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SUPER-SUMMATIVE

square-50cm-spacer.jpg A discussion paper by John Wood
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square-50cm-spacer.jpg Nurse Money Maginfying Glass.svg

ABSTRACT

This paper outlines some key criteria for re-designing unit-based money. It advocates an approach that replaces the exclusively summative nature of money with a relational mathematics that acknowledges the synergistic nature of collaboration. What we recognise as money (i.e. cash, digital banking and cryptocurrencies) were all designed to replace local social trust with accountancy that is universally uncontroversial. Unfortunately, its fungibility, lack of limits on upscaling and human greed mean that it will always be prone to speculation. A relational approach could enable it to encourage local trust and to reveal unforeseen opportunities. Where unit-based currencies use numbers in order to appear abstract and uniform (i.e. to mask internal synergies) a relational banking approach would be designed to cultivate new synergies at the community level.

Context

At the time of writing, the UK is grappling with a crisis in the 'care industries'. 'Food banks' have become the 'new normal' and a number of large UK towns will soon introduce 'warm banks'. However, rather than focussing directly on the behavioural causes of famines, fires, floods, and energy insecurity, governments focus on the management of monetary incentives and rewards. One thing the COVID pandemic reminded us is that care and money are incommensurable. As the Beatles explained, 'money can't buy you love'. Nor can it buy you trust, happiness, fun, or care. This is probably because it was designed for imperialistic expansion, rather than for sustaining local communities. While good fiscal policy can, admittedly, procure many of the conditions that underpin the wellbeing of citizens, it works by regulating the direction and flow of incentives, taxes and other financial instruments. These methods are too abstract, remote and indirect to orchestrate the complex feelings and subtle emotions that encourage goodwill and build trust within communities. Although nurses and care home workers obviously need remuneration in order to eat and to pay their bills, the nurturing and care they provide cannot be bought with money. A recent article cites a 10% increase in USA Care Home deaths after privatisation (see post-2019 study). Some are seeking to address this issue by making care systems more accountable.

Defining Money

Although economics is a huge field that looks well beyond the way that currencies are designed, much of the theory behind it reflects human behaviour in a money-driven world. Here, by 'money' I mean the bankable, unit-based media of exchange and investment that developed from fiat currencies. Unlike barter, money facilitates transaction without needing a ‘double coincidence of wants’. Traditional economists regard money as:

  1. A medium of exchange
  2. A standard of deferred payment.
  3. A unit of account
  4. A store of value

This paper accepts all but the fourth presumption. It disagrees with the claim that money can 'store' value.

Money Cannot Store Value

Storing value might seem like a reasonable aim when agricultural futures are favourable and trustworthy. Unfortunately, food security has become increasingly precarious of late. We are tied into into a global web of unpredictable and interdependent factors including military conflict, biodiversity losses, and climate change. These are already changing the 'value' of everyday things. If the ecological resilience afforded by Gaia is reduced, this could quickly erase the usefulness of money as a viable medium or standard of exchange, therefore money cannot store value. Just as the disconnect between clocks and their surroundings makes them ignorant of lived time, so the abstract and profoundly value-less nature of money disconnects it from the intimate micro-level exchanges that enable whole ecosystems to survive and flourish.

Ideally...

Here are some properties we might expect from a well-designed monetary system:

  1. It should resist speculation
  2. It should be free and ubiquitous
  3. it should encourage, not replace, mutual trust
  4. it should promote creative synergy.
  5. It should be relational (i.e. aware of its context)
  6. It should be super-summative

N.b. the notion of 'super-summative' reflects the observation that money is designed to 'add up', not to grow. In the real (i.e. practical) world, everything we put together exceeds what we can 'account for' in terms of assets. In order to reinvent currencies that would support a creative, mutually caring world we will probably need to study living systems. It is only very recently (in evolutionary terms) that we came to regard economic matters as more important than the ecosystem. The good news is that ecology and economy derive from the same Greek word, so we can learn from the similarities between ecosystems and economic systems. Biological organisms use the flow of elements, (e.g. water, oxygen) to retrieve and store energy within, and around, their bodies. Until now they could take these currencies for granted and certainly do not seek to find advantage by intervening in their availability or distribution. Biological organisms do not hoard oxygen or water in order to gain advantage (as financial markets do). Nor do they fetishise energy in itself in the way that money can be traded speculatively and hierarchically, using supertools of the derivatives markets.

Money Is Blind and Forgetful

In the 21st century, humans have begun to relinquish managerial control of derivatives with an increasing dependency on AI (McWaters, 2018). Money was invented around five thousand years ago for building, expanding and sustaining large cities, colonies and empires (Graeber, 2016). However, where tributes could take the form of services, commodities, or assets of value (e.g. in-kind), fiat money developed from decrees or promissory documents backed by an emperor or monarch. nature of unit-based money made it useful for commissioning very large, risky projects. Unfortunately, money works partly because coins and notes were designed to forget the value, context, meaning and purpose of each transaction. Reducing them down to arithmetical units enabled money to work across boundaries of territory, language and culture.

