The Growing Universe

The universe:

$$\Omega =\{\Phi ,\mathcal{F}\}$$

The “growing” universe:

$$\Omega (t)=\{\Phi (t),\mathcal{F}(t)\}$$

Where:

• $\Omega$ is the Universe
• $\Phi$ is the Objective Space
• $\mathcal{F}$ is the Functional Space By parameterising the Universe on time, we facilitate growth.

Some more definitions:

• $P^k=\{{\Phi }_i^k,{\Phi }_o^k,{\Phi }_p^k,f^k\}$
• ${\Phi }_o^k=F^k({\Phi }_i^k,{\Phi }_p^k)$. I’m a little dubious about this one. I cannot currently see the relationship between $f$ and $F$. Nor how an output space can be a function of input spaces. I think $F$ has to be a Function space, that is a space constructed of functions. This is very significant if we can nail this down.
• ${\phi }_o^k=f^k({\phi }_i^k,{\phi }_p^k)$
• ${\phi }_o^k(t)=f^k({\phi }_i^k,{\phi }_p^k,t)$

$$\Omega =\bigcup _{k=1}^N{P}^k$$ $$\Phi =\bigcup _{k=1}^N{\Phi }^k$$

with ${\Phi }^k=\{{\Phi }_i^k,{\Phi }_o^k,{\Phi }_p^k\}$

$$F=\bigcup _{k=1}^N{F}^k$$

I think $f^k\in F^k$

a Process $P^k$ is defined as the set of

flowchart LR
INPUT:::hidden -- IN --> P
P -- OUT --> OUTPUT:::hidden

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