Meeting/GautamGroup/Sep 3 2021

On September 3, 2021, 9PM Bali time, I attended a meeting with Gautam, Ray, and Probal. The meeting had a number of crucial observations, and we decided to write a paper together, starting from a draft that I will be producing to kickoff the process.

Absolute Symbols

In this meeting, Ray stated that people like Gregory Chaitin had thought of information must be represented in terms of digits or characters, such as 0s and 1s. This concrete representation of information can be limiting. He criticized that grounding the notion of numbers or digits as the most fundamental building blocks for manipulation may not be sufficiently universal. The world may not be grounded in a set of artificially defined symbols. Is it possible the have a set of symbols or building blocks that are relative in nature?

Some useful references

A few days later, on September 6, I found two papers that helps clear up the ideas in this discussion. The first one was a white paper:Stepping Beyond the Newtonian Paradigm in Biology, which referenced Chaitin's paper called:Life as Evolving Software, which shed some light on the positions of Chaitin on this subject, also presented some evidence to break the spell of the absolutism in Ray's challenge.

All computation are searches

Ray also mentioned that one of these prominent computing scientists (I remember he said Turing) had asserted that all computation are searches. This statement implies that all computation can be approximated using the universal property or unique up to isomorphism kind of argument in Category Theory.

Relative Symbolism

I proposed that all information being presented in terms of symmetry-breaking functions. Functions are made of at least two elements in contrasting positions. First, the function itself is an object, and the input component it take in to map to some other value is another. This mapping could map to some null value, but even that, we are still talking about at least two elements. Therefore, a function represents a unit of relative information content, relating input with functional outputs. For example, to define truth/false values in lambda calculus,, one can use the relative positions of two inputs, to denote the true/false values in terms of head/tail positions of an input argument list. This way to thinking about information, allows functions or symbols of arbitrary scales to retain the same property, head/tail, left/right, front/back. The notion of making a distinction between its possible alternative states. This way of using functions to represent information, creates a unity in the types of information. In other words, all information can be represented as function, or verbs, at the same time, all information can be encoded as one of the possible symmetry-breaking states, which are nouns. This allows information to be consistent in the ways that fit its preferred operational or representational context, while keep all content being intact in the chosen type.

This conversation prompted me to read up on the book: Digital Mantras. On page 217, it has the following statement, which can be used to help define how PKC can evolve:

Approaches to using computers in the creative process will vary. Some will take "cognitive modeling" as their point of departure. They will develop programs that are simulations of how the human mind works, or, at least, are based on theories of how the mind works. Harold Cohen aimed to simulate his own creative processes, from drawing a line or a circle a segment at a time to integrating knowl­ edge of the world as a foundation for drawing and painting. Koenig began with a goal of better understanding how he himself composed. A great deal of research, whether in natural language, problem solv­ing, vision, or artistic creativity, aims to create "artificial intelli­gences" that are precise models of human intelligence.

Symmetry-breaking and Pythagorean Philosophy

We also talked extensively about the idea of symmetries and their relations to cryptography. Digital Mantras also talks about Pythagorean theorem, the beauty in musical compositions/forms. These inspired me to think about that pythagorus theory provides a universal rule to compose two perpendicular orientations, horizontal and vertical, so that it informs a kind of potential symmetries across two orthogonal dimensions. This can be related back to the orthogonality between verb and noun, when they are represented in the dimension of functional space, or in the dimension of the labeled symmetries, or the named space, they both can be united through some common rule, such as the Pythagorean theorem, to unite the two different linear spaces into one planetary space, so that additional symmetries and beauties can be observed and identified.

What is the Mantra?

In the above case, the mantra could have been Pythagorean theorem, or more deeply, the notion of unification through symmetries in type consistency. All phenomenon can be represented in a consistent type, independent of the orientations, could be the ultimate mantra. Moreover, it is possible that symmetry-breaking being the deepest mantra, that gave the insight to Pythagorus, so that he was able to establish this longest strand of tapestry in human intellects. This lead to the mantra of all concepts are nothing but one mathematical construct: Kan extension.

Operationalizing the Mantra

By adopting a universal construct, such as the Kan extension or its other name:Logic model, to represent data has a clear advantage. It allows one to assess the condition by computing a function or observing its value. Either approach can be automated and generalized to many operational contexts.