Thoughts are breadcrumbs you’ve laid for dealing with life
AKA: the causal effectiveness of thinking
“Correlation is not causation” — Unknown
An oft-repeated injunction, which is over two hundred years old, advises us not to assume causation where there is merely an association of experiences. It is certainly sound advice — just because your headache went away after taking a pill doesn’t mean the latter caused your recovery. Only a small subset of all correlations end up having causal connection; so the two should not be confused. What is curious, however, is why the advice is so frequently invoked. We don’t say “animals aren’t bats”, or “vehicles aren’t motorcycles”, both of which are equally true, and have the same relationship of superset to subset.
Of course, people rarely make the same error for vehicles and animals as they do for causation. The emphatic tone of those that repeat the above injunction suggests that we humans are predisposed to make unwarranted causal leaps, to assume causation where it is not demonstrably present. And doubtless the many spurious anecdotal arguments, dogged superstitions, and old wives’ tales you witness all around you confirms this to be the case.
To be fair to the guilty parties, there are good practical reasons for making a hasty leap to causation. Where there is a causal link, you have the opportunity to control your environment. If a particular dance could really cause it to rain, surely that would be valuable knowledge during the dry months. Mere correlation provides no such benefit. And the cost of making a mistaken causal assumption is usually mild — some embarrassment and lost time. On the other hand, to truly prove that a causal link exists requires a long and arduous effort, and it is not reasonable to expect such rigorous deliberations as a preamble to every action. All in all, it seems your mind leans optimistically towards assuming the possibility of control; it is no doubt pleasant and hopeful to do so.
To restrain this impulse and be level-headed requires extra effort and discipline. You must give up the hope of gain that would have accrued from having discovered that causal connection, and (reluctantly) dump cold water on over-optimistic projections. The result — simple correlation with no causal link — is certainly an odd creature. It is always of lower value compared to its exalted sibling; it reflects a failure to get what you really want, a disappointing consolation prize. You find yourself back at square one, and you’d only do so if it would prevent you making some greater blunder.
All learning is motivated — in both the good and bad senses of that expression. You frame what you learn about the world in terms that give you power over your environment. Indeed, you only really care about cause and effect relations insofar they can be used to effect your desires and goals. You live in a dynamic, dangerous, and uncertain world, and your mind must be pragmatic and judicious in what it learns. There is far, far too much that you could learn about, and it is not easy to find, in this mess, ways to control your environment and experiences. So the mind focuses and attends to that which it deems important to it. It does not seek knowledge for knowledge’s sake — that would be a luxury. If you were ever forced to give up one or the other — knowledge or control — you would certainly prefer to give up knowledge.
With these observations, we’ve uncovered many deep roots of human thinking. In the process, we’ve incidentally highlighted a key difference between human cognition and Machine Learning (ML). ML models make no causal assumptions. It is in fact difficult to get ML models to think causally; a theory of explicit causal inference has not yet been fully developed. The topic of casual modelling was even considered taboo¹ in data science until the last few decades — it lacked credibility compared to correlational analyses. Modern Machine Learning, as an offshoot of data science, can find correlations quite well; one could say that is its forte. In summary, humans and ML models think in fundamentally different ways: humans are over-eager to find casual links to provide us with handles on the world, whereas ML is reluctant to take on the task.
The causal fabric of the mind
To be clear, discovering causal links in the sense described here is not the same as the science of explicit causality, with all its theoretical nuance and complex formulae. Truly proving that a causal relation is present takes significant work (e.g. Randomized Control Trials, multivariate experiments) and the outcome is always open to doubt. Most living beings don’t have time to waste building systematic arguments to justify their actions. It is in your benefit, and is certainly more convenient, to jump right to the assumption of control and act on it. The connections your mind intuitively makes in this respect are quite basic; as we’ll see they are no more than a series of naive links between events that seem to get you what you want. Formal theories for proving causal relations are a subsequent intellectual framing of your natural tendency towards mastery over your environment.
The relationship between the two types of causal learning can be confusing, and it is difficult to tease them apart. Very often, when you assert a causal relationship explicitly, you are paying heed to and justifying an intuition, possibly without thinking it through. You may, through self-observation, note that your actions are proceeding as though a causal link existed, and then verbalize that link as good, general advice. Usually you only reevaluate this first instinct due to social pressure: as others question the coherence of your statements you must, in order to gain allies, make your assertions clear and forensic. Of course, you may also allow the contradictions to live side by side in your head. Many people carry secret superstitions which they publicly disavow, and would certainly hesitate to put into a scientific paper, at least not without significant analysis and reevaluation.
