The Calculus of Ideas and Patterns

 Introduction.

When dealing with ideas, patterns, intuition, and brainstorming, we need operations or rules not unlike those of arithmetic. The goal is not proof, a finished device, or a fait accompli, but rather a foundation for further investigation and study. In some cases, these operations may yield a proposition, that is, something capable of being proved. In this sense, they form a practical logic of intuition. The article concludes with a few select examples from a variety of venues.

Setting.

We are working with a given idea, problem, or project, or simply just thinking. Our aim is to discover pathways, patterns, or conceptual connections that may be useful. The following operations describe ways in which ideas and patterns can be generated, transformed, or refined. These also work toward understanding the imagination. Yet, this framework is distinguished from formal logic and proof. We are tempted to call them as “soft logic” because while nothing is proved, reasons are paramount during the process.

Operations.

• Inspire
  To generate a new pattern that may prove useful, often without a clearly traceable origin.
• Combine
  To merge two distinct ideas or patterns into a single, unified pattern.
• Pare
  To strip away elements from two or more disparate ideas or patterns so that what remains connects into a new, coherent pattern.
• Bridge
  To discover a logical or conceptual method that connects two or more otherwise separate patterns. This could also be termed a splice.
• Excise
  To extract a distinct pattern from within a larger or more complex one.
• Compare
  To examine two patterns point by point, focusing on similarities (and, implicitly, differences).
• Patch
  To add a small modification to an existing pattern in order to enhance its usefulness or explanatory power.
• Hone
  To sharpen a pattern so that it becomes more clearly visible, precise, or dominant for a particular purpose.
• Meld
  To integrate two or more patterns into a new, more complex pattern that better captures what is needed.
• Import
  To introduce an external pattern into the current context in order to test its relevance or applicability.

Runners-up in the creative/pattern process include iteration, refinement, and prototyping, crucial steps for anyone involved in actual production, whether the output is a widget, an article, or a paper. You may have noticed that some "papers of the year" are chock-full of ideas that culminate in an action plan. Those of us exploring new concepts love to hear new ideas and see new patterns, even if they are not personally ours.

Once imagination, intuition, ideas, and patterns move past the "mystical frontier," these operations seem to come down to earth, implying they can be learned. This single fact is important. It also makes the work of geniuses more understandable. However, these processes are based on non-formal reasoning, which is often seen more clearly in group settings with many contributors. Interestingly, the ability to recognize patterns has its own psychological classification: Pattern Recognition Intelligence (PRI). This is the ability to identify, understand, and leverage rare patterns to make successful and productive choices. It is also significant to realize the pattern may not be recognized as an object, but that the pattern conveys a resonance to the observer, which is then imitated. This can be the source of a “style.”

It is possible to collectively classify these mental operations as generative, reductive, and integrative, giving more reality to what is happening deep in the recesses of the mind.

Figuratively, all this happens before the first shovel hits the ground.

Examples.

Let’s consider a few examples of highly creative people, some offered with only a maxim, others with more detail. These examples show that while the operations discussed above may satisfy many as to "how it’s done," there must be another layer resting upon them, glimpsed only by a few. Getting the idea or seeing the pattern is not always enough; persistence and perseverance, two other qualities we know well, must be proactive companions.

Steve Jobs. Jobs approached thinking with a blend of intuition, curiosity, and a relentless focus on the human experience, often merging technology with the humanities to drive innovation. His thought process was not linear or purely analytical; instead, it emphasized connecting disparate ideas, simplifying complexities, and pursuing passion-driven visions that challenged the status quo. Central to Jobs' thinking was the belief that creativity emerges from linking seemingly unrelated experiences rather than inventing from scratch. He viewed innovation as perceiving patterns others missed—an outcome that often felt like an obvious synthesis after accumulating diverse "dots." Jobs used meditation to calm the mind, allowing intuition to blossom and fostering the empathy needed to anticipate user needs without reliance on focus groups. He revered ideas as fragile and iterated relentlessly; for example, the iPhone was prototyped countless times. Jobs' legacy shows that innovative thinking thrives on curiosity, synthesis, and bold execution, turning abstract insights into world-altering realities.

Srinivasa Ramanujan. Ramanujan's mind operated through a deep, almost instinctive grasp of mathematical structures. He could perceive complex patterns and relationships in numbers that eluded others, generating theorems and formulas rapidly without the step-by-step reasoning typical of Western mathematics. A hallmark of Ramanujan's thinking was its mystical dimension. He attributed many breakthroughs to visions and dreams, particularly from the Hindu goddess Namagiri Thayar, whom he said revealed formulas to him during sleep or meditation. His notations were irregular, and proofs were often absent, making his work initially hard for others to evaluate. Indeed, some of his early results still lack formal proofs.

Successful Investors. Investors like Warren Buffett, Paul Tudor Jones, Carl Icahn, and Ray Dalio honed their pattern recognition skills early in their careers. Their highly developed observational and pattern recognition abilities allow them to make superior investment decisions.

The Arts. In the Arts, surely Leonardo da Vinci and Michelangelo reign supreme, but for pure creativity, imagination, and pattern usage, Monet, Picasso, and Klee also stand out. In music, one must place Mozart among the most creative of all composers, renowned for conceiving ideas fait accompli, fully realized in his mind before writing them down. In the more contemporary genre, the Beatles were outstanding.

Industrialists such as Elon Musk, Andrew Carnegie, and Henry Ford were truly creative and spent much of their time conjuring ideas and seeing patterns on how to accomplish their monuments. Amazon inventor, Jeff Bezos, began with a well-conceived idea to bring the local bookshop to all of America, and consequently brought the entire American mercantile enterprise with it. Alexander Graham Bell had this radical concept of communications via electricity and perseveres through multiple patterns to ultimately realize his dream.

 

 

 

References

1. Polanyi, M. (1966). The Tacit Dimension.
   Polanyi’s core thesis—that “we know more than we can tell”—directly supports your idea of operations of intuition that precede formal proof.
2. Peirce, C. S. (1931–1958). Collected Papers of Charles Sanders Peirce.
   Peirce introduces abduction—a logic of discovery distinct from deduction and induction—which closely parallels your Inspire, Bridge, and Import operations.
3. Kuhn, T. S. (1962). The Structure of Scientific Revolutions.
   Kuhn explains how new patterns (paradigms) emerge not through linear proof but through reorganization of ideas—very close to Meld, Excise, and Pare.
4. Hadamard, J. (1945). The Psychology of Invention in the Mathematical Field.
   A classic analysis of how creative mathematical ideas arise through intuition, incubation, and sudden pattern recognition.
5. Simon, H. A. (1969). The Sciences of the Artificial.
   Simon formalizes problem-solving as pattern manipulation and heuristic operations, strongly validating your “operations” framing

 

©2026 G Donald Allen