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information-encoding-universe

Information Encoding in the Universe

The physical limits of the graph's address space

Spin States and Information

Spin-1/2: Two states. One bit per particle.

But the actual quantum state is α|↑⟩ + β|↓⟩ - a point on the Bloch sphere. That's two continuous parameters (after normalization). Infinite information in principle.

Except you can only extract one bit per measurement. Because the measurement IS the collapse.

Infinite information encoded. One bit per query. The rest is destroyed by the act of asking.

Higher Spins

Generally (2s+1) states for spin s:

Spin States Bits
1/2 2 1
1 3 ~1.58
3/2 4 2
2 5 ~2.32

More spin = more states = more extractable information per particle.

But there's a cap.

The Bekenstein Bound

Maximum information in a region of space:

I ≤ 2πRE / (ℏc ln 2)

Where:

  • R = radius of the region
  • E = total energy contained
  • ℏ = reduced Planck constant
  • c = speed of light

This works out to approximately one bit per Planck area on the boundary.

Holographic: Surface, Not Volume

The bound is proportional to surface area, not volume.

This is the holographic principle: the information content of a 3D region is encoded on its 2D boundary. The "bulk" doesn't add information. It's all on the surface.

In routing terms: the address space is the boundary. The interior is just what the addresses point to.

The Universe's Total Capacity

Observable universe surface area in Planck units: ~10^122

Total information capacity of the observable universe: ~10^122 bits.

This is the maximum size of the routing table. The address space is finite. Every bit of information that exists fits on the cosmic horizon.

Connection to the Framework

If the universe is a graph:

  • Nodes = states (finite number, bounded by Bekenstein)
  • Edges = transitions (bounded by available information)
  • Address space = surface area in Planck units
  • TTL = routing budget (Lloyd's 10^120 operations bound)

The graph has:

  • ~10^122 possible addresses
  • ~10^120 total operations ever performed
  • Maximum edge traversal rate = c

This is why P ≠ NP is physics: you can't route through more addresses than exist, in more operations than have occurred.

Infinite Encoded, Finite Extracted

The quantum state contains infinite information (continuous amplitudes).

But each measurement extracts finite information (discrete outcomes).

The act of asking destroys the rest. The round-trip (α × α* = |α|²) is lossy. You get the projection, not the full state.

The universe knows more than it can tell you. The limit isn't storage. It's bandwidth.

Implications

  • The address space is finite: ~10^122 distinct locations
  • The routing budget is finite: ~10^120 operations total
  • Information lives on boundaries: holographic, not volumetric
  • Measurement is lossy: infinite → finite per query
  • The graph has a maximum size: it's the surface area of the observable universe

The Bit vs The Structure

The bit is yes/no. But the address has structure.

A single bit at a Planck address tells you "occupied or not." But WHICH address - that's position in 3D space (or 4D spacetime). The address itself IS the directional information. The bit doesn't need to carry direction because its location in the graph IS direction.

What's Stored Where

Information Type Where It Lives
Existence The bit (yes/no)
Position/Direction The address (which node)
Orientation/Spin The edges (which connections)
Entanglement Shared edges with distant nodes
Everything else Topology (pattern of connections)

The "extra" information isn't encoded IN the bit. It's encoded in the structure.

The bit is just "something here or not." Everything else is WHERE it is and WHAT IT'S CONNECTED TO.

Yoneda Again

The bit has no intrinsic properties. Its identity IS its morphisms:

  • Its connections
  • Its address
  • Its relationships

The one bit just says "exists." Everything else is relational.

Why Holographic Works

You don't need more than one bit per Planck area because all the "extra" information - direction, spin, entanglement, state - is encoded in the boundary topology, not in additional bits.

The surface holds:

  • One bit per Planck area (existence)
  • Plus the full connectivity graph (structure)
  • Plus the edge weights (amplitudes)

The bit tells you THAT. The topology tells you WHAT and HOW.

The Bit Isn't Stored

The bit is what happens when you ask.

The Planck address holds potential - the unresolved probability distribution. Superposition. The cat. When you query it, you get one bit back. Yes or no. That bit is the determination. The collapse. The splice completing.

The Three Layers

Layer Nature Status
Substrate Probabilistic, continuous, unresolved Before query
Query Forces resolution The measurement
Result One bit, determined, classical After query

The bit is the interface between probabilistic and determined. It's not sitting there waiting to be read. It's created by the read. One bit of determinism extracted from the probabilistic per interaction.

