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The extended excerpt below is from p. 73 of Richard David Precht's book Erkenne die Welt (my emphasis):

...selbst wenn der Pythagoras zugeschriebene Satz »Alles ist Zahl« erst aus späterer Zeit stammt, so schärfen die Pythagoreer zumindest den Blick darauf.

Eine besondere Aufmerksamkeit verwandten sie auf das Dezimalsystem. Es hatte den praktischen Vorteil, dass man gut mit den Fingern rechnen konnte. Schon im Alten Ägypten wurde es verwendet. Pythagoras, oder wahrscheinlicher seine Schüler, machen daraus eine Art mystischer Wissenschaft. Zählt man die Zahlen 1, 2, 3 und 4 zusammen, so ergibt dies zehn — die größte nicht zusammengesetzte Zahl. Sie soll den Pythagoreern gleichsam heilig gewesen sein. Für sie durchwaltet die Zehn den ganzen Kosmos und ordnet ihn nach mathematischen Gesetzmäßigkeiten. In den Quantitäten sieht die Schule des Pythagoras zugleich Qualitäten ausgedrückt. Die geraden Zahlen sollen weiblich und unbegrenzt sein, die ungeraden Zahlen männlich und begrenzt.

I cannot make sense of the emphasized phrase. According to every translation I have found so far, zusammengesetzte Zahl means composite number, and therefore, nicht zusammengesetzte Zahl here would mean prime number1.

If this is indeed the meaning that Precht intends, then the sentence emphasized in the excerpt above is doubly nonsensical: (a) there is no such thing as a greatest non-composite number (aka Euclid's theorem); and (b) 10 = 2 × 5 is obviously composite.

Granted, Precht is not a professional mathematician, but these are very elementary facts, and it is hard for me to believe that a university professor of philosophy like him is unaware of them. Therefore, I have to conclude that by zusammengesetzte Zahl he must mean something other than composite number, but I cannot figure out from the context what else this could be.


1 The number 1 is also generally regarded as neither composite nor prime, but clearly 10 ≠ 1, so we can safely disregard this as a possible interpretation of nicht zusammengesetzte in this context..

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    I am astonished, too, because zusammengesetzte Zahl means exactly what you say: composite number. The claim made in the quoted passage is clearly false. – Björn Friedrich Feb 25 at 19:38
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    I wonder whether the author mixed up some things and wasn't thinking about the mathematical meaning of composite, but about a linguistic meaning: deka as a non-composite word in contrast to composites like hen-deka (11) and do-deka. However, my knowledge in Ancient Greek is rather limited, so I'm not sure, whether deka really would be the largest number word that isn't composition of other number words. – Arsak Feb 25 at 20:01
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    I'm strongly with @Arsak's hypothesis about what he might have meant, but even then he would have been wrong: the classical Greek words for 100, 1000, and 10000 are "synthetic", too, similar to hundert and tausend. – phipsgabler Feb 26 at 7:34
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    I’m voting to close this question because it is not about the German language but about the history of mathematics. – Carsten S Feb 26 at 9:03
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    @CarstenS: Maybe the question needs to be slightly reworded, but I think the aspect of how native speakers would understand "zusammengesetzte Zahl" is indeed about the German language. And for what it's worth, my first intuitive interpretation of "zusammengesetzte Zahl" was that it refers to multi-digit numbers (= "aus mehreren Ziffern zusammengesetzt"), which makes the highlighted statement a possible off-by-one error (as 9 rather than 10 is the greatest single-digit number, at least when using 10 as a radix). – O. R. Mapper Feb 26 at 11:10
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Whatever Precht wants to say about the number 10, it is flawed. The problem is that he does not explain what he means by a "zusammengesetzte Zahl". Any reader who has a little mathematical background will certainly understand that in the sense of an integer which is not a prime number, thus a "nicht zusammengesetzte Zahl" should be a prime number. See here and here. So Precht's statement appears to be nonsense. See this Amazon customer review for a sharp criticism of this formulation.

So is that all we can say? The number 10 certainly played a special role for the Pythagoreans, but in a mystic sense, and I think this fact cannot explain Precht's statement that 10 is the biggest non-composite number. In a comment Arsak conjectures that it has a linguistic interpretation: 10 is the biggest number denoted by a non-composite Greek word (deka). This is a very good explanation although it is true only for numbers up to 99. The numbers 100 and 1000 are also expressed by non-composite words.

Here is my guess. Precht writes

Eine besondere Aufmerksamkeit verwandten sie auf das Dezimalsystem. Es hatte den praktischen Vorteil, dass man gut mit den Fingern rechnen konnte.

And in fact 10 is the biggest number which you can display in the obvious manner with ten fingers. There are methods to display bigger numbers with fingers (see here), but these involve additional actions and the numbers bigger than 10 may therefore be regarded as composite.

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Quoted from Wikipedia: Pythagoreanism:

Pythagoras is credited with discovering that the most harmonious musical intervals are created by the simple numerical ratio of the first four natural numbers which derive respectively from the relations of string length: the octave (1/2), the fifth (2/3) and the fourth (3/4).The sum of those numbers 1 + 2 + 3 + 4 = 10 was for Pythagoreans the perfect number, because it contained in itself "the whole essential nature of numbers".

So the paragraph quoted from Precht is definitely not concerning divisibility and primes but string length (frequency) ratios and musical intervals.

The Pythagoreans had the special name of tetractys for number 10 considered mystical in a special triangular arrangement of unit dots.

I admit, that it does not provide a clue concerning zusammengesetzt, and wikipedia: perfect numbers is also different.

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  • Precht spricht vom Dezimalsystem. Auch dann macht es keinen Sinn, weil auch 100 = 1x10^2+0x10^1+0x10^0 keine in diesem Sinne zusammengesetzte Zahl ist. Ratios and musical intervals don't explain it either (as you admit yourself). So - sorry to say that - your answer is just nonsense. – Olafant Feb 27 at 12:32

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