A non-deterministic system is not quite the same as a non-predictable one. This is where probability comes into play and makes me think we're really on the right track with currencies as tools for expressing/modeling complex, living systems.
[BTW, I still can't post replies, so I'm making this a main blog post even though it started out as a reply to Alan's post "Do currencies describe living systems?"]
Rain falling on a hillside is non-deterministic. We could never be sure about the path any drop will follow. However, taken as a whole with hundreds of thousands of drops, we can probably predict rather easily where water will run, where it will puddle, where much will soak in, etc.
That is what makes the design of a (monetary) currency SO IMPORTANT in the way it shapes behavior. It is non-deterministic -- it doesn't take away the free will of the actors. You might choose to burn that $20 bill in your wallet, but chances are good that you'll spend it... in a fairly bounded range of ways.
The design of a currency is like the shape of the landscape upon which the rain falls. Each drop follows its own non-quite-predictable path as each person performs their own not-quite-predictable transactions. But one of the things that I think fluency in flow language will make clear to us, is that taken as a whole, the probable pattern is VERY CLEAR.
Like with dollars being issued as debt which bear interest... That interest will compound, daily, forcing exponential growth until the debt load is growing faster than the economy can expand which causes collapse of the currency. The outcome is really as plain as day to anyone who looks at flow pattern.
However, it is not quite as clear exactly what day that collapse occurs. Or how hard the fall will be, because those factors are outside the inherent rules of the currency and are more like your chess game factors of how much sleep the players got or if they're playing for a big prize.
Even some of the pattern outside the explicit currency rules is visible when in play. The Bush administration as it greedily centralized wealth into the hands of the few, accelerated the collapse severely. Offering a "bail-out" which did more of the same (by handing it directly to the bankers) didn't slow the unraveling. Obama's bailout approach, which spreads short-term wealth around, will slow the collapse, perhaps for months or years.
However, they both are rooted in the same unsustainable core principle of dollars as a Ponzi scheme requiring us to perpetually mortgage our future with present debt. We cannot bear the tax burden to repay the "stimulus." It extends the downward spiral of compounding debt toward sure collapse.
Non-deterministic system --> Certain outcome.
Of course, this way lies madness for predicting on an individual level. It reminds me of Skinner's behaviorism and likely why his kids ended up institutionalized. Just because you can consistently get a pidgin to turn left to get you to release food does not demonstrate much flow language wisdom. The model is too one-dimensional to operate outside of a very artificially constrained environment.
Just like in most economic plans or corporate compensation plans where people think they're causing predictable behavior through monetary reward...but the plan is too one-dimensional to connect to the various layers of incentives of a whole human. This becomes painfully obvious when worker productivity drops instead of rises, or consumer confidence still falls even after $350B of bailouts. :)
Wednesday, January 28, 2009
Tuesday, January 27, 2009
Do currencies describe living systems?
I have been pondering this question about whether a CURRENCY is a set of rules that play out into the future, the state of a whole system at a specific time, or a representation of flows over time that manifested in the past. Linked to this question, is the question of whether a CURRENCY is deterministic and allows prediction about the behavior of systems as a whole, or whether it is open ended and only sets up a ground upon which interactions can play out.
Perhaps we should think about chess. Chess has a set of rules that govern how pieces interact with one another, and it sets up a start point (board at opening) and end point (checkmate) for the system. The rules of chess allow for the manifestation of around 10^100 (a 1 with 100 zeros after it) different games, but the rules say nothing about which game will be played at any given time. The rules of chess are non-deterministic, but they set up boundaries of interaction, i.e. no rook ever moves diagonally. If we want to actually predict the way a particular chess game will manifest, we will have to study intently the history of the players and how they have chosen to deal with given situations in the past. We might even take into account whether the players got enough sleep before the game, and whether there is a lucrative prize for winning. In all cases where we are trying to predict a specific game, we need information that cannot be found within the rules of chess.
Let’s look at a more biological example. Think of an ant colony. The behavior of the individual ants is relatively simple and probably determined in some way by the ant’s DNA, but the actual manifestation of a particular colony is highly complex and non-deterministic. This makes the ant colony quite different from a computer program, which will run the same every time. See Wikipedia's article on cellular automata for a great explanation of how this process differs from conventional computer programming.
