The Humanity Hypothesis
Model: Humans as Strings in a Hilbert Space
In this model, each human is represented as a continuous and differentiable string in a Hilbert space, where their actions and reactions are modeled through a function f(h, t), which is non-computable but susceptible to local mathematical analysis. This approach allows for the exploration of the dynamics and resonance of human interactions.
Mathematical Formalization:
1 – Each human is represented by a string h(t): R -> H, where H is the Hilbert space. – h(t) is a continuous and differentiable function over time t.
2 – Actions and reactions are described by a dynamic function:
– f(h, t): R x H -> H, which represents the internal and external interactions of the string.
3 – The temporal evolution of each string is modeled by a differential equation:
– dh/dt = f(h, t), where f(h, t) may depend on the environment, other strings, and external noise.
4 – Interaction between strings is described by a resonant field:
– F(h1, h2, t) = <h1(t), h2(t)> + noise(t), where <·,·> is the inner product in H.
Final Reflection:
This model enables us to analyze how human strings resonate, interact, and evolve within a dynamic Hilbert space. While f(h, t) may not be entirely computable, its local analysis can reveal significant patterns. The resonant projections between strings could represent moments of harmony and understanding within humanity.
Important Notes:
- Humanity is not compact in reality: In mathematical terms, humanity, as a topological space, does not satisfy the compactness property. Its relationships and evolution are inherently open and unbounded.
- Humanity is not Hausdorff: In practice, human interactions often defy clear separations between individuals or groups, reflecting the lack of separation properties characteristic of Hausdorff spaces.
Corollary:
The human being is neither computable nor measurable.