# 628

## Zero

## The book of science

Tom Sharp

Tom Sharp

Brahmagupta mathematics |

*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.

- 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.”

- 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.
- To reply “empty handed”
- 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.

- 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.

See also in

The book of science:Number system—Leonardo Pisano Bigollo (Fibonacci)Infinite and infinitesimal—John WallisPi—Johann Heinrich Lambert, Ferdinand von LindemannReadings on wikipedia: