Namespace

Namespace(Q873636) is a container of identifiers. It helps manage terminology precisely, and efficiently. Therefore it must be considered as a kind of resource pool, that can be considered as a symbolic space for representing any concepts, including the relational structures of spacetime. It is closely related to the field of knowledge management, and software engineering. A significant amount of insights about namespace management in mathematics, and number theory in particular.

Namespace management

To manage namespaces in a methodical fashion, one can use namespace management techniques or tools, developed in the database or container orchestration industries. The reason that namespace must leverage database technologies and container orchestration, is due to the fact that there are simply too many data points or names to be processed, therefore, some scalable instrumentation must be employed.

Namespaces as Catalogs

A namespace has the property that all entries should be distinguishable from each other, and ideally, not having too many overlapping names.

Individuals and Agencies

The identities of human users are managed using Authentication and authorization services such as distributed Keycloak services.

Products and Services

Products such as books, cars, and other manufactured products are managed by unique namespaces defined in PKC-managed namespaces. Services such as computational services, energy, water, hospitality, and other amenities can also be managed in PKC-managed namespaces. And PKC-managed namespace is defined using a hierarchical data structure, similar to XML or YAML.

Land Ownership

By using ideas borrowed from What3Words, one may come up with intuitive, yet convenient and succinct unique labeling of spatial locations, that enables the labeling of land masses and its association of time-based ownership. By associating a triple, composed of

$Triple=N_{location},N_{ownership},N_{duration}$

, this unique data content combination should define a unique status of land ownership.

Namespace in Mathematics

Henri Poincaré had an quote on namespace management:

Mathematics is the art of giving the same name to different things

This short sentence describes the essence of how math can be used as a formal language.

Names as a Resource

To measure the amount of resources, or keep accounts for event dependencies, names or symbols must be used with rigor. Therefore, namespace management is the ultimate control plane for accountability. This insight was explicitly revealed in Luca Pacioli's work on Summa de arithmetica. However, managing names at scale, requires the use of advanced computing devices, it is until the 20th century, that human started to have egalitarian access to personalized computing devices, so that a new way of managing resources became a force to change the way we realize ownership and discern scientific results. In other words, it is only after one realize the universal expressive powers of the symmetry-preserving, or balanced accounting equation, often shown in the following form:

Asset = Liability + Equity 

It is this simple equation, that both denoted the compositional admissibility of Liability + Equity and the equality relationship between the left hand side(LHS) and the right hand side(RHS) of the equation, that other forms of scientific disciplines, such as linear algebra, Hamiltonian mechanics, quantum physics can take on a reliable pattern of logical arguments. All logical arguments must be based on the conditions of symmetry-preserving and symmetry-breaking.

Time as a Resource in Namespace

A powerful insight to manage namespace is to be aware of the fact that temporal sequence is naturally asymmetrical, meaning that ordered sequences each can represent a different information item. This is utilized extensively in the management of data content, especially in the area of blockchain, and in the design and implementation of stateful systems, such as distributed databases.

A Universal Namespace constructed by Lambda Calculus

To see why sequential structures can be used to encode any information content, the best example would be using $\lambda -Calculus$ to encode Boolean logic. Using the sequential relations of input elements, one can denote TRUE and FALSE with just two primitive functions,FRONT(LIST(...)) and BACK(LIST(...)). For more detail, see the $\lambda -Calculus$ tutorial.

Implementation in MediaWiki

Another important revelation is that all the above concepts can be realized in a MediaWiki, or a Browser-based Network Computing interface. The dynamic behavior of every PKC page can be programmed with Lua if Scribunto extension is installed. Moreover, HTML and CSS and JavaScript can be customized and perform computation on the client side. This infrastructure enables PKC to work as a highly extensible repository of executable knowledge. From a software engineering viewpoint, PKC can be considered as a fully programming environment to manage the compositional effects of many networked resources.

Namespace in Linux

The term: Namespace has a special place in Linux Kernel. Explanation can be found in this web article. In other words, Linux has a strategy to separately refer to its resources accessible through distinguishable namespaces. They can be categorized as follows:

1. User namespace
2. Process ID (PID) namespace
3. Network namespace
4. Mount namespace
5. Interprocess communication (IPC) namespace
6. Unix Time-Sharing (UTS) namespace.

This is the first lecture of the course:Mathematics: make the invisible visible.