Observations and risk of confirmation/disconfirmation

It seems that a rational agent cannot guarantee their credence in a hypothesis H to go up by choosing what observation to perform. For if no matter what I observe, my credence in H goes up given my observation, then my credence should already have gone up prior to the observation—I should boost my credence from the armchair.

But this reasoning is false in general. For in performing the observation, I not only learn which of the possible observable results is in place, but I also learn that I have performed the observation. In cases where the truth of H has a correlation with whether I actually perform the observation, this can have a predictable direction of effect on my credence in H.

Suppose that the hypothesis H is the conjunction that I am going to look in the closet and there is life on Mars. By looking to check if there is a mouse in my closet, I ensure that the first conjunct of H is true, and hence I increase my credence in H—no matter what I find out about mice.

This is a very trivial fact. But it does mean that we need to qualify the statement that any observation that can confirm a hypothesis can also disconfirm it. We need to specify that the confirmation and disconfirmation happen after one has already updated on the fact that one has performed the observation.

Observation, collapse and circularity

The following four premises seem to be contradictory:

1. An observation of an event E is caused by the event E.

2. Observation causes collapse.

3. What is observed is the collapsed state.

4. There is no circular causation.

Here is my first attempt to get out of this, on behalf of those attracted to the observation-causes-collapse view. For concreteness, let’s suppose that we’re observing an electron in a mixed up-down spin state, and suppose that we observe that it’s in the up state. Distinguish these two events:

• O₁: Observing whether the electron is in an up or a down state.

• O₂: Observing the electron to be in an up state.

Then I think what the defender of observation-causes-collapse can say this: O₁ causes the collapsed state which in turn causes O₂. But this is rather strange. For O₁ and O₂ actually seem to be the same coarse-grained event, which makes that coarse-grained event be its own cause! Another way to see the problem is to note that O₁ is the disjunctive event of observing the electron to be in the up state or observing the electron to be in the down state. But then O₂ grounds O₁: disjunctions are grounded in their true disjunct(s). But then O₁ is causally prior to its grounds, which seems absurd.

A second attempt: deny (3). Compare Elizabeth Anscombe’s theory that an intention to ϕ in the successful case constitutes one’s knowledge that one will ϕ or Thomas Aquinas’s theory that God’s knowledge of the world is the cause of the world’s being as it is. On these cases, the direction of fit in the knowledge is reversed. Observation of quantum phenomena could be like that.

Third attempt: cut up an act of observation into two parts. Metaphorically speaking, we could imagine the mind querying the world: “Is the electron in an up or a down state?” In response, reality collapses, and the mind observes that reality is in an up state. Thus, we have a query event Q and an observation-proper O₂. It is Q that causes collapse, and P is then the observation of the collapse. This solves the circularity problem, but strictly speaking it’s incorrect to say that observation causes collapse. Rather, it is the pre-observation query event Q that causes collapse. And if simultaneous causation is possible, then Q and O₂ may be simultaneous.

I think the second and third attempts are the way to go, assuming we're keeping the basic idea behind observation-causes-collapse.

Constructive empiricism and pairs

Van Fraassen thinks that when we accept a scientific theory, we should be bracket the theory’s claims about unobservable entities, but believe everything else.

An oddity has occurred to me. Suppose a theory talks about certain microorganisms that are just under the minimum size for human visual observation. But when you have two things that are just under the minimum observable size side-by-side, the pair is observable. So, oddly, we will believe in pairs without believing in individuals.

For further oddity, now imagine that Alpha and Beta are such a side-by-side pair. Then we believe in Alphabeta, the pair of Alpha and Beta. Suppose Alpha swims a little away from Beta. Now, Alphabeta disappears from view. But Alphabeta is still observable. To observe Alphabeta, all we need to do is to coax Alpha and Beta to swim to each other. So on van Fraassen grounds, we should still continue to believe in Alphabeta even when temporarily we cannot see it due to the separation of Alpha from Beta. (Compare: a very thin sheet is still observable when it is edge-on, even though it can only be seen when tilted to the line of sight.)

But it is absurd to believe in a pair of organisms, at different ends of a test-tube, without believing in either organism.

One way out for van Fraassen is to adopt a sparse ontology on which there are no pairs. But while I like such an ontology, I don’t think van Fraassen will want to do that, as he wants to believe in observable objects that science talks about, such as planets.

A modified consciousness-causes-collapse interpretation of quantum mechanics

Here are two technical problems with consciousness causes collapse (ccc) interpretations of quantum mechanics. In both, suppose a quantum experiment with two possible outcomes, A and B, of equal probability 1/2.

