Concepts, Abstractions, and Problem-Solving
Summary of posts 1 to 10: A theory of Artificial General Intelligence (AGI) must begin by focusing on invisible, automatic mental behaviours that drive higher-level, complex ones. One such behaviour is “becoming aware of something”, either something external or within one’s own mind. This results in the formation of concrete memories/thoughts (sights and sounds) which can later be re-experienced as needed. You became aware of this because it was a solution to a problem. It was driven by a negative impulse, which we call a “tension”.
The last few posts have described an insight whose value to understanding the inner workings of your mind is far-reaching and profound. It is that the faculty of awareness, and therefore of consciousness, is an outcome of problem-solving behaviour. The theory can be summarized as follows: whenever a set of experiences registers as a problem (a tension), experiencing it again automatically triggers a process of waiting for a solution. Once a solution is discovered, the mind registers, aka learns, a new thought whose content is whatever came right before the problem was solved. You “become aware” of the solving experience as the content of a memory, which is then recreated in similar situations. The material of your consciousness is therefore dictated by this “search, notice, and learn” behaviour. As we’ll soon see, this pattern applies not only to concrete content like memories, but even to matter that at first glance appears to be abstract, such as feelings and qualia; all are merely content for awareness. And since the mechanism of becoming aware of something is automatic — outside of choice — it is a fundamental and ubiquitous process.
The only thing left to explain is how your mind learns to register certain things as solutions. For example, if you are looking for a job, there are a variety of experiences that qualify as having found one, because “job” is an abstract concept. Trying to understand how solutions form forces us to confront the more difficult topic of abstract concepts. Fortunately, as you’ll discover, the two problems are actually the same.
Let’s start with an example: looking for your keys. This searching activity usually has another motivation that is driving it, such as having to go out somewhere. You have, over time, built an anticipatory tension around stepping out of your house — “what if I get locked out?” This tension demands an a solution: the thought of where your keys are. The solution may come in a variety of forms, such as the thought of where they usually are (e.g. they’re always in your left pocket), the sight of them on a hook, the feel of them in your hand, or even someone telling you they found your keys. Any one of them leads to solving the problem, and to you becoming aware of it by forming a memory. This memory becomes a useful recollection later; when you step out the door you know where to reach for your keys. The self-generated image (thought) of its location guides your arm as effectively as if you saw it in front of you.
Finding keys seems like an obvious case, but there are subtler cases too. For example, when doing mental math, you “become aware” of intermediate steps — digits—during the process. These get stored at every step, and are recreated in later calculations, just as the thought of your keys was above. Other cases appear to elude this pattern; for instance when contemplating problems of metaphysics, a variety of abstractions like being and nothingness float around your mind and appear not to be associated with any concrete problem-solving pattern. Registering subtle feelings like the qualia of the colour red or the quality of the feeling of anger may also appear not to be solutions to problems. Moreover they cannot be stored or processed in the same manner as concrete thoughts and memories can.
These last examples seem to be exceptions because they don’t fit the model. Saying so, however, raises a key question: how did you realize that they are exceptions? In other words, what difference is there between a concrete thought like keys and an abstraction like existence, that you become aware of, and which convinces you the two are not the same type?
Anything you assert about your mind, or believe about your thoughts (e.g. that they are abstract), is something your mind became aware of at a specific moment in time. An explicit belief is a concrete statement based on what you realized in a moment of awareness. Regardless of what trends and probabilities drove you to that decision, at some point you had to make a choice of where to reach for your keys, or whether to assert that existence is or is not an abstraction. The truth about the objects in question is irrelevant; whether key is abstract or not is not the point. What matters is that you formed a belief about it; whatever that entails, and regardless of if it reflects the truth or not. There was a mechanism, a series of steps that led to that belief being what it was. Understanding the process by which you form beliefs is the first clue to disentangling the riddle of how your mind deals with abstractions.
Consider the following two cases:
If you were asked what colour a leaf in front of you was, you might say “it’s green”. If asked how your mind came to know that “the leaf is green”, you might say:
“Certain wavelengths of light hit the retina of my eye, activating colour receptors, which triggered a pattern of connections in my visual cortex. These, when connected to other brain areas triggered various patterns, including thoughts of the word “green”. Those were passed to speech controllers that made me say the word “green””.
