" It also sowed the seed for zero as a number, which is first described in a text called Brahmasphutasiddhanta, written by the Indian astronomer and mathematician Brahmagupta in 628AD." The development of zero as a mathematical concept may have been inspired by the region’s long philosophical tradition of contemplating the void and may explain why the concept took so long to catch on in Europe, which lacked the same cultural reference points.
“The Europeans, even when it was introduced to them, were like ‘Why would we need a number for nothing?’” said Du Sautoy. https://youtu.be/MrCPIrs90eg
I mean, it’s such a great quote. You just can’t see what you can’t see; and if all you can see is things, you miss the fact that it’s nothing that makes everything possible.
The section about zero was also the one that really gave me goose bumps when reading your post about the Budddha being at the origin of computer technology:
On the subject of mathematics without zero, if you are are interested in ‘older’ classical music, you may be familiar with a musical form called the “augmentation canon” or “diminution canon”.
Augmentation is a ‘canonic utility’ that allows one to create a polyphony ‘out of’ of a single line of music by having that line accompany itself played twice as slow, or twice as fast.
With clever planning, one can avoid creating harmonic collisions by applying a mathematical formula to each tone of the piece, in order to determine “which beat” that tone will be occurring on once the canonic utilities have been applied.
Where this becomes relevant to the OP is that in music, the first beat is “beat one”, not “beat zero”.
This means, that in music, if you want to apply a mathematical formula to a tone to see when else it will occur (after canonic utilities are implemented), you need to perform math that presumes no ‘zero’ as a “starting number”.
The formula to determine 3 voices for a 3-part augmentation canon (these voices being, respectively, X1, X2, & X3, with X being the “beat” on which a tone occurs in the line in questioning, which is indicated in subscript numeral), is:
X1 = X1
X2 = (X1 + 1)/2
X3 = (X1 + 3)/4
This can be used, essentially, to create a net of values, that show you which pitches will be simultaneous with which other pitches:
X1 = 1.00, 2.00, 3.00, 4.00, 5.00, 6.00, 7.00, 8.00, 9.00, [...]
X2 = 1.00, 1.50, 2.00, 2.50, 3.00, 3.50, 4.00, 4.50, 5.00, [...]
X3 = 1.00, 1.25, 1.50, 1.75, 2.00, 2.25, 2.50, 2.75, 3.00, [...]
All of this instead of a simple “divided by 1”, “divided by 2”, & “divided by 4”, if music “started” on “beat zero”.
Incidentally, after you do this, you might also to convert everything to base-8, or another base, depending on the number of beats-per-measure in your metre, if you want the resulting numbers to map into beats in measures.
Zeros are pretty helpful.
Does zero mean silence in music?
From the perspective of tone velocity (loudness), yes.
Time-wise, I suppose it means “before anyone starts playing”, which would be silent too, I suppose.
That’s amazing, you’re full of surprises! I knew that canons were highly formalized, but had no idea it could be so expressed.
Well, a while back, it took a lot of graph paper and a lot of pencil sharpening to figure it out! I don’t like to boast, but you won’t find that formula in any music theory textbook published by anyone, its only here on SuttaCentral!