Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

174 some considerations on infinity in physicsI think that what is truly infinite may just be the abyss of our ignorance. We keeplearning, but the little we already know is uncertain, limited in scope, and partial. Ourmind has evolved on earth to solve problems about scales included between millimetersand kilometers, and about time spans between seconds and decades. When we try touse this limited and mortal intelligence for looking much farther, we probe our limits.On the other hand, our brain contains more than a hundred thousand billion synapses.If each one of these can be activated or not, then the number of possible configurationsof our brain is something like a one followed by billions and billions of zeros. Thatis an immensely large number. This means that the space of possible thoughts is farlarger than anything we can even vaguely imagine. For all practical purposes, we canconsider this number infinite. The space of the thinkable is effectively infinite, and wehaven’t explored more than an infinitesimal corner of it. This is fantastic complexity;indeed, the natural object around us that we understand the least is the very one we usefor understanding – the few pounds of our own brain. But careful, “effectively infinite”does not mean infinite. It means “very large,” in the same way in which the quanta ofspace may be “very small,” but not “infinitely small,” and the universe may be “verylarge,” but not “infinitely large.”Thanks to this extraordinarily versatile tool that is our brain, we have found out thatwe can partly overcome some of our natural limits. We have evolved to think aboutmeters and kilometers, but so effectively that we can now talk about atoms and galaxies.We keep overcoming our limits. We have been able to do so repeatedly, thanks to thecomplexity of the harmonious dance of the billions and billions of neurons inside ourhead. But the world remains far more extended and complex than the smallness ofwhat this dance can grasp. The world remains far more extended and complex thanthe smallness of our spirit. Some limitations may very well be intrinsic. We may haveso many neurons, and feel so smart and profound, but none of us can even multiply379,887 times 88,699,673 in our mind, something that a tiny plastic machine can do ina beep. With all our neurons, we are very stupid indeed.I suspect that what we feel as infinity is only the immensity of what we realize thatwe cannot reach. Our emotional sense of infinity, the one that grasps us when we lookat the stars in the night, when we ponder the mathematics of the continuous, when wecontemplate the eons of time before and after us, when we keep asking, with Archytas,“what’s beyond?” – this is just the sense of our smallness, our frailty, our ignorance.We are ripples that last a moment over an immensity that we probably have no meansto understand.What science and the history of science teach us, I believe, is such a sense of theinfinity of what we do not know. With this comes immediately a profound suspicionfor all certitudes, especially those based on our own intuitions or direct personalexperiences, or the intuitions and the experiences of our ancestors, including the mostvivid of these. Science keeps telling us that it is so easy to nurture false convictionand beliefs. It is so easy to fill the unknown that the infinite represents with our emptyfantasies and our desires.Aristotle says in the passage about the argument by Archytas mentioned previously,“What is outside the heaven [is] supposed to be infinite because [it] never gives outin our thought” (Aristotle 1952, p. 203b22). However, our thought may very well bemisled, regarding distant reality.