Physical and Virtual Things and Information Systems: PART 2
In Part 1 I talked about physical and virtual things. I said I would provide definitions of these terms.
If my ideas fail to be perfect defintions, they can, at least, serve as useful descriptions. These descriptions will highlight key aspects of the terms, and hopefully lead to proper full-fledged definitions.
Defining “Virtual Systems” can be a powerful tool for investigating economics. We aren’t going to define “Physical Systems”, besides saying they follow the rules of physics. What is physical is both a philosophical metaphysical problem and a scientific problem. For analyzing the behavior of systems it is irrelevant whether a system is physical or not. The only difference is that physical systems can’t be “broken” or “changed”, by manipulating an underlying system.
Modeling how a system behaves won’t tell us how it is built underneath the hood or when it might break.
In economics, this is a major problem. Our financial systems are virtual systems built using political, legal, and social structures. The ability to perfectly describe the behavior of a financial system won’t help us if a problem comes from the underlying legal, political, or social environments. There are many circumstances where a financial system stops behaving as prescribed, and any conclusions from modeling finance become irrelevant.
Social economic problems often arise not because of poor design of a financial system, but because of a disconnect lower down the “stack”(as one would say in programming). Many people are unbanked or unemployed. When you are unbanked, it doesn’t matter how well banking works, you simply can’t take advantage of the system. When you are unemployed and without income, it doesn’t matter how well our factories, supply chains, or businesses work, they are simply inaccessible to you.
If we want to fix problems, we need to recognize whether a system A) Has problems arising from its design, or B) It fails to behave as designed due to underlying problems, or C) both of the above.
If you have both kinds of problems, you might be f***ed. Good luck with that economists!
Virtual Systems and Information Systems are Different
Initially, I failed recognize that virtual systems and information systems are different. Based on my interests computer science, moral philosophy, and social phenomena like economics, I have been trying to create terms and concepts that work across these domains. Such terms might include information, information system, knowledge, etc. Armed with such concepts, we could talk about the human mind(irregardless of your position on metaphyscial debates), simple deterministic machines, or complex emergent social phenomena using the same language and tools.
Exploring these concepts has made it clear that each type of these systems: physical, virtual, and informational, are related but distinct.
The Need for Virtual Systems
If you learn about differential equations, you’ll discover there are lots of processes in the physical world that don’t have a closed form, or equation, as a solution. I took a differential equations class as a college freshman in 2005. The progression of that course initially gave us the illusion that these tools could solve most problems. As long you were given an equation of the relationships between quantities, it appeared, you should be able to find an equation giving the values of those quantities over time. Though more complicated, it worked as smoothly as algebra, at least at first.
About midway through the course, our professor started showing examples without closed form solutions. This was surprisingly easy. It was clear the equations in our previous homework exercises had been cherry-picked for their solvability. It doesn’t take much complexity for equations to fail us, and it doesn’t take much uncertainty to throw a wrench in estimation techniques. Otherwise we could easily predict the future.
Later I took a class from the CS department on Algorithms. Among other things, we studied recurrence relations: discrete sequences where each successive value is computed using a simple equation with previous value(s) as input. Surprisingly, the techniques used for solving recurrence relations look very similar to the techniques used on differential equations.
Ultimately, both these mathematical processes, whether discrete or continuous, can be said to be “feedback”. The “output” of a system is also an “input” affecting its behavior.
The wikipedia page on feedback pulls a quote from Feedback Systems: An Introduction For Scientists and Engineers, by Astrom and Murray, to highlight the challenge of identifying causality in a feedback environments:
Simple causal reasoning about a feedback system is difficult because the first system influences the second and second system influences the first, leading to a circular argument. This makes reasoning based upon cause and effect tricky, and it is necessary to analyze the system as a whole.
I took a feedback/control theory course in 2010. We used the Astrom and Murray text quoted above. I struggled with that material much more than the content of the other courses mentioned here. Seeing a matrix in an exponent, or hearing the term: eigenvector, still triggers memories of gruelling mathematical labor, much of which I failed to complete or did incorrectly.
Even so, I feel the effort payed off, I learned some useful stuff, and somehow passed(thanks to generous grading by the professor).
