Symmetry and Continuity in Physics and Epistemology

From: jimruttshow8596

The Incommensuration Theorem (ICT), developed by Forrest Landry, is a theorem arising from his immanent metaphysics [00:00:48]. It fundamentally describes the relationship between symmetry and continuity, two concepts prevalent in mathematics and physics [00:02:16].

Defining Key Concepts

Symmetry

Symmetry, in the context of Landry’s work, refers to a type of constancy [00:02:25].

• Examples:
  • A geometric shape appearing the same when flipped [00:02:28].
  • The law of conservation of matter where the amount of matter remains constant over time [00:02:40].

Continuity

Continuity is primarily concerned with connectedness [00:02:59]. It implies the ability to move from one place to another through infinitesimally small steps without encountering hard edges or boundaries [00:03:04]. This is akin to the concept of a continuous function in mathematics [00:03:26].

Domain

A “domain” in this context is distinct from a mathematical set. While a set can be thought of as a “bag with things in it” where elements are abstract points [00:04:09], a domain includes a third notion: relationship [00:04:55].

• A set describes the content and context, but a domain explicitly incorporates the relationships between the elements and the relationship between the elements and the container itself [00:05:15].
• Domains can be understood as abstract containers for concepts (e.g., the “universe” as a domain contains the concepts of matter and energy) [00:06:17].
• A key aspect of Landry’s definition is that domains cannot be included in other domains [00:07:11]. If a broader category (like “computer languages”) contains specific domains (like “C++”), the specific domains are treated as elements or identities within the larger domain, not as enclosed domains themselves [00:14:38]. This avoids confusion with meta-universes or nested structures [00:08:57].

Core Concepts of a Domain

For understanding the universe as a domain, Landry posits three necessary and sufficient concepts: creation, existence, and interaction [00:16:15].

• Creation: Relates to the origin, like the Big Bang in physics [00:19:25].
• Existence: Refers to material things and their properties, like matter [00:18:52].
• Interaction: Pertains to forces and relationships between existing things [00:18:55]. Understanding these three concepts would allow one to know everything knowable about the domain of the universe [00:20:46]. This approach shifts the definition of a domain from being exclusively about its content (elements) to being a concept defined by other concepts [00:21:28].

The Role of Comparison/Measurement

The core of epistemic process (how we come to know something) is comparison [00:31:34]. Any act of knowing, observation, or measurement is a form of comparison [00:31:31].

Comparison involves six “intrinsics” [00:33:41]:

1. Objective: That which is outside the self or perceived [00:27:48].
2. Subjective: The self or perceiver [00:27:50].
3. Content: The specific object of perception, like the image within a painting [00:35:25].
4. Context: The environment or framework in which perception occurs, including the perceiver’s state of mind, like the wall and museum around a painting [00:35:46].
5. Sameness: The aspect of constancy or non-changingness [00:32:11].
6. Difference: The aspect of change or new information [00:32:19].

These intrinsics are inseparable. For example, there cannot be content without context, or sameness without difference [00:54:42]. Any first-person measurement inherently involves subjective and objective elements, and a change of state from “not knowing” to “knowing” [00:28:07].

Relating Symmetry and Continuity to the Intrinsics

These six intrinsics are used to define symmetry, asymmetry, continuity, and discontinuity [01:03:45]:

• Symmetry: A sameness of content across different contexts [00:58:00]. This represents lawfulness in the universe, where the same laws apply regardless of location [00:56:54].
• Continuity: A sameness of content within the same context [01:00:36]. This relates to continuous functions where small changes in input lead to small changes in output, often relevant at microscopic scales [01:00:48].
• Asymmetry: A difference of content within the same context. This implies an irreversible change of state, such as going from “unknown” to “known” [01:02:14].
• Discontinuity: A difference of content across different contexts. This implies distinctness and separateness [01:13:00].

These definitions are stated to be “explicit,” “exact,” and “totally inclusive” [01:04:48], and consistent with the natural usage of these terms in various fields [01:05:07].

Access Control Limits

Physics theories, particularly General Relativity and Quantum Mechanics, describe inherent “access control limits” on what can be known [00:46:12].

• General Relativity: Defines regions like the “absolute elsewhere” in Minkowski diagrams, from which no causal signal can be received [00:44:37]. This is analogous to a computer system’s wiring, where signals can only flow where connections exist [00:45:04].
• Quantum Mechanics: The Heisenberg Uncertainty Principle states that one cannot simultaneously know both the position and momentum of a particle beyond a certain scale (Planck constant) [00:46:36]. This imposes fundamental information access limits [00:46:53].
• Newtonian Mechanics: In contrast, Newtonian mechanics assumes a deterministic “clockwork universe” where, in principle, all information (past and future) is accessible [00:47:26]. These access limits highlight the inherent unknowability that defines boundaries of what is knowable within a given framework [00:52:17].

