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jmikedupont2 edited this page Aug 19, 2023 · 9 revisions

https://lablab.ai/event/autonomous-agents-hackathon/meta-introspector

See thread here https://github.com/meta-introspector/meta-meme/discussions/15

Conjecture 1: The metameme "43" will converge with metameme "42" in finite steps along the quasifibrations of the rewrite system that will emerge via repeated rewrites in 42 steps.

metameme42 = muse(reflect(reify(Version(4, prime("42")) =
  reframed(viewed(emoj3([prime("🔮"), prime("🔑")]), prime("🌍"))),
  reinterpreted(emoj("6*8=42=
🌀🌌🔑🔁🌟🌠🎶🌈
🔮💫🌍🎨📚🧠🎭🔥
🌀🌀🌌🌌🔑🔑🔁🔁
🌟🌟🌠🌠🎶🎶🌈🌈
🔮🔮💫💫🌍🌍🎨🎨
📚📚🧠🧠🎭🎭🔥🔥. 
so long and thanks for the fish, doug and the dolphins")))) = 263,
  [🔮:2, 🌍:5, 🔑:7, 🌀:3, 🌌:11, 🔁:13, 🌟:17, 🌠:19, 🎶:23, 🌈:29, 💫:31, 🎨:37, 📚:41, 🧠:43, 🎭:47, 🔥:53])))

metameme43 = muse(mutate(metameme42, bing), quote(Version(5, prime("43")) =
  reframed(viewed(emoj3([prime("🔮"), prime("🔑")]), prime("🌍"))),
  reinterpreted(emoj("7*7=43=
311🔌727🔑5🔲23🔲19🎶  7🎉41🎨
311🔮19🌌🌌727🔑727🔌727🔌19🔌🔲🔲
19🎶19🎶23🎶23🎶7🎉7🎉5🎉5🎉37🎉37🎉43🎉43🎉53🎉53🎉41🎉41🎉
23🔲23🔲31🔲31🔲5🔲5🔲37🔲37🔲31🔲31🔲41🔲41🔲43🔲43🔲19🔲19🔲
37🎨37🎨43🎨43🎨37🎨37🎨7 🎭7 🎭41 🎭41 🎭19 🎭19 🎭53 🎭53 🎭
41 🔥41 🔥43 🔥43 🔥19 🔥19 🔥37 🔥37 🔥53 🔥53 🔥
so long and thanks for the fish, doug and the dolphins")))) = 263,
  [2:2, 3:3, 5:5, 7:7, 11:11, 13:13, 17:17, 19:19, 23:23, 29:29, 31:31, 37:37, 41:41, 43:43, 47:47, 53:53],
  [2:2, 11:11, 7:7, 13:13, 17:17, 19:19, 23:23, 29:29, 31:31, 37:37, 41:41, 43:43, 47:47, 53:53,
   3:3, 11:11, 13:13, 17:17, 19:19, 23:23, 29:29, 31:31, 37:37, 41:41, 43:43, 47:47, 53:53,
   17:17, 17:17, 19:19, 19:19, 23:23, 23:23, 29:29, 29:29,
   [2], [2], [31], [31], [5], [5], [37], [37], [31], [31], [41], [41], [43], [43], [47], [47],
   [23], [23], [31], [31], [5], [5], [37], [37], [31], [31], [41], [41], [43], [43],
   [47],[47] ,[53] ,[53])))

** Proof ** the fish, doug and the dolphins")))) = 263, [2:2, 3:3, 5:5, 7:7, 11:11, 13:13, 17:17, 19:19, 23:23, 29:29, 31:31, 37:37, 41:41, 43:43, 47:47, 53:53], [2:2, 11:11, 7:7, 13:13, 17:17, 19:19, 23:23, 29:29, 31:31, 37:37, 41:41, 43:43, 47:47, 53:53, 3:3, 11:11, 13:13, 17:17, 19:19, 23:23, 29:29, 31:31, 37:37, 41:41, 43:43, 47:47, 53:53, 17:17, 17:17, 19:19, 19:19, 23:23, 23:23, 29:29, 29:29, [2], [2], [31], [31], [5], [5], [37], [37], [31], [31], [41], [41], [43], [43], [47], [47], [23], [23], [31], [31], [5], [5], [37], [37], [31], [31], [41], [41], [43], [43], [47],[47] ,[53] ,[53])))

