Critical feedback especially welcome as we explore whether this perspective might help resolve one of physics' deepest puzzles! /fin
November 14, 2024 at 1:29 AM
Critical feedback especially welcome as we explore whether this perspective might help resolve one of physics' deepest puzzles! /fin
Draft pre-print exploring these ideas:
Paper 📝:[https://github.com/aporeticaxis/CDR/blob/main/CDR_draft_nov11.pdf]
🎤 NotebookLM: [https://notebooklm.google.com/notebook/956b98f6-d8ff-4efd-a2a3-b0be9d40c95f/audio]
Paper 📝:[https://github.com/aporeticaxis/CDR/blob/main/CDR_draft_nov11.pdf]
🎤 NotebookLM: [https://notebooklm.google.com/notebook/956b98f6-d8ff-4efd-a2a3-b0be9d40c95f/audio]
November 14, 2024 at 1:29 AM
Draft pre-print exploring these ideas:
Paper 📝:[https://github.com/aporeticaxis/CDR/blob/main/CDR_draft_nov11.pdf]
🎤 NotebookLM: [https://notebooklm.google.com/notebook/956b98f6-d8ff-4efd-a2a3-b0be9d40c95f/audio]
Paper 📝:[https://github.com/aporeticaxis/CDR/blob/main/CDR_draft_nov11.pdf]
🎤 NotebookLM: [https://notebooklm.google.com/notebook/956b98f6-d8ff-4efd-a2a3-b0be9d40c95f/audio]
Much work remains - this is very much a draft exploring these ideas. But by thinking in terms of difference-relations rather than discrete/continuous, we might find new ways to approach these deep puzzles.
November 14, 2024 at 1:29 AM
Much work remains - this is very much a draft exploring these ideas. But by thinking in terms of difference-relations rather than discrete/continuous, we might find new ways to approach these deep puzzles.
Again, our aim wasn't mere philosophical wordplay, but rather a rigorous mathematical framework that makes testable predictions while illuminating why reality has the character it does.
November 14, 2024 at 1:29 AM
Again, our aim wasn't mere philosophical wordplay, but rather a rigorous mathematical framework that makes testable predictions while illuminating why reality has the character it does.
CDR points to pattern-formation as fundamental: not patterns OF something, but pattern-forming as the primary activity of reality.
November 14, 2024 at 1:29 AM
CDR points to pattern-formation as fundamental: not patterns OF something, but pattern-forming as the primary activity of reality.
Setting aside the technicalities for a second - CDR suggests something profound: the interplay of difference and relation shapes the very possibility of existence, understanding, and measurement itself.
November 14, 2024 at 1:29 AM
Setting aside the technicalities for a second - CDR suggests something profound: the interplay of difference and relation shapes the very possibility of existence, understanding, and measurement itself.
This connects to deep ideas in:
- Process philosophy (Whitehead)
- Category theory (Eilenberg-Mac Lane)
- Information theory (Bateson)
...but attempts synthesizing them into a novel mathematical framework.
- Process philosophy (Whitehead)
- Category theory (Eilenberg-Mac Lane)
- Information theory (Bateson)
...but attempts synthesizing them into a novel mathematical framework.
November 14, 2024 at 1:29 AM
This connects to deep ideas in:
- Process philosophy (Whitehead)
- Category theory (Eilenberg-Mac Lane)
- Information theory (Bateson)
...but attempts synthesizing them into a novel mathematical framework.
- Process philosophy (Whitehead)
- Category theory (Eilenberg-Mac Lane)
- Information theory (Bateson)
...but attempts synthesizing them into a novel mathematical framework.
[Importantly] This is a mathematical framework attempting to understand these patterns, /not/ a claim about ultimate reality. It's one possible way to understand how these seemingly contradictory aspects might coherently coexist
November 14, 2024 at 1:29 AM
[Importantly] This is a mathematical framework attempting to understand these patterns, /not/ a claim about ultimate reality. It's one possible way to understand how these seemingly contradictory aspects might coherently coexist
This has (potentially) profound implications for how we think about:
- Information as "differences that make a difference"
- Emergence as pattern-formation
- Observation as participating in reality's self-distinction
- Information as "differences that make a difference"
- Emergence as pattern-formation
- Observation as participating in reality's self-distinction
November 14, 2024 at 1:29 AM
This has (potentially) profound implications for how we think about:
- Information as "differences that make a difference"
- Emergence as pattern-formation
- Observation as participating in reality's self-distinction
- Information as "differences that make a difference"
- Emergence as pattern-formation
- Observation as participating in reality's self-distinction
One striking example:
A quantum measurement isn't a mysterious "collapse" from continuous to discrete. In CDR, instead it's viewed as a natural interplay of difference-making (measurement) and relation-forming (entanglement) processes.
A quantum measurement isn't a mysterious "collapse" from continuous to discrete. In CDR, instead it's viewed as a natural interplay of difference-making (measurement) and relation-forming (entanglement) processes.
November 14, 2024 at 1:29 AM
One striking example:
A quantum measurement isn't a mysterious "collapse" from continuous to discrete. In CDR, instead it's viewed as a natural interplay of difference-making (measurement) and relation-forming (entanglement) processes.
A quantum measurement isn't a mysterious "collapse" from continuous to discrete. In CDR, instead it's viewed as a natural interplay of difference-making (measurement) and relation-forming (entanglement) processes.
One surprising insight from the categorical cohomology: emergent classical properties correspond to non-trivial cohomology classes in CDR. This gives us a new way to understand why some quantum properties persist while others vanish.
November 14, 2024 at 1:29 AM
One surprising insight from the categorical cohomology: emergent classical properties correspond to non-trivial cohomology classes in CDR. This gives us a new way to understand why some quantum properties persist while others vanish.
