Tamari Attractor
Encyclopedia
In the mathematics of dynamical system
s, the Tamari attractor, named for Ben Tamari, is a 3-dimensional attractor
evolving from the dynamic system associated with the theory of a country's economics. This dynamical system is a set of partial differential equation
s that, by the theory of economics developed by Tamari, control the economics of a country. The main point of this economic theory is that the relation between the quantity of money to the country's output is what governs the country’s economic situation and outcome.
Where the parameters in these equations are:
___________________________________________________________
In rates terms: o (
dO/dt) is the growth, m (
dM/dt) is the printing, and p (
dP/dt) is the inflation, p = m – o, or as the old saying goes "Inflation occurs when too much money is chasing too few goods".
The first 2 equations are in fact Cremona equations, which Tamari had found suitable to depict the economic situation in the output-money space (
Keynes space [O, M,] ), because of their conservative nature. The third equation is the Feedback equation, which Tamari had developed in a manner of trial and error to fit the statistical data of the countries as found in the “International Financial Statistics" YEARBOOK, The parameters of these equations vary from country to country, according to the statistical data.
Tamari space [O, M, P,]) created by the solutions of the above equations. When the position is within the green boundary of the nest (see picture 1), the situation is stable, and forecasting and planning is possible in the short term. However, if the country's position has moved to the red part (usually after printing too much money due to political chaos, armed conflicts, dictatorships, election campaigns, etc…), the situation is unstable and may lose control.
Thus, finding the parameters:
, 
, 
, 
, 
, 
, 
, 
, 
, by statistical methods (from the statistical data of IMF yearbook), the Tamari attractor may serve to understand, control and predict the economic situation of a country. To show how it is worked, Tamari developed the economic simulator “Eco” (see picture 2).
Dynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...
s, the Tamari attractor, named for Ben Tamari, is a 3-dimensional attractor
Attractor
An attractor is a set towards which a dynamical system evolves over time. That is, points that get close enough to the attractor remain close even if slightly disturbed...
evolving from the dynamic system associated with the theory of a country's economics. This dynamical system is a set of partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s that, by the theory of economics developed by Tamari, control the economics of a country. The main point of this economic theory is that the relation between the quantity of money to the country's output is what governs the country’s economic situation and outcome.
The Tamari equations
The Tamari equations are (blue letters are variables and red are parameters):
Where the parameters in these equations are:
-
– Inertia
-
– Productivity
-
– Printing
-
– Adaptation
-
– Exchange rate
-
– Indexation (linking)
-
– Expectations
-
– Unemployment
-
– Interest
-
are GreshamGresham's LawGresham's law is an economic principle that states: "When a government compulsorily overvalues one type of money and undervalues another, the undervalued money will leave the country or disappear from circulation into hoards, while the overvalued money will flood into circulation." It is commonly...
coefficients.
-
denotes the country's output (gross domestic product, GDP (
), 
is the Money axis (the quantity of money, M1 (
) and 
is the Pricing axis - consumer price index, CPI (
), so the equations may also be written as:
___________________________________________________________
In rates terms: o (
dO/dt) is the growth, m ( dM/dt) is the printing, and p ( dP/dt) is the inflation, p = m – o, or as the old saying goes "Inflation occurs when too much money is chasing too few goods".The first 2 equations are in fact Cremona equations, which Tamari had found suitable to depict the economic situation in the output-money space (
Keynes space [O, M,] ), because of their conservative nature. The third equation is the Feedback equation, which Tamari had developed in a manner of trial and error to fit the statistical data of the countries as found in the “International Financial Statistics" YEARBOOK, The parameters of these equations vary from country to country, according to the statistical data.Economic consequences
Tamari's theory of a country's economic situation says that the situation of the country can be estimated by mapping the country's position on the nest ( Tamari space [O, M, P,]) created by the solutions of the above equations. When the position is within the green boundary of the nest (see picture 1), the situation is stable, and forecasting and planning is possible in the short term. However, if the country's position has moved to the red part (usually after printing too much money due to political chaos, armed conflicts, dictatorships, election campaigns, etc…), the situation is unstable and may lose control.Thus, finding the parameters:
, , , , , , , , , by statistical methods (from the statistical data of IMF yearbook), the Tamari attractor may serve to understand, control and predict the economic situation of a country. To show how it is worked, Tamari developed the economic simulator “Eco” (see picture 2).