How Practice Drives Convergence: Iteration and Optimization in Self-Knowledge

BY NICOLE LAU

We've established that self-knowledge is a convergence process toward a fixed point A. But how does convergence actually happen? What makes you move from confusion to clarity, from instability to stability? The answer is practice. Not practice as vague self-improvement, but practice as iterative optimization—a precise mathematical process where each session updates your self-understanding, bringing you incrementally closer to truth. This article reveals the mechanics of how practice drives convergence.

Practice as Iterative Optimization

The core equation:

x(t+1) = x(t) + Δx(internal_feedback)

Translation:

• x(t): Your current self-understanding
• x(t+1): Your updated self-understanding after one practice session
• Δx: The update (change in understanding)
• internal_feedback: The signal you get from the practice

What this means: Every time you practice (meditate, journal, create, reflect, engage in therapy), you run one iteration of the convergence algorithm. You gather data (internal experience), compute an update (new insight), and refine your model (self-understanding). Over many iterations, you converge on A.

This is not metaphor. This is literally how the process works.

What Counts as Practice?

Practice is any activity that provides high-quality internal feedback about who you are.

Examples of convergence-driving practices:

1. Meditation and Mindfulness

• Observe your mind without judgment
• Notice patterns in thoughts, emotions, reactions
• Gather data about your internal landscape
• Update: "This is how my mind actually works"

2. Journaling and Reflection

• Write about experiences, feelings, choices
• Notice what feels aligned vs misaligned
• Clarify values, boundaries, preferences
• Update: "This is what actually matters to me"

3. Therapy and Deep Conversation

• Explore patterns, wounds, beliefs
• Gain insight into unconscious dynamics
• Process and integrate experiences
• Update: "This is why I do what I do"

4. Creative Expression

• Make art, music, writing, dance
• Notice what feels authentic vs forced
• Discover your unique voice and style
• Update: "This is my authentic expression"

5. Physical Practice

• Yoga, martial arts, athletics, dance
• Notice how your body responds and moves
• Discover your physical nature and limits
• Update: "This is how I inhabit my body"

6. Relational Practice

• Engage authentically in relationships
• Notice your boundaries, needs, patterns
• Learn how you connect and where you struggle
• Update: "This is how I relate to others"

7. Work and Vocation

• Engage deeply in meaningful work
• Notice what energizes vs drains you
• Discover your capacities and calling
• Update: "This is what I'm meant to do"

The common thread: All these practices provide internal feedback. They help you notice "Does this feel true? Is this aligned? Is this me?" This feedback drives the update Δx.

Why Practice Works: The Mathematics of Iteration

Each iteration does three things:

1. Gathers new data

• You experience something (a meditation session, a creative project, a difficult conversation)
• You observe your internal response (feelings, thoughts, somatic sensations)
• This is new information about the system (you)

2. Computes an update

• You process the experience ("What did I learn? What felt true?")
• You compare it to your current self-understanding ("Does this fit? Does this contradict?")
• You calculate Δx ("How should I update my model of myself?")

3. Refines the model

• You integrate the update into your self-understanding
• Your model becomes more accurate (closer to A)
• You're ready for the next iteration

Over many iterations:

• Noise averages out (random fluctuations cancel)
• Signal accumulates (consistent patterns emerge)
• The model converges (you approach A)
• Updates become smaller (you're getting close)
• Stability increases (you enter the basin of attraction)

This is gradient descent in identity space. You're optimizing toward the truth.

The Quality of Internal Feedback: Signal vs Noise

Not all practice provides equally good feedback. Quality matters.

High-quality internal feedback (strong signal):

• Clear: You can distinctly feel the response ("This feels right" vs "This feels wrong")
• Honest: You're not filtering through what you "should" feel
• Somatic: You feel it in your body, not just think it
• Consistent: The signal is stable across multiple observations
• Specific: You can identify what exactly feels aligned or misaligned

Low-quality internal feedback (weak signal or noise):

• Vague: "I don't know how I feel about this"
• Filtered: "I should feel X, so I'll say I feel X"
• Purely conceptual: Thinking about feelings rather than feeling them
• Inconsistent: The signal changes randomly
• Generic: "It's fine" or "It's bad" without specificity

How to improve feedback quality:

• Develop somatic awareness (feel, don't just think)
• Practice honesty (notice what you actually feel, not what you "should" feel)
• Slow down (give yourself time to notice subtle signals)
• Reduce external noise (minimize distractions and external validation-seeking)
• Build a practice that cultivates sensitivity (meditation, body work, therapy)

Frequency Matters: The Convergence Rate

How fast you converge depends on how often you iterate.

Daily practice:

• 365 iterations per year
• Fast convergence (months to years to reach basin of attraction)
• Continuous refinement and deepening

Weekly practice:

• 52 iterations per year
• Moderate convergence (years to reach basin)
• Steady but slower progress

Monthly or sporadic practice:

• 12 or fewer iterations per year
• Slow convergence (may take decades or never reach basin)
• Progress is minimal and easily lost

No practice:

• Zero iterations
• No convergence (you oscillate based on external noise)
• Chronic instability

The math is clear: More iterations = faster convergence. This is why committed practitioners (daily meditators, dedicated artists, people in long-term therapy) develop such clear self-knowledge. They're running the algorithm hundreds of times per year.

