In a book called The Sleepwalkers by Arthur Koestler, he writes, "Numbers were regarded by the Pythagoreans as patterns of dots which form characteristic figures, as the sides of a dice; and though we use arabic symbols, which have no resemblance to these dot-patterns, we still call numbers 'figures', i.e. shapes." This makes it sound like they used their own unique form of writing numbers. Unfortunately, he doesn't continue to explain how the figures were actually written. How true is this statement? If true, how far outside of this group did this practice extend?
Also, on a related note, Koestler mentions that they, as a "religion," were able to survive through the discovery of irrational numbers by killing those who leaked the discovery. I'm curious about the veracity of this as well.
I know it's a fairly specific question, but any information you could provide would be helpful. Thanks!
I suspect that this refers more to a system of considering numbers rather than writing numerals -- when considered as patterns of dots, some numbers create interesting patterns, and the Pythagoreans were certainly interested in the meanings that might lie behind these patterns and coincidences.
I don't know about Samos specifically, but there was was a sort of hash mark counting called the Aegean number system that was used by the Minoans and other preclassical cultures.
The numbers 1 2 3 looked just like I II III (but no serifs)
II 4
II
III 5
II
III 6
III
IIII 7
III
IIII 8
IIII
III
III 9
III
Tens and hundreds kept the same shapes, but used different marks for the 'I' in that shape.
These numbers have been added to the unicode character set. Theoretically I could just type them in, but my browser does not have that font. Here they are in the unicode specification http://www.unicode.org/charts/PDF/U10100.pdf . Start at row 7 in the first column.