A few years ago, the Dutch Bach Society set a goal of performing all of Bach’s (Johann Sebastian) works, recording them on video and making them available to the world for free. A crazy cool plan. You could say a new beginning, were it not for the fact that they have already started. Bach’s work is numbered according to the BWV Index (Bach-Werke-Verzeichnis), which extends beyond 1100. In total, it includes 160 hours of music. It’s not ready yet, but you can immerse yourself in allofbach.com. (Or, if you don’t really like it, go for it. Although you don’t have to go to this site first.)
Much has been written about the similarities between Bach and mathematics. I don’t need to repeat that here, but I would like to say something about this completeness. Mathematics exists by virtue of completeness, which is why it is so beautiful that the Bach Society also wants to honor Bach in its completeness. Anyone who wants to prove a mathematical theory wants the theory to hold up for the entire area to which this theory applies. Take, for example, the well-known Pythagorean theorem. This applies to right triangles (triangles in which one angle is exactly 90 degrees), and it states that the sum of the two sides of a right rectangle (the two sides meeting at an angle of 90 degrees) is equal to a square of oblique silk. Or, as almost everyone knows the phrase: a2 + B2 = C2. If you want to prove this statement, you must prove that this statement is correct All Right Triangles. Once there was a right-angled triangle to which Pythagoras did not apply, it was no longer a theorem, but rather a cracked conjecture.
[Deze alinea mag u overslaan als u in uw weekend geen zin heeft in te veel wiskunde.]
Completion is a concept that returns in mathematics in various ways. In topology – a subfield of geometry – completeness says something about the density of a group – and how close its elements are to each other. The exact definition goes too far (even in this paragraph), so I’ll stick to an incomplete definition of completeness: the set is complete as it is for every converging row in that set – this is a row that converges to one term point – this term is also the point in the set. Take the set of all fractions, that is, all numbers in the form a / b, where a and b are random integers. This set is not complete. I can create a row that looks like this: 3 … 3.1 … 3.14 … 3.141 … 3.1415 … where each subsequent digit adds another decimal place to the number pi. (In fraction notation: 3/1, 10/31, 314/100, 3141/1000, etc.) The term for this row is pi, but pi cannot be written as a fraction. Therefore, the set of all fractions is incomplete.
[Welkom terug!]
I think everyone has a tendency to be complete to a greater or lesser degree. That’s why we love rhyme: It gives the temporary feeling that something is totally fine. That’s why we’re bringing our Caravan Peanut Butter to France: totally at home. This is why we feel offended when our prime minister says in a debate like this week about the formation group, “Yes, I lied, but I did it to my knowledge and belief.” A row of elements all chosen with “the best honor and conscience” cannot, in your opinion, end with a lie. Likewise, we do not accept that Mark Rutte claims that his memory is incomplete, while offering a complete overview in other areas. What remains, then, is an incomplete confidence.
This is devastating. Without trust, an alliance cannot be formed, because in our life – and certainly in politics – it is almost impossible to be perfect. Anyone who wants the full story at the table quickly gets desperate. Ask Pieter Omtzigt, or follow Lukas van der Storm on Twitter and in this newspaper. But the Bach association will pass the completion test. I am currently listening to BWV 733: Trip over the Magnificat, Played by Matthias Hinda on Organ Muller in Saint Bavo in Harlem. Then only one thing remains: complete surrender.
Jan Beoving is a mathematician and comedian. In his column he plays with natural sciences and language. Previous columns are by Jan Beufeng.