Or something along those lines. But if you were asked to explain how you know that “existence is the opposite of nothingness”, what chain of mental causation would you use to explain it? What’s the source of the belief? What are the intermediaries? If it’s based on reasoning, what is the origin of its premises? How do you know the conclusion is right?
These seem like more difficult questions to answer because they don’t deal with concrete concepts like “leaf” and “green”. But do they need to be more difficult? We have already discussed a few mechanisms that can help guide us. To begin with, any verbal question someone asks is a problem looking for a solution, specifically a verbal answer¹. Words, regardless of how abstract their referent, are still concrete sounds and speaking them is a concrete action. It is critical not to confuse the abstractness of the content of the thought (concepts like existence and nothingness are abstract), with abstractness of thinking itself. You can think concretely about abstract things, for example, by using language, diagrams and symbols. The thought that “existence is an abstract concept” is itself a concrete thought.
This insight gives us a foot in the door, and provides leverage to crack this riddle open. You no longer have to worry about explaining the arcane magic of abstract thinking, but instead you can address it through the problem of concrete thinking. The latter is much easier to explain and ultimately to formalize in AGI. The aforementioned magic of abstract thinking is now to be found in the pattern of concrete thoughts, in explaining why you think that “being” is “an abstract concept” (all in words). There is no need to shoehorn abstractions into some concrete physical explanation; that is an impossible task. A mental event is a real, concrete event, a specified response that happens in a particular moment. The persistence of the idea of, say, existence as an abstract entity is merely the persistence of those responses.
This is not an argument in favour of reductionism. We are not reducing concepts to their names and labels. We are explaining abstractions as the driving force that is causing the patterns of concrete thinking. They are like an invisible magnetic field that shapes iron filings, or the forces of gravity and wind that shape the waves. For example, when you say that the concept of ball includes roundness, you are having a series of thoughts which were shaped by certain learned patterns and forces. These caused you to have thoughts like an image of a specific ball and the word “round”. It is much easier for the mind to work with these, than with the concepts of ball and round since neither has a concrete mental correlate— balls come in various shapes and sizes, and “roundness” is an infinitely precise ideal that cannot be perfectly represented in a finite mind². What your mind can do is think of a specific example of a ball, and as round a shape as you ask it for. This approach has the added benefit of not requiring your mind to have perfect definitions before it can do any useful work; imperfection will do just fine.
The phrase “do just fine” suggests that concepts are somehow related to goals and motivations, and here is where we get back to the topic of problem-solving. Your thoughts serve a purpose, they must be useful before their presence can be justified. When looking for your keys, you might recognize certain key and key-like shapes because those shapes have been useful to your purposes of opening doors before. They register as solutions because they have led to solving problems, like getting in your house or car.
There is a symmetry here between the things you recognize as solutions and what you recognize as problems (tensions). In the previous post we discussed how rapid repetition of tensions (i.e. “inescapable” tensions) created new ones that caused you to learn how to avoid getting into those situations. Now we’re asking what makes an experience count as a general solution, as opposed to a solution to a specific instance of a problem.
When you engage in, say, the task of finding a red object, the word “solution” could apply both to the specific memory of the object you find, and the concept of redness that signalled to you that this object is a valid solution. The latter is the more powerful of the two. It signals that a certain broad set of experiences can be used as a proxy solution to a grander problem. Consider how the sight of cake in itself triggers positive responses even before you eat it. So saying that a tension should recognize a certain pattern as a general solution implies that there is a common feature among the diversity of solutions that designates it as a a good predictor of solving the underlying problem.
Let’s making this clearer by using an example. If I asked you to count the number of blocks in the image above, you would find the answer to be 11. The tension in this case was triggered not by the specific words or image of blocks, but by the perceived need to answer a question. This tension likely has its roots in social pressures (e.g. the desire to impress or please parents and peers). The answer, “11”, is not necessarily a general solution to many problems, but only to this specific one. The general solution pattern only requires that the thought must be a number. It is noteworthy that you could make an error and come up with a wrong answer (“12”), and your mind would still register that as an answer because it meets the criteria of being a number. Other passing thoughts like thoughts of your English teacher would not qualify, so they are passed over as junk and not remembered. You would only become aware of them if you got bored or distracted.
