There are two fundamental types of Infinity: quantitative and qualitative infinity. The difference between is simple: one is about the number of something, and the other is about the nature of that something.

Let’s think about this in the form of an analogy. Let’s say we have two rollercoasters: one is infinite in length, and the other is finite in length but is in the form of a loop with some kind of accelerator on it that keeps the cart going (think of the old Hot WheelsTM loop accelerators with D batteries inside).

The first rollercoaster is physically impossible because it would violate the First Law of Thermodynamics, i.e. that neither matter nor energy can be created or destroyed, only changed. The rollercoaster would consist of material, and thus it would have a lower limit; but since it would extend forever it would have no upper limit. So, having it extend infinitely in length without removing some of the pre-existing material in the process would mean one would have to obtain new material.

Alas, there is only so much wood/metal/etc. in the Universe, and thus it could not be infinite.

The second rollercoaster is a bit different: it is still quantitatively finite because it is in the form of a circle (or oval; or whatever you want…)—in other words, because it has the property of repetition. This latter version is therefore still physically possible.



Image Credit:

Original work released under a CC BY-SA 4.0 International license.


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