by Michael Kempe
We know that some things are connected. For example, Mark Bernstein is the author of the weblog that you are reading. (And that sentence connects in a different way to the opening of Italo Calvino’s if on a winter night a traveller.) That some things are connected to other things cannot be denied, but are these connections exceptional and instrumental, or are they ubiquitous? As a rule, I find that people who believe in ubiquitous connection embrace tools like Tinderbox, while those who disagree do not.
Leibniz (1646-1716) remains a central figure in the philosophical question of connectionism. Postulating that God is perfect and perfectly kind, Leibniz tried to deduce the natural laws that would follow. Famously, he reasoned that a perfect God would not create an inferior universe, nor one that inflicted unnecessary suffering on its inhabitants: ours must be the best of all possible worlds. Because stupidity and suffering are not hard to find, Leibniz concludes that they must be necessary, and intuits that they are necessary because paradise would not be paradise unless it were achieved by universal effort. So, for Leibniz, everything must be connected because it is God’s plan not to build a garden for his creation, but to allow his creation to build a better one.
In his work on automatic calculators and on languages, Leibniz discovered the trick of representing any text as a very large number. This is one of the crucial connections that Gödel and then Turing made in demonstrating the incompleteness of formal systems. Leibniz didn’t quite get there — he did not quite figure out that there is more than one infinity, and that focus on the one perfect God was a distratction. Still, Leibniz did understand that, if the events in life could be represented as texts (like the Sybil’s book), then eventually everything (and everyone) happening right now would happen again. (Leibniz eventually embraced the alternative view that events must be continuous in the way time seems to be, more like the Fate’s weaving than the Sybil’s writing.)