Schrödinger’s Cat

Erwin Schrödinger describes the context for his thought experiment with a cat:

The other alternative consists of granting reality only to the momentarily sharp determining parts – or in more general terms to each variable a sort of realization just corresponding to the quantum mechanical statistics of this variable at the relevant moment.

That it is in fact not impossible to express the degree and kind of blurring of all variables in one perfectly clear concept follows at once from the fact that Q.M. as a matter of fact has and uses such an instrument, the so-called wave function or psi-function, also called system vector. Much more is to be said about it further on. That it is an abstract, unintuitive mathematical construct is a scruple that almost always surfaces against new aids to thought and that carries no great message. At all events it is an imagined entity that images the blurring of all variables at every moment just as clearly and faithfully as does the classical model its sharp numerical values. Its equation of motion too, the law of its time variation, so long as the system is left undisturbed, lags not one iota, in clarity and determinacy, behind the equations of motion of the classical model. So the latter could be straight-forwardly replaced by the psi-function, so long as the blurring is confined to atomic scale, not open to direct control. In fact the function has provided quite intuitive and convenient ideas, for instance the “cloud of negative electricity” around the nucleus, etc. But serious misgivings arise if one notices that the uncertainty affects macroscopically tangible and visible things, for which the term “blurring” seems simply wrong. The state of a radioactive nucleus is presumably blurred in such a degree and fashion that neither the instant of decay nor the direction, in which the emitted alpha-particle leaves the nucleus, is well-established. Inside the nucleus, blurring doesn’t bother us. The emerging particle is described, if one wants to explain intuitively, as a spherical wave that continuously emanates in all directions and that impinges continuously on a surrounding luminescent screen over its full expanse. The screen however does not show a more or less constant uniform glow, but rather lights up at one instant at one spot – or, to honor the truth, it lights up now here, now there, for it is impossible to do the experiment with only a single radioactive atom. If in place of the luminescent screen one uses a spatially extended detector, perhaps a gas that is ionised by the alpha-particles, one finds the ion pairs arranged along rectilinear columns, that project backwards on to the bit of radioactive matter from which the alpha-radiation comes (C.T.R. Wilson’s cloud chamber tracks, made visible by drops of moisture condensed on the ions).

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

We see here the two elements described at the end of this earlier post. The psi-function is deterministic, but there seems to be an element of randomness when someone comes to check on the cat.

Hugh Everett amusingly describes a similar experiment performed on human beings (but without killing anyone):

Isolated somewhere out in space is a room containing an observer, A, who is about to perform a measurement upon a system S. After performing his measurement he will record the result in his notebook. We assume that he knows the state function of S (perhaps as a result of previous measurement), and that it is not an eigenstate of the measurement he is about to perform. A, being an orthodox quantum theorist, then believes that the outcome of his measurement is undetermined and that the process is correctly described by Process 1 [namely a random determination caused by measurement].

In the meantime, however, there is another observer, B, outside the room, who is in possession of the state function of the entire room, including S, the measuring apparatus, and A, just prior to the measurement. B is only interested in what will be found in the notebook one week hence, so he computes the state function of the room for one week in the future according to Process 2 [namely the deterministic  wave function]. One week passes, and we find B still in possession of the state function of the room, which this equally orthodox quantum theorist believes to be a complete description of the room and its contents. If B’s state function calculation tells beforehand exactly what is going to be in the notebook, then A is incorrect in his belief about the indeterminacy of the outcome of his measurement. We therefore assume that B’s state function contains non-zero amplitudes over several of the notebook entries.

At this point, B opens the door to the room and looks at the notebook (performs his observation.) Having observed the notebook entry, he turns to A and informs him in a patronizing manner that since his (B’s) wave function just prior to his entry into the room, which he knows to have been a complete description of the room and its contents, had non-zero amplitude over other than the present result of the measurement, the result must have been decided only when B entered the room, so that A, his notebook entry, and his memory about what occurred one week ago had no independent objective existence until the intervention by B. In short, B implies that A owes his present objective existence to B’s generous nature which compelled him to intervene on his behalf. However, to B’s consternation, A does not react with anything like the respect and gratitude he should exhibit towards B, and at the end of a somewhat heated reply, in which A conveys in a colorful manner his opinion of B and his beliefs, he rudely punctures B’s ego by observing that if B’s view is correct, then he has no reason to feel complacent, since the whole present situation may have no objective existence, but may depend upon the future actions of yet another observer.

Schrödinger’s problem was that the wave equation seems to describe something “blurred,” but if we assume that is because something blurred exists, it seems to contradict our experience which is of something quite distinct: a live cat or a dead cat, but not something in between.

Everett proposes that his interpretation of quantum mechanics is able to resolve this difficulty. After presenting other interpretations, he proposes his own (“Alternative 5”):

Alternative 5: To assume the universal validity of the quantum description, by the complete abandonment of Process 1 [again, this was the apparently random measurement process]. The general validity of pure wave mechanics, without any statistical assertions, is assumed for all physical systems, including observers and measuring apparata. Observation processes are to be described completely by the state function of the composite system which includes the observer and his object-system, and which at all times obeys the wave equation (Process 2).

It is evident that Alternative 5 is a theory of many advantages. It has the virtue of logical simplicity and it is complete in the sense that it is applicable to the entire universe. All processes are considered equally (there are no “measurement processes” which play any preferred role), and the principle of psycho-physical parallelism is fully maintained. Since the universal validity of the state function is asserted, one can regard the state functions themselves as the fundamental entities, and one can even consider the state function of the whole universe. In this sense this theory can be called the theory of the “universal wave function,” since all of physics is presumed to follow from this function alone. There remains, however, the question whether or not such a theory can be put into correspondence with our experience.

This present thesis is devoted to showing that this concept of a universal wave mechanics, together with the necessary correlation machinery for its interpretation, forms a logically self consistent description of a universe in which several observers are at work.

Ultimately, Everett’s response to Schrödinger is that the cat is indeed “blurred,” and that this never goes away. When someone checks on the cat, the person checking is also “blurred,” becoming a composite of someone seeing a dead cat and someone seeing a live cat. However, these are in effect two entirely separate worlds, one in which someone sees a live cat, and one in which someone sees a dead cat.

