36. Fine Grained Analysis: Kaṇāda’s Vaiśeṣika-sūtra

Curious about the Vaisesika argument for the existence of atoms derived from observing motes of dust in a shaft of light. If I recall correctly Lucretius uses the dance of dust motes observable in a shaft of light to argue that atoms are real, a line of reasoning that may go back to Epicurus. (Lucretius' argument in turn is sometimes compared to Einstein' 1905 argument for atoms using Brownian Motion, the paper which finally convinced the holdouts that atoms were real and not just useful constructs.) That dust-in-a-shaft-of-sunlight image is an odd coincidence, and if Lucretius' version goes back to Epicurus or even further back to Democritus, they are roughly contemporaneous. Is there a possible connection through transmission, or is it that observing dust in a shaft of light suggests a certain line of reasoning that transcends time and place?

The argument in favor of atomism here: If things can always be divided, everything is made of an infinite number of parts. And so a grain of rice is as large as a mountain. This is not so, so there must be a smallest part.

This is actually analogous to the Banach-Tarski paradox in mathematics. If you're not aware, the idea is that with a particular set of operations, you can take a sphere, cut it up into a finite number of parts and reassemble it into 2 spheres of the same size, then repeat, etc until, to take the earlier analogy, you have turned your grain of rice into a mountain. The interesting thing is that mathematicians actually have a response to that. It's called measure theory and to make things simple, it's a new way to measure things and basically it allows you to say that recombining the original sphere into two sphere will necessarily yield 2 smaller spheres.

I'm wondering if this kind of thing was brought up in response to the atomism of the Vaisesika school. Not likely in the modern form of measure theory, but maybe in the more general sense of "OK. The mountain and the grain both have infinitely many parts, but there are different concepts of size and when you say the two must be the same size if they have infinitely many parts, you're using the wrong concept of size. With the right concept of size, the two have infinitely many parts, but the mountain is bigger than the grain of rice."

The central idea of measure theory is the advanced concept of Lebesgue integration (https://en.wikipedia.org/wiki/Lebesgue_integration) contrary to Riemann-Stieltjes integration (https://en.wikipedia.org/wiki/Riemann%E2%80%93Stieltjes_integral), which fails in such cases like the Banach-Tarski paradox. One could say, that the Riemann-Stieltjes approach is the physical approach to integration, whereas Lebesgue is the metaphysical approach to it in a way. Also the Hindu way of energetic thinking (energy levels like e.g. in quantum mechanical theories of the atom) is quite in line with the viewpoint of Lebesgue integration and modern measure theory. Furthermore, one has to consider the differing metaphysical settings from modern math and measure theory and classical (Vaisiseka) philosophy. In philsophy epistemology and ontology are integral, whereas in our modern maths and physics view we are adhering to Cartesian rationalist philosophy, which separates the light of physics from the formless darkness of mathematics, very much like the gnostic sect (https://en.wikipedia.org/wiki/List_of_Gnostic_sects) of Priscillianism (https://en.wikipedia.org/wiki/Priscillianism) teaches separate kingdoms of light and darkness. From yet another teleological viewpoint the Lebesgue integration concepts are like all modern mathematical formalism a alchemistic cryptic seal to the ancient mysteries and therefore maybe the ancient mysteries are more important for people than the mathematical seals and concepts encrypting an veiling it.