Feedback and Control Theory offer more than just mathematical tools for predicting or manipulating the outcomes of the systems of our physical world.
Control Theory highlights the philosophical way we create boundaries dividing the world into seperate systems, and identify interactions as inputs and outputs.
Our philosophical boundaries are not simply arbitrary. Initially, it seems like we design the mathematical tools around our philosophical boundaries. We measure and relate things quantitatively based on the way we conceptually organize the world in our minds. But I would to suggest that the reverse happens as well. Our philosophical boundaries arise through learning the underlying mathematical structure of the relevant systems.
In Control Theory, the world is divided into 4 parts based on 2 distinctions: controllability, and observability.
There are things we both control and observe, things we observe but not control, things we can neither observe nor control, and surprisingly, things we control but can’t observe.
Even though they sound like something from the religious mantra popularized by Alcoholics Anonymous: “God grant me the … wisdom to accept what I can’t control.”, controllable and observable are precisely defined mathematical terms. They have definitions that look like something you would see in calculus or analysis.
I think it’s possible to relax mathematical terms into philosophical concepts while retaining intellectual integrity. Instead of “Controllability” and “Observability”, we can talk of “boundaries of knowledge” and “spheres of influence”.
We must recongize that these relaxed concepts ARE NOT the same thing. They are merely parallel or similar ideas. There are things which can be explored philosophically which we may not be able to describe mathematically or test scientifically. I think fields like economics especially, must concern themselves with such philosophical questions, because econ is closely related to both morality and politics, which can’t be put into simple equations.
Bertrand Russell, a famous mathematician, had some good insights as to the value of philosophy, while still being a careful rigorous thinker:
Building the Virtual Using The Physical
Precise, holistic, mathematical models of the physical world are hopelessly intractable.
And yet, as humans we are able to make many useful and accurate observations about the world around us. Even these hopelessly complex physical systems appear to be regulated by causal mechanisms we can observe and relate to. Is it all an illusion?
Before proceeding, let me reiterate, we are not going to be making a mathematical or scientific exploration, but a philosophical one. I want to be informed by science and mathematics as much as I can, and use their concepts when they fit, but there are many ideas and decisions we must grapple with as humans without an empirically established imperative.
The desire to use science to test knowledge and change our beliefs, is a moral position. Ironically, it is ultimately philosophy, and not science, that leads us to this moral position. Once embraced, positive experience reinforces the utilitarian value of scientific process. Science, philosophy, and math can work together.
It is ultimately information that is the glue between physical and virtual systems, that allows us to build our virtual realities in a physical world.
What is information?
The big philosophical question we must address, centers on the nature of information. What is the difference between a boat that travels across water, and a wave that similarly travels across water?
Boats have speed and direction. A wave has speed and direction. A wave might propagate in all directions, but that is not the defining difference.
The wave is not a thing itself, merely a pattern built on other things. It is a virtual thing. The pattern emerges because of the underlying relationships of the things on which it is built. In this case, the molecules in a wave of water have physical relationships that cause them to move in response to the movement of their neighbors.
There is much to explore here, but let’s cut to the chase. By that I mean the definitions/descriptions I promised earlier.
A) Information — Configuration independent of medium, comparable under an interpretation.
B) Interpretation — Mapping between configurations with similar or identitical computation. Some physical process is needed to perform this “map” between information encoded in different mediums.
C) Computation — Evolution of information, or evolution of configuration.
These descriptions appear to be circular. Is that a problem?
- Information is described using interpretation.
- Interpretation is described using computation, and finally,
- Computation is described using information.
But if you notice, we have a base case. The base case is this: computation can be the considered the evolution of information OR configuration. So descriptions A, B, and C above each depend on what we mean when we say configuration. That is a tricky question. It is worth exploring in detail, but we won’t do it here.
Suffice it to say, information exists on a medium, but the medium itself becomes irrelevant, only the computational evolution of that information matters. For example, waves can travel similarly through many different medium; the behavior of wave propagation in a medium can be described with simple coefficients. Two different medium could have the same coefficients even with different underlying material, in which case, the speed and energy loss would be the same. Identical waves can appear in different medium.
The wave, in this case, is the information. Pairs of waves in different mediums can have comparable interactions so long as you correspond them carefully.
