Preview · Didática block only · will be inserted between Onboarding and Prelude II
Didática · four faces, one object

This book has four faces.

Not a hierarchy, not a ladder — four surfaces of the same mathematical object, each of which you can enter first. They are Ler, Simular, Provar, and Ensinar — to read, to simulate, to prove, to teach. They travel in Portuguese through every Level. Meet them once, in the legend below, and afterward they will carry you.

Ler
/leɾ/
Read · C · Contract
From Latin legere, "to gather, to choose." In Portuguese ler is also the soft verb of attention — ler alguém, "to read a person." This is the face where the book speaks and you listen. Colour of the Contract operator, C.
Simular
/simuˈlaɾ/
Simulate · K · Curvature
From Latin simulare, "to make alike." Portuguese keeps the theatrical sense: simular is to stand in for, to play-act, to let a model take the part of the thing. This is the face where you move the controls and watch the math answer. Colour of Curvature, K.
Provar
/pɾoˈvaɾ/
Prove · F · Filter
From Latin probare, "to test." Portuguese keeps all three meanings alive at once: provar is to prove, to taste, and to try on clothes. A proof, in this book, is something the body checks — not only the mind. Colour of Filter, F.
Ensinar
/ẽsiˈnaɾ/
Teach · U · Unfold
From Latin insignare, "to point out, to mark." Ensinar is not authority — it is a finger pointing. This is the face where the book hands you an unfinished problem and you carry it forward. Colour of Unfold, U.

Every Level offers all four faces. Each closes by leaving one open problem in your hands. Not because the book forgot to solve it, but because that is how the book knows you are learning. This is Axiom 9 (Honest Incompleteness) made didática/d͡ʒiˈdatʃikɐ/Greek didaktikos, "apt at teaching"; PT keeps the noun feminine and the stress light — didática is the way, not the authority..

You, the reader, this book will call camará/kɐmaˈɾa/capoeira-companion, the one in the roda/ˈʁɔdɐ/"the circle," where the practice is done with you. Not student, not pupil. Companion in the circle. When a Level hands you back an open problem and you carry it out of the book, the sound of your work returning to the roda has a name in Portuguese: ressonância/ʁesoˈnɐ̃sjɐ/resonance, but in capoeira it is specifically the answer the circle gives to what you played..

"Every session leaves one open problem in the student's hands. This is Axiom 9 (Honest Incompleteness) made pedagogical." — Vol IV landing (3M), sibling page.
Didática · quatro faces, um só objeto

Este livro tem quatro faces.

Não é hierarquia, não é escada — são quatro superfícies do mesmo objeto matemático, e você pode entrar por qualquer uma delas. São elas Ler, Simular, Provar e Ensinar. Atravessam todos os Níveis sem tradução.

As quatro faces respondem às quatro cores do encadeamento operatorial herdado do Volume IV — C · Contract (Ler), K · Curvature (Simular), F · Filter (Provar), U · Unfold (Ensinar). Cada Nível oferece as quatro. Cada Nível se fecha deixando um problema em aberto nas suas mãos — não porque o livro esqueceu de resolvê-lo, mas porque é assim que o livro reconhece que você está aprendendo. Isso é o Axioma 9 (Incompletude Honesta) feito didática.

Você, leitor, este livro chama de camará. Não aluno, não pupilo. Companheiro na roda. Quando um Nível devolve um problema em aberto e você o carrega para fora do livro, o som do seu trabalho voltando à roda se chama ressonância.

"Cada sessão deixa um problema em aberto nas mãos do estudante. Este é o Axioma 9 (Incompletude Honesta) feito pedagogia." — Folha de rosto do Vol. IV (3M), página irmã.