Three Criteria Model of Elegance

1. Hierarchy: Independent levels of resolution.

This allows for zooming in and out. Different levels of focus may reveal different patterns. A non-linear relationship can sometimes be approximated as linear on a small scale. This is one of the main principles underlying the general theory of relativity. Manifolds appear Euclidean locally but may have a different emergent topology. Generally speaking, it is more convenient to work with lines than curves.

Systems theory and mathematics are in some sense the collection of rules that work across scale. Sets can be thought to transform into other sets. Such sets can contain elements or even other sets. The idea of containment is central to such theories and is so fundamental in our minds that it is often overlooked.

At times it may be best to ignore scale and isolate observations. This gives a clear view of the local data and shines light onto certain asymmetries or irregularities. Such information can be extremely useful when estimating the effects of aggregation.

2. Exclusivity: Parts are mutually exclusive when dividing wholes.

If the default state of a system is modeled with a monism, then identity is the only quality of interest. It is a whole that is not broken down into parts. Reduction cannot go on forever, therefore at some point an agent much stop at a whole. However, reduction is necessary for consciousness to exist at all. Apparent boundaries of existence define our reality. Without parts, there is not an alternative state or position within that existence. It is all just one thing.

Duality breaks the whole into two parts. Those parts can be further broken down into sub-dualities. If the parts of a whole are not mutually exclusive, then the distinction generates no information. The switch must either be on or off but such a certainty is not always practical. Confidence in distinguishing between two parts can be challenging when the signal is distorted by noise. At the human level, there is a significant amount of such noise due to the complexity/size ratio.

Binary classification trees are popular because of the low error rate when typing. Hence the use of transistors in computing and my use of binaries in personality theory. Selecting between two alternatives is more accurate than selecting between twenty. Though, this does not mean a binary encoding is optimal. A shallower, wider hierarchy can be quicker to navigate.

3. Symmetry: Parts of the same whole and resolution have equal impact.

Impact is sometimes hard to judge, especially across context. Setting a boundary is often hard due to our inability to accurately predict the consequences of non-linear interactions. Often, a measure is distributed according to a power law in some uniform space. Dividing down the middle in such a situation would lead to an asymmetric sampling of attention/time/energy in the space relative to the impacts of each side.

For instance, if you want to predict the future state of a market, then spending an equal amount of time researching every company in that market would be inefficient. Not every company has the same impact. A better strategy is to focus most of your time researching large cap companies and a relatively small amount of time researching mid/small cap companies (perhaps in accordance with a power law).

Overall, this is the most challenging criteria to meet yet is vital to the development of elegant models.