Everett mentions “the necessary correlation machinery for its interpretation,” because a mathematical theory of physics as such does not necessarily say that anyone should see anything in particular. So for example when Newton when says that there is a gravitational attraction between masses inversely proportional to the square of their distance, what exactly should we expect to see, given that? Obviously there is no way to answer this without adding something, and ultimately we need to add something non-mathematical, namely something about the way our experiences work.

I will not pretend to judge whether or not Everett does a good job defending his position. There is an interesting point here, whether or not his defense is ultimately a good one. “Orthodox” quantum mechanics, as Everett calls it, only gives statistical predictions about the future, and as long as nothing is added to the theory, it implies that deterministic predictions are impossible. It follows that if the position in our last post, on an open future, was correct, it must be possible to explain the results of quantum mechanics in terms of many worlds or multiple timelines. And I do not merely mean that we can give the same predictions with a one-world account or with a many world account. I mean that there must be a many-world account such that its contents are metaphysically identical to the contents of a one-world account with an open future.

This would nonetheless leave undetermined the question of what sort of account would be most useful to us in practice.

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Aristotle on Future Contingents

In Chapter 9 of On Interpretation, Aristotle argues that at least some statements about the future need to be exempted from the principle of Excluded Middle:

In the case of that which is or which has taken place, propositions, whether positive or negative, must be true or false. Again, in the case of a pair of contradictories, either when the subject is universal and the propositions are of a universal character, or when it is individual, as has been said,’ one of the two must be true and the other false; whereas when the subject is universal, but the propositions are not of a universal character, there is no such necessity. We have discussed this type also in a previous chapter.

When the subject, however, is individual, and that which is predicated of it relates to the future, the case is altered. For if all propositions whether positive or negative are either true or false, then any given predicate must either belong to the subject or not, so that if one man affirms that an event of a given character will take place and another denies it, it is plain that the statement of the one will correspond with reality and that of the other will not. For the predicate cannot both belong and not belong to the subject at one and the same time with regard to the future.

Thus, if it is true to say that a thing is white, it must necessarily be white; if the reverse proposition is true, it will of necessity not be white. Again, if it is white, the proposition stating that it is white was true; if it is not white, the proposition to the opposite effect was true. And if it is not white, the man who states that it is making a false statement; and if the man who states that it is white is making a false statement, it follows that it is not white. It may therefore be argued that it is necessary that affirmations or denials must be either true or false.

Now if this be so, nothing is or takes place fortuitously, either in the present or in the future, and there are no real alternatives; everything takes place of necessity and is fixed. For either he that affirms that it will take place or he that denies this is in correspondence with fact, whereas if things did not take place of necessity, an event might just as easily not happen as happen; for the meaning of the word ‘fortuitous’ with regard to present or future events is that reality is so constituted that it may issue in either of two opposite directions. Again, if a thing is white now, it was true before to say that it would be white, so that of anything that has taken place it was always true to say ‘it is’ or ‘it will be’. But if it was always true to say that a thing is or will be, it is not possible that it should not be or not be about to be, and when a thing cannot not come to be, it is impossible that it should not come to be, and when it is impossible that it should not come to be, it must come to be. All, then, that is about to be must of necessity take place. It results from this that nothing is uncertain or fortuitous, for if it were fortuitous it would not be necessary.

The argument here is that if it is already true, for example, that I will eat breakfast tomorrow, then I will necessarily eat breakfast tomorrow, and there is no option about this and no ability of anything to prevent it. Aristotle is here taking it for granted that some things about the future are uncertain, and is using this as a reductio against the position that such claims can be already true. He goes on to give additional reasons for the same thing:

Again, to say that neither the affirmation nor the denial is true, maintaining, let us say, that an event neither will take place nor will not take place, is to take up a position impossible to defend. In the first place, though facts should prove the one proposition false, the opposite would still be untrue. Secondly, if it was true to say that a thing was both white and large, both these qualities must necessarily belong to it; and if they will belong to it the next day, they must necessarily belong to it the next day. But if an event is neither to take place nor not to take place the next day, the element of chance will be eliminated. For example, it would be necessary that a sea-fight should neither take place nor fail to take place on the next day.

These awkward results and others of the same kind follow, if it is an irrefragable law that of every pair of contradictory propositions, whether they have regard to universals and are stated as universally applicable, or whether they have regard to individuals, one must be true and the other false, and that there are no real alternatives, but that all that is or takes place is the outcome of necessity. There would be no need to deliberate or to take trouble, on the supposition that if we should adopt a certain course, a certain result would follow, while, if we did not, the result would not follow. For a man may predict an event ten thousand years beforehand, and another may predict the reverse; that which was truly predicted at the moment in the past will of necessity take place in the fullness of time.

Further, it makes no difference whether people have or have not actually made the contradictory statements. For it is manifest that the circumstances are not influenced by the fact of an affirmation or denial on the part of anyone. For events will not take place or fail to take place because it was stated that they would or would not take place, nor is this any more the case if the prediction dates back ten thousand years or any other space of time. Wherefore, if through all time the nature of things was so constituted that a prediction about an event was true, then through all time it was necessary that that should find fulfillment; and with regard to all events, circumstances have always been such that their occurrence is a matter of necessity. For that of which someone has said truly that it will be, cannot fail to take place; and of that which takes place, it was always true to say that it would be.

Yet this view leads to an impossible conclusion; for we see that both deliberation and action are causative with regard to the future, and that, to speak more generally, in those things which are not continuously actual there is potentiality in either direction. Such things may either be or not be; events also therefore may either take place or not take place. There are many obvious instances of this. It is possible that this coat may be cut in half, and yet it may not be cut in half, but wear out first. In the same way, it is possible that it should not be cut in half; unless this were so, it would not be possible that it should wear out first. So it is therefore with all other events which possess this kind of potentiality. It is therefore plain that it is not of necessity that everything is or takes place; but in some instances there are real alternatives, in which case the affirmation is no more true and no more false than the denial; while some exhibit a predisposition and general tendency in one direction or the other, and yet can issue in the opposite direction by exception.