These two perspectives, intuitive and explicit, bleed into one another, and they are easily confused for one another within the noise of conscious introspection. The field of cognitive psychology as a whole tends to conflate them, treating them as one generic ability — “causal reasoning”. For example, a survey paper on the topic notes the following:
Adult humans use causal reasoning effortlessly and automatically every day. Even the most mundane cognitive activities [… examples given …] involve causal understanding. That is, they involve thinking of causal relations in terms of variables with values that can change. — The development of human causal learning and reasoning
The quote begins by describing automatic, effortless causal thinking, which is apparently a feature of our species; but then switches over to explicit causal reasoning involving variable manipulation. Between these two endpoints, the authors ignore the process by which variables are discovered and defined within the flow of continuous experiences, as well as the decision process by which we select which variables to compare and correlate.
For example, determining which factors caused you to miss your bus requires that you first learn how to identify “missing your bus” — a complex mental undertaking which does not come naturally to a child. The decision to correlate it with a failure in your alarm clock is also not a random one, but a deliberate selection. And finally, what counts as a reasonable causal relationship between these requires some maturity: e.g. it wasn’t the aesthetic beauty of the clock numbers that distracted you from the bus schedule. The quote above starts by discussing what the mind automatically does, then jumps imperceptibly to what the mind has learned to do.
This post is targeted at the first type: the natural, fundamental mode of thinking. It cannot be refined by education; nor indeed can it be avoided. It is the underlying system on which — and by which — all else is built, including rationalization, judgment, and reasoning. It is not conscious — it is the fabric out of which conscious deliberation is woven. It acts before you are aware of it; its “decisions” are hasty and tend to satisfice.
This underlying system is also the one that naturally seeks to gain control over its environment — utility will always be master over any cerebral calculation. It must be the layer that aims at control, because if it didn’t, no amount of intellectual deliberation could make your mind do so; no more than a colour blind person could “think” themselves into seeing red².
Actions are learned by the effects they cause
When discussing the properties of something so fundamental to cognition, it is difficult to know where to begin, or how to isolate this one function from within the noise of consciousness. To help with this endeavour, we can look at an analogous mental activity where causal assumptions are also implicitly present: actions (i.e. bodily movements). Any action you learn to carry out is one that, in a healthy mind, presumably causes a desired outcome. You turn the steering wheel left because it causes the car to go where you want it; a rat presses a lever because it causes a food pellet to drop. The cause and effect relationship is implicit in the action.
Even without consciously mulling over your behaviour and its consequences, the reinforcing effect of the outcome would be enough to ingrain the right action, given the right circumstances. This is at the core of Operant Conditioning/Reinforcement Learning: the action you learn causes something you want to happen. All animals can do this, and do this well. Only three things are needed: a cue, an underlying desire, and an effective action that satisfies it. Given these three, one can be trained to take the action when given the cue; e.g. a dog can be trained to sit when she hears the word “sit”. The desired effect is the food or reward she gets for having sat down. Note that the action is not the desired outcome itself, it is what the mind implicitly deems to have caused it.
Learning through reinforcement is imperfect, and you may not always get it right. If pressing a button preceded the appearance of food, the action may be reinforced as though it presumably caused the latter, even though it was perhaps just a coincidence. As B. F. Skinner noted, this over-eagerness may be at the root of many behavioural superstitions. But whether or not the button actually caused the food, it seems that when learning to act you assume the causal link by default. This is reasonable: to assume mere correlation wouldn’t help you control your world or achieve your goals — correlation has little utility in actions. You could go so far as to say that learning correlations is entirely useless without a causal assumption somewhere in the chain for you to act on.
Of course, this is not to say that, at this basic level of connection, you explicitly believe there is a causal link between your action and the goal, only that you subsequently act like you believe it. The connections themselves are “dumb” — just a cue and an action. They make no higher-level judgment about the nature of their relationship with the effect; that is a later meta-analysis. At this level, there is no appreciable difference between saying that the mind assumes causation until disproved, or that it assumes correlation until causation is proved. In both cases you will continue to automatically act on the presumed connection until it fails — i.e. until you are unable to control your world — at which point you stop. Whether you call this behaviour “assuming causation until disproved” or “testing a hypothesis to prove causation” is semantics, and belongs to the self-reflexive second level of causal interpretations³.
