Digital Infinity
Short essay by Nadia Palliser.
The concept of infinity has come a long way since Zeno of Elea (495 B.C). In his forty paradoxes of motion, he held the principle of "All is one", meaning there is no change -- in his world all remained static for "that which is moved must arrive at the middle of its course before it arrives at the end", just as the race of Achilles and the tortoise. The symbol for infinity -- ∞ -- was used by the Romans to represent the number 1000, a huge quantity at the time! Yet, mathematicians have always been weary of the depths of infinity; perhaps the lack of overview scared them off? Whatever the case, there were no signs of any serious approach towards infinity until the early 1600's, when Gallileo proposed that "infinity should obey a different arithmetic than finite numbers". Yet, it was not until the late 19th century that George Cantor (1845-1918), a German mathematician, finally put infinity on a firm logical foundation and described a way to do arithmetic with infinite quantities useful to mathematics. His basic definition was simple: "a collection is infinite, if some of its parts are as big as its whole". Cantor was able to demonstrate that there are different sizes of infinity. The infinity of decimal numbers that are bigger than zero but smaller than one is greater than the infinity of counting numbers. Yet the infinity of counting numbers as opposed to all possible fractions is exactly the same size!
The loss of control, as numerical as these examples might be, seems central to the concept of infinity. A strange and almost spiritual "weirdness" descends over the term, as the mind tries to grasp the idea of endlessness, mostly projected and explained by religion. On the other hand, the infinite calculations of the computer have no meaningful undercurrants whatsoever... the search engine swaps the symbol -- ∞ -- into the number 8734 churning out all links with the numbers 8734: a different kind of infinity all together... so does digital infinity offer us a rational sense of endlessness? What are we to do with it however? -- Watch yet accept our own inevitable end? Somehow the drive for infinity, apparent in all man-made media, continually betrays the urge for immortality... the constant obsession with duration, with life after death, memory and eternity. The difference lies only in the dynamics of digital infinity: instead of a gradual degeneration, it is a constant accumulation of data that entails infinity now, provoking the illusion of immortality once again in hard-core cyberspace. To mystify the never-ending calculation of the computer seems a farce, however: as endless as digital infinity might seem, is it not just meaningless duration, numbers unfolding in bland calculation? The synthetic, the zeros and ones of the digital medium deny all symbolism, so pervasive in the loaded analytic approach of the twentieth century: constantly on the look out for one-way meaning and signification. Perhaps, digital infinity finds different symbols in two-way communication? After all, the intensive nature of digital infinity seems quite bland and empty without being confused and distorted by the unlogical activities of humans.
