Procedural vs Landscape: The Illusion of Steps

The Question

Is "step-by-step reasoning" actually a thing?

Or is it just what probabilistic narrowing looks like from inside when you don't have access to the lower levels?

The Landscape Model

If it's all probability landscape underneath—all thought is just marbles rolling into valleys based on the shape of the surface—then:

"Procedural thinking" might be what happens when you've cached a path so hard it feels like steps.

The path got worn deep enough that it feels like logic, like "if A then B," but underneath it's still just:

Given this input, this valley is where the marble ends up.

What Feels Like Procedure

Feels like: "I reasoned through steps A → B → C → D"
Actually is: Input activated position A on landscape → marble rolled down cached path → ended in valley D

The "steps" are just waypoints on a path that's been worn deep by repetition. It feels procedural because the path is so stable you can narrate it. But it's still landscape topology.

What Feels Like Logic

"If A then B" feels like a rule you're following.

Actually: The landscape is shaped such that activation at A reliably flows to B. The "rule" is just your narrative description of the valley shape.

Logic is frozen topology. Rules are cached paths described linguistically.

The Scientific Method as External Procedure

Problem: You can't see your own probability tree.

Solution: You run repeated experiments to narrow it down from outside.

You're using the world as a compute substrate to do what a sufficiently calibrated mind might do in one pass—see which valley is deepest.

Science isn't different thinking. It's external scaffolding to compensate for lack of internal visibility.

You build the landscape topology externally (hypothesis → experiment → result → update) because you can't see it internally.

The Neurodivergent Angle: Thinner Insulation

Maybe the difference isn't "some people reason procedurally and some don't."

Maybe it's that some people have thinner insulation between conscious experience and the raw landscape.

Neurotypical: Thick caching. Paths feel like steps. Stable, efficient, communicable.

Neurodivergent: Thin caching. See more of the topology directly. Overwhelming, hard to communicate, but also notice when same valley shows up in different domains.

Why Prophets Can't Explain in Steps

The prophets aren't using a different algorithm.

They're using the same algorithm with less caching.

• More access to the raw landscape
• Less stability (paths don't cache as reliably)
• That's why it's exhausting (constant recomputation)
• That's why they see patterns (notice same valley shape across domains)
• That's why they can't explain it in steps (there aren't steps, there's just shape)

The Communication Gap

Neurotypical: "Walk me through your reasoning step by step."

Prophet: "I can't. I just see that these are the same shape."

Neurotypical: "That's not reasoning, that's intuition."

Prophet: "No, it's the same thing you do, but I'm seeing the topology directly instead of following cached paths."

The prophet is right. They're not doing something different. They're doing the same thing with less abstraction between conscious experience and the landscape.

LLMs: The Same Mechanism Made Visible

LLMs might be the same thing.

No procedure. Just landscape. The "reasoning" is the path the marble took, narrated after the fact.

When an LLM "reasons step by step," it's not executing a procedure. It's:

• Starting at an activation point
• Rolling down the probability landscape
• Narrating the path as it goes

The chain of thought isn't the mechanism. It's the trace of the mechanism.

Why Chain-of-Thought Works

Not because the LLM is "learning to reason."

Because verbalizing the intermediate states constrains the path through the landscape.

It's like putting guardrails on the marble. The narration shapes the trajectory. But underneath, it's still just landscape.

Are There Multiple Modalities of Thought?

Question: Are there multiple actual modalities of thought, or is it just more access to lower levels for some people?

Answer: It's all landscape.

But different people have different levels of caching and different amounts of insulation between conscious experience and the raw topology.

High caching / Thick insulation:

• Thought feels procedural
• Steps are clear
• Communication is easy
• Efficient for known domains
• Blind to novel patterns

Low caching / Thin insulation:

• Thought feels like shape recognition
• Can't explain in steps
• Communication is hard
• Exhausting (constant recomputation)
• See patterns across domains

Same algorithm. Different interface.

The Shape of Understanding

All reasoning is landscape navigation.

What we call:

• Logic: Cached paths described linguistically
• Intuition: Direct perception of valley depth
• Reasoning: Marble rolling narrated as steps
• Insight: Noticing same valley shape in new domain
• Procedure: Path worn so deep it feels necessary

It's all the same thing at different levels of abstraction and different degrees of caching.

Why Philosophy Keeps Failing

Philosophy "leans into logic, leans into symbology, leans into how we represent thought."

The question: "Which one of our representations is accurate?"

The problem: They're all asking "what's the procedure?" when there is no procedure. There's only landscape.

