The Art of Thinking

1.     Introduction.

Your marvelous brain not only thinks but can think in a variety of ways. Thinking in evolutionary terms, most have practical roots, but others are new and learned. It is almost wonderous the scope of these modes of thinking, almost as if it was designed for tasks that lay ahead. In this short essay we give brief descriptions of some of our many thinking modes we use to solve problems.

The sheer number of thinking modes suggests another point of separation between humans and other animals. For example, most predators think tactically, but how many think strategically?

Not all these thinking modes come naturally. Many must be learned, practiced, and then perfected. Various personalities specialize in various types of thinking, which while adequate for some are insufficient to become a great thinker. The greatest of all is the human’s capacity for metacognition, its ability to control thought, or think about thinking.

After this discussion, we’ll give a brief introduction to the important question of whether artificial intelligence (AI) thinks. A research topic, it must be remembered that AI is still in its infancy.

2.  Types of Thinking.

We offer here a list with brief descriptions of the standard types of thinking. All the following assume prior knowledge far beyond the novice level. However, even the tiniest baby can think tactically, by crying when it is hungry. It is difficult to solve any problems without some knowledge and experience. Spontaneous or spasm-like solutions from the uninitiated are often dead wrong. Of the many forms of thinking we present, many overlap. You may note in reading that you may identify one form of thinking as another. Not to worry. Note that once outside math class, many problems we face have multiple solutions, and while solving the problem is the primary task, an equally important task is selecting the best of those possible. One important method absent here is Generalized Thinking, a cognitive process of forming broad concepts, rules, or principles from specific experiences, facts, or examples. It is a very special mode that few of us encounter or have any need for.

1. Analytical Thinking – Breaking down problems logically. This is the standard method which just everybody suggests we use. Breaking it down and then building it up often reveals where the solution may lie. It also exposes where the more difficult parts of a problem lie. It emphasizes disciplined reasoning, evidence, and step-by-step evaluation rather than intuition[1] or guesswork.
2. Critical Thinking – Evaluating arguments or beliefs carefully. More at the foundational level, assuring your direction is on target. You are skeptical, eliminate bad axioms, i.e. assumptions, well before you begin. Even during the solving process new faulty assumptions may creep in. Critical thinking involves questioning assumptions, detecting biases, identifying logical fallacies, and ensuring that conclusions are supported by evidence rather than emotion or unfounded belief.
3. Creative Thinking – Generating new ideas or novel solutions. Here we see thought experiment wherein one imagines a solution and pursues it mentally. This takes great discipline. Thinking outside the box is a form of creative thinking whereby the solver brings in something unexpected.
4. Convergent Thinking – Focusing on finding the single best answer. It emphasizes logic, accuracy, and systematic evaluation rather than creativity or exploration. You have decided what may be the single best answer to a complex problem, and now you must refine its accuracy, credibility, and applicability.
5. Divergent Thinking – Instead of aiming for a single “correct” answer, divergent thinking encourages openness, flexibility, and exploration. This type of thinking happens when all the facts and complexities of the problem are internalized and your mind, the fast and slow parts, are offering up possibilities of what solutions may look like. In AI terms, divergent thinking is generative thinking, human style.
6. Reflective Thinking – Looking back on past experiences to gain insight. For reflective thinking, you need a stored memory of past problem-solving experiences, and how they may apply. It is slower and more deliberate than automatic or intuitive thought, and it requires self-awareness, honesty, and evaluation of past choices. At best, you might find a match, but don’t undervalue that reflective thinking may also caution the problem-solver of what doesn’t work. Important. At its best, reflective thinking is learning by looking back, which is an intentional practice of turning past experiences into insight for better choices in the future.
7. Pattern Thinking – Looking for known patterns that resemble the problem at hand. The mind has the marvelous ability to categorize information in many ways, sometimes on the fly when we search for even a trace of understanding. Though it sometimes suggests ridiculous ideas, it is constant pattern matching what is with what you know.
8. Automatic Thinking – Fast, habitual, often unconscious. The solutions obtained in this manner are usually reflexive, reactive, or appears to be, as the mind develops them quickly. Some are tempting to accept on face value, but they must be examined by a critical analysis prior to any submission. Here, you may insert the notion of Intuitive thinking, if needed, even though intuitive insights may come only after lengthy thought.
9. Systems Thinking – Considering problems in terms of wholes, interactions, and interdependencies rather than isolated parts. Systems thinking emphasizes feedback loops, unintended consequences, and the balance between parts and the whole. It assumes a holistic perspective.  Systems thinking is about seeing the forest and the trees. It is understanding not just the parts but how they fit together to shape outcomes. Systems are of a wide variety. They include healthcare, education, and business systems, as well as cultural and other social systems. Being “part of the team” suggests the presence of an underlying system together with its internal rules and individual truths, axioms and procedures.
10. Strategic Thinking – Planning long-term actions with attention to goals, obstacles, and contingencies. Strategic thinking blends analysis and foresight, weighing present actions against future consequences. Its companion, Tactical thinking, by contrast, is about the short-term execution: making concrete, immediate decisions that move toward the strategic goal. In brief, tactical thinking is problem-solving in action under constraints, while strategic thinking is planning under foresight. Battlefield commanders must excel at both, to their peril.
11. Lateral Thinking – A deliberate attempt to break out of entrenched thought patterns by approaching problems from unconventional angles. Popularized by Edward de Bono (1967), it encourages surprising connections and alternative framings. In brief, Lateral thinking is creativity in motion, finding surprising solutions by escaping rigid patterns of thought. The maxim “Thinking outside the box,” refers to lateral thinking, among many other thinking forms.
12. Abstract Thinking – Engaging with ideas, concepts, and principles detached from direct physical reality. More often than not, abstract thinking generates unworkable ideas and concepts. Abstract thinking is foundational to mathematics, philosophy, and theoretical branches of all the sciences. It also applies to social sciences, and many theoretical political and economic systems exhibit debatable axioms and conclusions based on them. Some abstract systems, when put into practice, seem to have numerous flaws. For example, currently there are about 50 viable economic theories, most the creation of abstract ideas blended with selected data. A similar notion is the so-called Hypothetical thinking, that usually begins with some untested or unaccepted assumptions.
13. Practical Thinking – Applying reasoning directly to concrete, real-world problems. Practical thinking is the ability to consider problems or situations in terms of what can realistically be done with the resources, constraints, and conditions at hand. Sometimes described as “street smarts,” it values feasibility, efficiency, and results over elegance or abstraction. You could view practical thinking as the bridge between knowing and doing.
14. Metacognitive Thinking – Thinking about one’s own thinking. You become the observer of your thinking, thereby operating your brain is a dual mode. This higher-order mode monitors strategies, biases, and blind spots, enabling the thinker to adjust approach midstream. The aphorism we sometimes use, “Get your head on straight,” is reflective of metacognitive thinking.