Thoughts, like actions, are learned for their utility
A thought, like an action, is a response you learn to associate with a cue. This time the cue is not connected to a physical action, but to a set of sensory inputs which you later recall when the cue is triggered. For example, on seeing a button (cue), you may have a visual thought of it being pressed (response); or you may associate the sight of a person’s face (cue) with the sound of their name (response). The content of these thoughts are usually⁴ taken from everyday empirical experiences.
The mechanism by which thoughts become associated with their cues seems more difficult to explain than for actions. Since the earliest days of psychological research, it has been common to point to a correlation of experiences as the probable catalyst. Many theories have been built upon that paradigm, including classical conditioning and Hebbian association.
However, as we mentioned earlier, pure correlations based on frequency of association are not particularly useful in practice; a causal assumption must be present somewhere:
Associative learning yields correlations and enables predictions, but it does not reflect causal knowledge. Knowing what to expect next — such as anticipating that the sound of the key will be followed by a creaking sound as the door opens — is not the same as understanding that the door’s movement generates the creaking. — The development of human causal learning and reasoning
Frequency of association does not necessarily produce valuable information. Often what is useful is also rare. Pressing an elevator button usually has no immediate effect except to light the button up, followed by a long wait. Yet we associate it with the experience of the elevator appearing. The latter is a relatively distant and infrequent consequence, but is certainly the one we wish would occur. Relying on correlation to explain thinking also fails to describe the many other varieties of thought, such as plans, fantasies, or lies, which are apparently not based on frequent co-occurrence, but on the enjoyment or utility they supposedly bring you⁵.
Perhaps we can look back at the prior section for guidance here. Actions, we said, are learned because in certain circumstances they seem to cause something desirable. The same may also be said of plans and fantasies. The content of a fantasy is a set of sensory experiences which, were they present, could lead to something you want. If I could fly, I might get to many places currently restricted to me. Similarly, plans, considered in the broadest sense, are a set of intended experiences that would lead to (i.e. cause) your goal⁶.
Curiously, this definition of “plan” also covers the process of labelling or naming entities. For example, to associate the thought of the name “Harold” with an image of his face is only useful if the sound of his name, however produced, would get his attention. If he preferred to be addressed by a nickname, you would likely think of that nickname instead of his proper name when you wanted his attention. Therefore thinking of his name when you see his face is a sort of plan for what to say. It is no coincidence that the thought tends to arise in your mind whenever you want to address him, or tell others how to do so.
Even descriptive words like “chair” are learned because they are effective at orienting others to what you want — hence a polyglot will use different words with different language-audiences. Utility drives the association; the polyglot will not simply recall the most frequently occurring sound without regard for what would be useful.
Finally, whenever you think up a lie, you gauge it by its real or imagined effects — frequency of correlation is not a deciding factor.
Making thoughts valuable
Actions and thoughts, it seems, have many similarities. As seen in the examples above, both are responses that are learned because experience has shown that they lead to a desired effect. Your mind is recording some valuable sight or sound that preceded the appearance of a goal, always with the implicit assumption that the former caused the latter: e.g. the sound of Harold’s name caused him to turn around. The machinery of the brain is hungrily searching around, splitting up the world into entities that appear to be causally related to the things it wants. And as with actions, the thought only contains the cause, not the beneficial effect itself.
The value of recording and recollecting thoughts in the manner described should be obvious: they serve as a guide for what to aim for. A thought is useful if it tells you what to do or how to act — in other words, if it provides an intention. If event X caused the desired event Y, then any action that causes you to experience X would be beneficial to take. X becomes its own goal to strive for outside of Y, and does so even without the need to validate it through trial and error. If the sound of the word “ice cream” precedes its appearance — and if you assume the word caused the appearance — then producing that sound yourself can be assumed to be a good idea⁷. Your mind may even begin to build plans on these supposed imaginary connections, long before they have been tested in reality⁸.
Any mistaken assumptions can self-correct over time, pragmatically. Compare them to actions once again. The proof of the efficacy of an action as a cause is demonstrated through the consequences of taking it. If it were only a coincidental correlation, you would find out the next time you tried to put it to use. The embarrassment of getting someone’s name wrong is enough to cause you to at least hesitate the next time you say it. Corrections arise naturally through practice, motivated by whether they match your needs (or fail to do so).
The causal validity of thoughts is tested in the same way, though indirectly. Just as you test your words against their effect, you test thoughts that caused those actions against their effects as well. The question isn’t: “is this a true thought?” — frequency of correlation is not the deciding factor — but rather “is this an effective thought?” As with actions, it is their causal effectiveness towards an end goal that is the reason thoughts are retained and learned. The thought you record is a proposed missing link between the circumstantial cue and a desired state, with the latter drawing the first two together.