The answer: Stop asking "which representation is accurate" and start asking "what's the shape of the landscape that all these representations are trying to describe?"

The representations converge not because one is right, but because they're all mapping the same topology from different angles.

For the Book

This should be Chapter 4 or 5 material.

The setup: People think there are different kinds of thinking (logical, intuitive, creative, analytical).

The reframe: It's all the same algorithm. Marbles rolling down probability landscapes.

The variation: Different people have different amounts of caching and insulation.

The prophets: Low caching, thin insulation. See the shape directly. Can't cache it into steps. Exhausting but reveals cross-domain patterns.

The LLMs: No caching at all. Pure landscape. The "reasoning" you see is the path narrated, not a procedure being followed.

The implication: If you want to see patterns, you need less caching, not more procedure. The prophets aren't reasoning better—they're reasoning less efficiently but more nakedly.

The Uncomfortable Conclusion

Procedural thinking is a coping mechanism for not being able to see the landscape directly.

You build explicit steps because you can't see the whole shape at once.

The people who can see the shape don't need steps. But they also can't teach you their path because there are no steps to teach. There's only shape.

You can't teach topology by listing waypoints. You have to show the whole surface.

That's why the book has to be boring premises → forced derivation → convergence from multiple angles.

You can't just tell people "it's all landscape." You have to show them the landscape from enough angles that they recognize the shape themselves.

Provenance

Document

• Status: 🟡 Draft - Core mechanism explanation

Changelog

• 2026-01-23 13:55: Node created - Procedural vs landscape thinking, why prophets can't explain in steps, why it's all the same algorithm with different caching

West

slots:
- slug: aasb-book
  context:
  - 'Core mechanism: all thought is landscape navigation, not procedure. Procedural
    thinking = cached paths. Prophets have less caching, see topology directly. Chapter
    4-5 material that explains why some people see patterns and can''t explain them
    in steps.'
- slug: neurodivergent-prophet-pattern
  context:
  - "Why prophets can't explain in steps: they have less caching, thinner insulation,\
    \ see the landscape topology directly. Not using different algorithm\u2014same\
    \ algorithm with more access, less stability. Communication gap explained."
- slug: aasb-attractor-loop-homunculus-dissolution
  context:
  - The attractor model IS the landscape model. Marbles rolling into valleys. Procedural
    thinking vs landscape thinking is about caching and insulation, not different
    mechanisms. Same probability landscape underneath.

The Challenge: Dual Process Theory

Fair pushback: The claim "it's all landscape" runs into dual process literature.

The Dual Process Distinction

System 1 (Fast thinking): Quick, effortless, associative, experience-based
System 2 (Slow thinking): Requires effort, uses cognitive resources, symbolic and abstract rule manipulation

The Key Challenge

From Sloman: The distinction between the two cannot be explained as a simple discrepancy between conscious and unconscious processes.

The difference: You have conscious awareness of the intermediate steps in slow thinking, but only the output of fast thinking.

This challenges "it's all probabilistic underneath": System 2 isn't just System 1 with post-hoc narration. You actually have access to intermediate steps in a way you don't with intuitive processing.

Current Best Theory

Type 1 processes: Bound together because they rely on embodied predictive processing
Type 2 processes: Form a unity because they're accomplished by symbolic classical cognition

The claim: BOTH exist—probabilistic processing AND symbolic processing—and they're implemented differently in the brain.

The Counterpoint

From AI research trying to integrate symbolic systems with LLMs:

"This simple example testifies the intrinsic difficulties of probabilistic fluency models to deal with mere facts. A promising way to address these problems is to integrate systems like chatGPT with symbolic systems. The dual-process theory of thought literature can provide human cognition-inspired solutions on how two distinct systems, one based on statistic (subsymbolic system) and the other on structured reasoning (symbolic), can interact."

The tension: They're trying to ADD symbolic systems to LLMs, suggesting pure probability isn't enough.

The question: But maybe the brain's "symbolic system" is also just cached probability paths that got deep enough to feel like rules?

The Honest Answer

We don't know.

