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Ashby’s Law of Requisite Variety: The Value of Diversity

Diversity is an attribute that can be beneficial in a large range of fields - from national economies to natural ecosystems, diversity is essential to survival, stability and even growth. At Viable Systems, we hold diversity in high esteem - after all, diversifying the Tezos ecosystem is one of the reasons why we set out to develop TezEdge, a new Tezos node shell written in the Rust programming language. In this article, we take a look at diversity from a novel angle, examining it through the Law of Requisite Variety, a theory which is at the core of our company’s philosophy.

In his 1952 book "Design for a Brain", the British biologist W. Ross Ashby coined The Law of Requisite Variety, a concept he described in the context of homeostasis, which is the method by which organisms living in changing environments succeed in maintaining critical variables (for example, internal body temperature) within tightly-defined limits.

Ashby identified variety as a measurement of the number of possible states of a system. His Law of Requisite Variety stated that for a system to be stable, the number of states that its control mechanism is capable of attaining (its variety) must be greater than or equal to the number of states in the system being controlled. Or, as he put it:

“Only variety can absorb variety.”

A common interpretation of the so-called Ashby’s Law is that for a system to be stable, the number of states that its control mechanism is capable of attaining (internal variety) must be greater than or equal to the number of states in the system being controlled (external variety). The ambiguous meaning of system is intentional - a great number of things can be considered systems, for instance organs, living beings, companies, organizations and machines.

Variety, diversity, heterogeneity - many words for the same property: the quality or state of being different or diverse; the absence of uniformity or monotony. When we apply Ashby’s Law outside of biology, we can see what makes it so special - the Law holds true across a wide variety of fields,

To provide a better understanding, here are five cases that demonstrate Ashby’s Law in action:

1. Cognitive science

Within a single organism, the variety of neurons determines the variety of circuits that can be built and, by extension, designates the variety of an animal’s behavioural repertoire.

In the 1960 book Design for a Brain, Ashby described the nervous system's unique ability to produce adaptive behaviour. The brain is a complex system with a high degree of internal variety. If the host organism is to thrive in its environment, it must respond to a great variety of external stimuli by tapping into an equal (or greater) variety of context-dependent behavioral responses. In Ashby’s words: “A variety of disturbances will therefore evoke a variety of matched reactions”.

Neural diversity, that is, the physical diversity among individual neurons within a single organism, may be key to the brain’s ability to generate a rich repertoire of behaviors based through neural interactions. A high degree of neural diversity may be the reason why neural dynamics do not get stuck in so-called attractor states, explaining why the brain can quickly react to environmental stimuli with a great variety of responses, and with less effort than a system where all cells are identical.

Comparing the nervous systems of nematodes, fruit flies, mice, rhesus macaques and humans shows increasing levels of internal variety. The more advanced nervous system are hierarchical structures, with increasing levels of complexity at higher levels. At the basic level, such advanced nervous systems are composed of the same elements that are found in basic computations made within cells (like in single cell organisms), but also computations made within networks of cells. This kind of architecture provides dynamic stability of the system while opening up a considerably greater variety of context-dependent behavior.

At the level of individual neurons, neural variety may allow information to be integrated over varying periods of time. At the population level, neural variety is proposed to be involved in

complex processes, including our representation and interpretation of the world, our capacity to form rich memories, and our capacity to produce appropriate, context-dependent behaviors.

The genetic, molecular, and morphological variety of the brain leads to a functional diversification that is likely necessary for the higher-order cognitive processes that are unique to humans.

The human brain may be the single most complex object known to mankind. We have become the powerful and widespread species on our planet, in large part aided by our keen ability to adapt to a variety of environments and situations.

The high variety of the human brain has, ironically, prevented us from fully understanding how the organ operates. This has been astutely described in the words of Emerson Pugh: “If our brains were simple enough for us to understand them, we’d be so simple that we couldn’t”.

2. Immune systems

Coming into regular contact with a greater variety of pathogens increases the variety of an immune system’s major histocompatibility complex (MHC) types, increasing its ability to defend against a greater variety of infectious diseases.

The European conquest of the Americas was preceded by a series of devastating epidemics that annihilated the native population. Between 1492 and 1650, it has been estimated that 80% of the native populations of Central and South America had succumbed to infectious diseases. However, the native populations had not lived in a pristine, disease-free environment. This begs the question; why didn't Indian diseases cause similarly devastating epidemics among the Europeans after they returned home?

