The most important tool that helps solve riddles is divergent thinking. This form of thinking demands that you survey and analyze all possible solutions to any given problem. In its opposite, convergent (or critical) thinking, we generally operate within a set of rules and use them to work our way to arrive at answers. However, in divergent thinking, the rules are immaterial, and we must explore any and all relevant solutions.
Other important tools include lateral thinking, which involves studying how we infer something from information given to us. Systems thinking calls on you to look at the bigger picture, namely how components of any idea or solution fit with one another to form a coherent whole. Lastly, inspirational thinking requires you to gain insight from some source, like a peak experience or an altered state of consciousness. This type of thinking lets our unconscious mind solve problems for us, allowing our conscious selves to benefit from it.
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Creativity and divergent thinking can be thought of as simultaneously subtypes and examples of one another, wherein the mind goes from a small, narrow, or limited perspective and opens up. This requires different types of frameworks to not be stuck in a box of our own creation.
Convergent thinking, on the other hand, goes the other direction and takes many strains of thought and ideas and boils them down to a narrower conclusion or solution. It’s finding a way inside the given rules rather than breaking them or seeking new rules and outside solutions. Insight comes from digging deeper rather than looking elsewhere.
This is a process of further understanding a narrower set of information and then attempting to draw conclusions from it via analysis and insight. These are both ways of problem solving, which is the true skill that riddles help us cultivate. Whether you go broader or more specific, it’s clear that our mental status quo can’t quite cut it.
The first thing to remember is that critical (step by step) thinking is not really all that separate from non-linear, insightful, or creative thinking. In fact, the two often go hand in hand, solving one another’s unfinished business. In developing all aspects of cognition, we equip ourselves with more tools to use on any problem or situation we’re faced with. We can expand in one moment (gathering data, exploring arguments, and taking in the general logic of a problem) before narrowing down again (drawing conclusions and fashioning a single solution). Either way, we are challenging ourselves and using different perspectives.
No style of thinking is better than the other—rather, it’s knowing which is most appropriate to use in each situation. Questions like, “What is the atomic weight of magnesium?” require a different kind of thinking than do more open-ended questions like, “How are we going to get our sales team to cooperate more in the office?” For some problems, you need as many answers as possible (or, there is no “right” answer), but for others, you really want to hone in on the single best solution. Riddles force you to alternate between them.
Critical thinking is broadly convergent instead of divergent—it seeks to whittle down, to find logical coherence, and to unpick the components of a problem in the same way you’d take apart an appliance. Though creativity is a kind of intelligence, and intelligent people are invariably deeply creative thinkers, it is critical thinking that’s most often regarded as thinking in general. People who wish to bolster their intelligence often train their analytical skills. We can ask the same question here as we did above. What are people actually doing when they think intelligently and logically about a problem?
The first step is usually identification. Actually seeing and acknowledging what the problem is, diagnosing the issue, and finding all the aspects influencing it. You can never provide adequate solutions if you don’t understand the problem sufficiently.
During this stage, you might ask questions like, what am I really looking at here? What’s the question/problem? Who are the actors and what are they doing? And why? Can I identify cause and effect relationships here? What am I trying to achieve, and what information am I missing? And so on.
The next step entails a little research. Once you’ve broadly identified the field in which your problem is taking place, you can begin to explore various options, arguments, or possible solutions. Look at information and consider its quality.
Verify your sources and independently look at arguments to see how persuasive they are, and how they’re making that argument. Evaluate different possibilities with an eye to a solution. These research skills are invaluable in making sure that you’re not using faulty assumptions or bad data to come to your conclusions. A great critical thinking skill is to routinely ask, “What do I think and why do I think this?”
What’s the evidence? You could also deliberately search for the opposing argument to counter your own unconscious bias. Rather than merely look for data that supports your already-held conclusions, it can help to ask yourself what you are not seeing! This is a step that most people don’t make it to, so if you’re getting to this stage, you’re already significantly ahead of the pack.
