Information and Energy Theory of Value
Introduction
The ideas of Marx have been cemented in history; despite the massive social and economic changes since his time, these ideas still remain popular in academia and continue to be debated and refined. Most of the focus is on Marxist conceptions of communism, capital, and historical materialism. These ideas are constantly reapplied to modern issues, and world events are continuously analyzed through a Marxist lens. Less discussed is Marx’s Labor Theory of Value (LTV), its successes, failures, and potential successors.
Background on LTV and the Way Forward
Briefly, some definitions and background. Any commodity has a use-value, that is, it has some value determined by its uses. For example, clothing has value because it can protect its wearer from the elements, food has value in keeping its consumer alive. In trading commodities, say clothes for food, an exchange-value also exists. While use-value relates to the value a commodity derives from its uses, exchange-value is its value in exchange with other commodities, essentially its price. Some portion of food can, on average, be traded for a given amount of clothing. This is the exchange-value of the commodities. One of Marx’s insights was that the average exchange-value of commodities will depend on the labor expended in producing them. If, on average, it takes 10 hours to produce a given amount of food and it takes 100 hours to produce a given amount of clothing, then that amount of food will have one-tenth the value of the clothing. This is the essence of the LTV.
The main strength of the LTV is that it allows the quantification of value, especially where averages are concerned. While there may be variance in the productivity of a given worker, an average productivity of many workers will tend to a fixed quantity for a population (by the weak law of large numbers). Then if the quantity of labor required to produce any given commodities is known, their exchange-value can be perfectly quantified. Any increase or decrease in the efficiency of producing a commodity will cause a decrease or increase in its exchange-value, respectively. This being said, weaknesses in the LTV are apparent.
One of these weaknesses is in addressing the problem of scarcity and externalities. Take oil for an example case: oil is relatively easy to acquire but fundamentally limited. Oil isn’t “easy” to acquire per se but the labor required to extract it from the Earth and refine it for combustion is much less than the labor required to harvest an equivalent amount of energy from another energy source. That is, by the LTV, oil should have a lower exchange value than other combustible energy sources, like wood. But, oil is fundamentally a limited resource, by considering only the labor required to extract it, a key portion of its value is missing: its scarcity. The LTV is missing the information that oil is limited.
Another case is in the value of gold. By Marx’s analysis, gold’s use-value is its exchange-value. That is, gold derives its use-value by the fact that is well suited for being a currency. It is resistant to tarnishing and intrinsically rare on the Earth’s surface. Copper has similar properties, though it is somewhat more prone to tarnish. Copper is more labor intensive to produce than gold, requiring more mining and more heat to refine. Thus, by a pure LTV, copper should be more valuable than gold. The higher value of gold derives from the information of its scarcity and its physical properties. This information is quantifiable, and therefore can be used to add a value to it that goes beyond the labor, taking into account its scarcity. To first approximation, both elements can be quantified in the Earth’s crust, and their relative value can be compared by their relative proportions. Going even further, the information of the location of deposits of each can be quantified, and thus contribute to understanding their relative value.
The previous two cases both argue that information is useful in valuation for quantifying scarcity, but that’s not the only reason for including it in a theory of value. Information is also required to specify the method of labor. For example, not just any sequence of actions can turn raw cotton into a shirt, but there also isn’t a single way to turn cotton into a shirt. There are multiple methods, some more efficient than others. Converting cotton into a shirt with a loom is much easier than without a loom. The labor required to produce a loom and a number of shirts will eventually be less than the labor required to produce the same number of shirts with no loom i.e. the efficiency gained will pay back the labor cost of the loom. Then the information specifying how to build a loom has a value to it. A worker building skill also reflects having greater information about their task. As they improve, they learn tricks to improve their efficiency, they learn to deal with complications, and to perfect their product.
Marx acknowledged some of these limitations in LTV, especially where it concerned more skilled workers, hence his frequent use of averages. The big problem in his time was quantifying information. Things have obviously changed since his time. In the age of computers, information, and machines, we are approaching a point where information can truly be quantified; the rigidity of a machine’s labor can allow the information in its labor to be quantified. The complexity of human labor makes it nearly impossible to quantify the information needed to complete, but this isn’t the case with machines. Information theory is what will allow the information in a machines labor to be quantified.
Background on Information Theory and Kolmogorov Complexity
Before discussing automation, we’ll need to cover some information theory. Information theory is a mathematical discipline that emerged with the growth of communications in the early 20th century. In the West, it was pioneered by Claude Shannon, who is generally considered to be the “Father of Information Theory”. We’ll be focusing on a different form of Information Theory, developed by Andrey Kolmogorov in the Soviet Union. While Shannon’s formulation was purely based on probability theory, Kolmogorov formulation also included aspects of the theory of computation. Kolmogorov’s complexity measure shall be central in our quantification of information, we will need some more background to define it though. The interested reader should explore the citations to gain the mathematical picture of Kolmogorov’s theory.
Let’s begin with the basics. A computer is a machine with some internal state that receives as input a program, which can change its internal state and may cause it to output a symbol. A universal computer is a computer that can simulate any other computer, that is, it can run a program to make its own operation identical to any other computer. Most computers are universal, including any that you are reading this on, whether that’s a tablet, a phone, or a desktop computer. The output of a computer can be many things, it could simply be the sequence of characters “Hello, world!” or it could be all the pixel values that represent a fast-paced battle in a modern video game. For our discussion, let’s interpret the output as a sequence of abstract symbols, which we’ll refer to as a string. The symbols could be ones and zeros, letters, or symbols specifying the RGB color of a pixel on a screen. Given a universal computer U
, the Kolmogorov complexity of a string x
is the minimum length computer program p
that can produce that string.
