Processes, Marks and Light-Spots

Alexander R. Pruss

 

Department of Philosophy

Georgetown University

 

March 6, 2007

 

1. Introduction

            The flow of water in a river is a causal process. A disc of light moving along a wall due to a rotating spotlight is only a pseudo-process. Perhaps the most easiest way to see that it is only a pseudo-process is to observe that while a spotlight that rotates sufficiently quickly will produce a disc of light moving faster than light if the wall is far enough.

            Salmon has attempted to distinguish causal processes from pseudo-processes by means of mark transmission. A process can be marked, and the mark will be transmitted by the process. Dump some dye in the river and the water will become colored downstream.

            It is essential to Salmon’s project of characterizing causal processes that the notion of mark transmission not be a causal one. Thus, Salmon defines mark transmission (MT) as follows:

Let P be a process that, in the absence of interactions with other processes would remain uniform with respect to a characteristic Q, which it would manifest consistently over an interval that includes both of the space-time points A and B (A ¹ B). Then, a mark (consisting of a modification of Q into Q’), which has been introduced into process P by means of a single local interaction at a point A, is transmitted to point B if P manifests the modification Q’ at B and at all stages of the process between A and B without additional interactions.[1]

This has led to several counterexamples in the literature that point out that some pseudo-processes do transmit marks by this non-causal definition of MT.[2] However, those counterexamples might be read not as objections to Salmon’s characterization of causal processes in terms of MT, but as objections to the particular non-causal characterization of MT given by Salmon, objections that could perhaps be circumvented by giving further conditions.

            Instead, I shall give a very simple example of MT by a pseudo-process. That the pseudo-process transmits a mark will be true not only by Salmon’s stipulative definition of MT, which might simply be a counterexample to that definition, but will be intuitively correct on any plausible notion of mark transmission, even a causal one. Therefore, Salmon’s theory cannot be fixed simply by repairing the definition of MT. The counterexample will show that a non-causal pseudo-process can causally transmit a mark.

2. The example

            Start with the paradigmatic example of a pseudo-process. A wall with a spot of light from a rotating spotlight. In this example, the spot of light moves quite slowly. You observe an experimenter who puts down a small black object on the spot of light. As the spot of light moves, the black object moves with it. This already seems to be a case of mark transmission by Salmon’s definition. The spot of light without a black object has been modified to a spot of light with a black object. The black object has been introduced by a single local interaction—the experimenter has put it in.

And it appears that no additional interactions take place. One might worry that there is an ongoing interaction between the black object and the modified process, but that would be mistaken. For the new process is the spot of light with the black object, and hence it is a mistake to describe the black object as interacting with the modified process even if the black object interacts with the spot of light, unless the prohibition of continuing interactions prohibits the self-interaction of a process. But of course if the prohibition of continuing interactions prohibited the self-interaction of a process, Salmon’s account would be a failure, since typical causal processes do exhibit some measure of self-interaction: thus in the growth of a plant, the various cells are interacting with one another.

Thus the pseudo-process transmits a mark by Salmon’s definition of MT. Thus, we have a counterexample either to Salmon’s account of MT or to his analysis of causal processes in terms of MT. I shall argue that the case can be elaborated in such wise that not only is it a counterexample to Salmon’s definition of MT, but to Salmon’s analysis of causal processes in terms of MT, since in fact we can elaborate this case in such a way as makes it clear that we have genuine MT here.

For suppose that we observe the process further. We see the experiment repeated a number of times, with the same results, and we observe that no little black objects appear without the experimenter putting down a little black object. Sometimes, the beam of light moves by a somewhat different path, and the little black object then follows that different path. We also observe that when the little black object is put down outside of the light spot, it moves about haphazardly. All of this gives us good reason to believe that the mark is causally transmitted. It is not mere coincidence or some independent force that makes the little black object move with the spot of light.

As a further refinement, we notice that the experimenter has a bucket of little black objects, and can put a number of them in the light spot, and the marked spot will move across the wall. Now our experimenter can use this to transmit information through the markings to a fellow experimenter at the far end of the wall: “One dark object, and we go out for dinner afterwards; two dark objects, and we skip dinner and go home; three dark objects, and the experiment is done.” Furthermore, we rule out the hypothesis of the little black object running on remote control.

Let us suppose that all the natural observational inferences are in fact correct. The counterfactual that the black objects would not move with the light spot if the light spot were not marked with them is true. The local interaction of putting down the black object and the interaction between the black object and the light spot cause the black object to be further down the wall when the light spot is further down the wall. There are no coincidences or otherwise deceptive non-causal correlations here. This is bona fide causation.

What is particularly interesting about the case as described in the previous paragraph is that the marked spot of light is now a causal process. Hence, one can mark a pseudo-process in such a way that the marked process is a causal process.

Thus, if the scenario is as described, then the pseudo-process does indeed transmit a mark, both by Salmon’s flawed definition and really. Hence MT cannot be the way to distinguish between causal processes and pseudo-processes.

Now one might ask whether the arrangement as described is actually possible. This really comes down to asking whether one can find little black objects sufficient to make the above claims true. Many readers at this point will probably have their own examples of objects that will make the story work. My personal favorite is a light-sensitive beetle, one that tracks the lit-up disc on the wall. The spot will have to move slowly, of course, for the beetle to follow it. The beetled spot of light or, equivalently, the beetle surrounded by light are going to be genuine causal processes.

3. An objection

I think the main objection to the example is whether the beetle’s continued tracking of the spot of light might not constitute the “additional interactions” that Salmon prohibits. I have, however, already argued that internal interaction in the marked process cannot disqualify the marking, since bona fide causal processes often do have significant internal causal interaction.

But perhaps, it will be argued, in this case the interaction is more significant. For the mark is only transmitted because of this continued interaction. However, this surely cannot count against the claim that we have mark transmission. Suppose I mark a deer by painting a spot on its back. Then the mark is surely transmitted when the deer runs with that spot on its back. But the mark is only transmitted by virtue of the continued interaction between the deer and the paint—when the deer moves, the paint, which continues to adhere to the deer, is pulled along. Now, adhering may be a less complex form of interaction than tracking, but surely that cannot make for the crucial difference. And, anyway, the chemical interactions in the paint’s adherence to the deer’s hair might well be quite complex.

Salmon himself gives as an example of mark transmission a car’s becoming dented and scratched and these dents and scratches being maintained as part of the structure of the process.[3] But the dents and scratches are maintained on the car only because of continuing electromagnetic interactions that maintain the shape of the car, including the shape of the dents and scratches.[4]

It thus seems that the no-continued-interaction condition should say something like: there is no continued interaction between the marked process and processes external to it. But that will not work, because typical causal processes, marked or unmarked, do interact with their environments, and often require specialized environmental conditions for their maintenance (think of living organisms). Rather, we need to say that any, or maybe any relevant, interaction with the environment that that the marked process has would also be there absent the marking. In the case at hand the marked process does have a continued external interaction, namely one with the source of the light-beam, but that interaction was there in the unmarked case as well.

But even if one insists that the marked process not have any relevant interaction with the environment, so that the interaction with the source of the light-beam rules out this example, we can modify the example. Instead of a spot of light from a beam, consider a wall covered with LEDs, each plugged independently into its own timer and power cell. By coincidence, the timers are set in such a way that an observer will see a (pixelated) disc of light process over the wall, simply as an artifact of individual LEDs turning off and on independently. This is a pseudo-process—indeed, if the timer values are right, the spot can move faster than light. Once again we mark with a beetle that follows the disc of light. But now there is no relevant continued interaction with the external environment, since there is no source of a beam of light.[5]