The Incommensuration Theorem (ICT)

The ICT arises from analyzing how the four fundamental concepts (symmetry, asymmetry, continuity, and discontinuity), defined by the intrinsics of comparison, can combine [01:07:07].

• Applying the principle that sameness and difference must always be paired [01:09:00], Landry concludes that perfected symmetry and perfected continuity cannot coexist [01:11:54].
• This means that if one wants perfect symmetry, one must accept perfect discontinuity; and if one wants perfect continuity, one must accept perfect asymmetry [01:12:03].
• The ICT asserts that there are two fundamental kinds of epistemic knowledge:
  1. Symmetry and Discontinuity: This describes knowledge of the “digital world” – a collection of distinct entities (like particles) with consistent properties [01:13:15]. This is typically associated with a third-person perspective [01:17:16].
  2. Continuity and Asymmetry: This describes the first-person experience of knowing, which involves an inherent connectivity between observer and observed, and an irreversible “arrow of time” (from unknown to known) [01:15:24]. This is associated with a first-person perspective [01:19:54].

Since symmetry and continuity cannot perfectly coexist, these two fundamental ways of understanding epistemic process are “incommensurate” [01:17:20].

Implications for Physics and Metaphysics

The ICT provides a framework for understanding the deep philosophical underpinnings of scientific knowledge.

Everyday Example: First-Person vs. Third-Person Experience

The ICT explains why humans experience consciousness as a continuum with an inherent asymmetry (the subjective flow of time, inability to predict the future with certainty) [01:19:00]. This is the first-person, embodied, and visceral experience of continuity and asymmetry [01:20:18].

Conversely, abstract scientific knowledge, such as mathematics or physics laws, is a third-person perspective. It consists of discrete, symmetrical patterns (laws) that are abstracted from direct experience [01:20:26]. Here, the subjective is factored out, and patterns are seen as “floating” and disconnected [01:20:48]. The ICT highlights that the “broken symmetry in time” that humans experience as conscious entities supports the idea that physics seems more symmetrical than first-person experience [01:22:51].

Bell’s Theorem and Quantum Interpretations

The ICT can be seen as a more general notion that supports Bell’s Theorem in quantum mechanics [01:25:20].

• Bell’s Theorem generally implies that reality cannot be both local and have hidden variables [01:27:15].
• From the ICT perspective, “lawfulness” (symmetry) and “locality” (continuity/connectedness) cannot perfectly coexist [01:25:31]. One must emphasize one and accept the implications of the other [01:25:51].
• Quantum interpretations can be categorized based on whether they prioritize the first-person (subjectivity, hard randomness, arrow of time) or third-person (absence of these) [01:35:50].
  • Many Worlds Interpretation (MWI): This interpretation is a perfected third-person view, assuming no hard randomness, subjectivity, or arrow of time [01:35:04]. It claims that every quantum event causes the universe to fork into multiple universes [01:27:52]. However, the ICT suggests that MWI is not a complete description because it implies “inherently unmeasurable and unknowable” universes that are not causally connected, thus exhibiting discontinuities that are not described by the theory itself [01:44:00].
  • Copenhagen Interpretation: This interpretation takes the opposite stance, asserting the existence of hard randomness, subjectivity, and an arrow of time [01:35:09].

Godel’s Incompleteness Theorem

The ICT also projects into mathematics itself through Godel’s Incompleteness Theorem [01:37:16].

• Godel’s Theorem states that any sufficiently complex axiomatic system cannot be both complete and consistent [01:38:20].
• Landry argues that “consistency” is isomorphic to “symmetry” (sameness of truth value across contexts) [01:38:31].
• “Completeness” is isomorphic to “continuity” (all true knowledge being connected in one field) [01:40:08].
• Therefore, Godel’s Theorem, which asserts that completeness and consistency cannot simultaneously exist, is a projection of the ICT into the realm of mathematics, essentially stating that one cannot have perfected symmetry and perfected continuity at the same time [01:40:47]. The ICT offers a simpler proof for this than Godel’s original [01:40:53].

The ICT offers a fundamental and coherent framework for understanding the limits of knowledge, the nature of reality, and the relationship between subjective experience and objective scientific inquiry [01:33:04].