1. The sleeping experimenter: The experimenter is dreamlessly asleep in the lab and the experiment is rigged to wake her up on measuring A by ringing a bell. If conscious observation causes collapse, then when A is measured, the experimenter is woken up, and collapse occurs. Presumably, this happens half the time. But what happens the other half the time? No conscious observation occurs, so no collapse occurs, so the system remains in a superposition of A and B states. But that means that when the experimenter naturally wakes up several hours later, and then collapse will happen. However, when collapse happens then, it has both A and B outcome options at equal chances. But that means that overall, there is a 75% chance of an A outcome, which is wrong.

2. Order of explanation: The experimenter is awake. On outcome A, a bell rings. On B, a red light goes on. In fact, A is observed. What caused the collapse? It wasn’t the observer’s hearing the bell, because the bell’s occurrence is explanatorily posterior to the collapse. But we said that it is conscious observation that causes the collapse. Which conscious observation was that, if it wasn’t the hearing of the bell? Note that the observer need not have been conscious prior to hearing the bell or seeing the light—the experiment can be rigged so that either the bell or the light wakes up the observer. Perhaps the cause of the collapse was the state of being about to hear a bell or see a red light, or maybe it was the disjunctive state of hearing a bell or seeing a red light. But the former is a strange kind of cause, and the second would be a weird case where the disjunction is prior to its true disjunct.

The first problem strikes me as more serious than the second—the second is a matter of strangeness, while the first yields incorrect predictions.

I’ve been thinking about a curious ccc interpretation that escapes both problems. On this interpretation, the universe branches like in Everett-style multiverse explanations, but a conscious observation in any branch causes collapse. Collapse is the termination of a bunch of branches, including perhaps the termination of the branch in which the collapse-causing observation occurred. The latter isn’t some sort of weird retroactive thing—it’s just that the branch terminates right after the observation.

In case 2, the universe branches into an A-universe and a B-universe (or into pluralities of universes of both sorts). In the A-universe a bell is heard by the observer. In the B-universe a red light is seen by her. When this happens, collapse occurs, and there is no future to the observer after the observation of the red light, because in fact (or so case 2 was set up) it is the observation of A that won out. Or at least this is how it is when the two observations would be simultaneous. Suppose next that the bell observation would be made slightly earlier. Then as soon as the bell observation is made, the B-branch is terminated, and the red light observation is never made. On the other hand, if the light observation is timed to come first, then as soon as the light observation is made in the B-branch, this observation terminates the B-branch, and shortly afterwards the bell is heard in the remaining branch, the A-branch.

Case 1, then, works as follows. The universe branches into an A-universe, with a bell, and a silent B-universe. As soon as the bell is heard in the A-universe, the observation causes collapse, and one of the branches is terminated. If it’s the A-branch that’s terminated, then the observer heard the bell, but the future of that observation is annihilated. Instead, a couple of hours later the observer wakes up in the B-branch, and deduces that B must have been measured. If it’s the B-branch that’s terminated, on the otehr hand, then the observer’s observing of the bell has a future.

Prior to collapse, on this interpretation, we are located in multiple branches. And then our multilocation is wholly or partly resolved by collapse in favor of location in a proper subset of the branches where we were previously located. What happened to us in the other branches really did happen to us, but we never remember it, because it’s not recorded to memory.

On this interpretation, various things are observed by us which we never remember, because they have no future. This is a bit disquieting. Suppose that instead of the red light in case 2, the experimenter is poked with a red hot poker. Then if she hears the bell ring, she is relieved to have escaped the pain. But she didn’t: for if the poking is timed at or before the ringing, then the poking really did happen to her, albeit in another branch and not recorded to memory.

Fortunately for us, the futureless unremembered bad things were very brief: they only lasted for as short a period of time as was needed to establish them as phenomenologically different from the other possible outcome. So in the poked-with-a-poker branch, one only feels the pain for the briefest moment. And that’s not a big deal.

I worry a bit about quantum Zeno issues with this interpretation.

When a non-observation is an observation

Consider a standard Stern-Gerlach setup. An electron with mixed up/down spin is sent through a magnetic field. Then there are electron detectors that detect whether it went up or down.

Now, the up detector is connected to a very loud bell. The down detector is connected to a dim light. On the standard consciousness-causes-collapse (ccc) theory, if there is an observer who can both hear and see, she collapses the wavefunction, with probabilities given by the Born rule.

But now suppose that our observer has fallen asleep. The bell would wake the observer. The light wouldn't. What happens?

I think that if we accept ccc, we should also accept that the wavefunction collapses in this case. Thus, sometimes the wavefunction collapses in favor of up and a bell, and sometimes it collapses in favor of down and a light. In the latter case, there is no observation made—the observer is unconscious. Thus, on this solution, while an unconscious observer is capable of collapsing a wavefunction.