To make things more concrete, consider the string of 100 sevens:
7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777
Simply writing it out takes 100 characters. However, the simple Python program:
print(100*"7")
takes only 14 characters. This program is not the minimal program, but it illustrates the central idea: strings are compressible and one way of expressing this is in the minimal length computer program to produce them. One neat exploitation of this fact is zip bombs, which can wreck havoc on a computer.
Kolmogorov proved that for any other computer, universal or not, no program shorter than the Kolmogorov Complexity capable of producing a given string exists. Since every string has a minimum length computer program to produce it, Kolmogorov complexity actually quantifies the complexity of a string. If the minimal program to produce a string is very long, then it is a very complex string. In this way, Kolmogorov complexity is a measure of the information contained in a string.
Kolmogorov Complexity and Automation
Our output string doesn't need to be words or pixel values, it can also be symbols that control a motor or machine. In this way, the output of a computer controlling a machine can be considered to be a sequence of actions by the machine. Thus, the information required for a machine to convert raw material to an output commodity can be quantified with Kolmogorov complexity. This does depend on the machine in question: a more precise machine would require either a longer string or more symbols to specify how to perform a given action. Nonetheless, Kolmogorov complexity serves as a basis for quantifying the information required for a machine to convert a raw material into a different commodity. It presents a lower bound on the information required to perform a task. From this fact, we can propose a successor to the LTV, the Information-Energy theory of value (IETV). Since Kolmogorov complexity can quantify the information required to complete a task, it can be used to place an economic value on the complexity of a machine’s labor. Along with the energy required to perform this labor, the value added to a commodity by the labor can be precisely quantified.
There is one major problem: Kolmogorov complexity is not generally computable This isn’t the end though. The length of program to complete a given task is still quantifiable, we simply won’t always be able to find the minimal length to complete the task. In a competitive program market, a shorter length program to run on a given computer-machine pair will necessarily be more useful. It will take less time to compute, consume less computational energy, and will require less memory to store. Thus, competition will serve to drive the complexity of programs towards their Kolmogorov complexity. Keeping in mind that these programs will be those controlling manufacturing robots and 3D printers, small advantages in one program’s efficiency will mean a lot for overall productivity, as manufacturing in this way can be very costly in time and resources.
What is Labor and What is the IETV
The working definition of labor used here is that labor is the information and energy necessary to convert some materials into other materials. In other words, any labor requires energy and the specifications for performing the task at hand. In Marx’s time, most labor was performed by humans and animals, little was performed by machines. Because of this, the information necessary to perform a task was practically unquantifiable that is, it could not be converted to a numeric value. With the ubiquity of machines and the constant rise of automation, this is no longer true. The information needed to specify a task can be quantified by the complexity of the program performing that task, and can thus be added to calculations of economic value. The information to program a machine and the energy to run the machine can determine the gain in value by its operation on raw materials. Even the values of the materials can be calculated, from the energy to extract and transport them and the information to find them and perform the extraction and transportation process.
The labor theory of value can therefore be superseded by an information and energy theory of value. Not only does information better describe the effects of market behavior on value than that of LTV, IETV also allows physical grounding of costs. Energy and information are both calculable through thermodynamics, value can then be converted into universal quantities based on the laws of Nature. IETV is thus a better basis for valuation when dealing with extraterrestrial beings, which may very well be necessary in the future.
Subjectivity, Value and Nature
For a human being, value is inherently subjective. That doesn’t mean that is doesn’t depend on external or objective factors, it simply means that it will vary between individuals and even between the same individual at different times. Both LTV and IETV are concerned with economic value, essentially the exchange rates of commodities. They don’t claim to have the power of determining a universal value of a thing. That being said, the IETV has much more power compared with LTV for evaluating economic value of commodities with unclear use-value.
How can the LTV be used to find the economic value of art? Marx acknowledged the use-value of art, saying that it derived from the enjoyment it brings human beings. By a LTV, the exchange-value (price) of a piece of art should be quantified by the labor time put into it. This clearly falls apart though, as the labor time put into an artistic production is not necessarily a reflection of its quality. Information about a piece of art must be used to determine its economic value. Historically, this may be information about its age, the artist that produced it, or its ownership. The economic value of a piece of art is at least theoretically calculable with IETV, with plain LTV there is no satisfying way to find it.
The value of nature is also poorly quantified by LTV. At best, LTV evaluates the economic value of region based on its potential productivity for human beings. An IETV can quantify the value of a region by the information in it. The economic value of a rainforest can be calculated by the genetic complexity of its denizens and not merely by the lumber or food than can be produced by it. IETV is more amenable to a naturalistic outlook of the world, which doesn’t reduce living beings to their potential productivity, instead valuing things by their inner nature, quantified with the tools of information theory.
Conclusion
The ideas of Marx have been a source of great controversy and strife in the world. While his ideas on socialism and historical materialism are often addressed, his ideas on value are often overlooked. By replacing his labor theory of (economic) value with one based on energy and information, a theory of economic value in the digital age can be created. We now can quantify energy and information to a degree never before possible; this new ability will aid us in understanding economic value in the age of automation, and could even allow us to base economic value in the laws of physics itself.
Thomas M Cover and Joy A Thomas. Elements of information theory. Wiley, 2012.
Karl Marx, 1818-1883. Capital, a Critique of Political Economy. Chicago :H. Regnery, 1959.