Obsessions on Infinity

Plato had his triangles and his numbers, abstract objects which he called universals or ideals. Such ideals do not exist spatially or temporally, or anywhere else in our physical world. The lines that represent a triangle’s sides are perfectly thin and perfectly straight. They cannot be perceived; only conceived. They existed independently of Plato’s thinking about them. Although a purist might not agree with such a formulation, triangles, numbers, and other ideals existed long before any humans thought about them and will exist long after humans; that is, they’ll exist forever.

Like numbers (yet subtly different) infinity and eternity are also ideals. If you were to throw an open bag of coins up in the air and all the coins were to land on their edges, which would be a most improbable event, but it’s inevitable given an infinite amount of time. The probability of such an occurrence would be much smaller than the probability of my winning the Powerball Lottery, especially considering I don’t purchase lottery tickets; however, given an infinite period of time (an eternity), it’s inevitable that the coins would all land on their edges not only once but an infinite number of times.

The Kardashev Scale measures a civilization’s level of technical advancement. Nikolai Kardashev designated three categories, which he called types I, II, and III. Type I civilizations should be able to use and store the energy reaching their planet from their neighboring star. Type II civilizations should be able all the energy of a star (e.g., a Dyson sphere). Type III civilizations should know everything there is to know about energy and use that knowledge to travel between galaxies. Others have proposed extensions to the basic Kardashev Scale, such as types 0, IV, and V, as well as measurements unrelated to energy. Of course the Kardashev Scale is only hypothetical since we only know about our own civilization. According to Carl Sagan, we’re at about 0.724 (Type 0, possibly attaining Type I within 100 – 200 years).

Thinking about the Kardashev Scale and its variants, I’d like to propose a variant based on intelligence. Type I would be one or more species of life on a planet accidentally acquiring intelligence (consciousness, sense of self, world view, empathy, judgment, will, etc.). Type II would be artificial intelligence programmed by an intelligent species, Type III would be artificial intelligence programmed by artificially intelligent artifacts. Type IV might represent the spread of intelligence like a virus around an entire planet. Type V might represent intelligent stars along with their solar systems. Type VI might represent intelligent galaxies. Type VII might represent an intelligent universe.

These obsessive ramblings may sound far-fetched to the casual bystander but, given all the time in the world, given an eternity, all types are inevitable.

Mike Stone

Raanana Israel


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