Not all infinities are made equal. Vishwa Shah Now a mathematically well-known fact, this According to Jain mathematics, quantities can wasn’t a trivial claim to make back in 400 be divided into three major categories (each of BCE, when the Jain mathematical text Surya which has several subcategories)2: Prajnapti was written. Accepted by both ◼ Enumerable (Sankhya): quantities you can Shwetambars (Upang Agams) and Digambars count to, like how many Dravyas (substances) (Karnanuyog), this Jain canonical text extenthere are in the universe sively defines mathematical principles that ◼ Innumerable (Asankhya): practically infi1 guide Jain cosmology. While I have not read the nite numbers that are rigidly bounded, mostly text itself, the depth of exposition Jains have on used to define smaller units of infinite quanmathematical and logical systems amazes me tities — it’s not something the average person (or, I, ◼ Infinite (Anant): boundless quantities, like at least) would expect from a religion. how many souls there are
Fun Fact: Hemchandra Acharya, a prominent Jain monk, independently devised the Fibonacci sequence. Amidst all its mathematical exposition, the Surya Prajnapti extensively defines large quantities. This is what backs much of the detail in Jain cosmology, especially for units of time and space. In modern times, the concept of infinity is associated deeply with mathematics. However, philosophical experiments with unbounded quantities actually predate (and arguably motivated) subsequent mathematical experiments. Indians and Greeks were two of the earliest documented cultures to toy with the idea of infinity, and both did so from a philosophical angle, rather than a formalized mathematical one.
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1 Jain Study Center of North Carolina. (n.d.). Appendix – Summary of Swetambar Jain Agams. JainWorld.com. https:// jainworld.com/literature/jain-agams/jain-agam-literature/ upang-agams/
The bounds of each of these are defined in depth, mathematically. If you’re interested in learning more, check out the QR code on the right. For the sake of this article, I’ll focus on understanding them in context; after all, innumerable and infinite quantities already exist to represent numbers our brains cannot process. Enumerable quantities are fairly straightforward to understand; for example, there are only six Dravyas (substances). But how much of each of those substances exist in the universe? Moreover, how big is the universe? Depending on your depth of Jain cosmological knowledge, you may know the answer to both of those questions is “infinite.” But these infinities are not all equivalent quantities.
2 U. (2011). Jainism, Key to Reality: Tattvārthasūtra by Āc Umā Swāmi. India: Digambar Jain Trilok Shodh Sansthan.
