A few years ago, the Netherlands Bach Society set itself the goal of performing all of (Johann Sebastian) Bach’s works, recording them on video and making them freely available to the world. A fantastic and insane plan. You would say a new start if it weren’t for the fact that they have already started. Bach’s works are numbered according to the BWV (Bach-Werke-Verzeichnis) index, which extends beyond 1100. In total, this is 160 hours of music. They are not ready yet, but you can indulge yourself at allofbach.com. (Or, if you really don’t like it, your shoulders. Although you don’t have to go to this website first.)
Much has been written about the parallels between Bach and mathematics. I don’t need to repeat it here, but I would like to say something about this comprehensiveness. Mathematics exists by virtue of completeness, which is why it is so beautiful that the Bach Society also wants to honor Bach in its entirety. Anyone who wants to prove a mathematical theorem wants the theorem to be valid for all the space to which this theorem applies. Take, for example, the famous Pythagorean theorem. This goes for right triangles (triangles in which an angle is exactly 90 degrees), and indicates that the sum of the squares of the two sides of the right rectangle (the two sides that meet at that 90 degree angle) is equal to the square oblique silk. Or as almost everyone knows the statement: a2 + b2 = c2. If you want to prove this statement, you have to show that this statement is true for all right triangles. As soon as there was a right triangle for which Pythagoras does not apply, it was no longer a theorem, but a cracked conjecture.
[Deze alinea mag u overslaan als u in uw weekend geen zin heeft in te veel wiskunde.]
Complete is a concept that comes up in mathematics in various ways. In topology – a subfield of geometry – completeness says something about the density of a set – how close its elements are to each other. The precise definition goes too far (even in this paragraph), so I will stick to an incomplete definition of exhaustiveness: a set is complete as for each convergent row of this set – that is to say a row converging to a limit point – this limit point is also in the collection. Consider the set of all fractions, that is, all numbers of the form a / b, where a and b are arbitrary integers. This collection is not complete. I can create a line that looks like this: 3… 3.1… 3.14… 3.141… 3.1415… where each following number adds another decimal to the number pi. (In fraction notation: 3/1, 31/10, 314/100, 3141/1000, etc.) The limit for this line is pi, but pi cannot be written as a fraction. The set of all fractions is therefore incomplete.
I think each person more or less tends to be complete. That’s why we love rhyme: it gives a momentary feeling that something is just right. That’s why we bring our own peanut butter to the trailer in France: a complete home feeling. And that is why we are offended when our Prime Minister says in a debate like this week on the fate of the formation: “Yes, I lied, but I did it to the best of my knowledge and my conscience. ” A row made up of items that have all been chosen with “the best of honor and conscience” cannot, in your opinion, result in a lie. Likewise, we do not accept that Mark Rutte claims to have incomplete memory, while showing full insight in other areas. What remains then is incomplete confidence.
And it is devastating. Without trust, no coalition can be forged, because in our lives – and certainly in politics – it is almost impossible to be complete. Anyone who wants the whole story on the table quickly becomes desperate. Ask Pieter Omtzigt or follow Lukas van der Storm on Twitter and in this newspaper. But the Bach Society will pass the completeness test. I am currently listening BWV 733: Flight over the Magnificat, played by Matthias Havea on the Müller organ of the St. Bavo in Haarlem. Then there is only one thing left: complete abandonment.
Jan Beuving is a mathematician and comedian. In his column, he plays with the natural sciences and language. Previous columns by Jan Beuving.