Abstract
A defining characteristic of modern science is its ability to make immensely successful predictions of natural phenomena without invoking a putative god or a supernatural being. Here, we argue that this intellectual discipline would not acquire such an ability without the mathematical zero. We insist that zero and its basic operations were likely conceived in India based on a philosophy of nothing, and classify nothing into four categories—balance, absence, emptiness and nonexistence. We argue that zero is a tangible representation of nonexistence and constitutes all nonzero numbers, which together represent existence. It appears that zero’s journey out of India somewhat separated its mathematical and philosophical aspects, with the former being more valued by some cultures and the latter by others. The European culture, in which modern science grew, largely ignores a philosophy of nothing due to a deep-rooted Greek philosophical base, although this science relies on the notion of nonexistence through zero. Consequently, zero is a mere number of convenience without its foundational philosophy in science, and techniques to circumvent zero are developed. We insist that, while such techniques contribute to the progress of science and mathematics within the current framework, a tendency to avoid zero and its philosophy leads to approximations and may hinder a deeper understanding. Finally, we argue that nonexistence may notionally constitute existence, and hence may be the fundamental. This implies that, if a supernatural being exists, it is not the fundamental. The independence of modern science from a supernatural being is consistent with this.
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Notes
Iraq and around.
The Mayan civilization flourished in Mexico and Central America during around 300 BCE–900 CE.
Western part of Turkey.
For example, in the astronomical treatise Almagest, written by the notable Alexandrian astronomer Ptolemy in the second century CE.
Ṛg-Veda: 10:129.
See Bilimoria (2012) for a discussion on nothing, also in the Indian context.
Indian philosophical texts. Some of them could have been composed in the first half of the first millennium BCE (Radhakrishnan 2008, vol. 1, pp. 106–220).
See Bilimoria (2017) for a brief and systematic discussion on Nāgārjuna’s philosophy.
Śūnyatāsaptati: verses 2 and 71.
E.g., I have zero money instead of I have no money.
Unlike absence, which refers to the absence of a specific thing (see ‘Nothing’).
Note that a child can distinguish between increase and decrease, before he/she learns mathematical operations.
The word Ch’an came from the Indian word dhyana, which means ‘meditation’.
The divine wager of Pascal, based on a probabilistic calculation, was an example.
Note that a degree of subjectivity was mentioned in the Copenhagen interpretation of quantum theory (Heisenberg 2000, pp. 19–25).
Implausibility of self-sustenance is briefly mentioned in ‘Implications for the Fundamental’.
Although, the basics of calculus were developed within trigonometry in fifteenth century CE in India by the Kerala School of mathematics (Webb, 2014).
Note that an approximation hinders a further deeper understanding. As a crude example, suppose 23.473 centimeter is the measured length of a rod, and we approximate it to be 23.5 centimeter. Once we accept this approximation, neither will it be meaningful nor will we be motivated to measure the length of the rod more precisely, and to find out, for example, if it is 23.4727 centimeter or 23.4732 centimeter.
This notion is mentioned in ‘Invention of Zero’.
Here is an example. Consider a pure iron bar made of iron atoms. Which is more fundamental, an iron atom or the iron bar? The bar cannot exist without atoms, but an atom can exist without the bar. So, while the bar contains all atoms, an atom is more fundamental. However, this is a simplistic example, because an iron atom is fundamentally different from nonexistence.
For example, considered by Martin Heidegger in twentieth century CE (see, for example, Robinson & Groves 2012, p. 121).
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We thank Navin Sridhar for critically reading this paper.
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Bhattacharyya, S. Zero—a Tangible Representation of Nonexistence: Implications for Modern Science and the Fundamental. SOPHIA 60, 655–676 (2021). https://doi.org/10.1007/s11841-021-00870-4
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DOI: https://doi.org/10.1007/s11841-021-00870-4