Now that which is must needs be when it is, and that which is not must needs not be when it is not. Yet it cannot be said without qualification that all existence and non-existence is the outcome of necessity. For there is a difference between saying that that which is, when it is, must needs be, and simply saying that all that is must needs be, and similarly in the case of that which is not. In the case, also, of two contradictory propositions this holds good. Everything must either be or not be, whether in the present or in the future, but it is not always possible to distinguish and state determinately which of these alternatives must necessarily come about.

Let me illustrate. A sea-fight must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow. Since propositions correspond with facts, it is evident that when in future events there is a real alternative, and a potentiality in contrary directions, the corresponding affirmation and denial have the same character.

This is the case with regard to that which is not always existent or not always nonexistent. One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good. The case is rather as we have indicated.

Basically, then, there are two arguments. First there is the argument that if statements about the future are already true, the future is necessary. If a sea battle will take place tomorrow, it will necessarily take place. Second, there is the argument that this excludes deliberation. If a sea battle will take place tomorrow, then it will necessarily take place, and no place remains for deliberation and decision about whether to fight the sea battle. Whether you decide to fight or not, it will necessarily take place.

Unfortunately for Aristotle, both arguments fail. Consider the first argument about necessity. Aristotle’s example is that “if it is true to say that a thing is white, it must necessarily be white.” But this is hypothetical necessity, not absolute necessity. A thing must be white if it is true that is white, but that does not mean that “it must be white, period.” Thus for example I have a handkerchief, and it happens to be white. If it is true that it is white, then it must be white. But it would be false to simply say, “My handkerchief is necessarily white.” Since I can dye it other colors, obviously it is not simply necessary for it to be white.

In a similar way, of course it is true that if a sea battle will take place, it will take place. It does not follow at all that “it will necessarily take place, period.”

Again, consider the second argument, that deliberation would be unnecessary. Aristotle makes the point that deliberation is causative with respect to the future. But gravity is also causative with respect to the future, as for example when gravity causes a cup to fall from a desk. It does not follow either that the cup must be able not to fall, nor that gravity is unnecessary. In a similar way, a sea battle takes place because certain people deliberated and decided to fight. If it was already true that it was going to take place, then it also already true that they were going to decide to fight. It does not follow that their decision was unnecessary.

Consider the application to gravity. It is already true that if the cup is knocked from the desk, it will fall. It does not follow that gravity will not cause the fall: in fact, it is true precisely because gravity will cause the fall. In a similar way, if it true that the battle will take place, it is true because the decision will be made.

This earlier discussion about determinism is relevant to this point. Asserting that there is a definite outcome that our deliberations will arrive at, in each case, goes against our experience in no way. The feeling of “free will,” in any case, has a different explanation, whether or not determinism is true.

On the other hand, there is also no proof that there is such a determinate outcome, even if in some cases there are things that would suggest it. What happens if in fact there is nothing ensuring one outcome rather than another?

Here we could make a third argument on Aristotle’s behalf, although he did not make it himself. If the present is truly open to alternative outcomes, then it seems that nothing exists that could make it be true that “a sea battle will take place,” and false that “a sea battle will not take place.” Presumably if a statement is true, there must be something in reality which is the cause of the statement’s truth. Now there does not seem to be anything in reality, in this scenario, which could be a cause of truth. Therefore it does not seem that either alternative could be true, and Aristotle would seem to be right.

I will not attempt to refute this argument at this point, but I will raise two difficulties. First of all, it is not clear that his claim is even coherent. Aristotle says that “either there will be a sea battle or there will not be,” is true, but that “there will be a sea battle” is not true, and “there will not be a sea battle” is not true. This does not seem to be logically consistent, and it is not clear that we can even understand what is being said. I will not push this objection too hard, however, lest I be accused of throwing stones from a glass house.

Second, the argument that there is nothing in reality that could cause the truth of a statement might apply to the past as well as to the future. There is a tree outside my window right now. What was in that place exactly 100 million years ago to this moment? It is not obvious that there is anything in the present world which could be the cause of the truth of any statement about this. One might object that the past is far more determinate than the future. There are plenty of things in the present world that might be the cause of the truth of the statement, “World War II actually happened.” It is hard to see how you could possibly have arrived at the present world without it, and this “necessity” of World War II in order to arrive at the present world could be the cause of truth. The problem is that there is still no proof that this is universal. Once things are far enough in past, like 100 million years, perhaps minor details become indeterminate. Will Aristotle really want to conclude that some statements about the past are neither true nor false?

I will more or less leave things here without resolving them in this post, although I will give a hint (without proof at this time) regarding the truth of the matter. It turns out that quantum mechanics can be interpreted in two ways. In one way, it is a deterministic theory, and in this way it is basically time reversible. The present fully determines the past, but it equally fully determines the future. Interpreted in another way, it is an indeterministic theory which leaves the future uncertain. But understood in this way, it also leaves the past uncertain.

Employer and Employee Model of Human Psychology

This post builds on the ideas in the series of posts on predictive processing and the followup posts, and also on those relating truth and expectation. Consequently the current post will likely not make much sense to those who have not read the earlier content, or to those that read it but mainly disagreed.

We set out the model by positing three members of the “company” that constitutes a human being:

The CEO. This is the predictive engine in the predictive processing model.

The Vice President. In the same model, this is the force of the historical element in the human being, which we used to respond to the “darkened room” problem. Thus for example the Vice President is responsible for the fact that someone is likely to eat soon, regardless of what they believe about this. Likewise, it is responsible for the pursuit of sex, the desire for respect and friendship, and so on. In general it is responsible for behaviors that would have been historically chosen and preserved by natural selection.

The Employee. This is the conscious person who has beliefs and goals and free will and is reflectively aware of these things. In other words, this is you, at least in a fairly ordinary way of thinking of yourself. Obviously, in another way you are composed from all of them.

Why have we arranged things in this way? Descartes, for example, would almost certainly disagree violently with this model. The conscious person, according to him, would surely be the CEO, and not an employee. And what is responsible for the relationship between the CEO and the Vice President? Let us start with this point first, before we discuss the Employee. We make the predictive engine the CEO because in some sense this engine is responsible for everything that a human being does, including the behaviors preserved by natural selection. On the other hand, the instinctive behaviors of natural selection are not responsible for everything, but they can affect the course of things enough that it is useful for the predictive engine to take them into account. Thus for example in the post on sex and minimizing uncertainty, we explained why the predictive engine will aim for situations that include having sex and why this will make its predictions more confident. Thus, the Vice President advises certain behaviors, the CEO talks to the Vice President, and the CEO ends up deciding on a course of action, which ultimately may or may not be the one advised by the Vice President.