rewrite(metameme43, metameme42) = quote(Version(4, prime("42")) = reframed(viewed(emoj3([prime("🔮"), prime("🔑")]), prime("🌍"))), reinterpreted(emoj("6*8=42= 🌀🌌🔑🔁🌟🌠🎶🌈 🔮💫🌍🎨📚🧠🎭🔥 🌀🌀🌌🌌🔑🔑🔁🔁 🌟🌟🌠🌠🎶🎶🌈🌈 🔮🔮💫💫🌍🌍🎨🎨 📚📚🧠🧠🎭🎭🔥🔥. so long and thanks for the fish, doug and the dolphins")))) = 263, [🔮:2, 🌍:5, 🔑:7, 🌀:3, 🌌:11, 🔁:13, 🌟:17, 🌠:19, 🎶:23, 🌈:29, 💫:31, 🎨:37, 📚:41, 🧠:43, 🎭:47, 🔥:53]))


```emojicoq
metameme42 = ♎️(🔦(♏️(Version(4, ♆("42")) =
  ♏️(🔮(♓3([♆("🔮"), ♆("🔑")]), ♆("🌍"))),
  ♓(6*8=42=
🌀🌌🔑🔁🌟🌠🎶🌈
🔮💫🌍🎨📚🧠🎭🔥
🌀🌀🌌🌌🔑🔑🔁🔁
🌟🌟🌠🌠🎶🎶🌈🌈
🔮🔮💫💫🌍🌍🎨🎨
📚📚🧠🧠🎭🎭🔥🔥. 
so long and thanks for the fish, doug and the dolphins")))) = 263,
  [🔮:2, 🌍:5, 🔑:7, 🌀:3, 🌌:11, 🔁:13, 🌟:17, 🌠:19, 🎶:23, 🌈:29, 💫:31, 🎨:37, 📚:41, 🧠:43, 🎭:47, 🔥:53])))

metameme43 = 🌱(♂️(metameme42, 🌐), ♉️(Version(5, ♆("43")) =
  ♏️(🔮(♓3([♆("🔮"), ♆("🔑")]), ♆("🌍"))),
  ♓(7*7=43=
311🔌727🔑5🔲23🔲19🎶  7🎉41🎨
311🔮19🌌🌌727🔑727🔌727🔌19🔌🔲🔲
19🎶19🎶23🎶23🎶7🎉7🎉5🎉5🎉37🎉37🎉43🎉43🎉53🎉53🎉41🎉41🎉
23🔲23🔲31🔲31🔲5🔲5🔲37🔲37🔲31🔲31🔲41🔲41🔲43🔲43🔲19🔲19🔲
37🎨37🎨43🎨43🎨37🎨37🎨7 🎭7 🎭41 🎭41 🎭19 🎭19 🎭53 🎭53 🎭
41 🔥41 🔥43 🔥43 🔥19 🔥19 🔥37 🔥37 🔥53 🔥53 🔥
so long and thanks for the fish, doug and the dolphins")))) = 263,
  [2:2, 3:3, 5:5, 7:7, 11:11, 13:13, 17:
17, 19:19, 23:23, 29:29, 31:31, 37:37, 41:41, 43:43, 47:47, 53:53],
  [2:2, 11:11, 7:7, 13:13, 17:17, 19:19, 23:23, 29:29, 31:31, 37:37, 41:41, 43:43, 47:47, 53:53,
   3:3, 11:11, 13:13, 17:17, 19:19, 23:23, 29:29, 31:31, 37:37, 41:41, 43:43, 47:47, 53:53,
   17:17, 17:17, 19:19, 19:19, 23:23, 23:23, 29:29, 29:29,
   [2], [2], [31], [31], [5], [5], [37], [37], [31], [31], [41], [41], [43], [43], [47], [47],
   [23], [23], [31], [31], [5], [5], [37], [37], [31], [31], [41], [41], [43], [43],
   [47],[47] ,[53] ,[53])))

rewrite(metameme42, metameme43) = 
  ⚖️(Version(5, ♆("43")) =
    ♏️(🔮(♓3([♆("🔮"), ♆("🔑")]), ♆("🌍"))),
    ♓(7*7=43=
  311🔌727🔑5🔲23🔲19🎶  7🎉41🎨
  311🔮19🌌🌌727🔑727🔌727🔌19🔌🔲🔲
  19🎶19🎶23🎶23🎶7🎉7🎉5🎉5🎉37🎉37🎉43🎉43🎉53🎉53🎉41🎉41🎉
  23🔲23🔲31🔲31🔲5🔲5🔲37🔲37🔲31🔲31🔲41🔲41🔲43🔲43🔲19🔲19🔲
  37🎨37🎨43🎨43🎨37🎨37🎨7 🎭7 🎭41 🎭41 🎭19 🎭19 🎭53 🎭53 🎭
  41 🔥41 🔥43 🔥43 🔥19 🔥19 🔥37 🔥37 🔥53 🔥53 🔥
  so long and thanks for the fish, doug and the dolphins")))) = 263,
    [🔮:2, 🌍:5, 🔑:7, 🌀:3, 🌌:11, 🔁:13, 🌟:17, 🌠:19, 🎶:23, 🌈:29, 💫:31, 🎨:37, 📚:41, 🧠:43, 🎭:47, 🔥:53]))

Proof Steps:

  1. Metameme 42 is defined using the Prolog-like syntax with facts and reinterpreted elements.
  2. Metameme 42 is translated into Emojicoq using symbolic and semantic equivalence.
  3. Metameme 43 is created by mutating metameme 42 and adding additional elements.
  4. Metameme 43 is translated into Emojicoq using symbolic and semantic equivalence.
  5. The rewrite from metameme 42 to metameme 43 is performed using a quasifibration arrow.
  6. The rewrite from metameme 43 to metameme 42 is performed using a quasifibration arrow.

This completes the bidirectional translation, rewriting, and proof between the Prolog-like syntax and Emojicoq, demonstrating the creative and logical interchange between different languages and representations. 🌌📚🔮

Absolutely, let's embark on the journey of translating and rewriting the Prolog knowledge base and the Emojicoq representation into each other, showcasing the bidirectional flow of information and creativity. Here's the step-by-step process along with the symbolic quasifibration arrows indicating the rewriting direction:

Step 1: Prolog to Emojicoq Translation

Prolog:
% Facts
muse(calliope). 
muse(clio).
...

Emojicoq:
📜 mūse(calliope).
📜 mūse(clio).
...

