• Mathematics

    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 √2, π, and e in the real world, but they appear to have infinite irreducible complexity. Similarly, many rational numbers such as 1/3 have infinite digits in them. Unlike negative numbers which are fully understood but never seen, rational and irrational numbers are seen but never fully understood. In what sense are these numbers then…

  • Mathematics

    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 these concepts real when they cannot be represented in the real world, now presents a problem of mathematical realism, which remains unresolved today. This post discusses the issues of realism in mathematics outlining how there are two ways of counting, only one of which involves negative numbers, while the other doesn’t. Why both schemes are…

  • Logic,  Mathematics

    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 nature of space and time, etc. But there is no single place where we have collected them so far. This is what this podcast achieves to do. I will follow this up with a few posts on the nature of numbers.