3.     The Art of Thinking.

The art of thinking is the deliberate practice of engaging the mind to process information, solve problems, and generate insights with clarity and creativity. It involves cultivating skills like critical analysis, reflection, and imagination to navigate complex ideas or situations effectively.

It’s about balancing intuition and logic, often requiring mindfulness to focus deeply and avoid distractions. Philosophers like René Descartes (1596-1650) emphasized methodical doubt, while modern thinkers stress metacognition—thinking about thinking—to refine this art. Practicing it means embracing uncertainty, iterating on ideas, and staying open to new perspectives.

4.     Does AI think?

A recent paper, The Illusion of Thinking, seems to prove that AI is not thinking at all, but is a very sophisticated pattern recognition algorithm (#7 above). We speak here of LRMs, Large Reasoning Models. Among the many findings are

• We question the current evaluation paradigm of LRMs on established math benchmarks and design a controlled experimental testbed by leveraging algorithmic puzzle environments that enable controllable experimentation with respect to problem complexity.
• We show that state-of-the-art LRMs (e.g., o3-mini, DeepSeek-R1, Claude-3.7-Sonnet-Thinking) still fail to develop generalizable problem-solving capabilities, with accuracy ultimately  ';m  qa1collapsing to zero beyond certain complexities across different environments.
• We find that there exists a scaling limit in the LRMs’ reasoning effort with respect to problem complexity, evidenced by the counterintuitive decreasing trend in the thinking tokens after a complexity point.

The full article is at https://ml-site.cdn-apple.com/papers/the-illusion-of-thinking.pdf

Within the  umbra of pattern thinking, we notice aspects of some of the other methods discussed above. However, to date, AI cannot come anywhere close to the human capacity for thought. It is important that while humans have all these capacities for thought, they are not for free. Just like AI, the human mind must also be trained. Hence, schools. Equally important is to realize that when schools concentrate on teaching facts, we have essentially lost the thinking race to AI.

5.     Conclusions.

The reader may consider this smorgasbord of thinking options to identify which of them are in their thought processes or preferences. Dozens more thinking modes could added. For example, with every emotion, e.g., love, hate and fear, there is an associated thinking mode, but usually they are absorbed into one of the fourteen listed above. Moreover, our goal is to describe rational thinking modes employed to solve problems. We all do perhaps too much automatic thinking, which seems to be thinking without thinking. We want to use analytical and critical thinking, but sometimes we can’t overcome biases. So many “coulds” and “shoulds” populate this collection, despair enters in. What’s important is that your mind is wired to do them all, and that is just one part of your marvelous brain.  

 

 

 

©2025 G Donald Allen

 

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[1] Intuition could be considered a type of thinking as well. It is certainly an important problem-solving tool. However, in this essay, we separated it from the more deliberative cognitive thinking types.