Scientific Divulgation of Mathematic

(Traduzir)

Mathematical formalism is sometimes exaggerated by the standards of everyday life. Even the scientific method is already quite absurd in our reality, in which to succeed in 3 or 4 attempts seems to be sufficient to determine an “absolutely safe and faithfully tested method”.

Thus, the mathematical formalism that aims to develop a tautology around the facts is very far from a reality that defines “truths” based on a few empirical results. With this in mind, the focus of this blog is to address mathematical argumentation, the formation of its properties and applications through relationships with the world. The posts were developed to address themes that, although artificial, are comic or capable of arousing the reader’s curiosity, sometimes relating them in contexts of literary / audiovisual fictions, playful constructions or other aspects considered to be leisure, linked to a totally different field. abstract that is mathematical formalism. From these constructions of their own meanings, we hope to promote the valuation of the study of formal mathematics, the interest in demonstrations, in addition to presenting in a light way several properties and theorems of nature that are not very contextualizable.

In this way, I consider this blog a collection of texts for scientific dissemination, as I try to present mathematics linked to a formation similar to the monastic one, led by the so-called “pure mathematicians”, to a middle ground in which the common person can read and understand these constructions abstract. The focus in this case is not the teaching of mathematics, although through the reading of these texts and their differentiated approaches, this learning can occur or be used by teachers as resources for their didactic practices.

In fact, there are legal issues to talk about in the middle of a pizzeria, and it is unlikely to be any of the posts on this blog. For several years I realize that these are more boring subjects than politics, football or catastrophes, people just don’t get together in pizzerias to hear how surprising a probabilistic event was, or how sets relate. Nor are these subjects of the curriculum that interest students or concurseiros.

That way, when I set out to work with science dissemination in the area of ​​mathematics, I tried to be cool, talk about cool things, attract the cool guys … that failed, I failed again and then again, until I joined a scientific blog project. The magic of this group is its very existence as a community, because in it we supported each other to increase the publicity and take the “boring” themes to those who find them fun. At the beginning of this work I needed to define a theme for the blog, and then following with the proposal that I had already worked on, I decided to relate playfulness to the rigid structures of mathematical formalism. So it would be neither, for the bad luck of several mathematicians who have come to criticize me about “my demonstration is not 100% complete”.

With this in mind, the blog was made with a name that would refer to mathematics in multiple ways and with an unchanged meaning for different languages, a number that did not come naturally, although it is “natural” to see it in all places, Zero .

I realized in this period working with other blogs of scientific dissemination, that the work on the blog Zero was quite peculiar, because the mathematics in the context of the dissemination often seems centered on its teaching as curricular content. People wouldn’t come to a mathematician with practical questions about how the microwave works, how a virus proliferates … and even if they did, the answer would probably be: I don’t know. Our area is centered on a theme of a more abstract nature and at the same time distant from our practical and utilitarian world. Despite this, there is a range of interesting concepts and content that when we have enough time to discuss them, we realize that “understanding” is the real benefit of this study. Knowing how to choose a pizza using optimization, or even reading an internet meme about π, are several useless things that together are no longer so uninteresting and divulging them is somewhat laborious, but directly proportional.

The main stimulus for this work was my perceptions of the world itself with its mathematical properties, which, when I try to tell others, I notice an immense difficulty in understanding. It is as if I saw things very simply, and just a verbal explanation was not enough for other people to understand. So I started this production with the intention of telling some of those “fun” things that I see all the time, and which is easier to explain with texts, calculations and descriptive drawings.

For example, if there is a bijector relationship between the members of a WhatsApp group and students in a course, everyone in the group will be students and all students will be in the group.

bijector relationship

Course students

WhatsApp Group

João→

Maria→

Pedro→

Júlia→

←João

←Maria

←Pedro

←Júlia

If there is an injective relationship of course students in the WhatsApp group, we would be sure that all students are in the group, but we could not guarantee that everyone in the group would be students.

injective relation

Course students

WhatsApp Group

João→

Maria→

Pedro→

Júlia→

João

Maria

Pedro

Júlia

Cláudio

Likewise, if there is an overjective relationship of course students in the WhatsApp group, we would be sure that everyone in the group is a student, but we could not say that all students are in the group.

overjective relation

Course students

WhatsApp Group

João

Maria

Pedro

Júlia

←João

←Maria

←Pedro

Thus, a bijector relationship is both injective and overjective. A very simple concept and present in modules of disciplines with distance monitoring:

1. We do not want people outside the course in the group;

2. We don’t want to leave anyone on the course outside the group.

If there is a bijector relationship between the course participants and the group members, then we are sure that these two interests are achieved. Similarly, if we have the class divided to work on several projects, each group must have an overlapping relationship with the class (only students of this course will participate in the group), but not injective (we do not want the whole group together in one project) .

Featured image credit:
https://xkcd.com/435/

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