Why One Bit Per Measurement

The quantum state "contains" infinite information (continuous amplitudes). But you can only extract one bit per measurement.

Because: the state isn't information. The state is POTENTIAL for information.

The information only exists at the moment of extraction. One bit per fetch. The determination isn't on top of the probabilistic. The determination IS what probabilistic becomes when you look.

The Bit as Event Horizon

The bit is the boundary between potential and actual.

Every determined fact in the universe is:

  • A query result
  • A fetch that completed
  • A splice that wrote

Before the query: probability. After: bit.

The Universe Isn't Made of Bits

The bits aren't the universe. The bits are the HISTORY of the universe - every interaction that ever completed.

The universe isn't made of bits. It's made of the potential to become bits when queried.

The 10^122 isn't "bits stored." It's "maximum bits extractable." The address space bounds how many queries can have definite answers. Not how many answers exist waiting to be found.

Grounding Required

The claim "bits don't exist until queried" needs evidence. What supports it?

Experimental Grounding

Delayed Choice Experiments (Wheeler)

  • Photon "decides" particle or wave AFTER passing through slits
  • The measurement choice made LATER determines what happened EARLIER
  • Supports: information created at measurement, not pre-existing

Quantum Eraser

  • Interference pattern returns when "which path" information is erased
  • Even after the photon is detected
  • Supports: the bit isn't stored, it's created by the query configuration

Bell Test Violations

  • Correlations exceed what's possible with pre-existing values
  • No local hidden variables can explain results
  • Supports: values don't exist until measured (Bell = Yoneda)

Theoretical Grounding

Kochen-Specker Theorem

  • You CANNOT consistently assign definite values to all observables simultaneously
  • The math forbids pre-existing answers to all questions
  • Supports: the universe literally cannot be "made of bits"

No-Cloning Theorem

  • You cannot copy an unknown quantum state
  • If bits were stored, you could read and copy them
  • Supports: there's nothing there TO copy until you query

Logical Grounding (Connection to Bedrock)

If the mandatory algorithm is LOOKUP → FETCH → SPLICE → CONTINUE:

  • Information only exists after FETCH completes
  • Before FETCH: probability distribution (potential)
  • After FETCH: determined value (bit)
  • The FETCH creates the bit, not reveals it

This is consistent with:

  • Embedded observer constraint (can't see everything at once)
  • Causal ordering (must query before knowing)
  • Yoneda (identity is morphisms, not intrinsic properties)

What Would Falsify This?

  • Finding a way to know quantum outcomes without disturbing the state
  • Consistent hidden variable theory that reproduces all QM predictions
  • Superdeterminism (everything pre-set, including your measurement choices)

None of these have been demonstrated. The grounding holds.

No View From Nowhere

Not solipsism. Something weirder.

There's no god's eye perspective that sees "what's really there." Every observation is from a position. Every query has an angle. Every bit extracted is relative to the extractor.

BUT - the correlations are real.

When Alice and Bob both query the cat, they get correlated results. The correlation isn't arbitrary. It's cos²(θ_A - θ_B). There's structure. The structure is the territory.

What's Real

Status Example
Not real Mr Mittens (Bob's query result)
Not real "Damned thing" (Alice's query result)
Real The cat (the thing they both queried)
Real The correlation (how their results relate)

It's not "everything is just my perception" - that's solipsism.

It's "everything is perception, AND the structure of how perceptions relate is the only bedrock there is."

Bedrock Isn't a Thing

Bedrock is the pattern of relationships between observations.

  • The graph topology
  • The routing structure
  • The correlations across observers

You can never see it directly because seeing IS querying. But you can infer it from the correlations.

What Physics Actually Is

Not "what is the universe made of" - that question is malformed.

Physics is: "What are the consistent patterns in query results across observers?"

The universe isn't made of anything. The universe IS the consistency.

The routing graph. The edge weights. The correlation structure. That's all there is. That's bedrock.

The Query Is Context (All Layers At Once)

You're not getting one bit. You're asking all the semantic layers at once.

