The idea of ‘Infinity’ has long attracted the mathematically adventurous. And the philosophically credulous.
The symbol ‘0’ has been around for a long time. But the symbol ‘∞’ for ‘Infinity’ however is relatively new, less than 500 years old, coincident with the birth of Science and its need for abstract measurements [the Universe is ‘Finite but Unbounded’?!].
The grizzled Dharmic monks and the geezers around the fountain-square in old Athens didn’t like the word very much, rarely used it. [It parallels their reluctance to grant the ‘Principle of Induction’ the status of ‘Law’]. And why not?
‘Infinity’ is a notoriously slippery idea. The slightest misstep and you will spin around forever in self-referential loops. And most annoyingly, you will not even notice it.
‘Infinity’ is from the Latin In-finitas, for ‘Unbounded, Unbordered’. The bells should go off right there. To give definition is to mark a boundary. And here we begin by defining something as the ‘Unbounded‘.
From the Isavasya, the briefest of the principal Upanishads: ‘When taken away from the Infinite Whole [Purnam], the Infinite Whole remains the Infinite Whole’.
Infinity minus ten trillion is still Infinity. That’s the definition for this formally ‘Undefined Concept’. ‘Infinity’ is that which doesn’t budge when you take something away from it. Or add something to it.
We don’t quite know what Infinity is. But we are quite sure that ‘Infinity plus one’ is the same as it. The functional definition of this idea has remained pretty much the same since antiquity.
‘Infinite Regress’? A term coined to suggest its user needs serious psychiatric help. The resolution of the Self-Eating Expression is ‘Infinite Regress’ in its most militant form.
The always effective threat of the Preacherman that brings the obdurate to their knees: ‘Thou shalt fry for all Eternity’ [Infinity on a Time-Axis].
Have you ever had the compelling desire to fly faster than Light? Yes?
We’ll, you can’t do it. And why can’t you do it? The folks who worked out the Theory of Relativity found that as you approach the speed of Light, the amount of energy needed to move you an inch [or for that matter, a single electron] ‘Tends to Infinity’.
[Before I forget, let me remind you to close the curtains, make sure no light enters the room when reading the speed-meter you have set-up to measure the above speed of light. Else thing can get loopy, seriously circuitous.]
While you snuggle into the empty space of a vacuum tube [‘Tends to Zero’], enthusiastic Scientists are vigorously seeking a ‘Theory of Everything’. Any such theory, by that very fact, invalidates itself.