Rings bells with background processing as well for me, pushing incomplete tasks into the background, letting the brain work on them.
How they do stick and keep popping up until resolved in some way, which can be very useful imho.
I can attest to this.
Let the words/topic/thought "marinate" is the concept behind it.
I remember solving -not advanced but fairly complex network problems-, while in P4nd3m1C in home office when I had work.
I was trying so solve a technical problem so hard consciously that the things I tried didn't worked and got frustrated, then after some 45 minutes of nonstop trying things, I just dropped it (not out of despair, but off of tiredness) and then I lay in bed just remained calm with eyes closed, like when your release something you had a tight grip on... A sort of "pseudo sleep" (not even a nap) just closing my eyes completely forgetting about the problem and then it came with the solution: almost automatically and instantly, but the conscious effort I was exerting previously was FULL, my brain just needed SPACE to solve this problem. Happened to me twice.
I remembered I read that in The book named: How to think like Leonardo da Vinci, had a similar tip like this and it was the moment to put it to test, and it worked.
Definitely worth the try.
Tips for Solving Complex Problems Leonardo Style (Deep seek feedback)
In How to Think Like Leonardo da Vinci, Michael Gelb adapts Leonardo's genius into 7 key principles (Curiosità, Dimostrazione, Sensazione, Sfumato, Arte/Scienza, Corporalità, Connessione). While the entire book teaches how to develop these da Vincian thinking habits, the most direct framework for complex problem solving is presented as the "Solution Finding" process, primarily outlined in Chapter 11 ("Arte/Scienza: Developing the Balance of Science and Art").
Here are the complete steps/tips Gelb provides for solving complex problems, synthesized from the "Solution Finding" section:
Define the Question (Curiosità Driven):
Ask: "What is the real question I'm trying to answer?" "What is the core problem?"
Reframe: Look at the problem from multiple angles. Challenge initial assumptions.
Use Questions: Employ Gelb's "Power Questions" (e.g., "What's missing?", "What if...?", "How else can I look at this?").
Gather Information (Dimostrazione & Sensazione):
Research: Collect relevant facts, data, and knowledge from diverse sources (books, experts, history).
Direct Observation: Use your senses! Look closely, listen intently, touch, taste (if appropriate), smell. Leonardo learned by intensely observing nature and life.
Experience: Test things out practically where possible. Learn from hands-on experimentation.
Deepen Sensory Awareness (Sensazione):
Engage All Senses: Consciously involve sight, sound, touch, smell, and taste to gather richer, more nuanced information about the problem and potential solutions.
Visualize: Create vivid mental images of the problem and potential solutions.
Allow for Mess & Uncertainty (Sfumato):
Tolerate Ambiguity: Don't rush to premature closure. Accept that the path isn't clear yet.
Brainstorm Wildly: Generate a large quantity of ideas without judgment. Encourage absurd, unconventional possibilities. Use mind maps.
Welcome Contradictions: Explore opposing ideas simultaneously. See what insights emerge from the tension.
Incubate (Sfumato & Corporalità):
Step Away: Consciously put the problem aside. Let your subconscious mind work on it.
Engage Body & Rest: Do something physical (walk, exercise), creative (draw, play music), or relaxing (take a bath, nap). This is crucial for insight.
Trust the Process: Understand that breakthroughs often come when you're not actively forcing the solution.
Integrate & Synthesize (Connessione & Arte/Scienza):
Look for Patterns & Connections: How do the ideas, information, and potential solutions relate? Look for analogies in nature, art, science, history.
Combine Opposites (Connessione): Can seemingly contradictory ideas be merged into a novel solution?
Balance Logic & Imagination (Arte/Scienza): Use both analytical thinking (science) and creative, holistic, pattern-based thinking (art). Draw diagrams, make models, sketch ideas.
The "Aha!" Moment: This is where the insight or breakthrough solution often surfaces, often after incubation.
Refine & Define (Dimostrazione):
Test & Evaluate: Subject your insights and solutions to rigorous testing. Ask: "Does this really solve the core problem?" "What are the potential flaws?"
Seek Feedback: Share your ideas with others and get constructive criticism.
Iterate: Be prepared to go back to earlier steps based on feedback and testing. Refine your solution.
Define the Solution Clearly: Articulate the final solution precisely.
Key Da Vincian Principles Embedded in this Process:
Cyclical, Not Linear: Gelb emphasizes this is rarely a straight path. You may loop back between steps (e.g., gathering more info after testing, incubating again after integrating).
Wholeness: True solutions often emerge when engaging the whole mind (logic + intuition), body (senses, movement), and spirit (curiosity, wonder).
Embrace Paradox: Sfumato (tolerance for ambiguity) is essential for navigating the messiness of complex problems.
Interconnectedness (Connessione): Solutions often lie at the intersection of different disciplines or perspectives.
Crucial Takeaway from Gelb: Solving complex problems like Leonardo isn't just about a checklist; it's about cultivating the underlying mental habits (the 7 principles) that make this process natural and effective. The "Solution Finding" steps provide the structure, but your developed Curiosità, Dimostrazione, Sensazione, etc., fuel the process.
This framework encourages moving beyond purely analytical approaches, embracing creativity, ambiguity, sensory input, and the power of the subconscious to unlock innovative solutions to truly complex challenges.