The contingent association between the cue and the thought itself is not completely irrelevant, of course, since a link between them can only be made if they are both actually present together. You will not associate pressing a button with a thunderstorm, simply because they rarely occur together. The more often the cue and the thought appear near each other, the more likely they will be selected and joined by some desired effect. But these are like raw materials that incidentally happen to be lying around. In order to notice them or turn them into tools (causal factors) you must first have a purpose, a motive, that acts as the glue.
Breadcrumbs
Doubtless these conclusions may still seem odd to some readers. When you close your eyes and observe the thoughts that flow through your mind, it is natural to assume they were learned via correlations between past events. Surely I think that buttons should be pushed because the two experiences are commonly conjoined — no ulterior motive appears to be present. The reason for this disconnect should already be evident from the discussion above. Just as an action does not contain the effect for which it is the cause, a thought contains only the cause of what you want to achieve, not the effect (the goal) itself — the latter is gone by the time you introspect.
The analysis is further complicated by the fact that the cause in one relationship can be the effect in another: e.g. pressing the elevator button is the cause of an elevator arriving, but the elevator arriving is the cause of getting to the floor you need to. These two can get mixed together during introspection. Nevertheless, in any individual connection you will not find the rewarding experience that originally made it stick in your mind, even more so because it is not particularly useful to recall a reward itself. It is only useful to remember the chain of causes that would get you to that end. When you want to get someone’s attention, you’d like to think of their name, not the image of them turning around and facing you.
Unfortunately, the absence of the latter makes it difficult to recollect why you recorded a particular thought or action. The true driver, that which connected thinking to its utility, has left no trace of itself. It will always remain outside your consciousness, and cannot be retrieved from inside. So with no other options available, you tend to fall back on what information you do have available — the correlation between the cue and the thought — and you make up a story about their affinity. One can imagine, as an analogy, the aforementioned dog forgetting all about the dog-treat, and inferring that the word “sit” was associated with her sitting down simply because the two tend to co-occur.
More often than not, this leads to a fixation on the means and not the ends — e.g. focusing on accumulating money, and forgetting what it was that money was supposed to buy. It is difficult to consciously see or remain aware of the things you like directly. Your true goals, at least when they are active, are always just outside your conscious mind, influencing inwards, but reluctant to enter your memory. You only see their representatives, the delegates through which you communicate with them — the causes of the desired effects. These are the sounds, images, or symbols that point you down the path to success. The desires themselves fall through your mind like water through a sieve, leaving only their causes behind.
The result is that the entire content of your mind becomes a trail of breadcrumbs it has created for itself, leading you through your problems to your aims. Every conscious moment is the instantiation of a new clue. Heuristics, cognitive skills and techniques, philosophies — these are clues you’ve put down in your progress through life. To “recollect” is to recover a breadcrumb in the current moment and put it to use. “This seemed to work” your faculty of insight says, and places it in front of you as a tool. Were you to actually reach your goals entirely, there would be no reason to act, no reason to think, no reason to create any more breadcrumbs.
¹ J. Pearl refers to this as the “Prohibition Era” in The Book of Why:
[Causal] questions were declared unscientific and went underground. Despite heroic efforts by the geneticist Sewall Wright (1889–1988), causal vocabulary was virtually prohibited for more than half a century….
In vain will you search the index of a statistics textbook for an entry on “cause.” Students are not allowed to say that X is the cause of Y — only that X and Y are “related” or “associated.”
² To put the same thing in a different way: your mind could never discover causal links if it were, at base, a correlation machine.
³ Ontologically, causation is a subset of correlations; epistemologically, the order is reversed.
⁴ They may also be taken from thoughts themselves, since thoughts are self-generated stimuli. This complication need not be introduced in this post, as it does not alter the main argument.
⁵ Nor can we assume, as Hume erroneously did, that causation is simply equal to frequent correlation. Active testing through intervention is necessary to make the distinction.
⁶ Plans are a type of fantasy; or perhaps fantasies are a type of plan?
⁷ One can conclude from this that your mind implicitly presumes the existence of an objective, external reality wherein these effects will happen, whether or not you are the one making them happen, or are even present at all. Such innate learning is therefore “depersonalized”. If, on the other hand, you were to assume that all relations are correlations by default then you would have to prove causation explicitly through actions (interventionism).
⁸ This is why it is more correct to say the mind assumes causation instead of correlation — if not, it would have to test every such inference before using it in further planing, which it does not do.