Why We Chose Money

Some anthropologists have noted a correlation between cranium size and average group size that is true for all mammals (Dunbar, *). A few hundred thousand years ago, our brains evolved in size and our cognitive capacities grew. According to this hypothesis, Homo sapiens should be living in groups of around 100 to 150, because peer-based democracies become less effective for dispute settlement at a greater scale. The evolution of cities therefore required hierarchies at the social and managerial level. Somewhere between 6,500–3800 BCE in Mesopotamia, there appears to have been an unprecedented shift from 'responsibility' to 'accountability' as a basis for dispute resolution. In Dunbar-scale communities, most communication depends on local references and assumptions. Scaling up beyond the local led to a switch from orality to alphabetical writing. For trading, unit-based money became a low common denominator that would work for users in diverse cultures. As Georg Simmel (1900) explained it, the quality of money "consists exclusively in its quantity".

The Logic of Counting

As already noted, accountability (see 3 above) has been a key feature of money. Obviously, the term derives from the act of counting. The logic behind this depends on the shared assumptions that make addition and subtraction seem perfectly natural and reasonable. For example, there needs to be a tacit agreement that units of the same denomination are sufficiently identical to behave like numbers. If the uniqueness of each physical coin were to be too noticeable, disputes would make it less useful. David Graeber suggests that our sense of fairness ("I owe you one") and willingness to return the favour became the basis for unit-based currencies. By confining money to the logic of summation, rather than re-combination we made money 'add up'. Unfortunately, the concept of infinity is a recent one, in evolutionary terms. Although most humans can grasp the idea we are poor at imagining even moderately large quantities (Du Sautoy, 2009) and we readily confuse qualities with quantities (c.f. Kahneman & Tversky, 2011).

Money as a Tool

Our species has been digging up hard minerals for over 3 million years and making hand tools for around 2.5 million years. This presumably left us with a profound understanding of the logic of mining. Even cryptocurrency designers use metaphors of 'mining', 'exploitation', 'speculation' and granular reasoning when discussing their work. Graeber suggests that these processes would have given certain physical objects (talismans or tokens) a magical status (Graeber, 2001). This might also explain why money is, in essence, 'granular'. Money allows the spender to act remotely, i.e. to procure and despatch without needing to touch anything. It also works as type of tool in the sense that we use it to commission actions as though we had 'made' them. Georg Simmel has described it as "the purest example of the tool” (Simmel, 1900).

Money as a Supertool

We tend to think of the 'tool' as an exemplar of the local and the physical. In English we speak of 'calling a spade a spade'. (c.f. Heidegger). But scaling up social groups beyond the Dunbar number meant making unit-based money fungible. In effect, every transaction immediately 'launders' its previous context and purpose, whether good or evil. This is a form of alienation, as it requires users to visualise abstract possibilities that cannot be experienced directly. The Babylonian 'Code of Hammurabi' (1792–1750 BC) was the earliest known legal framework for delivering assets at a future date. This set the agreed price and date for future transactions. In this sense it established a basis for the first derivatives markets. In other words it made currency speculation more thinkable.

Collection as Addiction

Today, the richest individuals make their money by trading in buying and selling 'debts', or by buying the technologies that will do so. In 1900, Georg Simmel researched the habits of collectors, noting that “regardless of the amount, the liveliness of attached hopes gives money a glow” (Simmel, 1900). Gabor Mate is an addiction expert who believes that our whole society is now driven by compulsive behaviours (e.g. smartphones, workaholism, dieting, substance abuse, etc.). Marketing experts know how anticipation has become a powerful driver within capitalism. Scientific studies show how dopamine secretions in the brain can drive repetitious habits such as trading. The infamous 'invisible hand' of self-interest was once invoked to explain how money would trickle down to the needy. Unfortunately, it is trickling upwards in vast amounts. This is not only an issue of social justice. Money is shaping the Anthropocene in ways that are detrimental to living systems.

Quantifying Relations

Relations are much more than quantities or ratios. When distributing a finite number of equal 'things', ratios (perhaps, in the form of fractions, or percentages) may be helpful. However, relations cannot be represented adequately without including a rich set of relevant intrinsic qualities, in addition to their context. Working with simple ratios invokes a 'Law of Decreasing Returns' because these relational qualities are missing. Instead, by focusing more on relations, rather than on the parts they comprise, it is possible to harness the 'Law of Increasing Returns'. As Paul Romer said, “...possibilities do not add up. They multiply.” (Romer, 1991). This suggests that money should be used to trade in synergies, rather than in quantities.