The criteria for the solution is that it be “a set of digits” or a number. This criteria, unlike the thought of “11”, is abstract. It raises the obvious issue of how your mind knows that something is “a set of digits”. The natural intuition is that there is a sort of abstract “node” in the mind that is activated any time a digit appears. But asking how this abstract concept of number gets created presents its own riddle. Why did your mind create it? How did you define the limits of the concept? Modern mathematical notation employs a variety of symbols; why separate the digits 0 to 9 as useful in their own right? What about letters like O and l, which resemble numbers; how does the mind keep them out of the concept number? Should it include digits written in different scripts? And the formalization of Peano numbers? Despite being representations of numbers, few people would accept Peano notation as an answer to a counting problem. Number, it seems, is a surprisingly tricky concept.
So how did the concept of numerical digits get created in your mind in the first place? And how did it come to be that a set of such digits was recognized as an answer to a counting problem?
Although these seem like two different questions, the answer is the same for both. All that is required is to reverse your common perception of which of the two comes first. It’s easy to think that you first learn digits separately from the problem of counting, then use them while solving counting problems. But in fact, digits are learned because they are solutions to counting problems. Although mature adults treat number as an abstract, idealized concept during childhood all the various parts of the notion of number are learned piecemeal, as solutions to specific problems — in the same way you would learn the names of each of your friends, one at a time. A toddler could learn to identify that there are 2 objects in front of her, and even 3, yet not need to understand that this pattern can be continued indefinitely.
The ultimate formalization of number as an abstraction is a separate set of concrete thoughts which solve higher-level academic problems— and this step is not even necessary; no more than it is necessary for children to learn the rules of grammar before they can speak. Both can be learned in a fragmentary manner. What binds digits together under a single concept is the problem that they all solve. Inclusion of, say, Chinese digits in “the set of digits” would depend on if those digits ever solved a counting problem for you.
Once you understand this reversal of priority, you can use it to address the questions raised in this post. It can explain how the mind can learn pieces of solutions that are still acceptable: it is not necessary that you learn all the digits, and all about numbers, just to answer your parents’ first counting questions. It provides flexibility for exceptions and extensions: you can add units to the numbers, or the negative symbol (-), or fractions, etc. as needed, on a problem-by-problem basis. And it explains how thoughts are useful to the mind: they are the aggregate of solutions to problems.
This reversal of standard thinking about concepts can be applied to all kinds of domains, and can even resolve outstanding conundrums about how the mind learns concepts. For example, you don’t learn what words are, and then use them solve communication problems, rather a word is first defined as anything that solves a certain set of communication problems. This allows you to include exceptions like sign language or so-called leet-speak that would not otherwise match the definition of words. As another example: you don’t learn the about set of components that makes up a game, then use those to have fun; anything that lets you have fun is defined as a game.
You can finally even explain how concepts like existence and nothingness come to be defined in the mind: when you are searching for something that others have doubts about, existence is finding it; i.e. you can declare “it exists”. Once you have this basic foundation for using the word “exist”, you can add all kinds of addenda to it, such as that existence “is opposed to nothingness”. Bit by bit you may create the complex, abstract concept of existence, but you don’t need to recognize any of this when you first use the word. Similarly, nothing is how you convey your disappointment when you fail in your search.
This approach may seem convoluted and imprecise. Why go through this rigmarole? For the simple reason that there is no other way. To date there is no theory at all that explains how the mind acquires abstract concepts like superego or consciousness, or grounds them in real experiences. And though solving image classification problems may suffice for learning types that are easy to name, like tigers or teacups, there is a lot of subjectivity in concepts like game or even existence; which is to say individuals solve those problems in different ways, and thus have incompatible definitions. This presents an opportunity for creativity.
The goal of this post is to describe the connection between thinking, concepts, and problem-solving. For the sake of keeping it short, I’ll defer the question of what is involved in the exact moment of defining solution criteria to the next post.
Next post: Machinery for generating insights
¹ Excluding some rare exceptions, like the question “may I see your passport”.
² It also ignores exceptions like the oddly-shaped American football.