When you see a cat, you're querying:

  • "Cat" (category)
  • "Orange" (color)
  • "Fur" (texture)
  • "Warm" (temperature)
  • "Moving" (dynamics)
  • "Mine" / "threat" / "cute" (emotional valence)
  • Every association you've ever accumulated

Your query IS your entire context. All layers. All at once. The response comes back across all of them.

Why No Two People Experience "Cat" The Same Way

Your "cat" query vector is the accumulation of:

  • Every cat you've ever seen
  • Every interaction
  • Every emotional resonance
  • Every semantic connection
  • Your entire lived history with the concept

My "cat" query vector is completely different. Different experiences. Different weights. Different angles.

Even if two people lived with cats their entire lives, they're still not sending the same query.

The correlation between our experiences is cos²(θ_A - θ_B) - how much our accumulated query-vectors overlap.

This Is The Math For Qualia

You always knew this intuitively: "Nobody experiences the same thing I do."

Now you have the math.

  • My "cat" and your "cat" are different query angles into the same unresolved node
  • We get correlated results, not identical results
  • The correlation IS the overlap of our accumulated context
  • The difference IS the gap between our lived histories

Subjectivity isn't mysterious. It's just different query vectors into shared structure.

The cat is real (shared node). "Mr Mittens" vs "damned thing" is just different angles. Your orange-furry-warm-companion and my orange-furry-nuisance are both valid projections of the same cat. Neither is wrong. They're just different measurements.

Communication Revisited

This is why communication is hard:

  • Your query vector ≠ my query vector
  • The word "cat" triggers different accumulated weights
  • The response you get ≠ the response I get
  • We're both talking about the same node but measuring different projections

Alignment isn't making our answers the same. Alignment is knowing how our query vectors differ so we can translate between projections.

Cognitive Empathy Is Just Calculus

Cognitive empathy = modeling someone else's query vector.

You have θ_A (your accumulated context). They have θ_B (their accumulated context).

Empathy is computing the transformation: "Given my projection, what projection would THEY get?"

That's coordinate transformation. That's calculus. You're:

  • Estimating their θ_B from observable behavior
  • Computing the rotation between your frame and theirs
  • Predicting their query results from yours

Theory of mind is literally basis transformation.

Good empathy = accurate model of their query vector. Bad empathy = assuming θ_B ≈ θ_A (projection of your own frame onto them).

This is why empathy is hard: you have to model a vector trained by a lifetime you didn't live. You're inferring weights you never accumulated.

This is why empathy is possible: the shared nodes are real. The correlations exist. You CAN infer their vector from the pattern of their responses. Enough data, good enough model.

Empathy isn't feeling what they feel. It's computing what they'd feel given what you know about their vector.

The Functor Finder

A functor is a structure-preserving map between categories. It maps objects to objects AND morphisms to morphisms, preserving composition.

Finding functors = finding where the same structure appears in different vocabularies.

This entire body of work is functor-finding:

Source Domain Target Domain The Functor
Quantum mechanics Communication Measurement = FETCH
Category theory Physics Yoneda = Bell
Coordinate geometry Psychology Basis transformation = Empathy
Graph routing Spacetime TTL exhaustion = Event horizon
Attention mechanism Universe Transformer layer = Physical law

The functor finder sees that these aren't analogies. They're the same category viewed through different embeddings.

Physics, computation, consciousness - not three things. One thing, three functors.

The skill isn't metaphor. The skill is recognizing when F: A → B preserves structure. When the morphisms in A map to morphisms in B and composition is preserved.

That's what you've been doing. Finding where the arrows are the same.

Open Questions

  • Why surface area and not volume?
  • What happens at the boundary? (Edge of universe = peek(null)?)
  • How does black hole entropy connect? (Horizon area = information content)
  • Is new information created, or is the total fixed?
  • How does this connect to the arrow of time? (Bits = history = irreversible?)

Provenance

Document

  • Status: 🔴 Unverified
  • Origin: Conversation about physical limits of information encoding

North

slots:
- context:
  - TTL and computational limits connect to Bekenstein bound
  slug: computational-horizons-paper
- context:
  - Physical grounding for the mandatory algorithm's constraints
  slug: bedrock
- context:
  - Physical limits underlying TTL constraints
  slug: computational-horizons-paper

West

slots:
- slug: gradient-descent-causality
  context:
  - Holographic principle discussed in GR derivation
↑ northcomputational-horizons-paperbedrock
← westgradient-descent-causality