Structure - Apophysics

Sense from Ideas

In Foundation, I worked up to the point of an apophysical non-space. If we take this space to be maximal, it contains the exact data-like measurements of all the things in a universe. Those things may be whatever physical things you take to be most fundamental to reality, so long as they are measurable in principle. This maximal space would also include every possible relationship between every possible thing, including hypothetical relationships—those that have no real instances. These relationships are generated by relational operators. That is, in this maximal space, we compute every possible combination of every thing in the universe, and we can view these combinations as non-exclusive relationships between things according to the rules of their relational operators.

How does this work? Relational operators can be understood as binary operators.¹ These binary operators, according to the logic that defines them, either pass a thing, including it in the resulting group of included things, or fail a thing, indicating that it does not belong to the resulting group of included things. In this way, it follows that the things that are admitted to the group are related precisely by the binary operator used. If we are to consider the maximal number of relational operators, then we have a combinatory explosion of all possible permutations of all things. Assuming that the universe is finite, the maximal number of relational operators remains finite, albeit inconceivable!

How are we to make any sense of these relationships? Perhaps we can understand them from the perspective that they offer us structure. Whereas individual, fundamental-to-reality things do not really tell us anything, perhaps carefully selected relational operators will be more helpful. Imagine we could manipulate and view the data of these things and of relational operators as if we were using a sufficiently powerful computer. What if we ordered, sorted, filtered, and otherwise “played with” these data? This would allow us to use our own rationality to evaluate reality itself. What do you think are some interesting ways to sort out these data?²

My inclination would be to look for larger structures of things and for simple relational operators that generate large networks of relationships. In seeking to understand the data, I would filter out relational operators with exceedingly long definitions. These, which are understood as binary operators, would list the exact data-like definitions of many things and arbitrarily assign a pass or fail status to each. After filtering these out, I would continue by looking for exceedingly short rules that nevertheless generate large groups of related things. I imagine that such groups would describe small but frequently occurring particles and molecules. Rules like these might be constructed in a formal or perhaps fuzzy logic format; that is, the data contain this or that and are like this and not like that.³

Another route of inquiry I would take is that of looking for relational operators that group things that I think are important. With enough effort and computational power, I could find the relational operators that include all people, for example. With some additional effort, perhaps I could prove that some such groups include all possible people, real or imagined, and include only people.⁴ By definition and construction, these relational operators would be acceptable philosophical definitions of people. I might do this for everything that I identify as an object, like phones, trees, and chairs.⁵ Finally, the answer to what a chair is is at our fingertips, never to be used to torture undergrads again!

This is not to say that “definitions” are fixed and immutable. Indeed, while I may define persons in a particular way, you may do so differently, especially considering that we would have to address every hypothetical variant. Our groups of people might look different, or we might use different rules to get to the same place. This is not due to inaccuracies in the data, but to differences within our opinions and definitions.

Once I have “defined” these interesting objects and have some understanding of the relational operators that are used to generate the groups of defined objects, I might start to look for relationships between the objects. The data would starkly reveal the similarities and differences between objects. What do rabbits, fish, and giraffes all have in common? What do all animals have in common? What do all animals and plants have in common? Discovering the relational operators that form the answer to each of these questions (and many others) is akin to exploring the categorical and taxonomical distinctions in nature.

In this way, I might filter and group relational operators until I have narrowed them down to a list that generates every group that I find to be interesting. Every person, place, and thing could be defined rigorously by relational operators. This includes patterns in the data that define the ideas that people have. Because the apophysical non-space would need to recognize something like time in its rigorous data-like definition of fundamental things, this approach works for things that persist or unfold over time. This might include behaviors or patterns of behavior. The sky is the limit.⁶

With the inconceivable number of rules now filtered down to a far more conceivable list, we have the definitions and classifications of all things at our fingertips. We can clearly see the similarities and differences among everything that we have worked to define. But is this the structure that we were looking for?

