The poets who counted first
Fibonacci in Sanskrit prosody, centuries earlier
Tap a figure with no two adjacent yin lines and read its Sanskrit metre: each yin with the yang above is a long syllable.
Long before Fibonacci, the prosodists of India (Virahanka, Gopala, Hemachandra) were counting the metres: sequences of short syllables (laghu, duration 1) and long ones (guru, duration 2). How many metres of duration n are there? The last one can be a short over a metre of n−1, or a long over one of n−2: C(n) = C(n−1) + C(n−2). Out come 1, 2, 3, 5, 8, 13, 21: the Fibonacci numbers, written here centuries earlier (Singh, 1985).
Take a figure of 6 lines with no two adjacent yin (the 21 of Fibonacci), add a sentinel yang on top and read from the bottom up: every yin with the yang immediately above it is a long syllable (2); every unpaired yang, a short one (1). The metre always lasts 7, and there are exactly 21: the same ones India was counting.
Two civilisations counted the same thing with different symbols: yin and yang here, short and long there. The transfer-matrix method is the same in both cases, and the count of figures with no two yin is the binary version of the problem. India wrote it first; the laboratory merely exhibits the bridge.
Sanskrit prosody counted the metres of short (1) and long (2) syllables, and the count satisfies C(n) = C(n-1) + C(n-2): 1, 2, 3, 5, 8, 13, 21, the Fibonacci numbers, formulated by Virahanka, Gopala and Hemachandra centuries before Fibonacci.
The 21 figures of 6 lines with no two adjacent yin lines are in bijection with the 21 metres of duration 7: a sentinel yang is added and each yin is paired with the yang above it as a long syllable. Two civilizations counted the same thing with different symbols.
verificar_prosodiaThe types of claim and the full bibliography (APA) are in Foundations.