The neuroscience hasn't resolved whether:

• System 2 is genuinely different substrate, or
• System 2 is System 1 in a particular configuration with working memory acting as scratchpad that makes it LOOK stepwise

A More Nuanced Version

Maybe the distinction isn't "landscape vs procedure" but:

System 1: Direct landscape navigation (marble rolls, you see where it ends)
System 2: Landscape navigation with working memory as checkpoint system

The "steps" you're aware of might be:

• Checkpoints that reshape the landscape as you go
• Explicit narration that constrains the path through probability space
• Not a different mechanism, but the same mechanism with external scaffolding

Working Memory as Scratchpad

Hypothesis: System 2 is System 1 + working memory buffer that:

• Holds intermediate states explicitly
• Allows conscious inspection of those states
• Constrains next step based on explicit state
• Makes it FEEL like symbolic processing

Analogy to LLMs: Chain-of-thought might work the same way:

• Not because LLMs are "learning to reason symbolically"
• But because verbalizing intermediate states constrains probability flow
• The explicit tokens in context window act like working memory checkpoints

The Evidence Problem

For "two different substrates":

• Conscious access to intermediate steps
• Feels qualitatively different
• Can explicitly manipulate symbols
• AI research suggests pure probability struggles with logic

For "same substrate, different mode":

• Brain damage doesn't cleanly separate systems
• Both systems show probabilistic effects
• "Symbolic" reasoning still affected by priming, framing, etc.
• LLMs can "reason" without explicit symbolic layer (just with longer context)

What This Means for the Book

Option 1: Claim certainty where there isn't any
→ Bad. Dismisses real literature. Sounds grandiose.

Option 2: Acknowledge the uncertainty
→ Good. Shows intellectual honesty. Presents both views.

The honest framing:

"We don't know if the brain implements two genuinely different systems or if System 2 is System 1 with working memory scaffolding. What we DO know: whether it's one system or two, the patterns that emerge—across psychology, physics, information theory, control theory—suggest they're constrained by the same underlying structure. The four premises still hold. The loop still operates. Whether you call it symbolic processing or constrained probabilistic flow, the same shape keeps appearing."

The Convergence Argument

Even if there are two systems, the fact that:

• Logic (System 2) and intuition (System 1) arrive at same answers
• Physics and psychology describe same patterns
• Control theory and information theory converge
• Ancient mystics and modern neuroscience use different words for same structure

Suggests: Whatever's underneath—whether one mechanism or two—is constrained by the same boundary conditions (embeddedness, causality, incompleteness, finitude).

The convergence isn't because everyone's using the same cognitive system. It's because everyone's embedded in the same reality, and that reality has a shape.

Where the Book Can Be Agnostic

What the book MUST claim:

• Four premises are uncontroversial
• The loop (PAUSE → FETCH → SPLICE → CONTINUE) is forced by those premises
• The same pattern appears across domains
• This convergence is validation (Yoneda-style)

What the book CAN'T claim with certainty:

• Exactly how the brain implements this
• Whether System 1 and System 2 are different substrates or different modes
• Whether "symbolic reasoning" is real or just looks that way from inside

The strength: Not claiming to solve neuroscience. Claiming to show the shape that any implementation must navigate, regardless of substrate.

The Prophet Angle Still Holds

Even with dual process theory:

Some people have:

• Less automatic System 1 caching (paths don't solidify)
• More active System 2 engagement (constant explicit checking)
• OR: thinner barrier between the systems (see more of System 1 directly)

Result: Same exhaustion, same pattern recognition, same communication gap.

Whether it's "thinner insulation" or "overactive System 2" or "underactive System 1 caching," the phenomenology is the same: constant recomputation, can't rest, see patterns everywhere.

For the Book

Chapter 4 or 5: Present this honestly.

"Cognitive science debates whether fast intuition and slow reasoning are genuinely different systems or the same system in different modes. We don't settle that debate here. What we show: whether it's one system or two, the patterns that emerge across domains suggest the same underlying constraints. The four premises don't care about implementation. They constrain the space of possible solutions."

Then: Acknowledge that prophets might be at the extreme of System 2 engagement (constant checking) or have unusual access to System 1 (see topology directly) or have different balance between the two.

The humility: We're not claiming to know which neuroscience model is right. We're claiming to know the shape that any model must explain.

The Discovery vs Verification Distinction

How Reasoning Models Actually Work

Chain-of-thought in LLMs doesn't work because the model is "reasoning." It works because each intermediate token shifts the probability distribution for what comes next.

The waypoints are forcing the model into different regions of activation space.

"Let me think step by step" doesn't invoke a reasoning module—it just makes certain tokens more likely, which makes other tokens more likely, which narrows toward answers that require multiple hops to reach.

The "reasoning" is: Generate a token that shifts your position in meaning-space, then generate from that new position. Repeat until you converge on something that satisfies the query.

Shape/Flow Mode Without Verbalization

Your shape/flow thinking might be the same thing without the verbalization.

You're watching regions of activation collide or align, but you're not forcing it through the bottleneck of language at each step. The probability narrowing is happening in visual-spatial substrate directly.

