# 628

## The book of science

Tom Sharp

 Brahmagupta mathematics

## Zero

• Brāhmasphuṭa-siddhānta
• (“Correctly Established Doctrine of Brahma”) by Brahmagupta
• is the first known text to describe how to use zero as a number.
• It covers addition, subtraction, multiplication, and division with zeros
• and whether the result is positive or negative.
• Brahmagupta also gave rules
• for solutions to general linear equations,
• for calculating roots, powers, and sums of powers,
• for handling fractions,
• for calculating Pythagorean triples,
• for calculating the area of cyclic quadrilaterals,
• and for the value of π.

## Zeros

• The Chinese used a space in their counting-rod system
• as a placeholder for zero.
• The Incans used the absence of a knot
• in their knotted cord device.
• The Babylonians had a symbol used as a placeholder
• in other numbers, to distinguish, for example, 105 from 15.
• So did the Olmecs in Mesoamerica
• in the numeral system for their long-count calendar.
• Ptolemy and the Romans had a symbol for the lack of a quantity,
• but they did not perform arithmetic with it.
• Mathemeticians in India used the the Sanskrit word
• “ś ūnya” to refer to zero or void.
• For Brahmagupta, zero is a positive number;
• today we say it is neither positive nor negative.
• For Brahmagupta, a fraction could have a zero denominator;
• today we say division by zero is undefined.
• Brāhmasphuṭa-siddhānta was translated
• into Arabic by 1050.
• The Arabic word ŝifr gives us our words
• “zero” and “cipher.”

## Something

• Zero is nothing but nothing itself,
• the same as the empty set.
• The empty set is a subset
• of all other sets,
• including the empty set,
• which is probably not why
• seeing the emptiness in everything
• is a key to spiritual enlightenment.
• A photon is the zero
• of elementary particles;
• it’s a mass of nothing
• whose energy is all in its frequency.
• is not an empty reply;
• it’s better than not replying.
• There is only one empty set,
• nothing being the same in all circumstances.
• Really, no response
• is the same as no banana.

## Nothing

• For the time being,
• I enjoy my temporary existence
• loving many who are here
• and many who are gone,
• and it makes me think
• how close we are to nothing at all.

We make a distinction between 0, the number of nothing, and 0, a digit that is used in numbers written with digits in our positional number system.

History shows that the digit 0 came first (using various symbols). The history of the number 0 came from Brahmagupta. The Islamic world already had the positional number system. Brahmagupta gave them the number 0. The Persian, Muḥammad ibn Mūsā al-Khwārizmī (the inventor of algebra), oversaw translation of Brahmagupta into Arabic. Al-Khwārizmī’s work in Latin translation in the twelfth century introduced the Hindu-Arabic numeral system to the Western world. Fibonacci, having learned from Arabic mathematicians, contributed to its adoption in the thirteenth century.