The framework's power comes from its colimit construction: quantum behavior "flows" into classical behavior through decoherence. We model this via a functor D: CDR → Class that tracks how quantum systems become classical.
November 14, 2024 at 1:29 AM
The framework's power comes from its colimit construction: quantum behavior "flows" into classical behavior through decoherence. We model this via a functor D: CDR → Class that tracks how quantum systems become classical.
The mathematical architecture predicts specific behaviors: when a quantum system S interacts with environment E, the colimit colim(D(S ⊗ E)) recovers classical phase space - with experimentally testable consequences for decoherence rates.
November 14, 2024 at 1:29 AM
The mathematical architecture predicts specific behaviors: when a quantum system S interacts with environment E, the colimit colim(D(S ⊗ E)) recovers classical phase space - with experimentally testable consequences for decoherence rates.
The mathematical architecture predicts specific behaviors: when a quantum system S interacts with environment E, the colimit colim(D(S ⊗ E)) recovers classical phase space - with experimentally testable consequences for decoherence rates.
November 14, 2024 at 1:29 AM
The mathematical architecture predicts specific behaviors: when a quantum system S interacts with environment E, the colimit colim(D(S ⊗ E)) recovers classical phase space - with experimentally testable consequences for decoherence rates.
Excitingly, we propose specific experiments sketches for testability/falsifiability. One key prediction: when quantum systems interact with their environment, the emergence of classical behavior should follow a precise mathematical pattern we can test in labs.
November 14, 2024 at 1:29 AM
Excitingly, we propose specific experiments sketches for testability/falsifiability. One key prediction: when quantum systems interact with their environment, the emergence of classical behavior should follow a precise mathematical pattern we can test in labs.
The math reveals this deep structure:
- Quantum mechanics: entanglement shows relation without separation
- Category theory: focuses on morphisms between objects
- Topology: studies preserved relations under transformation
- Quantum mechanics: entanglement shows relation without separation
- Category theory: focuses on morphisms between objects
- Topology: studies preserved relations under transformation
November 14, 2024 at 1:29 AM
The math reveals this deep structure:
- Quantum mechanics: entanglement shows relation without separation
- Category theory: focuses on morphisms between objects
- Topology: studies preserved relations under transformation
- Quantum mechanics: entanglement shows relation without separation
- Category theory: focuses on morphisms between objects
- Topology: studies preserved relations under transformation
If this perspective holds water, it offers precise mathematical tools for:
- Quantum computing error correction
- Complex systems analysis
- Quantum field theory (QFT)
...each grounded in the same underlying patterns.
- Quantum computing error correction
- Complex systems analysis
- Quantum field theory (QFT)
...each grounded in the same underlying patterns.
November 14, 2024 at 1:29 AM
If this perspective holds water, it offers precise mathematical tools for:
- Quantum computing error correction
- Complex systems analysis
- Quantum field theory (QFT)
...each grounded in the same underlying patterns.
- Quantum computing error correction
- Complex systems analysis
- Quantum field theory (QFT)
...each grounded in the same underlying patterns.
Consider understanding itself: we experience both discrete "aha" moments AND (a perceived) continuous flows of potential connections. But crucially - neither emerges from the other. They're two aspects of a single pattern-forming dynamic that might reflect deeper principles.
November 14, 2024 at 1:29 AM
Consider understanding itself: we experience both discrete "aha" moments AND (a perceived) continuous flows of potential connections. But crucially - neither emerges from the other. They're two aspects of a single pattern-forming dynamic that might reflect deeper principles.
These patterns of difference and relation appear everywhere - from quantum mechanics to cognitive science, suggesting something fundamental about how reality organizes itself.
November 14, 2024 at 1:29 AM
These patterns of difference and relation appear everywhere - from quantum mechanics to cognitive science, suggesting something fundamental about how reality organizes itself.
CDR captures this mathematically through:
- Difference morphisms (δ): Create distinctions
- Relation morphisms (r): Form connections
...each implying and requiring the other in a precise categorical framework.
- Difference morphisms (δ): Create distinctions
- Relation morphisms (r): Form connections
...each implying and requiring the other in a precise categorical framework.
November 14, 2024 at 1:29 AM
CDR captures this mathematically through:
- Difference morphisms (δ): Create distinctions
- Relation morphisms (r): Form connections
...each implying and requiring the other in a precise categorical framework.
- Difference morphisms (δ): Create distinctions
- Relation morphisms (r): Form connections
...each implying and requiring the other in a precise categorical framework.
Every difference implies a relation (to be different from) and every relation implies differences (to be related to). This isn't mere philosophical wordplay - it points to something fundamental about how reality structures itself.
November 14, 2024 at 1:29 AM
Every difference implies a relation (to be different from) and every relation implies differences (to be related to). This isn't mere philosophical wordplay - it points to something fundamental about how reality structures itself.
Enter the Category of Difference-Relation (CDR), framework suggests reality manifests through patterns of difference and relation - not as separate "discrete" and "continuous" aspects, but as two faces of a single pattern-forming dynamic.
November 14, 2024 at 1:29 AM
Enter the Category of Difference-Relation (CDR), framework suggests reality manifests through patterns of difference and relation - not as separate "discrete" and "continuous" aspects, but as two faces of a single pattern-forming dynamic.
While approaches like loop quantum gravity suggest fundamental discreteness and quantum field theory (QFT) relies on continuous fields, each perspective faces its own challenges. The interplay between discrete and continuous aspects remains mysterious.
November 14, 2024 at 1:29 AM
While approaches like loop quantum gravity suggest fundamental discreteness and quantum field theory (QFT) relies on continuous fields, each perspective faces its own challenges. The interplay between discrete and continuous aspects remains mysterious.