A good place to look to unpack this issue further is Ilya Prigogine’s theory of life being a dissipative structure. According to Prigogine, life is an OPEN system far from equilibrium. A non-living system is one that comes to rest as all interactions are played out. This resting point is its state of equilibrium. Systems that are closed tend towards equilibrium, but in living systems equilibrium is synonymous with death. A system is dead when no more interactions are occurring between its constituent parts. This means that life must inherently be energetically OPEN to sources outside the system. Think of the earth as a whole. The earth is open to energy from the sun, and the sun is what keeps the whole earthly dance moving. This means that life is a pattern that maintains cohesion in a constantly changing stream of matter and energy.
The other big piece of the definition of living systems, is that they can adapt themselves to changes in the environment. Warm-blooded animals maintain their body temperature across a wide range of external conditions; ants have adapted to live on six of seven continents, and so forth. A good place to read further on this is Wikipedia’s article on self-organization.
So how does this relate to the metaphors we have been using so far to explore the flow language? Let’s look a circuit diagram. A circuit diagram represents a system that is not evolutionary. Sure electricity moves through the system, but the structure of the system itself does not change depending on the conditions. Even if there are complex relations between the parts in a circuit that do allow it to change to match some external conditions, the determination of how the system will manifest cannot change except by outside agency (the electrical engineer). Hence, it is completely deterministic. Here is where we see the difference between living and non-living systems. In contrast, a living system modifies its own internal structure to adapt to external conditions in novel and creative ways. What is probably going on in living systems is something akin to a bifurcation in a chaotic system. It is inherently unpredictable for this reason, and is determined by conditions within the boundary of the system rather than external conditions.
What makes this all especially complicated is the fact that living systems are within the realm of the biosphere, where as currency is more in the realm of the noosphere (mind). This means that meaning becomes part of the system. In biospheric systems, meaning isn’t really all that important to determining flows, but in noospheric systems meaning is an essential component. I think of currency design as permaculture of the noosphere.
To sum up, in my humble (and very possibly wrong) view, a CURRENCY is a set of rules that govern a particular flow within a complex open system in a non-deterministic way. As multiple currencies interact, even predicating outcomes in the short-term becomes less and less feasible. However, this doesn’t mean that we can’t make useful statements about the system derived from these rules. One feedback loop a currency complex can have is the communication of the state of the whole to the parts. This information flow affects how the parts behave and helps create cohesion in the system. This view of the whole is the holoptic view. In fact, it is the ability of the parts to know and interact with the state of the whole that may give the system meaning as a whole in and of itself.
Perhaps we should think about chess. Chess has a set of rules that govern how pieces interact with one another, and it sets up a start point (board at opening) and end point (checkmate) for the system. The rules of chess allow for the manifestation of around 10^100 (a 1 with 100 zeros after it) different games, but the rules say nothing about which game will be played at any given time. The rules of chess are non-deterministic, but they set up boundaries of interaction, i.e. no rook ever moves diagonally. If we want to actually predict the way a particular chess game will manifest, we will have to study intently the history of the players and how they have chosen to deal with given situations in the past. We might even take into account whether the players got enough sleep before the game, and whether there is a lucrative prize for winning. In all cases where we are trying to predict a specific game, we need information that cannot be found within the rules of chess.
Let’s look at a more biological example. Think of an ant colony. The behavior of the individual ants is relatively simple and probably determined in some way by the ant’s DNA, but the actual manifestation of a particular colony is highly complex and non-deterministic. This makes the ant colony quite different from a computer program, which will run the same every time. See Wikipedia's article on cellular automata for a great explanation of how this process differs from conventional computer programming.
A good place to look to unpack this issue further is Ilya Prigogine’s theory of life being a dissipative structure. According to Prigogine, life is an OPEN system far from equilibrium. A non-living system is one that comes to rest as all interactions are played out. This resting point is its state of equilibrium. Systems that are closed tend towards equilibrium, but in living systems equilibrium is synonymous with death. A system is dead when no more interactions are occurring between its constituent parts. This means that life must inherently be energetically OPEN to sources outside the system. Think of the earth as a whole. The earth is open to energy from the sun, and the sun is what keeps the whole earthly dance moving. This means that life is a pattern that maintains cohesion in a constantly changing stream of matter and energy.