In Foundation, I described the data that relational operators point to as ideas. This is right, in a sense, but notice that in this paper I have avoided that term, instead focusing on relationships. The substance is the same, but the perspective is different. When we allow ourselves to consider the full scope of what an idea can be, in both the technical and colloquial senses, it is not just an exact data-like measurement of material things. In accordance with how complicated the relational operator is, we can generate ideas that have meaning, imbued by our own intellect in constructing or selecting the relational operator. These ideas can contain complex relationships and abstractions. Indeed, they are higher-order relationships of relationships within things; that is, ideas on ideas…⁷ This is exactly the sort of structure needed to “practically” convert an apophysical non-space back to the physical space — or, rather, the space of all ideas. While it may be helpful to think of ideas as sums of relational operators — these “sums” being the intersection of a set of relational operators — it is still valid to say that relational operators point to ideas, as relational operators should be additive, and thereby any set is able to be “combined” into a single relational operator.⁸

The abstractions within any given field, space, or type of relational operator must be satisfactorily identified to distinguish structural categories. If we’re focused on people, how are we examining them? What sort of abstractions in the data are we using to describe them? If we’re focused on ideas, what are the categories of ideas, and can we identify “higher” or “parent” ideas?⁹ This is the sort of thing that we can do in an apophysical non-space.

Yes, I think this is something like the structure that we are looking for; at least, the structure that I am seeking. Perhaps you would like to do otherwise? I am quite satisfied with the understanding gained by rigorously identifying the relationships between things and relationships of things. In this way, we can make sense of reality.

Of course, there is the issue that all of this is imaginary. We do not have the data of an apophysical non-space to play with, nor do we have a computer that can process this type or quantity of data. But we do have something…

1. The term “relational operator” is closer to the idea I’m going for, while the term “binary operator” concretizes the sort of things that these operators can do. In some cases, it makes more sense to view relational operators as higher-order, non-binary operators, but computationally or mathematically, any well-defined operator in an apophysical non-space could be reduced to a binary operator.

2. If you haven’t worked with data in a computer much, using something like SQL or regex, this may be a difficult question. Even with such experience, something like creative philosophical thinking is also necessary. I’m not sure that I even have the answer—at this stage, this is truly a thought experiment.

3. This does not introduce ambiguity into the rules; rather, it gives us a more robust toolset for defining relational operators. Fuzzy logic rules can still be reduced to binary operators, of course. Likewise, I argue that we could make increasingly complex relational operators, until we have something akin to natural language operators. So long as the underlying rules are understood correctly, layers of abstraction can be safely added to our operators. The notion of a programing language is not far away.

4. This sort of rule may have many forms that fulfill the requirements. In accordance with Ockham’s Razer, I would likely give preference to the shortest rule.

5. It is an open question just how short these rules might be, and in what format they might be best understood. Complicated binary operators do not lend themselves to human intelligibility, nor do they necessarily offer intuitive definitions for the relationships that they generate. For example, if we isolate some feature of the data that only applies to people — something like identifying in the data a human-like head, heart, and spine combination — we will not have a particularly interesting or complete definition of a human. Nevertheless, this discussion highlights the multiple ways one might work with the data. If biological definitions seem unsatisfactory to you, you could try behavioral definitions or something completely different.

6. An alternate way of viewing this is with snapshots, where each apophysical non-space has only data concerning the moment to which it corresponds. This highlights the persistence problem, which could be resolved by noting that all fundamental things persist in the subsequent apophysical non-space altered only by the laws of physics, which are beyond the scope of this model. Well, you would be able to derive physics by evaluating the data postulated by this model — that’s exactly what the notion of physics is — but by doing so, you would be working on a practical question which these papers provide no guidance for. The point is that understanding things over time works whether you are using the snapshot model or the more general model wherein all data across all time exist in the apophysical non-space.

7. As I noted in Foundation, relational operators should not be nested or recursive to prevent infinite regress and group-related fallacies. Nevertheless, there is no harm is constructing simple logical expressions of relational operators, as the result would simply be another relational operator.

8. As computational “filters” for an apophysical non-space, selecting certain patterns of data, or filtering out certain patterns of data, relational operators are definitionally additive by computing one after the other sequentially. Each relational operator takes as input a space of data (either the apophysical non-space, or a subset thereof), and outputs a subset thereof.

9. The Platonic divided line should come to mind here. However, the differences between Plato’s model and my own are too significant to make much of a comparison.