While neither the CEO nor the Vice President is a rational being, since in our model we place the rationality in the Employee, that does not mean they are stupid. In particular, the CEO is very good at what it does. Consider a role playing video game where you have a character that can die and then resume. When someone first starts to play the game, they may die frequently. After they are good at the game, they may die only rarely, perhaps once in many days or many weeks. Our CEO is in a similar situation, but it frequently goes 80 years or more without dying, on its very first attempt. It is extremely good at its game.

What are their goals? The CEO basically wants accurate predictions. In this sense, it has one unified goal. What exactly counts as more or less accurate here would be a scientific question that we probably cannot resolve by philosophical discussion. In fact, it is very possible that this would differ in different circumstances: in this sense, even though it has a unified goal, it might not be describable by a consistent utility function. And even if it can be described in that way, since the CEO is not rational, it does not (in itself) make plans to bring about correct predictions. Making good predictions is just what it does, as falling is what a rock does. There will be some qualifications on this, however, when we discuss how the members of the company relate to one another.

The Vice President has many goals: eating regularly, having sex, having and raising children, being respected and liked by others, and so on. And even more than in the case of the CEO, there is no reason for these desires to form a coherent set of preferences. Thus the Vice President might advise the pursuit of one goal, but then change its mind in the middle, for no apparent reason, because it is suddenly attracted by one of the other goals.

Overall, before the Employee is involved, human action is determined by a kind of negotiation between the CEO and the Vice President. The CEO, which wants good predictions, has no special interest in the goals of the Vice President, but it cooperates with them because when it cooperates its predictions tend to be better.

What about the Employee? This is the rational being, and it has abstract concepts which it uses as a formal copy of the world. Before I go on, let me insist clearly on one point. If the world is represented in a certain way in the Employee’s conceptual structure, that is the way the Employee thinks the world is. And since you are the Employee, that is the way you think the world actually is. The point is that once we start thinking this way, it is easy to say, “oh, this is just a model, it’s not meant to be the real thing.” But as I said here, it is not possible to separate the truth of statements from the way the world actually is: your thoughts are formulated in concepts, but they are thoughts about the way things are. Again, all statements are maps, and all statements are about the territory.

The CEO and the Vice President exist as soon a human being has a brain; in fact some aspects of the Vice President would exist even before that. But the Employee, insofar as it refers to something with rational and self-reflective knowledge, takes some time to develop. Conceptual knowledge of the world grows from experience: it doesn’t exist from the beginning. And the Employee represents goals in terms of its conceptual structure. This is just a way of saying that as a rational being, if you say you are pursuing a goal, you have to be able to describe that goal with the concepts that you have. Consequently you cannot do this until you have some concepts.

We are ready to address the question raised earlier. Why are you the Employee, and not the CEO? In the first place, the CEO got to the company first, as we saw above. Second, consider what the conscious person does when they decide to pursue a goal. There seems to be something incoherent about “choosing a goal” in the first place: you need a goal in order to decide which means will be a good means to choose. And yet, as I said here, people make such choices anyway. And the fact that you are the Employee, and not the CEO, is the explanation for this. If you were the CEO, there would indeed be no way to choose an end. That is why the actual CEO makes no such choice: its end is already determinate, namely good predictions. And you are hired to help out with this goal. Furthermore, as a rational being, you are smarter than the CEO and the Vice President, so to speak. So you are allowed to make complicated plans that they do not really understand, and they will often go along with these plans. Notably, this can happen in real life situations of employers and employees as well.

But take an example where you are choosing an end: suppose you ask, “What should I do with my life?” The same basic thing will happen if you ask, “What should I do today,” but the second question may be easier to answer if you have some answer to the first. What sorts of goals do you propose in answer to the first question, and what sort do you actually end up pursuing?

Note that there are constraints on the goals that you can propose. In the first place, you have to be able to describe the goal with the concepts you currently have: you cannot propose to seek a goal that you cannot describe. Second, the conceptual structure itself may rule out some goals, even if they can be described. For example, the idea of good is part of the structure, and if something is thought to be absolutely bad, the Employee will (generally) not consider proposing this as a goal. Likewise, the Employee may suppose that some things are impossible, and it will generally not propose these as goals.

What happens then is this: the Employee proposes some goal, and the CEO, after consultation with the Vice President, decides to accept or reject it, based on the CEO’s own goal of getting good predictions. This is why the Employee is an Employee: it is not the one ultimately in charge. Likewise, as was said, this is why the Employee seems to be doing something impossible, namely choosing goals. Steven Kaas makes a similar point,

You are not the king of your brain. You are the creepy guy standing next to the king going “a most judicious choice, sire”.

This is not quite the same thing, since in our model you do in fact make real decisions, including decisions about the end to be pursued. Nonetheless, the point about not being the one ultimately in charge is correct. David Hume also says something similar when he says, “Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them.” Hume’s position is not exactly right, and in fact seems an especially bad way of describing the situation, but the basic point that there is something, other than yourself in the ordinary sense, judging your proposed means and ends and deciding whether to accept them, is one that stands.

Sometimes the CEO will veto a proposal precisely because it very obviously leaves things vague and uncertain, which is contrary to its goal of having good predictions. I once spoke of the example that a person cannot directly choose to “write a paper.” In our present model, the Employee proposes “we’re going to write a paper now,” and the CEO responds, “That’s not a viable plan as it stands: we need more detail.”

While neither the CEO nor the Vice President is a rational being, the Vice President is especially irrational, because of the lack of unity among its goals. Both the CEO and the Employee would like to have a unified plan for one’s whole life: the CEO because this makes for good predictions, and the Employee because this is the way final causes work, because it helps to make sense of one’s life, and because “objectively good” seems to imply something which is at least consistent, which will never prefer A to B, B to C, and C to A. But the lack of unity among the Vice President’s goals means that it will always come to the CEO and object, if the person attempts to coherently pursue any goal. This will happen even if it originally accepts the proposal to seek a particular goal.

