## 5 Complete ToE - Formalization  
This section formalizes the CToE selection principle and what accounts for a CToE. Universal Turing machines are used to formalize the notion of programs as models for generating our universe and our observations. I also introduce more realistic observers with limited perception ability. **Objective ToE. ** Since we essentially identify a ToE with a program generating a universe, we need to fix some general purpose programming language on a general purpose computer. In theoretical computer science, the standard model is a so-called Universal Turing Machine (UTM) [6]. It takes a program coded as a finite binary string \(q\in\{0,1\}^{*}\), executes it and outputs a finite or infinite binary string \(\{0,1\}^{*}\cup\{0,1\}^{\infty}\). The details do not matter to us, since drawn conclusions are typically independent of them. In this section we only consider \(q\) with infinite output  
\[\text{UTM}(q)=u_{1}^{q}u_{2}^{q}u_{3}^{q}\,...=:u_{1:\infty}^{q}\]  
In our case, \(u_{1:\infty}^{q}\) will be the space-time universe (or multiverse) generated by ToE candidate \(q\). So \(q\) incorporates items (i) and (e) of Section 4. Surely our universe doesn't look like a bit string, but can be coded as one as explained in Sections 2 and 7. We have some simple coding in mind, e.g. \(u_{1:N}^{q}\) being the (fictitious) binary data file of a high-resolution 3D movie of the whole universe from big bang to big crunch, augmented by \(u_{N+1:\infty}^{q}\equiv 0\) if the universe is finite. Again, the details do not matter. **Observational process and subjective complete ToE. ** As we have demonstrated it is also important to localize the observer. In order to avoid potential qualms with modeling human observers, consider as a surrogate a (conventional not extra cosmic) video camera filming=observing parts of the world. The camera may be fixed on Earth or installed on an autonomous robot. It records part of the universe \(u\) denoted by \(o=o_{1:\infty}\). (If the lifetime of the observer is finite, we append zeros to the finite observation \(o_{1:N}\)). I only consider _direct_ observations like with a camera. Electrons or atomic decays or quasars are not directly observed, but with some (classical) instrument. It is the indicator or camera image of the instrument that is observed (which physicists then usually interpret). This setup avoids having to deal with any form of informal correspondence between theory and real world, or with subtleties of the quantum-mechanical measurement process. The only philosophical presupposition I make is that it is possible to determine uncontroversially whether two finite binary strings (on paper or file) are the same or differ in some bits. In a computable universe, the observational process within it, is obviously also computable, _i.e._, there exists a program \(s\in\{0,1\}^{*}\) that extracts observations \(o\) from universe \(u\). Formally  
\[\text{UTM}(s,u_{1:\infty}^{q})=o_{1:\infty}^{sq} \tag{2}\]  
where we have extended the definition of UTM to allow access to an extra infinite input stream \(u_{1:\infty}^{q}\). So \(o_{1:\infty}^{sq}\) is the sequence observed by subject \(s\) in universe \(u_{1:\infty}^{q}\) generated by \(q\). Program \(s\) contains all information about the location and orientation and perception abilities of the observer/camera, hence specifies not only item (l) but also item (o) of Section 4. A Complete ToE (CToE) consists of a specification of a (ToE,subject) pair \((q,\!s)\). Since it includes \(s\) it is a Subjective ToE. **CToE selection principle. ** So far, \(s\) and \(q\) were fictitious subjects and universe programs. Let \(o_{1:t}^{true}\) be the past observations of some concrete observer in our universe, e.g., your own personal experience of the world from birth till today. The future observations \(o_{t+1:\infty}^{true}\) are of course unknown. By definition, \(o_{1:t}\) contains _all_ available experience of the observer, including e.g., outcomes of scientific experiments, school education, read books, _etc_.