thousands to billions of elements, and require a SNFT or other similar mechanism for the automated characterization, monitoring, and control of their activity. A theoretically-grounded model is needed, and smart network theories based on statistical physics (statistical neural field theory and spin-glass models), information theory (the AdS/CFT correspondence), and model systems are proposed. Generically, a SNFT (conventional or quantum) is a field theory for the characterization, monitoring, and control of smart network systems, particularly for criticality detection and fleet-many item management.
2.4.1 Theory requirements: Characterize, monitor, and control
The purpose of SNFTs is the characterization, monitoring, and control of smart network systems. The first objective is characterization. It is necessary to develop standard indicators and metrics to easily identify specific behaviors in smart network systems as they evolve and possibly grow in scalability and deployment. Both positive (emergent innovation) and negative (flash crash) behaviors should be assessable by the theory.
The second objective of an SNFT is to provide monitoring, at both the individual element and overall system level, of current and evolving behavior. Monitoring pertains to smart network operations that are currently unfolding, and also may be developing in the future. For example, in the farther future, deep thinkers (advanced deep learning systems) might go online. Although deep learning networks are currently isolated and restricted to certain computational infrastructures, it is imaginable that learning algorithms might be introduced to the internet. Risk management is a key concern. A Deep Thinkers Registry could be a safeguard for tracking an entity’s activity, with possible annual review by a Computational Ethics Review Board for continued licensing. This is a future example that demonstrates the intended extensibility of SNFTs, and the uncertain future situations that they might help to facilitate.
The third objective of an SNFT is control, for the coordination of fleet-many items. Orchestrating fleet-many items is a clear automation economy use case for smart network technologies. This involves the ability to securely coordinate fleet-many items in any kind of internet-connected smart network system, which could include autonomous vehicles, drones, blockchain peer-to-peer nodes, deep learning perceptrons, smart city IoT sensors, home-based social robots, medical nanorobots, and supply chain shipment-receiving. The longer-term range of deployment of smart network technologies could extend to the very small, such as the cellular domains of the body, and the very large, such as civilization building in space.
2.4.1.1Fleet-many coordination and system criticality
Whereas the practical application of SNFT is the automated coordination of fleet-many items, the risk management application is being able to detect and possibly avert unwanted critical moments such as potential phase transition. A crucial aspect of an SNFT is the predictive risk management of system criticality. It is important to have a mathematical and theoretical basis for understanding smart networks so that the critical points and phase transitions may be predictively managed to the extent possible. The events that could constitute criticality and phase transition in smart networks are both expected and emergent situations from both within and outside the network. Some examples are financial contagion, network security, novel technology emergence, and electromagnetic pulses.
SNFTs could also be useful in the well-formed design of smart network systems. They provide a formal scientific basis for studying smart networks as new technological objects in the contemporary world, particularly since smart networks are a nascent, evolving, and high-impact situation.
2.5Smart Network Field Theory Development
More precisely, an SNFT is any formal method for the characterization, monitoring, control of smart network systems such as blockchains and deep learning networks. Although there are different kinds of smart networks, blockchain and deep learning are the focus for developing a field theory because they are the most sophisticated, robust, and conceptually novel.
2.5.1 The “field” in field theory
The term “field” is meant both analogically and literally (in the physical sense). Other terms invoked in this work such as temperature and pressure also may have both precise analytical meanings in the physical context and conceptual meanings. Terms may be applied conceptually as to the purpose and function they are serving in smart network systems.
There are two primary meanings of field in the conceptual sense. First and most generally, field refers to the ability to control multiple items as one unit. The requisite functionality of the SNFT is to manage fleet-many items. One idea is to control them as a field, in which the term field might be dynamically-defined based on location, energy, probability, gradients, or other parameters. The concept of field might be used to coordinate thousands and millions of constituent elements (such as blockchain peer-to-peer nodes or deep learning perceptrons). An example of an existing smart network field operation is optogenetics (in which neurons express a protein that makes their electrical activity controllable by light) (Boyden, 2015). Optogenetics is a “light switch for a field of neurons” in that it conveys the ability to turn on or off a field of neurons all at once. Thus, an SNFT is created, in that optogenetically enabled cells are controlled as a field as opposed to individually (Swan, 2021).
The second meaning of field in SNFTs is that a field might refer to the situation in which each element in a system has its own measure and contribution to an overall metric or network activity (possibly being used to calculate a Hamiltonian or other composite measure of a system). This concept of field (from effective field theory development in physics) suggests that every point in a landscape has a computable value, generally referring to the idea that a function has a value everywhere throughout the space, at every location in the field.
2.5.1.1Scalar, vector, and tensor
SNFTs may be structured in scalar, vector, and tensor terms. A tensor is a complex mathematical object (a geometric object that maps functions and interacts with other mathematical objects). The simplest tensors are scalars (zero-rank tensors) and vectors (first-rank tensors). A scalar is a tensor with magnitude but no direction (a zero-rank point), and is described by one number. Mass and temperature are scalars. A vector is a tensor with magnitude and direction (representable by a first-rank tensor or vector line). A vector is often represented as an arrow, and defined with respect to a coordinate system. Force and velocity are vectors. A tensor is a multidimensional structure, representable by a matrix. Tensors are seen in the context of deep learning. Google’s tensor processing units (TPUs) and TensorFlow software use tensors in the sense conducting very-fast matrix multiplications. A tensor is representable by a multi-dimensional matrix, and TPUs and TensorFlow are fast because they flow through matrix multiplications directly without storing intermediate values in memory.
2.5.2 Statistical physics
A convenient theoretical approach to SNFT is based on statistical physics. Statistical physics is selected because of its focus on probability and inference in large systems. The two model systems used to elaborate the SNFT are also based on statistical models in physical systems (the brain and disordered magnets).
All of physics in my view, will be seen someday to follow the pattern of thermodynamics and statistical mechanics
— John Archibald Wheeler (1983, p. 398)
Statistical physics is a catchall that includes statistical mechanics, probability, and thermodynamics. The great benefit of statistical physics is that it provides a generalized method, based in probability, for linking microscopic noise to macroscopic labels (Mayants, 1984, p. 174). Smart networks are also fundamentally based on probability. Smart network technologies such as blockchain and deep learning are probabilistic state machines that coordinate thousands to millions