Consider this real life example from a relationship between an employer and employee:

 

Employer: Please construct a schedule for paying these bills.

Employee: [Constructs schedule.] Here it is.

Employer: Fine.

[Time passes, and the first bill comes due, according to the schedule.]

Employer: Why do we have to pay this bill now instead of later?

 

In a similar way, this sort of scenario is common in our model:

 

Vice President: Being fat makes us look bad. We need to stop being fat.

CEO: Ok, fine. Employee, please formulate a plan to stop us from being fat.

Employee: [Formulates a diet.] Here it is.

[Time passes, and the plan requires skipping a meal.]

Vice President: What is this crazy plan of not eating!?!

CEO: Fine, cancel the plan for now and we’ll get back to it tomorrow.

 

In the real life example, the behavior of the employer is frustrating and irritating to the employee because there is literally nothing they could have proposed that the employer would have found acceptable. In the same way, this sort of scenario in our model is frustrating to the Employee, the conscious person, because there is no consistent plan they could have proposed that would have been acceptable to the Vice President: either they would have objected to being fat, or they would have objected to not eating.

In later posts, we will fill in some details and continue to show how this model explains various aspects of human psychology. We will also answer various objections.

Truth and Expectation III

Consider what I said at the end of the last post on this topic. When our Mormon protagonist insists that his religion is true, he improves the accuracy of his expectations about the world. His expectations would actually be less accurate he decided that his religious beliefs are false.

Now we said in the first post on truth and expectation that in part we seem to determine the meaning of a statement by the expectations that it implies. If this is the case, then why should we not say that the Mormon’s beliefs are definitely true? In fact, in the post linked above about truth in religion, I suggested that people frequently do mean something like this when they say that their own religion is true. Nonetheless, it is easy to see that truth in this particular sense does not imply that each and every claim in the religion, understood as a claim about the world, is true.

But why not, if one’s expectations become more accurate, just as with statements that are clearly true? As I noted in the earlier post, to say that “that man is pretty tall” is a statement about the man. It is not a statement about myself, nor about my expectations, even if the meaning is partly determined by these things. So ultimately the truth or falsehood of the claim about the man is going to be determined by facts about the man, even if they need to be understood as facts about the man in relation to me and my expectations.

Consider again Scott Sumner’s anti-realism. Scott claims that we cannot distinguish between “our perception of reality, and actual reality.” As I said there, this is right in the sense that we cannot consistently hold the opinion, “This is my opinion about reality, but my opinion is false: reality is actually different.” But we can recognize the distinct meanings in “my perception of reality” and “actual reality.” Scott’s failure to recognize this distinction leads him to suggest on occasion that our beliefs about certain matters are just beliefs about what people in the future will believe. For example, he says in this comment:

You misunderstood Rorty. He is not recommending that you try to trick you colleagues into believing something that is not true. Rather he is merely describing what society regards as true. And who can deny that society tends to regard things as true, when they believe them to be true. No you might say “but what society believes to be true is not always really true.” But Rorty would say that statement means nothing, or else it means that you predict that a future society will have a different view of what is true.

Most people, without even realizing it, assume that there is some sort of “God-like” view of what is “really true” which is separate from what we believe is true, and or will believe in the future to be true. Rorty is an atheist. He believes that what society’s experts believe is the best we can do, the closest we can come to describing reality. Rorty would suggest to Hayek “if you want to convince other economists, use persuasive arguments.” I think that is very reasonable advice. It is what I try to do on this blog.

This is much like Bob Seidensticker’s claim that moral beliefs are beliefs about what society in the future will believe to be moral. In both cases, there is an unacceptable circularity. If our belief is about what people in the future will believe, what are the future people’s beliefs about? There is only one credible explanation here: people’s beliefs are about what they say their beliefs are about, namely the very things they are talking about. Moral beliefs are about whether actions are good or bad, and beliefs describing the world are about the world, not about the people who hold the beliefs, present or future.

This does not imply that there is “some sort of ‘God-like’ view of what is ‘really true’.” It just implies that our beliefs are distinct from other things in the world. Sumner is suggesting that a situation where everyone permanently holds a false belief, forever, is inconceivable. But this is quite conceivable, and we can easily see how it could happen. Just now I counted the cups in my cupboard and there are exactly 14 (if anyone is surprised by that value, most of those are plastic.) It is entirely conceivable, however, that I miscounted. And since I also have some cups that are not currently in the cupboard, if I did, I will probably never get it right, since I will just assume there was some other assortment. And since there is presumably no way for the public to discover the truth about this, society will be permanently deluded about the number of cups in my cupboard at 11:16 AM on July 14, 2018.

What would it mean, then, if it was not “actually true” that there were 14 cups in my cupboard? It would be determined by facts about the cups and the cupboard, not by facts about me, about society, about my expectations or society’s expectations. It would not be actually true if there were, in fact, only 13 cups there, even if no one would ever know this.

This all remains related to expectations, however. I don’t think I miscounted, so I think that if I go again and count them, I will get 14 again. If I did miscount, there is a good chance that counting again would result in a different number. Now I don’t intend to bother, so this expectation is counterfactual. Nonetheless, there are at least conceivable counterfactual situations where I would discover that I was mistaken. In a similar way, to say that the Mormon holds false religious beliefs implies that there are at least counterfactual situations where the falsehood would be uncovered by a violation of his expectations: e.g. if he had been alive at the time and had followed Joseph Smith around all the time to see whether there were any golden plates and so on.

Nonetheless, one cannot ultimately separate the truth of a statement from facts about the thing the statement is about. A statement is true if things are the way it says they are, “the way” being correctly understood here. If this were not the case, the statement would not be about the things in the first place.

Truth and Expectation II

We discussed this topic in a previous post. I noted there that there is likely some relationship with predictive processing. This idea can be refined by distinguishing between conscious thought and what the human brain does on a non-conscious level.

It is not possible to define truth by reference to expectations for reasons given previously. Some statements do not imply specific expectations, and besides, we need the idea of truth to decide whether or not someone’s expectations were correct or not. So there is no way to define truth except the usual way: a statement is true if things are the way the statement says they are, bearing in mind the necessary distinctions involving “way.”