This is how information is an abstraction of various possible physical configurations with similar interactions.
Note that interaction and evolution are necessary for information to exist. If there are no interactions or evolutions, it’s impossible to say whether two different configurations of physical mediums are really comparable.
Often we “store” information, in that we encode it into a fixed, unchanging, medium. This fails to be information unless we can then extract it again, transfering it into another medium that performs interactions or computations.
A storage medium is only an holding stage for information between computation mediums.
Note also: often, interpretation creates configurations that are only comparable, not computationally identical. Our imagination is a computation medium that processes information from the world around us or information encoded in media we consume like books or television. The imagination usually reproduces the original computational environment imperfectly. Barring mental logic and mental math, the imagination only computes approximately. It is a lossy interpretation. This is why we don’t really consider the imagination to be “real”, even though imagination is a physical process.
An information system is a system that has structures imposed to perform interpretations and computations. We talk about information systems on an information level, the underlying physical medium and underlying physics is irrelevant. Computation is consistent interactions of comparable configurations across medium.
I’m sure you can see the strong influence of computer science here, but also hope you see how these ideas can be applied to the human mind or human society, even without perfect physical descriptions of how each of these work.
Now that we have described information, computation, and information systems, we need to talk about virtual systems.
Virtual Systems: Constrained Interactions of Typed Information
Virtual systems are built on information systems, but calling something a virtual system implies the existence of abstractions imposed on the information, in addition to requiring consistent computation occurring across comparable configurations of different physical media.
So basically, in Computer Science lingo, Virtual Systems go beyond mere information systems, by imposing types on the encoded data.
In a computer, the data is not merely ones and zeros, but ones and zeros encoded to represent something abstractly. The type tells you what the data represents.
Types can involve all different levels of abstraction. A type of data could be an integer or a number, or it could be an integer or number that represents something specific, like temperature or the temperature of a specific room.
Types always impose constraints on the way information is used in computation. For example, integers can be added, multiplied, or divided, but it doesn’t really make sense to concatenate integers. Concatenating integers breaks the abstraction, because the operation then depends on the representation.
If you assign units to a number or an integer, that further constrains how you use the underlying data.
You can’t add inches and seconds together. To add seconds and years you must convert units.
Virtual entities exist on virtual systems where types dictate abstractions imposed on information and constrain the way that information interacts or equivalently what computations may be performed on that data. These restrictions lead to virtual entities that follow virtual rules as opposed to physical entities which follow physical rules.
Virtual is REAL!!!
It’s very important to emphasize that virtual systems and virtual entities are real. We sometimes forget this because there are a lot of possibilities for how you can organize virtual systems. The possibilities are so diverse it almost seems invented, contrived, or imaginary, unlike the physical world which has such clearly defined limitations. But Virtual systems are very real, even if they involve patterns of interactions agnostic of medium(computation), and abstractions imposed on information constraining computation(types, or virtual entities).
As humans we are virtual entities. Our physical matter could be replaced without changing our identity or what makes us who we are. The same could be said of society or a computer program.
The capabilities of our virtual systems, whether the human mind or human society, can be used to better describe and predict the behavior of the physical systems on which they are built. By recognizing imposed structures and computation, even if they are imposed by a system subject to underlying failure, we can effectively simplify the physical world into virtual interactions.
A mistake we could make, would be to not recognize the true constraints of our virtual systems, falsely treating them like a physical system, instead of accurately representing the rules they follow.
Another fatal mistake would be failing to recognize the relationships that create these virtual systems.
Physical Matter cannot be created or destroyed, thanks to the law of conservation of matter, but there is no such limitation on accounting information, or better yet, virtual resources allocated through accounting virtual information systems.
It can be INCREDIBLY empowering to recognize the true constraints and capabilities of our virtual systems. That allows us to act up to the boundaries of these systems and realize our full potential if desired.
It is also EXTREMELY important to recognize the foundations of these virtual systems. In the case of finance, what social, political, and legal relationships help create these productive financial relationships? What things might lead these underlying relationships to break down, which would then require us to give attention to social, political and legal issues, assuming we want financial relationships to continue to function?
I don’t have the all the answers, I’m trying to find the right concepts to be able to ask insightful questions.