Money is Alienating

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INTIMATE
DIRECT
SYNERGISTIC
Fairness in Mammals
Grooming in Primates
Family Caring
Institutional Caring
Cash Payment
Digital Payment
Currency Trading
Derivatives Trading
Super-Summatives
?
?

Accounting for Nature

Daniel Wahl (2016) highlights the non-numerical nature of the living world and some (e.g. Stefan Heidenreich) envision a world without money (Heidenreich, 2018). Kate Raworth offers a template for re-calibrating the relationship between economic and ecological health. Many worthy environmentalists and politicians use the term 'stewardship' to argue that humans must 'care for', or 'take care of' the planet. This concept is familiar within Christianity. It evokes images of pastoral care that pre-date modern industry and Enlightenment reasoning. Unfortunately, stewardship in the original sense, cannot be scaled up to modern megacities or corporations. This explains why Tony Juniper (the chairman of Natural England), applies pragmatic reasoning (i.e. "render to Caesar"), when arguing that, when trying to persuade big business to protect biodiversity, we must put a price on Nature. This is an irrational position to take. Whereas accountants are paid to make numbers add up, living systems are unique, multi-dimensional and emergent. They multiply according to mathematics that would be super-summative, elusive and incomplete.
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Above: John's slideshow & audio from a workshop at Goldsmiths University of London (16th Sept. 2019).

The Pleasure is All Mine

Utilitarian reasoning (e.g. "From each according to his ability, to each according to his needs" - Marx, 1875) applies idealistic, individual-oriented reasoning in pursuit of efficacies across the board. In monetary terms, each transaction should balance (every transaction will add up to 100%) in terms of a finite amount of money. This is reasonable when discussing issues of remuneration and fairness. However, as it uses inert (i.e. lifeless) identical tokens it is exclusively summative. It cannot 'grow'. However, beyond summative logic all relationships are manifold and synergistic. Celebratory exchanges are, therefore, 'super-summative'. Their totality exceeds the sum of their parts. There is a polite phrase sometimes used to camouflage the embarrassment of being thanked for a good deed: "Oh no, the pleasure is all mine". In monetary payment it is possible for one party to own everything. Of course, in (non-monetary) reality, nobody can ever experience all of the pleasures.

Some Non-Summative Mathematics

Kids are still taught to apply summative reasoning to team tasks, such as digging holes. This wrongly implies that the contribution of each member amounts to 100% of the whole task. However, if we focus on the efficacy of collaborative actions (i.e. by seeing things relationally) rather than by counting the individual output of each worker we will reach different conclusions. When we analyse the mathematical ratios that pertain among team members and the number of relationships among them we find, for example, that:

  • In a team of 8, each team member is responsible for 25% of all relations
  • In a team of 4, each team member is responsible for 50% of all relations
  • In a team of 3, each team member is responsible for 66.6% of all relations
  • In a team of 2, each team member is responsible for 100% of all relations^

Euler's Intrinsic Profit

In the simplest terms, a synergy may consist of two existing 'assets' that become combined to create a new, additional asset. The more ingredients we use, the more possible synergies we may find. For example, if we combine three assets we get the same number of synergies as the assets we started with. (i.e. 3 ingredients gives us 3 relations). By adding just one additional (fourth) asset we can get up to six synergies. Hence, a quartet is six times more synergistic, potentially, than a duet. Beyond combinations of three, the number of possible synergies will always deliver this numerical 'profit' of two. Euler (1707-83) explains this visually by referring to polygons. Here, the number of vertices denotes the number of existing 'things', or 'assets'. The number of lines that join them denotes the number of relations that may be seen as synergies.

Euler's Law (1751) states that V + F = E + 2 where -

  • V represents the number of vertices
  • F represents the number of faces
  • E represents the number of edges


A 4-fold Relational Currency Map
tetrad-ABCD-1.jpg

square-50cm-spacer.jpg Where:
square-50cm-spacer.jpg A - the donor
square-50cm-spacer.jpg B - the recipient
square-50cm-spacer.jpg C - the transactional purpose (e.g. covenanting future support as goods and/or services)
square-50cm-spacer.jpg D - the circumstances of the transaction (immediate / local / global etc.)
This implies that we would benefit from moving from a granular, object-defined logic of money to one that seeks to map relations in clusters that are small enough for humans to grasp, cognitively (e.g. say, four or five). The following example uses a tetrahedron as a standard figure for visualising six simultaneous relations. In practical terms, we are continuing to use this model as a template for revealing multiple synergies in which the 'intrinsic profits' are (meta)designed to serve up to six beneficiaries.

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