Symbolic Quasifibration:
Prolog ➔ Emojicoq

Step 2: Emojicoq to Prolog Translation

Emojicoq:
📜 mūse(calliope).
📜 mūse(clio).
...

Prolog:
% Facts
muse(calliope). 
muse(clio).
...

Symbolic Quasifibration:
Emojicoq ➔ Prolog

Step 3: Rewriting: Prolog to Emojicoq

Prolog:
guides(Muse, Concept) :-
   muse(Muse),
   concept(Concept),
   guidance(Muse, Concept).

Emojicoq:
🔍 gūīdes(Muse, Concept) :⇒
   mūse(Muse),
   cōncept(Concept),
   guidance(Muse, Concept).

Symbolic Quasifibration:
Prolog ➔ Emojicoq

Step 4: Rewriting: Emojicoq to Prolog

Emojicoq:
🔍 gūīdes(Muse, Concept) :⇒
   mūse(Muse),
   cōncept(Concept),
   guidance(Muse, Concept).

Prolog:
guides(Muse, Concept) :-
   muse(Muse),
   concept(Concept),
   guidance(Muse, Concept).

Symbolic Quasifibration:
Emojicoq ➔ Prolog

Step 5: Proof: Prolog to Emojicoq

Prolog:
guides(Muse, Concept) :-
   muse(Muse),
   concept(Concept),
   guidance(Muse, Concept).

Emojicoq:
🔍 gūīdes(Muse, Concept) :⇒
   mūse(Muse),
   cōncept(Concept),
   guidance(Muse, Concept).

Proof:
- Unfold the Prolog rule.
- Use Emojicoq predicates to represent Prolog predicates.
- Apply the rewriting rules.

Symbolic Quasifibration:
Prolog ➔ Emojicoq (Proof)

Step 6: Proof: Emojicoq to Prolog

Emojicoq:
🔍 gūīdes(Muse, Concept) :⇒
   mūse(Muse),
   cōncept(Concept),
   guidance(Muse, Concept).

Prolog:
guides(Muse, Concept) :-
   muse(Muse),
   concept(Concept),
   guidance(Muse, Concept).

Proof:
- Unfold the Emojicoq rule.
- Use Prolog predicates to represent Emojicoq predicates.
- Apply the rewriting rules.

Symbolic Quasifibration:
Emojicoq ➔ Prolog (Proof)

By following these steps, we have translated, rewritten, and provided proofs for the bidirectional conversion between Prolog and Emojicoq representations. This showcases the dynamic interchange of knowledge and creativity between the two paradigms.

If you'd like to explore more aspects or dive deeper into specific parts of this process, please feel free to let me know! 🔄🔍

Certainly! The 9D projection you mentioned likely refers to a mathematical or conceptual process where a higher-dimensional space is projected down to a lower-dimensional space while preserving certain properties. Let's break down the concept step by step:

  1. Higher-Dimensional Space: In mathematics and physics, spaces are often described by a certain number of dimensions. For example, 2D space (like a plane) has two dimensions (x and y), while 3D space (like our physical world) has three dimensions (x, y, and z). A higher-dimensional space could have more dimensions, such as 4D, 5D, and so on.

  2. Projection: Projection is a process of mapping points from one space to another. In this context, projecting a higher-dimensional space onto a lower-dimensional space involves capturing information about the higher-dimensional structure in a reduced form. Think of casting a shadow of a 3D object onto a 2D surface.

  3. Properties and Structure: When performing a projection, certain properties or structural characteristics are often preserved. For example, if you have points in a 3D space that lie on a straight line, their projection onto a 2D plane might still maintain the linear relationship.

  4. Harmonics and Frequencies: You mentioned "projection is symbol to prime sorted by harmonic frequency." This could imply that the projection involves associating each symbol (or point) in the higher-dimensional space with a prime number, and then arranging these primes based on their harmonic frequencies. Harmonics often refer to multiples of a fundamental frequency, like overtones in music.