The other big piece of the definition of living systems, is that they can adapt themselves to changes in the environment. Warm-blooded animals maintain their body temperature across a wide range of external conditions; ants have adapted to live on six of seven continents, and so forth. A good place to read further on this is Wikipedia’s article on self-organization.
So how does this relate to the metaphors we have been using so far to explore the flow language? Let’s look a circuit diagram. A circuit diagram represents a system that is not evolutionary. Sure electricity moves through the system, but the structure of the system itself does not change depending on the conditions. Even if there are complex relations between the parts in a circuit that do allow it to change to match some external conditions, the determination of how the system will manifest cannot change except by outside agency (the electrical engineer). Hence, it is completely deterministic. Here is where we see the difference between living and non-living systems. In contrast, a living system modifies its own internal structure to adapt to external conditions in novel and creative ways. What is probably going on in living systems is something akin to a bifurcation in a chaotic system. It is inherently unpredictable for this reason, and is determined by conditions within the boundary of the system rather than external conditions.
What makes this all especially complicated is the fact that living systems are within the realm of the biosphere, where as currency is more in the realm of the noosphere (mind). This means that meaning becomes part of the system. In biospheric systems, meaning isn’t really all that important to determining flows, but in noospheric systems meaning is an essential component. I think of currency design as permaculture of the noosphere.
To sum up, in my humble (and very possibly wrong) view, a CURRENCY is a set of rules that govern a particular flow within a complex open system in a non-deterministic way. As multiple currencies interact, even predicating outcomes in the short-term becomes less and less feasible. However, this doesn’t mean that we can’t make useful statements about the system derived from these rules. One feedback loop a currency complex can have is the communication of the state of the whole to the parts. This information flow affects how the parts behave and helps create cohesion in the system. This view of the whole is the holoptic view. In fact, it is the ability of the parts to know and interact with the state of the whole that may give the system meaning as a whole in and of itself.
Monday, January 26, 2009
Systems Theory on Wikipedia
Maybe if I had a degree in Systems Theory, I'd be able to know what we (society) know about mapping systems.
Although, as I read the Wikipedia article (linked above), they seem to still be doing actors-objects, just large groups of them. True? Not so much relation-of-relations or all-verb kind of thing. Or is there that kind of thing in Systems Theory?
Anyone want to call a professor?
Flow Language Continued
In the hopes of improving our understanding of what a flow language is all about, I want to share an excerpt from an ongoing email discussion with Arthur Brock, Eric Harris-Braun, and Katin Imes. Arthur had the following response to my last post about flow language basics:
So a flow language probably still needs containers of some sort, but what makes it different from subject / predicate is that instead of mapping linear piece-meal relationships between containers it maps a collection of relationships that when perceived / expressed together make up a greater holon of some sort. To the extent it needs to define containers, it differentiates, and to the extent it maps wholes, it integrates. It is these rules for interactions between subjects (and indeed the rules that define the subjects we are dealing with in the first place), that are the CURRENCY.
This is distinct from the actual manifest state of the system at any given time, and from the list of potential states of the system. The currency is instead the process through which these states may be realized. Particular processes will, through playing out, create basins of attraction around certain system states. I am reminded of the butterfly effect. The butterfly graph of the Lorenz attractor in phase space shows a bounded state of possibilities for the system, but it can't predict what state the system will be in at a given time, and indeed there are an infinite number of potential states.
So, these subjects are integrated into a new whole that is bound by these interactions between them. It is the rules themselves that enable the integration into a larger whole. Without a coherent rule set, the parts would simply be heaps rather than new wholes. It also might be the case that not every rule set produces coherent and functional wholes, but that determination seems like it would have to play out over time. Again, I am reminded of chaotic systems that, over time move towards basins of attraction. Different currency rule sets, would likely create different basins of attraction.
This concept is made more complicated by the fact that a representation of the state of the system as a whole could be in a container as a part of its own system. This is analogous to the play itself being a character in the play. The ability of systems to represent themselves to themselves becomes an important way for the system to feedback on itself (and maintain stability). The rules governing the system (or one CURRENCY within the currency complex) would include rules about how to represent the whole as a subject within the whole. This might be a round about way of describing the nature of a holoptic view. If subjects can interact with the whole, then that representation of the whole becomes a discreet part within the whole itself. The holoptic view would have to filter data about the whole and construct some sort of representation of the whole with that data that the parts can interact with. This is kind of mind bending stuff, I'd say!
