It is often said that Indians invented the zero, which then allowed the invention of negative numbers, complex numbers, and then modern mathematics and physics. The Roman numeral system (which followed the Greek system of counting) did not have zero. After all, zero represented “nothing”, which was purely conceptual but not physical. When zero is …

# Mathematics

## The Implications of Compression and Incompressibility

No two people are completely alike. No two roses look exactly the same. No two oranges are identical. Even as we classify the world into concepts, those classifications do not entail that two things are exactly alike. This fact is accommodated in modern physics by permitting different distributions of matter and energy, subject to some …

## An Illustration of Semantic Addition

As a follow-up to an earlier post, where I described how natural laws arise as a result of qualities, this post explores this idea further using an example. Since modern science grew out of the idea that matter is res extensa—i.e., that it has only one property of extension in space—this post also illustrates the …

## The Reality of Rational and Irrational Numbers

In the previous post we talked about the problem of mathematical realism of negative and complex numbers; the issue was that you can construct these numbers logically and conceptually, but you will never find them in the real world. The problem of irrational numbers is the opposite: you can easily find irrational numbers such as …

## Do Negative and Imaginary Numbers Exist?

Numbers for the greater part of history have been viewed alternately as concepts and as quantities. Now, this raises problems about many types of numbers, which include negative numbers and imaginary numbers, because these cannot be viewed as quantities although there are compelling theories that can treat them logically as concepts. In what way are …

## Mathematical Novelties in Vedic Philosophy

This is the transcript of the eighth episode of my podcast. In this episode, we talk about a number of unique problems that arise in trying to make Vedic philosophy more rigorous in a logical and mathematical sense. I have been presenting some of these ideas while discussing the theories of creation, cosmology, linguistics, the …

## The Arithmetic of Concepts

In all religious philosophies, God is the original person, Who creates all else. If we were to count things, then God would represent 1. In Vedic philosophy, additionally, all that is created is also a part of God, Who is then described as the complete truth. In effect, since God is the complete truth, everything …

## The Sāńkhya Theory of Five Elements

This post elaborates on the Sāńkhya theory of the five “gross” elements. The theory is rather complicated, and not well-understood today. One primary source of confusions is a comparison between the Sāńkhya elements and the Greek elements going by the same name. This post will hopefully illustrate how the Sāńkhya elements are deeply enmeshed with …