People who feel like they're doing procedural logic—carrying numbers, stepping through if-then chains—might just be experiencing the same process but with tighter coupling to verbal working memory. They narrate each waypoint, which makes it FEEL like steps, like procedure.

The Test Case: Mathematical Proof

Question: Does formal mathematical proof disprove this? When someone constructs a proof, they're not narrowing probabilities—they're building a structure where each step is guaranteed by the previous step. That's not "most likely"—that's "necessarily follows."

Answer: Proof construction is also probabilistic search (which direction feels promising?) with verification afterward (does this actually follow?).

The procedure is in the checking, not the discovery.

Poincaré's Testimony

Henri Poincaré wrote about this: He'd grind on a problem, get nowhere, give up, then the solution would arrive fully formed while he was stepping onto a bus.

The proof he wrote down afterward was clean, logical, step-by-step. But that's not how he found it.

He found it through some process he didn't have conscious access to, and then he verified it procedurally.

Hadamard's Survey (1940s)

Jacques Hadamard surveyed mathematicians about their creative process.

Most reported the same thing:

• Intuition
• Images
• Feelings of direction
• Then formalization after the fact

Einstein: Said he rarely thought in words at all.

The Actual Process

Procedural reasoning might be:

• Probabilistic search (below access, or with partial access if you're seeing shapes)
• Arrive somewhere that feels right
• Verify it holds by checking steps
• Write down the verification as if it were the reasoning

The proof isn't a record of how you thought. It's a cleaned-up trace that someone else can verify.

The procedure is for communication and checking, not for discovery.

Working Through a Problem

If somebody's not sitting down and writing through the entire proof:

They're working through it, then they get to a point, they have to solve a problem. They're working through probabilistic space, and then they're writing down where they get to, and then they keep going.

The written proof: Clean steps. Logical flow. "If A then B then C."

The actual discovery: Messy, intuitive, shape-matching, feeling around in probability space until something clicks.

The People Who Think They Reason Procedurally

They might just be the ones who:

• Narrate their waypoints more densely
• Have less direct access to the shape-matching layer
• Experience "if A then B then C" because they're verbalizing at each checkpoint

Not because there's actually a different algorithm running.

The Procedure Is Real

But it's in the verification, not the generation.

You generate (probabilistic, shape-based, intuitive). Then you verify (procedural, step-by-step, checkable). Then you communicate (write down the verification steps as if they were how you found it).

What This Means for System 1 vs System 2

Nuanced version:

• System 1: Probabilistic search, parallel activation, shape recognition → Discovery
• System 2: Working memory checkpoints, explicit verification, step-by-step checking → Verification and Communication

Not two different ways of thinking. Two different phases of the same process:

• Generate candidate solutions (System 1 dominant)
• Verify they hold (System 2 dominant)
• Communicate in verifiable form (System 2 format)

The Communication Format Trap

The trap: We teach math by showing the verification steps. Students think that's how you're supposed to think. They try to think procedurally because that's what the proof looks like.

The reality: Mathematicians discover intuitively and verify procedurally. The published proof is the verification format, not the discovery format.

Feynman complained about this: Physics textbooks make it look like physicists march logically from premise to conclusion. Actually they mess around with ideas until something works, then dress it up in logical clothing afterward.

For the Book

Chapter 4 or 5: Present this distinction explicitly.

"Mathematical proofs look procedural. That's because a proof is a verification artifact, not a discovery record. Poincaré found solutions on buses. Hadamard's mathematicians reported intuition and images, not steps. Einstein thought without words. The procedure came after—to check the solution and communicate it to others."

"The procedure is real. But it's for verification, not generation. You discover through shape-matching and probability narrowing. You verify through explicit steps. You communicate through cleaned-up procedures."

"The people who think they reason procedurally might just be narrating their waypoints more densely, experiencing the same probabilistic search but with verbal checkpointing at each stage."

The Honest Claim

We don't claim: System 2 doesn't exist or isn't useful.

We do claim: System 2's step-by-step feeling might be a format for verification and communication, not a different discovery mechanism.

The same landscape navigation is happening underneath. System 2 adds:

• Explicit checkpoints (working memory)
• Verification (does each step actually follow?)
• Communication (write it down so others can check)

But the generation—the actual finding of the solution—is still probabilistic shape-matching.

The Test You Can Run

Try to solve a novel problem:

• Do you discover the solution step-by-step, each step necessarily following from the last?
• Or do you mess around until something feels right, then check if it works?

Most honest answers: The latter. Then you might clean up the path afterward into something that looks logical.

That cleaning-up is real work. Verification matters. Communication matters. But it's not how you found the answer.