"...I wonder if we are talking about some sort of "container." Each container has rules for how it holds things, transforms things and transacts them with other containers. A container is defined by boundaries or membranes...Thanks Arthur for this excellent summation! These containers (or accounts) are bounded and have rules that govern what happens inside them, as well as what happens as they interact with other containers. I think it might be worth looking at the subject / predicate form in this light a little. Words in many ways seem to be containers. The sentence, "The sky is blue." puts the sky in one container (differentiated from the ground), and relates it with blue (differentiated from other colors). It interesting to note in this context that in reality the color spectrum is continuous rather than separated, integrated rather than differentiated. We have merely drawn lines in certain places in the spectrum and defined those as colors. So a subject / predicate sentence draws one container (subject) and relates it to another (predicate). Even in the case of "The sun rises." we have a container around the idea of rising and know that there is some quality of action that can be differentiated from other actions that is similar to what the tides do and what bread does.
...In a monetary currency, an account is a kind of container and can transact with any other account it is connected to. If you need to transact across banks, countries or currencies, there are rules about the transformational containers the transaction moves through, the fees/overhead of those transformations, and how long it takes for funds to become available... ...A currency (as a word in flow language) is a model or map of the interaction capacities of a set or multiple sets of containers..." - Arthur Brock
So a flow language probably still needs containers of some sort, but what makes it different from subject / predicate is that instead of mapping linear piece-meal relationships between containers it maps a collection of relationships that when perceived / expressed together make up a greater holon of some sort. To the extent it needs to define containers, it differentiates, and to the extent it maps wholes, it integrates. It is these rules for interactions between subjects (and indeed the rules that define the subjects we are dealing with in the first place), that are the CURRENCY.
This is distinct from the actual manifest state of the system at any given time, and from the list of potential states of the system. The currency is instead the process through which these states may be realized. Particular processes will, through playing out, create basins of attraction around certain system states. I am reminded of the butterfly effect. The butterfly graph of the Lorenz attractor in phase space shows a bounded state of possibilities for the system, but it can't predict what state the system will be in at a given time, and indeed there are an infinite number of potential states.
So, these subjects are integrated into a new whole that is bound by these interactions between them. It is the rules themselves that enable the integration into a larger whole. Without a coherent rule set, the parts would simply be heaps rather than new wholes. It also might be the case that not every rule set produces coherent and functional wholes, but that determination seems like it would have to play out over time. Again, I am reminded of chaotic systems that, over time move towards basins of attraction. Different currency rule sets, would likely create different basins of attraction.
This concept is made more complicated by the fact that a representation of the state of the system as a whole could be in a container as a part of its own system. This is analogous to the play itself being a character in the play. The ability of systems to represent themselves to themselves becomes an important way for the system to feedback on itself (and maintain stability). The rules governing the system (or one CURRENCY within the currency complex) would include rules about how to represent the whole as a subject within the whole. This might be a round about way of describing the nature of a holoptic view. If subjects can interact with the whole, then that representation of the whole becomes a discreet part within the whole itself. The holoptic view would have to filter data about the whole and construct some sort of representation of the whole with that data that the parts can interact with. This is kind of mind bending stuff, I'd say!
One system-flow view: circuit schematics
Here's an idea for how to express systems and flows: use a parallel set of symbols and methods as used in electronics for schematics. When an engineer looks at a schematic of a circuit, he doesn't see nouns-predicates, he sees a flowing system with modifiers and transformations.
(Check out a crystal tester circuit schematic. Read the Wikipedia entry on schematic diagrams.)
A circuit modulates and flows electricity to create a desired effect. The current, electricity, flows in predictable (but not always intuitive) ways through the components. An electronic engineer can look at a schematic and "see" what the circuit does.
What if we could schematically diagram the Community Way system, for example? Would it become obvious to see that it only runs a short period of time (3-6 months)? Would it be easy to calculate the transaction fees required for overhead and system management? Would we be able to see the same effects as the spreadsheet numerically showed us, only in a flow diagram?
Would the symbols be directly equivalent to the most common electronic components? Capacitors store an amount of current and will release it back into the circuit when it becomes the largest store & potential. Resistors drain away power (converting it to heat). Transformers change the characteristics of the currency, shifting voltage (pressure) and current.