Most infectious epidemic diseases originated in domesticated animals. Measles, smallpox and tuberculosis came to humans from cattle, flu came from pigs and ducks, and pertussis (whooping cough) came from pigs and dogs. Due to its large size and horizontal shape, the Eurasia continent had a rich variety of animal species suited for domestication (dogs, horses, sheep, pigs, cows), in addition to certain species that lived side by side with humans (cats, rats). On the contrary, pre-Columbian societies in the Americas kept fewer animals (llamas, guinea pigs, chicken). Additionally, their spread across the continent was further limited by the large differences in climate and seasonal cycles between the more north-south axis of the Americas.

Europeans therefore had a greater variety of domesticated animals. Co-existing with these animals resulted in the spread of animal-borne diseases, which in turn lead to an increase of major histocompatibility complex (MHC) types in the immune systems of Eurasians. MHC types are proteins that teach immune cells how to recognize which molecules to attack and which to allow into our body. When European settlers made landfall on the American coasts, the native Americans had few MHC types in their immune systems, and as a result they were overpowered by the spread of several epidemic diseases that had originated in Eurasian animals (smallpox, measles, influenza, typhus, bubonic plague). The effects were devastating for native populations across the Americas, with the death toll numbering between 57% to 95% for various communities. This reduction in populations paved the way for the eventual European conquest.

3. Ecosystems

The diversity of species within an ecosystem allows it to withstand a variety of environmental changes without collapsing.

Ecosystems are systems that manage nutrient cycles and energy flows by incorporating a number of living and nonliving components. Through photosynthesis, energy enters the system and is incorporated into plant matter. Animals feed on plants and other animals, which aids the movement of matter and energy through the ecosystem. Carcasses and left-overs decompose and enrich soil, which promotes the growth of new plant life.

Ecosystems regularly experience changes. Some are more subtle, others more dramatic and sudden; wildfires, droughts, floods and so on. There are also changes that occur on a structural level, such as climate change, ice ages or the acidification of oceans. Thus, ecosystems must constantly undergo internal changes to find ways to cope with these new conditions.

Ecosystems may possess a wide range of species diversity. Water-starved deserts contain a relatively low diversity of species, while dense rainforests are among the most diverse ecosystems in the world. In high-diversity ecosystems, several species are thought to perform the same functional role. While there is some redundancy across multiple species performing the same role, the loss of one individual species might not affect the overall functioning of an ecosystem.

On the other hand, a harsh environment such as a polar desert contains little diversity and is reliant on a select few species that are capable of surviving in such difficult conditions. In Taylor Valley, Antarctica, a single nematode species, Scottnema lindsayae, is responsible for a significant portion of carbon cycling. Researchers found that a regional drop in temperatures led to a 65% reduction in nematode population, which in turn led to a 32% loss of function in carbon cycling. On the other hand, the extinction of one species of beetle in the highly diverse South American rainforest is less significant, as there are many other beetle species (or other insects in general) ready to fulfill its role.

The lower the diversity of a species within an ecosystem, the more fragile it becomes to changes in its environment. Conversely, the higher the diversity of species, the more robust an ecosystem becomes to these changes.

Species diversity across different ecosystems is not only fascinating to observe, but it is also a crucial tool in the survival of life on Earth. We can never know what the future holds, significant changes can come rapidly and without much of a warning. What we can do is prepare ourselves as best as we can, which means preserverving the rich diversity of animal and plant species, creating a rich variety of organisms that can fulfill the various roles needed in the preservation of life on our planet.

4. Organizations

Increasing the variety of an organization’s membership allows it to overcome an increased variety of problems in the pursuit of its goals.

Organizations—whether they are businesses, political parties or militaries—benefit from an increased variety among their members. A diverse group consisting of individuals with a variety of backgrounds will be able to tackle a greater variety of problems. Contrary to the cliche image of the modern multi-ethnic office, variety is not limited to race—real variety is beyond skin-deep.

Cultural background, residence, social class, education, character traits, temperament, even seemingly minor aspects such as personal interests or favorite music genres, all of these items contribute to an individual’s variety. The greater the variety of individuals within an organization, the richer is it’s aggregate variety, allowing it to draw upon a larger range of ideas, viewpoints and opinions, which improves its ability to solve problems and achieve goals.