Perhaps one disagrees that the wavefunction collapses here. Then the observer in the lab is in a superposition of awake and asleep states. This by itself seems unacceptable. It seems that the whole point of ccc was to ensure that we did not have to worry about the weirdness of superpositions between different conscious states. But a superposition between a conscious and a non-conscious state is just as weird. Moreover, supposing that our observer is in a superposition of awake and asleep states, we can imagine a second observer coming into the lab. As soon as the second observer notes whether the first is asleep, we will have collapse. If that happens, then suddenly the first observer comes to be in a pure state. Some of the time, that pure state will be one of remembering being woken up by a bell. But that memory is false: she was never woken up by a bell, but was in a superposition of woken and non-woken states. So this interpretation leads to us having to attribute false memories to observers. And we should avoid that.

This line of thought suggests that we should treat non-observation as a kind of observation. Collapse happens whether the bell is observed or not. Collapse occurs always to exclude superpositions between different observational states, where non-observation counts as an observational state.

Suppose we do this outside of quantum mechanics? Well, this could have some implications for Sleeping Beauty. It would suggest that the Sleeping Beauty problem where one is woken on Monday and Tuesday on tails (with amnesia induced in between) and only on Monday on heads is equivalent to the variant where on heads one is also woken on Tuesday and informed that there was heads. For the non-observation on heads on Tuesday in the first problem should be thought of as a kind of observation. I think thirding is quite plausible on the variant on standard Bayesian grounds, so this supports thirding in the original.

We also get a variant of that lighthearted answer to verificationist worries about Christianity. The lighthearted answer is that whether Christianity is true is verifiable. Just wait until you're dead, and you'll see. Well, not quite, goes the riposte: you will see if there is an afterlife, but if there is no afterlife, you won't. But if we treat non-observation as a kind of observation, then you in effect do "observe"—through genuine observation if there is an afterlife and without one otherwise.

How far do we take the principle that non-observation can count as observation? Do non-observations by non-existent persons count? Quite possibly. Suppose that a lab apparatus is set up so that a conscious being is produced when the up electron detector is triggered and not otherwise. Similar reasoning to the above suggests that we should have collapse here, even if no conscious being is produced. The mere possibility of producing one triggers collapse.

Of course, ccc may be false.

Beauty, observation and objectivity

The following fact is typically seen as evidence for the subjectivity of beauty:

1. Very long necks look beautiful to the Padaung but not to contemporary Americans.

But the following fact is not typically seen as evidence for the subjectivity of beauty:

2. Van Gogh's Wild Roses is looks very beautiful by visible light but not so much by x-ray.

Why do we not see (2) as evidence for subjectivity about beauty? I think the answer is simple: Wild Roses is no more meant to be viewed by x-ray light than the Moonlight Sonata is meant to be viewed visually in Fourier transform. Wild Roses and the Moonlight Sonata are intended to be beautiful in those respects that are perceived visually or aurally, respectively, and they succeed admirably at these aims.

We can be a bit more subtle here. A microscopic examination of Wild Roses is not going to reveal the relevant beauty of the work, nor will an auditory examination of the individual notes of the Moonlight Sonata. These works are beautiful in respect of those features that are salient to the appropriately trained "eye" or "ear"—and of course it is not the literal eye or ear that is mainly being trained.

But why not say the same thing about long neck of the Padaung woman, then? She intends her long neck to be beautiful in those respects that are salient to trained Padaung observers. Maybe she is beautiful in respect of her long neck in contemporary North America, too, but we lack the training to make salient to us the features that make her beautiful.

Moreover, it is important to note that the features that make something beautiful may very well be relational features. A part of what can make a work beautiful is precisely the allusions to other works and to the outside world—what makes Anna Karenina a great work of art is in part that the people in it are like real people (which does not mean that every work of literature needs to have people in it that are like real people). Thus it may be that the Padaung woman's long neck is beautiful in part precisely by its relation to particular social practices (and hence when she travels to North America, and is no longer appropriately related to these social practices, she ceases to be beautiful in respect of her neck). Recognizing the aesthetic role of such relations is not a form of subjectivism, relativism or contextualism—it is no more that than recognizing the aesthetic role of the reality of the characters in Anna Karenina makes one a subjectivist, relativist or contextualist.

(Of course, there is also the possibility that the Padaung are simply wrong in their aesthetic judgment. But it is hard to say that without their training. And the possibility of their being wrong is significant evidence for objectivism about beauty.)

[Edited on March 16, 2011, to remove near-contradiction. -ARP]

Two kinds of scientific accounts

Science can provide two kinds of accounts in response to our observations:

1. Sometimes, science explains why it is that the things we observe are as we observe them.
2. At other times, science will explain why it is that we make the observations we do despite these observations not matching reality.

I think there ought to be a strong preference for the first kind of scientific account. Thus, we should prefer a story on which the universe evolves from a Big Bang to a story on which the universe comes into existence full-blown five minutes ago with false memories of a longer past. Likewise, we should prefer a story on which other people are conscious to a solipsist story explaining why we ascribe consciousness to others.