All of these things are present in ecological systems, transport and goods trading systems, and monetary systems. One question would be, what would be the "battery" or supplier of electricity in a monetary-circuit diagram? More over, what would actually be the electricity or motive force? What is actually in motion in a monetary system?
I think this would be a worthy perspective to add to the thought experiment and our exploration.
Sunday, January 25, 2009
Reaching to Systems Expression with Language
Eric mentioned something that I think stirred something within me. He said, to paraphrase and apply all my filters to it, that we are at a catch-22: we can't imagine what we really need to get to the level of holoptic systems thinking until we can be thinking at the level of holoptic systems. A tangent quote (was it Einstein?), "The current scope of problems cannot be solved by the same thinking that created them."
I want to find methods for getting my brain to inhabit the world of bigger-picture, whole-systems thinking. Not subject-predicate language but relation-of-relation language. Not discrete component language, but whole-system-at-once language. But how to get there?
We are handicapped as humans in this place in time because we really don't think systematically at all. My way of saying this is that we are a very clever race, but we aren't very smart. Examples I give here include things like:
-- we can build a ceramic internal combustion engine that'll run 100,000 miles without a tune-up, but the problem of rush-hour traffic stumps us.
-- we can build MRI machines that can sense physiological events as tiny as changes in the brain in real time, yet we instantiate and operate a health care system that has doctors frustrated, consumers bankrupt, and insurance companies complaining.
-- we can operate thousands of intricate and capable satellites and put a man on the moon, yet we don't seem to even be able to decide if global warming is real concern or not.
Humans are great at Descarte-style details, but we really rather suck at working systems gestalt. Predicting emergent effects of even moderately complex systems just plain boggles us, and even near-time extrapolations of basic systems behavior seems beyond our common capability as thinkers.
I want to find methods for getting my brain to inhabit the world of bigger-picture, whole-systems thinking. Not subject-predicate language but relation-of-relation language. Not discrete component language, but whole-system-at-once language. But how to get there?
We are handicapped as humans in this place in time because we really don't think systematically at all. My way of saying this is that we are a very clever race, but we aren't very smart. Examples I give here include things like:
-- we can build a ceramic internal combustion engine that'll run 100,000 miles without a tune-up, but the problem of rush-hour traffic stumps us.
-- we can build MRI machines that can sense physiological events as tiny as changes in the brain in real time, yet we instantiate and operate a health care system that has doctors frustrated, consumers bankrupt, and insurance companies complaining.
-- we can operate thousands of intricate and capable satellites and put a man on the moon, yet we don't seem to even be able to decide if global warming is real concern or not.
Humans are great at Descarte-style details, but we really rather suck at working systems gestalt. Predicting emergent effects of even moderately complex systems just plain boggles us, and even near-time extrapolations of basic systems behavior seems beyond our common capability as thinkers.
So how do we get our brains to inhabit a higher level of thinking about the concepts of systems? Language is one way. If we had an 'alphabet' of systems primitives, we could string them together into words and then sentences. It may need to be a really radical departure from what we think of now as language; for example, a holoptic-systems language might be all verbs and relational words only, no nouns. For in a way, in the systems flow view, there are no nouns or things, there are only processes.
Is this kind of language-thought required to implement a distributed-multi-currency management system that works? No. Might it help in the design of competent currencies and systems that manage the relationships between currencies (currency complexes)? I would say definitely.
Will we figure out a flow-language - or as Eric & Arthur call it, an expressive capacity about flow systems - in time to have it available as a tool for design of a distributed-multi-currency system? I doubt it. Is that any reason to stop cooking efforts at a flow-language, even just as a brain-builder if nothing else? Not at all!
All aboard for the Magical Mystery Tour.
Friday, January 23, 2009
Flow Language Basics
I wanted to summarize a fascinating conversation Eric Harris-Braun, Arthur Brock, Katin Imes, and I all had yesterday. Arthur and Eric have been developing the idea of a "flow language" for a while, but on the call we were all trying to make sense of what this new type of language is actually all about. The following is my crude attempt to describe the basics.
The purpose of a flow language is to enable the expression of flows in a system as opposed to discreet causal events. The standard form of language is subject / predicate. This structure makes differentiation between objects / actions very easy, but integration of those objects / actions into coherent patterns within wholes very difficult. Individual relationships can be easily isolated, but patterns in the whole are very difficult to express (or even perceive). A flow language makes these larger scale patterns visible and able to be engaged with efficiently.
