% uncontrol-undercontrol. That's where you can make mystics, but that's where you can have great ideals. And just to finish this recap, let's go to the definition of thinking. I already gave another one in lecture two, I said thinking is mostly about using simplification and crafting simplification. And, it's another way. It's a way to paraphrase but thinking is so important that probably two definitions relevant.
