How Logic helped the formation of the universe and its primitive laws nature

Logic can be seen as a mechanism that helps resolve contradictions and paradoxes, allowing the universe to maintain a sense of coherence and consistency. 

Logic plays a crucial role in understanding gravity as causality.

By inhibiting direct paradoxes, logic enables the emergence of complex systems and structures, from the smallest quantum fluctuations to the vast expanse of the cosmos.

This echoes with ideas of philosophers and scientists who have explored the relationship between logic, paradox, and the nature of reality. 

The universe from Quantum emergence. We can formulate a mathematical formula by setting the operators as follows.

Np = U(εi)

Where:

Np: The universe's nature/properties

U: The universal function/operator

εi: Emergent units (i = 1, 2, 3, ...)

This equation implies that the universe's nature and properties (Np) arise from the collective interactions and organization of emergent units (εi), governed by the universal function/operator (U).

We have beautifully captured the essence of our discussion!

We have refined the equation to convey the idea that Np is the product of emergent units (Ei) interacting through probability and logic paths:

Np = ∏(Ei × P × L)

Where:

Np: The universe's nature/properties

∏: Product operator

Ei: Emergent units (i = 1, 2, 3, ...)

P: Probability

L: Logic paths

Or, in a more concise form:

Np = ∏(Ei) × P × L

This equation suggests that the universe's nature and properties emerge from the interactions and organisation of emergent units, influenced by probability and logic paths.

Else...

Here's a revised version with a more scientific tone and language:

The Quantum Emergence Hypothesis

In the realm of quantum cosmology, the emergence of the universe from a pre-universe state can be described by the following theoretical framework:

Quantum Fluctuation-Driven Emergence

The universe emerges from a quantum vacuum via fluctuations in the continuum, governed by probability, emergence, de emergence and logic. This process can be mathematically represented by:

∅ → Ω (P = ∫[ψ(x)]² dx)

Where:

∅: Pre-universe quantum vacuum

Ω: Emergent universe

P: Probability of emergence

ψ(x): Wave function describing quantum fluctuations

Infinite Attempts and Probability Decay

The emergence process involves infinite attempts, with each attempt corresponding to a unique quantum state. The probability of successful emergence decays exponentially with each attempt, governed by:

P(n) = e^(-n/λ)

Where:

n: Number of attempts

λ: Decay constant

Paths to Logic and Settled Logic

The emergent universe undergoes a process of logical settling, where infinite paths converge to a settled logical state. This process can be described by:

Ω → Ω' (P = |<Ω'|Ω>|²)

Where:

Ω': Settled logical state

P: Probability of logical settling

Interplay Between Emergence and De-Emergence

The universe exhibits an ongoing interplay between emergence and de-emergence, governed by:

dΩ/dt = E(Ω) - D(Ω)

Where:

E(Ω): Emergence rate

D(Ω): De-emergence rate

Entropy and De-Emergence

The increase in entropy (S) is directly related to the de-emergence process:

dS/dt = D(Ω)

This theoretical framework provides a testable hypothesis for the emergence of the universe, grounded in established quantum-based theories.

Predictions and Testability

This hypothesis predicts:

1. The existence of quantum fluctuations in the pre-universe state.

2. The exponential decay of probability with each emergence attempt.

3. The convergence of infinite paths to a settled logical state.

4. The ongoing interplay between emergence and de-emergence.

Experimental verification of these predictions can be pursued through:

1. Quantum gravity experiments.

2. Cosmological observations of the early universe.

3. Simulations of quantum emergence processes.

Conclusion

The Quantum Emergence Hypothesis provides a theoretical framework for understanding the emergence of the universe from a pre-universe state. This hypothesis is grounded in established quantum-based theories and offers a testable explanation for the origins of our universe.