The most basic “word” in a flow language is a currency. A currency allows one flow to be described. For instance, if we were going to describe the flow of water in an ecosystem, we would want to know how the water cycles through the ecosystem as a whole and how this flow affects the different parts. These parts are the core units, the relationships between which describe the flow in the system. Think of these units as accounts. A currency only exists as a series of relationships between accounts. Accounts are analogous to "letters" in the flow language since they make up the most basic unit, but they lack meaning in and of themselves.
Boundaries between accounts can be arbitrarily drawn. For instance, in the currency describing the water cycle, we could describe three accounts: land, ocean, sky. There are certain basic relationships between these accounts. We know that water does not flow from the ocean to the land unless it goes through the sky first. We know that the sky can rain water onto the ocean or the land. And that the land can transpire water to the sky or run off into the ocean. While this is a very crude mapping of the water cycle, the relationships between these three accounts do tell us something useful. We could easily get much more granularity by drawing account boundaries with more differentiation. For instance, we could draw a grid on the land, each square with its own account. This might allow us to see which parts of the land transpire the most water, and what parts allow it to run off. There is of course a series of relationships between these accounts that could be described (non-proximal squares of land can’t directly have water pass between them without going through the sky first). We could also draw account boundaries between species, or even between individual life forms. In any case, the account is the “letter,” and the currency is the “word” (describing the relationships between the accounts).
If we want a sentence in flow language, we must look at the interplay between currencies. To continue our metaphor, we might also look at the flow of nitrogen in our ecosystem. We could similarly divide the space into the necessary (and sensible) accounts, and examine the relationships between them. Perhaps where nitrogen accumulates, we see more plant life, which in turn allows the land there to hold more water and transpire it directly to the sky without running off to the ocean. It is these interrelations between currencies that allow for the full construction of a flow sentence. For now, I have been calling a “flow sentence” a “currency complex.” As dozens of currencies interplay with each other we see that more and more complex flow sentences can be constructed.
The purpose of a flow language is to enable the expression of flows in a system as opposed to discreet causal events. The standard form of language is subject / predicate. This structure makes differentiation between objects / actions very easy, but integration of those objects / actions into coherent patterns within wholes very difficult. Individual relationships can be easily isolated, but patterns in the whole are very difficult to express (or even perceive). A flow language makes these larger scale patterns visible and able to be engaged with efficiently.
The most basic “word” in a flow language is a currency. A currency allows one flow to be described. For instance, if we were going to describe the flow of water in an ecosystem, we would want to know how the water cycles through the ecosystem as a whole and how this flow affects the different parts. These parts are the core units, the relationships between which describe the flow in the system. Think of these units as accounts. A currency only exists as a series of relationships between accounts. Accounts are analogous to "letters" in the flow language since they make up the most basic unit, but they lack meaning in and of themselves.
Boundaries between accounts can be arbitrarily drawn. For instance, in the currency describing the water cycle, we could describe three accounts: land, ocean, sky. There are certain basic relationships between these accounts. We know that water does not flow from the ocean to the land unless it goes through the sky first. We know that the sky can rain water onto the ocean or the land. And that the land can transpire water to the sky or run off into the ocean. While this is a very crude mapping of the water cycle, the relationships between these three accounts do tell us something useful. We could easily get much more granularity by drawing account boundaries with more differentiation. For instance, we could draw a grid on the land, each square with its own account. This might allow us to see which parts of the land transpire the most water, and what parts allow it to run off. There is of course a series of relationships between these accounts that could be described (non-proximal squares of land can’t directly have water pass between them without going through the sky first). We could also draw account boundaries between species, or even between individual life forms. In any case, the account is the “letter,” and the currency is the “word” (describing the relationships between the accounts).
If we want a sentence in flow language, we must look at the interplay between currencies. To continue our metaphor, we might also look at the flow of nitrogen in our ecosystem. We could similarly divide the space into the necessary (and sensible) accounts, and examine the relationships between them. Perhaps where nitrogen accumulates, we see more plant life, which in turn allows the land there to hold more water and transpire it directly to the sky without running off to the ocean. It is these interrelations between currencies that allow for the full construction of a flow sentence. For now, I have been calling a “flow sentence” a “currency complex.” As dozens of currencies interplay with each other we see that more and more complex flow sentences can be constructed.
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