The invocation that opens the Isha Upanishad is recited before study across most Vedantic settings. Purnam adah purnam idam, purnat purnam udachyate, purnasya purnam adaya purnam evavashishyate. That is whole, this is whole; from the whole the whole arises; taking the whole from the whole, the whole alone remains. Five uses of one word in a single verse, and the effect on a first hearing is of a riddle rather than a statement.
It is a statement about a specific property. For finite quantities, removing a part leaves less, and this is so basic that we do not notice we are assuming it. The verse is asserting that whatever it is describing does not have that property: taking the whole from it leaves the whole intact. This is not word-play but a precise claim that the subject under discussion is not the kind of thing that diminishes when drawn from, which is exactly what distinguishes the infinite from the very large.
Mathematics arrived at the same structural point much later and rigorously. An infinite set can be put into one-to-one correspondence with a proper subset of itself, so that removing infinitely many members leaves a set of the same size, which is Hilbert’s hotel and Cantor’s result. The resemblance is genuine and it is a resemblance in logical structure, not evidence that the Upanishadic composers were doing set theory. What both are registering is that infinity behaves differently under subtraction, and the verse uses that to say something about what underlies everything: that the world arising from it takes nothing away.
A verse recited before study, asserting that nothing was lost when everything appeared. To see what it is describing, explore more of The Living Sanatan Timeline.
Part 12 of 100 — Series I: From the Beginning
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