On the conscious level, I would distinguish between thinking about something is true, and wanting to think that it is true. In a discussion with Angra Mainyu, I remarked that insofar as we have an involuntary assessment of things, it would be more appropriate to call that assessment a desire:

So rather than calling that assessment a belief, it would be more accurate to call it a desire. It is not believing something, but desiring to believe something. Hunger is the tendency to go and get food; that assessment is the tendency to treat a certain claim (“the USA is larger than Austria”) as a fact. And in both cases there are good reasons for those desires: you are benefited by food, and you are benefited by treating that claim as a fact.

Angra was quite surprised by this and responded that “That statement gives me evidence that we’re probably not talking about the same or even similar psychological phenomena – i.e., we’re probably talking past each other.” But if he was talking about anything that anyone at all would characterize as a belief (and he said that he was), he was surely talking about the unshakeable gut sense that something is the case whether or not I want to admit it. So we were, in fact, talking about exactly the same psychological phenomena. I was claiming then, and will claim now, that this gut sense is better characterized as a desire than as a belief. That is, insofar as desire is a tendency to behave in certain ways, it is a desire because it is a tendency to act and think as though this claim is true. But we can, if we want, resist that tendency, just as we can refrain from going to get food when we are hungry. If we do resist, we will refrain from believing what we have a tendency to believe, and if we do not, we will believe what we have a tendency to believe. But the tendency will be there whether or not we follow it.

Now if we feel a tendency to think that something is true, it is quite likely that it seems to us that it would improve our expectations. However, we can also distinguish between desiring to believe something for this reason, or desiring to believe something for other reasons. And although we might not pay attention, it is quite possibly to be consciously aware that you have an inclination to believe something, and also that it is for non-truth related reasons; and thus you would not expect it to improve your expectations.

But this is where it is useful to distinguish between the conscious mind and what the brain is doing on another level. My proposal: you will feel the desire to think that something is true whenever your brain guesses that its predictions, or at least the predictions that are important to it, will become more accurate if you think that the thing is true. We do not need to make any exceptions. This will be the case even when we would say that the statement does not imply any significant expectations, and will be the case even when the belief would have non-truth related motives.

Consider the statement that there are stars outside the visible universe. One distinction we could make even on the conscious level is that this implies various counterfactual predictions: “If you are teleported outside the visible universe, you will see more stars that aren’t currently visible.” Now we might find this objectionable if we were trying to define truth by expectations, since we have no expectation of such an event. But both on conscious and on non-conscious levels, we do need to make counterfactual predictions in order to carry on with our lives, since this is absolutely essential to any kind of planning and action. Now certainly no one can refute me if I assert that you would not see any such stars in the teleportation event. But it is not surprising if my brain guesses that this counterfactual prediction is not very accurate, and thus I feel the desire to say that there are stars there.

Likewise, consider the situation of non-truth related motives. In an earlier discussion of predictive processing, I suggested that the situation where people feel like they have to choose a goal is a result of such an attempt at prediction. Such a choice seems to be impossible, since choice is made in view of a goal, and if you do not have one yet, how can you choose? But there is a pre-existing goal here on the level of the brain: it wants to know what it is going to do. And choosing a goal will serve that pre-existing goal. Once you choose a goal, it will then be easy to know what you are going to do: you are going to do things that promote the goal that you chose. In a similar way, following any desire will improve your brain’s guesses about what you are going to do. It follows that if you have a desire to believe something, actually believing it will improve your brain’s accuracy at least about what it is going to do. This is true but not a fair argument, however, since my proposal is that the brain’s guess of improved accuracy is the cause of your desire to believe something. It is true that if you already have the desire, giving in to it will improve accuracy, as with any desire. But in my theory the improved accuracy had to be implied first, in order to cause the desire.

The answer is that you have many desires for things other than belief, which at the same time give you a motive (not an argument) for believing things. And your brain understands that if you believe the thing, you will be more likely to act on those other desires, and this will minimize uncertainty, and improve the accuracy of its predictions. Consider this discussion of truth in religion. I pointed out there that people confuse two different questions: “what should I do?”, and “what is the world like?” In particular with religious and political loyalties, there can be an intense social pressure towards conformity. And this gives an obvious non-truth related motive to believe the things in question. But in a less obvious way, it means that your brain’s predictions will be more accurate if you believe the thing. Consider the Mormon, and take for granted that the religious doctrines in question are false. Since they are false, does not that mean that if they continue to believe, their predictions will be less accurate?

No, it does not, for several reasons. In the first place the doctrines are in general formulated to avoid such false predictions, at least about everyday life. There might be a false prediction about what will happen when you die, but that is in the future and is anyway disconnected from your everyday life. This is in part why I said “the predictions that are important to it” in my proposal. Second, failure to believe would lead to extremely serious conflicting desires: the person would still have the desire to conform outwardly, but would also have good logical reasons to avoid conformity. And since we don’t know in advance how we will respond to conflicting desires, the brain will not have a good idea of what it would do in that situation. In other words, the Mormon is living a good Mormon life. And their brain is aware that insisting that Mormonism is true is a very good way to make sure that they keep living that life, and therefore continue to behave predictably, rather than falling into a situation of strongly conflicting desires where it would have little idea of what it would do. In this sense, insisting that Mormonism is true, even though it is not, actually improves the brain’s predictive accuracy.

 

Skeptical Scenarios

I promised to return to some of the issues discussed here. The current post addresses the implications of the sort of skeptical scenario considered by Alexander Pruss in the associated discussion. Consider his original comparison of physical theories and skeptical scenarios:

The ordinary sentence “There are four chairs in my office” is true (in its ordinary context). Furthermore, its being true tells us very little about fundamental ontology. Fundamental physical reality could be made out of a single field, a handful of fields, particles in three-dimensional space, particles in ten-dimensional space, a single vector in a Hilbert space, etc., and yet the sentence could be true.

An interesting consequence: Even if in fact physical reality is made out of particles in three-dimensional space, we should not analyze the sentence to mean that there are four disjoint pluralities of particles each arranged chairwise in my office. For if that were what the sentence meant, it would tell us about which of the fundamental physical ontologies is correct. Rather, the sentence is true because of a certain arrangement of particles (or fields or whatever).