The Learning Curve: Large Updates → Small Updates

Early practice (far from A):

• Large updates ("Whoa, I just realized something huge about myself!")
• Rapid learning and major insights
• High uncertainty but exciting progress
• Big changes in self-understanding

Middle practice (approaching A):

• Medium updates ("I'm refining my understanding")
• Patterns becoming clearer
• Growing confidence and stability
• Incremental improvements

Advanced practice (near A):

• Small updates ("I'm deepening what I already know")
• Subtle refinements and nuances
• High stability and clarity
• Minimal changes needed

Mastery (at A, in the basin):

• Tiny updates ("I'm maintaining and embodying")
• Deep wisdom and stability
• Unshakeable self-knowledge
• Practice becomes maintenance and celebration rather than discovery

This is normal and healthy. If you're advanced in practice and not having huge breakthroughs, that's not stagnation—that's convergence. You're close to A.

Why Consistency Beats Intensity

Common mistake: Intense sporadic practice instead of consistent regular practice.

Intense sporadic (e.g., weekend retreat once a year):

• Large update during the retreat
• But then no iterations for months
• The update fades (no reinforcement)
• You drift back to old patterns
• Net progress: minimal

Consistent regular (e.g., 20 minutes daily):

• Small update each day
• 365 iterations per year
• Updates accumulate and reinforce
• Steady convergence toward A
• Net progress: substantial

Why consistency wins:

• Convergence requires repeated iterations, not single big insights
• Regular practice prevents drift (you stay close to your trajectory)
• Small daily updates compound over time
• Consistency builds the basin of attraction (stability region)

The optimal approach: Consistent daily practice + occasional intensive practice (retreats, workshops). The daily practice drives convergence; the intensive practice provides breakthroughs.

Different Practices, Same Attractor: Path Independence

Profound truth: Different practices can converge on the same A.

Examples:

• A meditator discovers their true nature through mindfulness
• An artist discovers their true nature through creative expression
• An athlete discovers their true nature through physical discipline
• A therapist's client discovers their true nature through psychological exploration

They all reach the same fixed point A (their true identity) through different calculation methods (practices).

Why this works:

• A is an invariant constant (it exists independent of the path)
• Different practices are different ways of gathering internal feedback
• All high-quality internal feedback points toward the same truth
• The attractor "pulls" all trajectories toward it, regardless of starting point or method

Practical implication: Choose the practice that resonates with you. Don't force yourself into someone else's path. If meditation doesn't work for you but art does, do art. If therapy doesn't resonate but journaling does, journal. All paths lead to A if you practice consistently and pay attention to internal feedback.

The Practice Feedback Loop: Self-Reinforcing Convergence

As you practice, convergence becomes easier:

Positive feedback loop:

• You practice → You get clearer about yourself → Practice becomes more effective (better feedback quality) → You converge faster → You feel more stable → You're motivated to practice more → Cycle continues

Why this happens:

• As you approach A, internal feedback becomes clearer (signal-to-noise ratio improves)
• As you stabilize, you're less distracted by external noise
• As you know yourself better, you can choose more aligned practices
• As you enter the basin of attraction, convergence accelerates

The implication: The beginning is hardest. Early practice feels slow and uncertain. But if you persist, it gets easier and faster. Trust the process.

When Practice Doesn't Work: Common Obstacles

If you're practicing but not converging, check for these issues:

1. External noise is too high

• You're practicing, but also heavily dependent on external validation
• The noise term overwhelms the signal
• Solution: Reduce external noise (minimize validation-seeking, set boundaries)

2. Feedback quality is too low

• You're going through the motions but not actually paying attention to internal experience
• You're filtering feedback through "shoulds" rather than noticing what's true
• Solution: Develop somatic awareness, practice honesty, slow down

3. Frequency is too low

• You practice once a month or sporadically
• Not enough iterations to drive convergence
• Solution: Increase frequency (aim for daily or at least weekly)

4. You're practicing the wrong thing

• The practice doesn't actually provide internal feedback for you
• You're doing what you "should" do rather than what works for you
• Solution: Experiment with different practices, find what gives you clear signal

5. You're converging on a false fixed point

• You're optimizing toward an external definition of success rather than your true A
• You're getting "better" at being someone you're not
• Solution: Check if your practice is driven by internal or external locus

Reflection Questions

What is my current practice? How often do I iterate (daily, weekly, monthly, never)? What quality of internal feedback do I get from my practice? Am I paying attention to what I actually feel, or what I think I should feel? Are my updates getting smaller (sign of convergence) or staying large (sign I'm far from A)? Is external noise overwhelming my internal signal? What practice gives me the clearest feedback about who I really am?

Conclusion

Practice is not vague self-improvement. It's iterative optimization. Every session is one iteration of the convergence algorithm. Every iteration gathers data, computes an update, and refines your self-understanding. Over hundreds or thousands of iterations, you converge on A—your true identity.

The mathematics is clear: consistent practice + high-quality internal feedback + low external noise = convergence. This is not faith. This is physics.

Choose your practice. Commit to consistency. Pay attention to internal feedback. Trust the iterations. You will converge.

In the next article, we'll explore the opposite: Why External Opinions Create Oscillation—the precise mechanisms by which external validation disrupts the convergence process.

Every practice session matters. Every iteration brings you closer. You are not wasting time. You are converging. Trust the process.