Last week I showed that the whole math needs to be re-invented, as I proofed that that 1 is indeed equal to 2, thereby boiling down all maths to just -1, 0, and 1. There were some replies, and it was interesting to see that the testers you read my blog entry were indeed critical enough to challenge the proof. Simon Morley, Chad Patrick and Matt Heusser did a great job to counter-proof that there is no such real number, so that between that number and 1 there isn’t any additional real number. So, the proof I showed was in fact flawed right from the start.

In honor to Jerry Weinberg’s alliterations in The Secrets of Consulting, I thought up a name for this revelation. As the first one who pointed out the flaw to me was my old math teacher Mr. Beckmann, I named it Beckmann’s Broad Brush (thanks to Matt Heusser for the help):

From a wrong premise you can draw any conclusion.

Interesting Beckmann’s Broad Brush works on different levels as well. While thinking over it, it seems to be a generalization of Weinberg’s Zeroth Law of Software (Quality Software Management Volume 1 – Systems Thinking, page 275):

If the software doesn’t have to work, you can always meet any other requirement.

So, since I can conclude anything from a wrong premise, then I can also meet any requirement for a software that does not have to work. It’s that simple.

This leads me to the interesting question how to get aware of wrong premises? Heuristics help to get aware of a problem here. Today I came across James Bach’s Essence of Heuristics which explains why heuristics can help you to get aware of wrong premises. On another take, heuristics are fallible, as James explains. So heuristics alone won’t solve your overall problem, but they might make you aware about troubles. So, keep your lights on and make sure, that your measurement system still is functional. The combination of these may guide you your way.

## 2 thoughts on “Beckmann’s Broad Brush”

1. This “math” is related to Bertrand Russell’s proof of his theorem that if you grant him one wrong axiom, he can prove anything.

Starting with the axiom 1=2, he proved that Bertrand Russell was the Pope! Great stuff, and in a great tradition.

You can google many accounts of this “proof.” One, for example, is at http://blogs.warwick.ac.uk/dangoodman/entry/self-deception

1. Thank you for this reference. I wasn’t aware of it, since a math student introduced me to the proof when I was still in school, but I doubt that he had the same reference. He introduced it to me as a “weird math proof” he got taught in one of his lectures.

Some more things learned on my side:

1. Some good ideas are longer around. Doing some reference research does not harm.
2. Philosophy may be a topic deliberately ignored for too long from my side.