This leads naturally to the next step (although all these functions typically overlap): “identifying bias.” This requires something we don’t often acknowledge when we think of intelligence—the ability to be discerning. Information needs to be appraised as neutrally and objectively as possible. To do this requires humility, honesty, and a lot of maturity—plus a little creative thinking to look into your own blind spots!
Debate with yourself. Find the flaws, weak points, and assumptions in how you’re thinking. Actively take an opposing view to understand your own flaws and potential weak points. Challenge yourself to find evidence for your beliefs and assumptions—and be ready to abandon those that are genuinely incorrect. This is the only way learning can ever happen! The worst thing you can do is assume that you are correct, and that there are elements of your thinking that are infallible and not worthy of testing.
This aspect of critical thinking is perhaps more important than any raw, intellectual power—because even the best arguments and most useful information will be ignored if too much ego is involved, or if someone has simply failed to consider all the facts at hand. Our world is overflowing with information, but not all of it is high quality. Yes, that even includes some of yours. If you find yourself resisting a question or assertion, take a second to pause and ask yourself if you are truly dedicated to finding the truth of the matter, or simply defending something else (like your ego).
We need to consistently ask who is presenting the information, and why (what is their agenda and how do they benefit from these claims?). Is it logical, relevant, incomplete, up to date? This may not seem immediately applicable when it comes to riddles, but many riddles do in fact trick us when we fail to properly appraise the problem, or fully consider the nature and quality of the information presented to us.
Inference or the closely related deduction, is the act of arriving at a conclusion given the information, or premises, in front of you. This is a process of extrapolation—guessing at some unknown piece of information based on known pieces of information.
For example, if you discovered that someone hadn’t worked for twenty years, you may infer that their unemployment was unfortunate and maybe due to some sort of disability (in this example, you can see that inferences can be incorrect—the person may well be independently wealthy, or someone like a monk or nun who doesn’t work at all). An inference is an educated guess, but it’s still just a guess and is only as good as the premises it’s based on.
More specifically, a deduction (in the classic philosophical sense, at least) is used when there is no possibility of the conclusion being wrong, given the premises. For example, I can have the following: “All students scoring below fifty percent fail the test,” as well as, “This student has obtained forty-two percent.” Using deduction, I can make the conclusion, “This student has failed the test.” I have moved from a general principle to a special case.
Deduction of this kind is rarer in real life than general inference—but sometimes mistakes can be avoided by simply knowing which one you’re actually dealing with! Induction, the opposite, is more informal logic and moves from a specific case to a general principle. For example, “The sun rose yesterday and it rose today as well. It will probably rise tomorrow, too.”
To improve inferential thinking, you need only improve the quality of the information you’re basing your conclusions on. Many of the riddles we’ll look at are deliberate tricks in that they withhold a crucial piece of information that’s needed to come to the right conclusion. Clues are always useful in critical thinking—but always remember that they’re just that, clues.
Another aspect of critical thinking is determining relevance. All the above steps assume that you’re only considering information that is actually pertinent to the situation at hand. This in itself requires some skill. How do you know when to stop looking, or whether a piece of data is worth including in your analysis? You don’t want to get sidetracked with totally irrelevant data, but you also don’t want to miss out on crucial information.
The best approach is to have a goal in mind and constantly measure new information against this goal—with many goals, you might need to rank them in order of importance. When you find yourself encountering repeated data, it’s a sign you’ve thoroughly explored the space, but you may have to be satisfied with enough information to merely allow you to identify trends. Like biases, information should constantly be checked for its value in the bigger picture—can you omit a dozen weak ideas in favor of a single better and more representative one?
Finally, curiosity is a vital but sometimes overlooked part of critical thinking. The truth is, information seldom comes to find us and present itself perfectly formed! Rather, it is us who has to go and seek it out deliberately, sometimes asking, “Why?” many times over to get to the crux of an issue. It’s easy to lose the curiosity habit and take things at face value, but sometimes the best critical thinking is done when people are not satisfied with the standard answer. Critical thinking is solutions-oriented and convergent, but that doesn’t mean you can’t regularly ask yourself, “Is this all there is?” and go poking around until something catches your interest. Keep things open-ended—at the end of every solution, you often find three more interesting problems!