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I am putting together a proposal for a system of economic exchange which links a transaction of money through a period of time, and subjective relationship evaluation between two people. How can it be modelled mathematically?

4.1 fundamental generalised contract - “double your money” How does this work? The basic mechanism is “double your money”. When you are invited to the entity, the person who invites guarantees the invitee will return with double what they bring. So, if I am invited to visit for £10, I bring £10, leave it at the door, do whatever is required for an hour, and when I leave, the person who invited me gives me £20. This money is guaranteed. It is all black. In fact, they match the initial £10 at the beginning of the hour.

Imagine a glass plate. People on the inside plaster money to the inside. People on the outside see the money and plaster money to the outside. There is a matching of inner and outer money. Once a person enters, they leave this money there, and only when they return do they pick it up if they have been invited in. Otherwise, money floats around on the inside to match up with more money from outside.

The generalised transaction is simple:

enter image description here


f(2x,p) = v ...where x is the base value of the invitation, p is the time period, and v is the value (the enumeration of which is subjectively determined).


“double your money”

Money is tagged to time. Since our time, each of us being human, is the same (at least in this first proposal, since it may be varied by intensity, wrt children and so on). The amounts and periods are given below.


4.3 scale of contract Looking more closely at the membrane of the eco^2 entity, we can see that this doubling of money is tagged to time. For the sake of simplicity, perhaps merely for this proposal but perhaps for an actual working model, there are fixed levels of engagement.

enter image description here

Notice that the function of the money for time, gives rise to an internal environment that is concerned exclusively with the production of value. This may appear strange, but it is actually what a company or government or any social body does, even one as small as a family. Money is pushed to the outside, while inside, people engage, collaborate, work together, learn at universities, play in teams, hang out, and lounge around with family. This entity is more like a family than a company. A company, a legal entity, has a strict structure, something like a cell wall which surrounds this membrane. And these cell walls are rather rigid, positions and roles. And these positions are tagged to money. Even though an “executive” and a “receptionist” both spend the same amount of time at the office, their pay is hardly comparable. Indeed the ratio can be as high as 500:1. Which is to say, one person’s time is 500 times as valueable as another’s. And if we include the financial gear ratios to “developing” countries, the underlying interpretation starts getting inhuman.

The membrane is not only the social contract of money, but that of time. The security of working for a year, is more relaxing than the security of working for a year of hours, not knowing if one is to be asked to return. Security is not only in terms of monetary value, but in terms of duration of contract.

At a certain level, the membrane translates money into value. The inviter is risking their money, whereas the person who is invited is risking their time. They shall only be invited back if during the time that they give, value is created. In standard “employment” terms, an individual is brought in to do something specific, sow some shoes together, draw up some designs, project manage, and when they leave, they are paid. It is about producing value. Somewhere along the line, in a traditional company, this value is converted into another monetary transaction, and we will consider this later. For this aspect of the membrane, the “double your money” invitation, the function of “employment” deals with the conversion of money into value.

The scale of contract, the money-time vector, may be considered as “quanta of money”, though I am not sure how useful the adoption of language may be, eg wrt concepts and equations from quantum physics. Sounds good though.


4.5 is the money that people bring used in any way? The individual who brings money, determines whether that money is “fixed”, which means it can not be touched, or it is “fluid” and can be used for the duration of the period they shall be within the entity. The ratio of “fixed” and “fluid” at the different levels of scale, determines the integrity of the membrane of the entity in time. It is important then for the inviter to be aware of the type the person they are inviting is willing to play.

Consider the “fixed” type. Perhaps a person is risking everything, and really needs to see a return. Or perhaps they unsure, they are playing with a sum of money they are nervous about, and they don’t trust the entity will continue existing. They want to be absolutely sure that they leave with the money they came with it. Hence, it is “fixed”.

The response to such a fixed person may be valid. And to reassure such a person, they may still be invited, even though this means the money they bring will be as fixed as the money that the inviter is guaranteeing. Effectively, this turns the transaction into a guaranteed “double your money” investment. A high return bank. Perhaps the inviter is not as interested in the money as the value that the invitee might be able to produce during the period of time of the contract. Remember, if they choose “fixed” and do not produce any significant worthwhile value beyond this “investment”, they may not be asked to return.

The additional advantage of inviting even a “fixed” player is that during the time that they are part of the entity, this can be leveraged to invite other players, players of equal or higher scales. By inviting in higher scale players, this is not only a higher level of income but a longer period of existence for the entity. Nevertheless, a “fixed” player locks the money for a period of time, and might be considered a cool relationship, and cold if no value is produced.

A “fluid” player is willing to take the risk of letting their money be used. That is, they can invite others, guaranteeing their return. Normally this will occur at lower levels of scale. For example, a person who is invited at the £1000-week level can invite a few people throughout that week.

The “fluid” player allows a certain amount of flexibility to enter into the system. Specifically, the vertical transfer of money down. This can only be sustained by the rate at which higher scale players are invited. This creates a funnel effect, attracting more players, and greater returns. See below.

Needless to say, those who are not invited or gifters can not “fix” their money, and indeed, once the money has moved, it will not return. Still, gifters will get a return of guarantee if they are invited; hence gifters are playing an equality game. Guarantors also are automatically “fluid”, because they do not expect any kind of return since they are not invited. If the system is healthy, however, guarantors fluid money will be covered by other fluid money by the end of the period of their participation.

The mathematical model should show that the ratio of “fixed” to “fluid” will determine the rate of growth of the entity. Specifically the increase of numbers as it scales into larger quanta of money. The entity may collapse if the ratios are not healthy, at different levels of scale.

Anyone interested in modelling this? And if not here, where...?

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apologise for the lack of skill in defining it mathematically, but i hope this provides enough of an explanation.... –  happyseaurchin Jan 20 '12 at 21:58
The (complex-analysis) tag is for "the theory of functions of one complex variable with an emphasis on the theory of complex analytic functions of one complex variable". Please read the tag summaries offered in the tag selection interface if you're not sure which tags to use. –  joriki Jan 21 '12 at 14:17
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