If there is such a broad range of fundamental ontologies that “There are four chairs in my office” is compatible with, it seems that the sentence should also be compatible with various sceptical scenarios, such as that I am a brain in a vat being fed data from a computer simulation. In that case, the chair sentence would be true due to facts about the computer simulation, in much the way that “There are four chairs in this Minecraft house” is true. It would be very difficult to be open to a wide variety of fundamental physics stories about the chair sentence without being open to the sentence being true in virtue of facts about a computer simulation.

If we consider this in light of our analysis of form, it is not difficult to see that Pruss is correct both about the ordinary chair sentence being consistent with a large variety of physical theories, and about the implication that it is consistent with most situations that would normally be considered “skeptical.” The reason is that to say that something is a chair is to say something about its relationships with the world, but it is not to say everything about its relationships. It speaks in particular about various relationships with the human world. And there is nothing to prevent these relationships from co-existing with any number of other kinds of relationships between its parts, its causes, and so on.

Pruss is right to insist that in order for the ordinary sentence to be true, the corresponding forms must be present. But as an anti-reductionist, his position implies hidden essences, and this is a mistake. Indeed, under the correct understanding of form, our everyday knowledge of things is sufficient to ensure that the forms are present: regardless of which physical theories turn out to be true, and even if some such skeptical scenario turns out to be true.

Why are these situations called “skeptical” in the first place? This is presumably because they seem to call into question whether or not we possess any knowledge of things. And in this respect, they fail in two ways, they partially fail in a third, and they succeed in one way.

First, they fail insofar as they attempt to call into question, e.g. whether there are chairs in my room right now, or whether I have two hands. These things are true and would be true even in the “skeptical” situations.

Second, they fail even insofar as they claim, e.g. that I do not know whether I am a brain in a vat. In the straightforward sense, I do know this, because the claim is opposed to the other things (e.g. about the chairs and my hands) that I know to be true.

Third, they partially fail even insofar as they claim, e.g. that I do not know whether I am a brain in a vat in a metaphysical sense. Roughly speaking, I do know that I am not, not by deducing the fact with any kind of necessity, but simply because the metaphysical claim is completely ungrounded. In other words, I do not know this infallibly, but it is extremely likely. We could compare this with predictions about the future. Thus for example Ron Conte attempts to predict the future:

First, an overview of the tribulation:
A. The first part of the tribulation occurs for this generation, beginning within the next few years, and ending in 2040 A.D.
B. Then there will be a brief period of peace and holiness on earth, lasting about 25 years.
C. The next few hundred years will see a gradual but unstoppable increase in sinfulness and suffering in the world. The Church will remain holy, and Her teaching will remain pure. But many of Her members will fall into sin, due to the influence of the sinful world.
D. The second part of the tribulation occurs in the early 25th century (about 2430 to 2437). The Antichrist reigns for less than 7 years during this time.
E. Jesus Christ returns to earth, ending the tribulation.

Now, some predictions for the near future. These are not listed in chronological order.

* The Warning, Consolation, and Miracle — predicted at Garabandal and Medjugorje — will occur prior to the start of the tribulation, sometime within the next several years (2018 to 2023).
* The Church will experience a severe schism. First, a conservative schism will occur, under Pope Francis; next, a liberal schism will occur, under his conservative successor.
* The conservative schism will be triggered by certain events: Amoris Laetitia (as we already know, so, not a prediction), and the approval of women deacons, and controversial teachings on salvation theology.
* After a short time, Pope Francis will resign from office.
* His very conservative successor will reign for a few years, and then die a martyr, during World War 3.
* The successor to Pope Francis will take the papal name Pius XIII.

Even ignoring the religious speculation, we can “know” that this account is false, simply because it is inordinately detailed. Ron Conte no doubt has reasons for his beliefs, much as the Jehovah’s Witnesses did. But just as we saw in that case, his reasons will also in all likelihood turn out to be completely disproportionate to the detail of the claims they seek to establish.

In a similar way, a skeptical scenario can be seen as painting a detailed picture of a larger context of our world, one outside our current knowledge. There is nothing impossible about such a larger context; in fact, there surely is one. But the claim about brains and vats is very detailed: if one takes it seriously, it is more detailed than Ron Conte’s predictions, which could also be taken as a statement about a larger temporal context to our situation. The brain-in-vat scenario implies that our entire world depends on another world which has things similar to brains and similar to vats, along presumably with things analogous to human beings that made the vats, and so on. And since the whole point of the scenario is that it is utterly invented, not that it is accepted by anyone, while Conte’s account is accepted at least by him, there is not even a supposed basis for thinking that things are actually this way. Thus we can say, not infallibly but with a great deal of certainty, that we are not brains in vats, just as we can say, not infallibly but with a great deal of certainty, that there will not be any “Antichrist” between 2430 and 2437.

There is nonetheless one way in which the consideration of skeptical scenarios does succeed in calling our knowledge into question. Consider them insofar as they propose a larger context to our world, as discussed above. As I said, there is nothing impossible about a larger context, and there surely is one. Here we speak of a larger metaphysical context, but we can compare this with the idea of a larger physical context.

Our knowledge of our physical context is essentially local, given the concrete ways that we come to know the world. I know a lot about the room I am in, a significant amount about the places I usually visit or have visited in the past, and some but much less about places I haven’t visited. And speaking of an even larger physical context, I know things about the solar system, but much less about the wider physical universe. And if we consider what lies outside the visible universe, I might well guess that there are more stars and galaxies and so on, but nothing more. There is not much more detail even to this as a guess: and if there is an even larger physical context, it is possible that there are places that do not have stars and galaxies at all, but other things. In other words, universal knowledge is universal, but also vague, while specific knowledge is more specific, but also more localized: it is precisely because it is local that it was possible to acquire more specific knowledge.

In a similar way, more specific metaphysical knowledge is necessarily of a more local metaphysical character: both physical and metaphysical knowledge is acquired by us through the relationships things have with us, and in both cases “with us” implies locality. We can know that the brain-in-vat scenario is mistaken, but that should not give us hope that we can find out what is true instead: even if we did find some specific larger metaphysical context to our situation, there would be still larger contexts of which we would remain unaware. Just as you will never know the things that are too distant from you physically, you will also never know the things that are too distant from you metaphysically.

