The First Process

See Attempting the First Process for the first try at this. Then The Second Process for and extension of this

Do we extend the Universe to include the Model?

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

or is the Universe the Model?

What The Identity Space brought to my attention is that the Object Identities are intrinsic to the Model, and are not found in the natural environment, they are a contribution to the Universe by the Model. So perhaps we define an Identity Space in our Universe?

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

And the Identity Space is strictly a structure that provides the naming of Objects and Processes in our Universe.

The simplest Process I can think of is one that emits discrete Objects of the same kind.

This Process $\mathcal{P}(t)=\{{\Phi }_o,\tilde{\Phi },\mathcal{F},\mathcal{I}\}$

$\mathcal{I}(0)={\mathbb{N}}_0$

and the way $f$ operates is to embed $\mathcal{I}$ into ${\Phi }_o$.

$${\phi }_o(i,t)$$

Let’s say that for the infinite lifetime of this Universe that we only have one Process ${\mathcal{P}}^1$, which does not change over time, in any way, and the only function of that process is to create a series of discrete Objects of the same kind.

$$\Omega =\{\Phi ,\mathcal{F},\mathcal{I}\}$$ $${\mathcal{P}}^1=\{{\Phi }_o^1,{\tilde{\Phi }}^1,{\mathcal{F}}^1,{\mathcal{I}}^1\}$$

and for simplicity $\Omega (t)=\Omega \forall t$. i.e. this is a Static Universe.

Let $\Phi =\{{\Phi }_1,{\Phi }_2,{\Phi }_3\}$ where:

• ${\Phi }_1:=\text{size}:={\mathbb{Z}}^{+}$
• ${\Phi }_2:=\text{colour}:=\{\text{green},\text{red},\text{blue},\text{black}\}$
• ${\Phi }_3:=\text{density}:={\mathbb{Z}}^{+}$ ${\mathcal{I}}^1={\mathbb{N}}^{+}$

This is a fully measured process, so ${\Phi }_o^1={\tilde{\Phi }}^1={\Phi }_1\cup {\Phi }_2\cup {\Phi }_3\cup {\mathcal{I}}^1$ A sequence of measurements are made in the course of the lifetime of the Process, such that ${\tilde{\phi }}^1=\{[7,\text{green},5.6,0],[4,\text{black},8.6823,1],\dots ,[0,\text{blue},6,332]\}$.

${\phi }_o^1=f({\tilde{\phi }}^1)={\tilde{\phi }}^1$

And there we have our first fully-defined Process. Yes, really. That’s it.

This is the simplest example. But it is indeed, nonetheless, complete.