A 2015 McKinsey report on diversity evaluated 366 public companies from a range of industries in Canada, Latin America, the United Kingdom, and the United States. Focusing on metrics such as employee diversity (racial, gender) and financial returns, the study found that “the unequal performance of companies in the same industry and the same country implies that diversity is a competitive differentiator shifting market share toward more diverse companies.”

Conversely, companies that are in the bottom quartile both for gender and for ethnicity or race are statistically less likely to achieve above-average financial returns than the average companies in the data set. In other words, they are lagging behind the average rather than just not leading.

Similarly to the report from McKinsey, researchers at the University of Michigan found that diverse groups solve problems more effectively than a more homogenous team. The researchers created a mathematical model that proved the concept of diverse organizations having a greater arsenal of solutions for solving problems. In a problem-solving context, a person's value to the organization depends on their ability to improve the collective decision. Therefore if competition depends on continuous innovation and the introduction of new products, firms with organizational forms that take advantage of the power of functional diversity will perform better than those that do not.

5. Macroeconomics

A sufficiently diverse economy is capable of producing a large variety of products and services, enabling it to adapt to a greater variety of situations in the global economic environment while being a strong predictor for continued economic growth.

In 2009, Harvard University economists Ricardo Hausmann and Cesar Hidalgo published a paper in which they identified economic diversity (referred to by them as economic complexity) as a predictive tool for economic growth.

The value of diversifying a country’s economy is clear. Take, for instance, oil-rich countries such as Norway and Chile that have used money from the sale of fossil fuels to expand other economic sectors (particularly manufacturing and services). Such countries are well-equipped to handle fluctuations in the prices of oil because even if it drops, they can rely on other sectors of their economy. Whereas an economy such as Russia’s (which has diversified little and is still heavily-reliant on oil money) suffers when oil prices collapse.

Hidalgo and Hausmann argue that not only does economic diversification help a country survive through a crisis, but also that it is an indicator of continued economic growth. “The Economic Complexity Index (ECI) measures the productive capabilities of large economies. In particular, the ECI looks to explain the knowledge accumulated in a population and that is expressed in the economic activities present in a city, country, or region.”

What this means is that to attain a high degree of economic complexity, a country does not necessarily have to invest evenly into a great variety of industries, but rather that it must foster the knowledge necessary to build up a variety of industries, even if the industries themselves are relatively small.

Simply put, economic complexity is formed by how many products and services the country is capable of producing. This means that even though a country may, for instance, have a very small car-manufacturing industry, it is the technology (tools, knowledge, and particularly the know-how) behind the production of a car that makes the industry valuable to the country in terms of economic complexity.

Economic complexity is highly accurate in predicting future growth, “which it has been shown to do better than any other single measure in predicting growth”. In a 2021 paper, Hidalgo described how an “economy’s future level of income (such as GDP per capita) was correlated with the ECI after controlling for its initial level of income and other factors. As Ricardo Hausmann stated “poor countries produce few things that everyone knows how to produce, while rich countries produce many things including some things few countries know how to produce. Growth is being driven by a process of diversification to enter more, and increasingly more complex, production.”

Diversity and Tezos

Like any system, the Tezos blockchain ecosystem benefits from an increase in the diversity of its nodes (multiple implementations across a range of different programming languages & operating systems). Adding a new Rust-based node shell in the form of the TezEdge node will allow us to verify that the protocol is unambiguous, keeps the door open for innovation and secures the honesty of all participants.

Even if there is an attack vector or bug in any of the Tezos implementations, the network will remain intact as there is a diverse range of nodes available. Ashby’s law is present even in the case of blockchain ecosystems, as it is in a multitude of other scenarios.

When multiple teams work on a variety of nodes, it becomes easier to detect and fix bugs before they can negatively affect the ecosystem. Since the responsibility for validating the chain does not lie on any single implementation, bugs are effectively quarantined in a limited subset of nodes and are therefore unlikely to affect the entire blockchain.

For all references and sources, please see the Google Document with Chicago-style footnotes.

We hope you have enjoyed this week’s article. Diversity is a core value of our company. Through this article, we aim to explain our appreciation for diversity, and hope to inspire our readers to similarly view its positive effects through the analytic lens of Ashby’s Law. To read more about Tezos and the TezEdge node, subscribe to our Medium, follow us on Twitter or visit our GitHub.

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