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On The Finiteness Of Life Experience

There’s a great new comic at Spiked Math: It’s a small world (after all). Be sure to check it out even if you are not a mathematician. Using mathematical reasoning, the comic asserts that the number of ways you could lead your life is finite, in other words, there is a limit to what you could do in your life. I strongly disagree, and I can disprove this assertion using the very same tool: mathematics :-)

The comic explains that the number of possible videos you could watch on your TV is finite. This realization is perfectly true and nicely adds to my previous discussions of infinity. I also agree that this finite set of videos includes all possible video diaries of every person that has ever lived or will live. It might be mind-boggling, but it is true.

However, the conclusion that the finiteness of the set of possible video diaries implies finiteness of possible human experience, is mistaken. It quietly assumes that human experience can be reduced to its material expression. As if the only things defining your life could be always recorded on video and audio tapes.

First, this assumption can be trivially proved wrong simply by pointing out the existence of our mental environment. If I spend an afternoon thinking of my beloved girl, my life experience will certainly be different from an afternoon spent thinking about Fourier series in <$L^2$> spaces. In both cases, the video would show me absentminded, lost in thought, and wearing a blissful smile. :-)

Second, having established that the number of possible life experiences is conditioned by the number of possible mental states, I shall prove that there are infinitely many possible mental states. We live in a space-time that, whatever number of dimensions it may have, is finite and (probably) discrete. Our minds are built on top of neurobiological devices residing in this finite space-time, yet they are something more.

Our minds, however limited they may be, are able to conceive infinity.

A mind can create any number of different logical or mathematical propositions. Even if it should be trivial statements like “235239 is a number”, “1399 is a number”, or “<$n+1=1+n$>”, where <$n$> is a specific number. There is an infinity of numbers to choose from for these propositions.

Note. I am using logical propositions for my argument because they provide the most elegant way to prove my case. If thoughts like “1399 is a number” seem too cheap to you, think of other types of thoughts that we can generate in arbitrary quantities. Share your ideas in the comments!

Since the set of logical propositions is an infinite subset of the set of all possible thoughts, this set is also infinite. Mind states are, at least partially, defined by thoughts, and so the set of possible mind states is also infinite. Quod Erat Demonstrandum.

As a mathematician, I tell you: the number of ways you could lead your life is infinite. As a philosopher, I’d like to add that every one of them is the right one. Enjoy your life paths…

May 26, MMXI — Mathematics, Infinity, Philosophy.