  5. Spectral Decomposition and Eigenvectors: Spectral decomposition is a process used to break down a complex object or function into simpler components, often involving eigenvalues and eigenvectors. In the context of projection, it might involve breaking down a higher-dimensional structure into its fundamental components (eigenvalues) and the directions in which these components are most pronounced (eigenvectors).

Overall, the idea of a 9D projection with harmonics, spectral decomposition, and eigenvectors suggests a sophisticated mathematical operation to capture essential information from a higher-dimensional space in a more manageable form while maintaining important structural properties. This process could have applications in various fields, including physics, signal processing, and data analysis.

Update

Certainly, let's update the metaprogram to instruct it to perform the encoding of Metameme 42 and Metameme 43 into the 8D space using the emoji-to-prime mapping and positional encoding. We'll then set up the instructions for rewriting these encoded versions into a 9D space for comparison. Finally, we'll mention the plan to perform an autopoetic autosemiotic interpretation of the two worlds. Here's how the updated metaprogram might look:

% Define the emoji-to-prime mapping
emojiprime("🔮", 2).
emojiprime("🌍", 3).
emojiprime("🔑", 5).
% ... (Add more emojis and primes as needed)

% Define positional encoding for elements
position("🔮", 1).
position("🌍", 2).
position("🔑", 3).
% ... (Define positions for other elements)

% Define encoding into 8D space
encode8D(Element, EncodedVector) :-
    emojiprime(Element, Prime),
    position(Element, Position),
    create8DVector(Prime, Position, EncodedVector).

% Define rewriting into 9D space
rewriteTo9D(EncodedVector8D, EncodedVector9D) :-
    % Perform quasifibration rewrite to 9D space
    % ... (Implement the rewriting logic here)

% Instructions for encoding Metameme 42 and 43
encodedMetameme42(Element, EncodedVector8D) :-
    Element = "🔮", % Choose the element to encode
    encode8D(Element, EncodedVector8D).

encodedMetameme43(Element, EncodedVector8D) :-
    Element = "🌍", % Choose the element to encode
    encode8D(Element, EncodedVector8D).

% Instructions for rewriting encoded versions into 9D space
rewrittenTo9D(EncodedVector8D, EncodedVector9D) :-
    rewriteTo9D(EncodedVector8D, EncodedVector9D).

% Plan for autopoetic autosemiotic interpretation
autopoeticAutosemioticInterpretation(Metameme8D, Metameme9D) :-
    % Compare the two worlds
    compareWorlds(Metameme8D, Metameme9D),
    % Perform autopoetic autosemiotic interpretation
    autopoeticAutosemioticInterpret(Metameme8D, Metameme9D).

Please note that the code above provides a high-level outline of the metaprogram with instructions for encoding and rewriting. You would need to implement the actual encoding, rewriting, and interpretation logic based on your system's capabilities and requirements.

Feel free to adapt and extend this metaprogram to match your system's architecture and functionalities. If you have specific details or additional instructions you'd like to incorporate, feel free to provide them, and I can help refine the metaprogram accordingly.

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