1. Let's start by stating the problem: You want to model a concept where "darkness" and "no darkness" regions influence matter and energy, explaining gravity, dark matter, and dark energy as an influence rather than a force. 2. To translate this idea into mathematics, we can think of "darkness" and "no darkness" as scalar fields or potentials in space. Let $\phi(x,t)$ represent a scalar potential field where regions of "no darkness" correspond to minima or maxima of $\phi$. 3. Gravity in physics is often modeled by a potential field $\Phi$ satisfying Poisson's equation: $$\nabla^2 \Phi = 4 \pi G \rho$$ where $\rho$ is mass density and $G$ is the gravitational constant. 4. Your idea suggests that the influence between darkness and no darkness regions can be modeled as gradients of a potential field $\phi$, where matter moves towards regions of lower or higher $\phi$ (depending on interpretation). This is similar to how gravity causes matter to move towards potential wells. 5. To incorporate your idea, define a potential field $\phi$ such that: $$\nabla^2 \phi = S(x,t)$$ where $S(x,t)$ is a source term representing the distribution of "darkness" and "no darkness". 6. The force or influence $\mathbf{F}$ on matter can be modeled as: $$\mathbf{F} = -\nabla \phi$$ meaning matter moves along the gradient of $\phi$. 7. For dark matter and dark energy effects, you can extend $\phi$ to include time-dependent or large-scale terms that modify the potential, for example: $$\phi = \phi_{gravity} + \phi_{darkmatter} + \phi_{darkenergy}$$ where each term satisfies its own field equation or contributes to $S(x,t)$. 8. To summarize, your mathematical model can be: - Define a scalar potential field $\phi$ representing darkness/no darkness. - Matter moves under influence $\mathbf{F} = -\nabla \phi$. - The potential satisfies a Poisson-like equation $\nabla^2 \phi = S(x,t)$. 9. This framework aligns with classical gravity but reinterprets the source term $S(x,t)$ to include your concept of darkness and no darkness regions. 10. Further refinement would require specifying $S(x,t)$ based on observational data and testing predictions. Final answer: $$\boxed{\mathbf{F} = -\nabla \phi, \quad \nabla^2 \phi = S(x,t)}$$ where $\phi$ is the potential field representing darkness/no darkness influence, and $S(x,t)$ encodes the distribution of these regions.