Thursday, June 15, 2006

The Limits Of Human Knowledge

I have been reading The Infinite Book which is both an eye-opener and a mind-twister. One (of the many) novel concepts from the book that has become a particular mindworm for me is the difference between the Visible Universe and the Actual Universe. I am going to have to paraphrase this a lot, but let me run it by you. (Yes, reading Thoughtport can make you smarter, as well as more good-looking.)

Given that the Actual Universe is 14.6 billion years old. Given that light moves at a constant one light-year per chronological year. Given that we know the distant objects, galaxies nebulae etc, that we can observe are moving away from us. Then, from our vantage point here on earth, even if we had a theoretically perfect telescope, the furthest object we could ever see would have to be at most 14.6 billion light-years from earth. Anything more distant than that and its light can never reach the Earth, there not being enough time elapsed from the beginning of the universe. Thus, you can describe an imaginary sphere around the earth with a 14.6 billion light-year radius. This is what scientists call the ‘Visible Universe’, that is the only part we can ever hope to observe directly. Our Visible Universe is constantly expanding, by one light-year per year, or even by a few light-minutes in the time it has taken you to read this post.

If the Actual Universe turns out to be truly infinite, rather than merely being boundless, then no matter how large our own Visible Universe ever becomes, according to the laws of mathematics it could never be any more than an infinitesimally small fraction of the Actual Universe. So while a sphere of 14.6 billion light years radius is a massively inconceivable volume to us, you could just keep on adding-in an infinite number of equally inconceivably-large sized spheres into such an infinite space and never fill it.

This sphere then defines the Ultimate Limits of Human Knowledge. As someone with great belief in the ability of the human mind to explore, discover, rationalise, analyse and expand the sum total of its knowledge, it is disappointing to discover that there are some things that we can not ever know and places we can never get to see.

Time for a rousing chorus of that old Monty Python song: “I am just an infinitesimal dot...”

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