# Fundamental Level

### From TechWiki

# Mathematical Models of Reality

*This is a technical overview, for a more illustrative overview go to the j-node section.*

- Definition
*State Space*Ω:

- Set of abstract and physically distinct states of of a subset of the observable world.

- Definition
*Observables**f*_{i}:

are rules associating physically distinct states in the state space with real numbers.

- Note:
- Ω can be finite, infinite, uncountable.
- The notion of
*physically distinct states*depends on the observer and is not a property of the system

- Definition
*Natural System N*:

- Definition
*Equations of State*:

- describes the dependency relations of the observables.

- Example
*Ideal Gas Law*:

- Notion of a
*Formal System F*:- Constructs of the human mind.
- Provides basis for making
**predictions**about*N*, using rules of inference in*F*. -
*F*is a*formal description*of*N*, if*N*can be**encoded**into*F*:

- Note: The inverse mapping

- gives the decoding back into the natural system, i.e., the
**predictions**

**Sources**: Casti, J.L. (1989). *Alternate Realities - Mathematical Models of Nature and Man*. New York: Wiley and Sons.

# Illustrations

Can be found here: Slides: From Fundamental to Complex.