I previously advocated patience as a way to avoid excessively detailed claims. There is nothing wrong with this, but here we see that it is not enough: we also need to accept our actual situation. Rebellion against our situation, in the form of painting a detailed picture of a larger context of which we can have no significant knowledge, will profit us nothing: it will just be painting a picture as false as the brain-in-vat scenario, and as false as Ron Conte’s predictions.

Self Reference Paradox Summarized

Hilary Lawson is right to connect the issue of the completeness and consistency of truth with paradoxes of self-reference.

As a kind of summary, consider this story:

It was a dark and stormy night,
and all the Cub Scouts where huddled around their campfire.
One scout looked up to the Scout Master and said:
“Tell us a story.”
And the story went like this:

It was a dark and stormy night,
and all the Cub Scouts where huddled around their campfire.
One scout looked up to the Scout Master and said:
“Tell us a story.”
And the story went like this:

It was a dark and stormy night,
and all the Cub Scouts where huddled around their campfire.
One scout looked up to the Scout Master and said:
“Tell us a story.”
And the story went like this:

It was a dark and stormy night,
and all the Cub Scouts where huddled around their campfire.
One scout looked up to the Scout Master and said:
“Tell us a story.”
And the story went like this:
etc.

In this form, the story obviously exists, but in its implied form, the story cannot be told, because for the story to be “told” is for it to be completed, and it is impossible for it be completed, since it will not be complete until it contains itself, and this cannot happen.

Consider a similar example. You sit in a room at a desk, and decide to draw a picture of the room. You draw the walls. Then you draw yourself and your desk. But then you realize, “there is also a picture in the room. I need to draw the picture.” You draw the picture itself as a tiny image within the image of your desktop, and add tiny details: the walls of the room, your desk and yourself.

Of course, you then realize that your artwork can never be complete, in exactly the same way that the story above cannot be complete.

There is essentially the same problem in these situations as in all the situations we have described which involve self-reference: the paradox of the liar, the liar game, the impossibility of detailed future prediction, the list of all true statementsGödel’s theorem, and so on.

In two of the above posts, namely on future prediction and Gödel’s theorem, there are discussions of James Chastek’s attempts to use the issue of self-reference to prove that the human mind is not a “mechanism.” I noted in those places that such supposed proofs fail, and at this point it is easy to see that they will fail in general, if they depend on such reasoning. What is possible or impossible here has nothing to do with such things, and everything to do with self-reference. You cannot have a mirror and a camera so perfect that you can get an actually infinite series of images by taking a picture of the mirror with the camera, but there is nothing about such a situation that could not be captured by an image outside the situation, just as a man outside the room could draw everything in the room, including the picture and its details. This does not show that a man outside the room has a superior drawing ability compared with the man in the room. The ability of someone else to say whether the third statement in the liar game is true or false does not prove that the other person does not have a “merely human” mind (analogous to a mere mechanism), despite the fact that you yourself cannot say whether it is true or false.

There is a grain of truth in Chastek’s argument, however. It does follow that if someone says that reality as a whole is a formal system, and adds that we can know what that system is, their position would be absurd, since if we knew such a system we could indeed derive a specific arithmetical truth, namely one that we could state in detail, which would be unprovable from the system, namely from reality, but nonetheless proved to be true by us. And this is logically impossible, since we are a part of reality.

At this point one might be tempted to say, “At this point we have fully understood the situation. So all of these paradoxes and so on don’t prevent us from understanding reality perfectly, even if that was the original appearance.”

But this is similar to one of two things.

First, a man can stand outside the room and draw a picture of everything in it, including the picture, and say, “Behold. A picture of the room and everything in it.” Yes, as long as you are not in the room. But if the room is all of reality, you cannot get outside it, and so you cannot draw such a picture.

Second, the man in the room can draw the room, the desk and himself, and draw a smudge on the center of the picture of the desk, and say, “Behold. A smudged drawing of the room and everything in it, including the drawing.” But one only imagines a picture of the drawing underneath the smudge: there is actually no such drawing in the picture of the room, nor can there be.

In the same way, we can fully understand some local situation, from outside that situation, or we can have a smudged understanding of the whole situation, but there cannot be any detailed understanding of the whole situation underneath the smudge.

I noted that I disagreed with Lawson’s attempt to resolve the question of truth. I did not go into detail, and I will not, as the book is very long and an adequate discussion would be much longer than I am willing to attempt, at least at this time, but I will give some general remarks. He sees, correctly, that there are problems both with saying that “truth exists” and that “truth does not exist,” taken according to the usual concept of truth, but in the end his position amounts to saying that the denial of truth is truer than the affirmation of truth. This seems absurd, and it is, but not quite so much as appears, because he does recognize the incoherence and makes an attempt to get around it. The way of thinking is something like this: we need to avoid the concept of truth. But this means we also need to avoid the concept of asserting something, because if you assert something, you are saying that it is true. So he needs to say, “assertion does not exist,” but without asserting it. Consequently he comes up with the concept of “closure,” which is meant to replace the concept of asserting, and “asserts” things in the new sense. This sense is not intended to assert anything at all in the usual sense. In fact, he concludes that language does not refer to the world at all.

Apart from the evident absurdity, exacerbated by my own realist description of his position, we can see from the general account of self-reference why this is the wrong answer. The man in the room might start out wanting to draw a picture of the room and everything in it, and then come to realize that this project is impossible, at least for someone in his situation. But suppose he concludes: “After all, there is no such thing as a picture. I thought pictures were possible, but they are not. There are just marks on paper.” The conclusion is obviously wrong. The fact that pictures are things themselves does prevent pictures from being exhaustive pictures of themselves, but it does not prevent them from being pictures in general. And in the same way, the fact that we are part of reality prevents us from having an exhaustive understanding of reality, but it does not prevent us from understanding in general.

There is one last temptation in addition to the two ways discussed above of saying that there can be an exhaustive drawing of the room and the picture. The room itself and everything in it, is itself an exhaustive representation of itself and everything in it, someone might say. Apart from being an abuse of the word “representation,” I think this is delusional, but this a story for another time.