October 29, 2007

Berkeley, Computers, and Time

I read a very interesting paper by James Van Cleve today, regarding a pair of arguments originally made by Jorge Luis Borges to the effect that either Berkeley's idealism or Leibniz's principle of the identity of indiscernables could be used to prove the unreality of time. The paper is "Time, Idealism, and the Identity of Indiscernables," Philosophical Perspectives 16 (2002): 379-393. Van Cleve identifies three "axioms of time order" which Borges' arguments are designed to undermine:

  1. Given any two events e and f, either e precedes f or f precedes e or e and f are simultaneous.

  2. If e precedes f, then f does not precede e. (As a corollary, no event precedes itself.)

  3. If e precedes f and f precedes g, then e precedes g. (p. 379, emphasis original)

Van Cleve's paper is focused on showing that Borges' arguments, while valid, rely on an interpretation of Leibniz that is actually implausible (that is, a defensible interpretation according to which Leibniz asserts something that is not plausibly true), and an interpretation of Berkeley that is both exegetically and actually implausible. However, he also finds time to report a challenge to axiom 2:

... it must be noted that there are thinkers who do not take the irreflexivity of temporal precedence [i.e. the principle that no event precedes itself] as sacrosanct. Henri Bois objected to Neitzsche's doctrine of eternal return that it was not what it purported to be - that the supposedly infinitely repeating linear sequence of ABCDEA'B'C'D'E', etc. would really be a loop, given the identity of A and A', B and B' ... Bois apparently takes seriously the possibility of an event's preceding itself ... In other words the failure of our irreflexivity axiom is not taken to be a breakdown of time, but is taken instead to be precisely what is involved in looping time. In a similar vein, Goedel [sic] and others have pointed out there are solutions to the field equations of general relativity that involve closed timelike curves, in which an event is preceded by itself ...

At any rate, there is arguably nothing iimpossible about an event's preceding itself if it happens as part of a loop in time. Matters are otherwise if it happens as part of a linear series such as ABCDAXYZ, in which the second occurence of A is identified with the first. Here numerically identical events would have different sequels, in volation of the Indiscernibility of Identicals. (pp. 388-389)

Reformulating axiom 2 will be challenging if time is continuous. If time were discrete, we could say "if an event A has two immediate predecessors B and C, then B and C are simultaneous, and if A has two immediate successors, D and E, then D and E are simultaneous." However, for continuous time, we cannot define a rigorous notion of immediacy in this context, and relativity only makes things worse.

Nevertheless, Van Cleve does seem to succeed in saving Berkeleian idealism from Borges' charge that it leads to the unreality of time. Another problem remains, however, for the idealism, and that is to get a shared timeline for all minds. Van Cleve rightly notes (p. 382) that God's perceptons can save us a lot of trouble, but it still seems that Berkeley needs to explain how my mental events can exist in the same timeline as yours and how we can know the ordering for those events for which we seem to think we know the ordering.

An observation I want to make here, which I think will lead to a solution, is that an idealist world is an information system, like a computer network. Berkeley's world, in particular, is one in which all information is routed through a central server (namely, God). Other "network architectures" are imaginable, but it is the "central server" architecture that guarantees the coherence of the universe.

Now, Berkeley's world resembles a computer network (or a single multi-processor computer) in one respect that is particularly relevant here: in each computer processor, there is a series of discrete events, called clock cycles. A crystal emits an electrical signal in a sine wave, and one computation takes place in each period of the sine wave. When you have a network of computers, it is often necessary to have them all keep consistent time with one another but, as it turns out, this is quite difficult. Network packets don't always take the same amount of time to arrive and the clocks have to be continually resynchronized, since tiny variations in temperature will change the period of the wave. This means that the problem can't be solved in such a way as to create an ordering of events according to the ticking of some 'absolute' clock, but there are, nevertheless, several algorithms to order all the clock cycles of all the computers such that they satisfy the previously mentioned time order axioms. I'll briefly describe the general approach shared by the major solutions from my notes on Matt Blaze's 2005 operating systems class.

We define a few rules, using the predicate Pxy for "x precedes y", and standard logical notation, with a bit of English mixed in:

  1. ∀x∀y[(x and y are events in the same process)&(x is executed before y)->Pxy]

  2. ∀x∀y[(x is a sending event)&(y is the corresponding receiving event)->Pxy]

  3. ∀x∀y∀z[(Pxy&Pyz)->Pxz]

  4. ∀x∀y[(~Pxy&~Pyx)->x and y are concurrent]

This means that some events are simultaneous for one observer and not for another (in particular, if you have network packets n1 and n2 where n1 precedes n2 and no other packets are between n1 and n2, computer c1 will regard all events on computer c2 in between n1 and n2 as simultaneous, but computer c2 will see its own events as having an internal ordering), but we already had that from relativity. Now, this doesn't define an absolute time (which, again, relativity says we can't do anyway), but what's interesting from a Berkeleian perspective is that it does seem (to me) to capture how it is that we have a shared timeline: that is, certain sense events are shared between people, and by applying rules like these we get a shared timeline. Of course, we don't each have exactly the same ordering of events, but there is enough commonality for coherence between one observer's perceptions and another's.

What's going to complicate things even further is that under relativity (as Lauren has just been explaining to me) in certain specific circumstances (namely, circumstances where the spatial separation between event a and event b is such that llight from a cannot reach b or vice versa), some observers may disagree on the order of a and b. In the computer case, that doesn't generally happen. That is, if Sxy is "x and y are simultaneous", we may have one computer saying Sab and another saying Pab, but we will never have one computer saying Pab and another saying Pba. It seems to me that someone should say something interesting about this message passing thing in connection with this relativity and light cone stuff, but since I don't know what this interesting observation is, that someone must not be me.

The long and short of it is, it seems that an idealist/phenomenalist can get a timeline out of this that is as intersubjective as anyone can hope for, post-relativity.

Posted by Kenny at October 29, 2007 5:43 PM
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