Year’s Best SF 15 Read Free

infinity. What a deep and beautiful concept, thinks Abdul Karim! Perhaps there are infinities in us too, universes of them.
    The prime numbers are another category that capture his imagination. The atoms of integer arithmetic, the select few that generate all other integers, as the letters of an alphabet generate all words. There are an infinite number of primes, as befits what he thinks of as God’s alphabet…
    How ineffably mysterious the primes are! They seem to occur at random in the sequence of numbers: 2, 3, 5, 7, 11…There is no way to predict the next number in the sequence without actually testing it. No formula that generates all the primes. And yet, there is a mysterious regularity in these numbers that has eluded the greatest mathematicians of the world. Glimpsed by Riemann, but as yet unproven, there are hints of order so deep, so profound, that it is as yet beyond us.
    To look for infinity in an apparently finite world—what nobler occupation for a human being, and one like Abdul Karim, in particular?
    As a child he questioned the elders at the mosque: What does it mean to say that Allah is simultaneously one, and infinite? When he was older he read the philosophies of Al Kindi and Al Ghazali, Ibn Sina and Iqbal, but his restless mind found no answers. For much of his life he has been convinced that mathematics, not the quarrels of philosophers, is the key to the deepest mysteries.
    He wonders whether the farishte that have kept him company all his life know the answer to what he seeks. Sometimes, when he sees one at the edge of his vision, he asks a question into the silence. Without turning around.
    Is the Riemann Hypothesis true?
    Silence.
    Are prime numbers the key to understanding infinity?
    Silence.
    Is there a connection between transcendental numbers and the primes?
    There has never been an answer.
    But sometimes, a hint, a whisper of a voice that speaks in his mind. Abdul Karim does not know whether his mind is playing tricks upon him or not, because he cannot make out what the voice is saying. He sighs and buries himself in his studies.
    He reads about prime numbers in Nature. He learns that the distribution of energy level spacings of excited uranium nuclei seem to match the distribution of spacings between prime numbers. Feverishly he turns the pages of the article, studies the graphs, tries to understand. How strange that Allah has left a hint in the depths of atomic nuclei! He is barely familiar with modern physics—he raids the library to learn about the structure of atoms.
    His imagination ranges far. Meditating on his readings, he grows suspicious now that perhaps matter is infinitely divisible. He is beset by the notion that maybe there is no such thing as an elementary particle. Take a quark and it’s full of preons. Perhaps preons themselves are full of smaller and smaller things. There is no limit to this increasingly fine graininess of matter.
    How much more palatable this is than the thought that the process stops somewhere, that at some point there is a pre-preon, for example, that is composed of nothing else but itself. How fractally sound, how beautiful if matter is a matter of infinitely nested boxes.
    There is a symmetry in it that pleases him. After all, there is infinity in the very large too. Our universe, ever expanding, apparently without limit.
    He turns to the work of Georg Cantor, who had the audacity to formalize the mathematical study of infinity. Abdul Karim painstakingly goes over the mathematics, drawing his finger under every line, every equation in the yellowing textbook, scribbling frantically with his pencil. Cantor is the one who discovered that certain infinite sets are more infinite than others—that there are tiers and strata of infinity. Look at the integers, 1, 2, 3, 4…Infinite, but of a lower order of infinity than the real numbers like 1.67, 2.93, etc. Let us say the set of integers is of order Aleph-null, the set of real