Price Inflation Fractal Coastlne Paradox
Here, I hypothesise that price inflation is a fractal phenomenon equivalent to or a real-life example of the coastline paradox.
The coastline paradox says the measurement of a coastline is related to the length of the 'measuring stick' being used: the shorter the measuring stick, the longer the coastline - right to infinity. I say the unit of money is the measuring stick, the coastline, the price of the object, and, therefore, the size of the economy. If the currency is decreased in value, the (nominal) size of the economy will exponentially increase (hyperinflate).
Just what is inflation?
Of course, we have the textbook answer, a general increase in the average price level - over time, but to be fractal, it must be a universal definition and go beyond the prices of goods.
A fractal explanation must demonstrate the following - I am convinced that the general fractal does.
A fractal explanation for inflation
When we look at the Koch Snowflake development/production (below), what is it that inflates - the area, the number of 'triangles', or the perimeter - or nothing?
Inflation and perimeter
I have become convinced that inflation is represented by the perimeter of the fractal. The reason is that the area of the Koch is finite, while the perimeter is infinite as the fractal iterates (grows). Also, note that area and perimeter are related through the base length of the triangle side, too.
This came to me after thinking about the perimeter length of an island or the length of a piece of string. The fractal theory says both are infinite and that the result depends on the actual length of the measuring stick. The shorter the stick, the larger the perimeter length, while, at the same time, the shape—the object—remains the same or at equilibrium. This measuring problem is well described from around 2 minutes into the following BBC: How long is a piece of string?
To me, this is also analogous to price inflation and the concept of value in economies: (Domestic) Production (GDP), where the measuring stick is units of currency or money.
Measuring an economy's GDP should follow the same principle as measuring an island or the Koch snowflake's perimeter; in this context, the only measuring tool is money or currency.
To go any further, do we need to clarify what money is? By definition, money should be - with the help of the circular flow of income model: Y=P=E - a liquid means of exchange, derived from income (Y), which comes from production (P), and will, in turn, be what expended or spent (E).
It follows that if the Product (the production) of the Koch snowflake is the triangle bits, then these bits represent money as a means of exchange.
As the fractal grows (as demonstrated in the fractal zoom below), the sides and bits get smaller and smaller while the perimeter gets larger and larger.
Veritasium: What Is The Coastline Paradox?
Just what is inflation?
Of course, we have the textbook answer, a general increase in the average price level - over time, but to be fractal, it must be a universal definition and go beyond the prices of goods.
A fractal explanation must demonstrate the following - I am convinced that the general fractal does.
- The increase in the descriptive value placed upon an 'unchanging' object
- requires a devaluation of a kind of measuring stick.
- There must be a notion of equilibrium, where one gets used to the new nominal change or size
A fractal explanation for inflation
When we look at the Koch Snowflake development/production (below), what is it that inflates - the area, the number of 'triangles', or the perimeter - or nothing?
Inflation and perimeter
I have become convinced that inflation is represented by the perimeter of the fractal. The reason is that the area of the Koch is finite, while the perimeter is infinite as the fractal iterates (grows). Also, note that area and perimeter are related through the base length of the triangle side, too.
This came to me after thinking about the perimeter length of an island or the length of a piece of string. The fractal theory says both are infinite and that the result depends on the actual length of the measuring stick. The shorter the stick, the larger the perimeter length, while, at the same time, the shape—the object—remains the same or at equilibrium. This measuring problem is well described from around 2 minutes into the following BBC: How long is a piece of string?
An animation showing the increasing length of the coastline with decreasing measuring units (coarse-graining length)
Coastline paradox. (2023, August 15). In Wikipedia. https://en.wikipedia.org/wiki/Coastline_paradox
P= s.l
The perimeter (P) of the Koch snowflake fractal is calculated by multiplying the number of sides (s) by the length of a side (l). The diagram below shows that as the fractal iterates and the shape develops towards equilibrium, at iteration 7 (plus or minus 2), the perimeter of the snowflake rises exponentially to infinity. This is due to the relationship between the diminishing length of each side and the exponentially rising quantity of sides.
To me, this is also analogous to price inflation and the concept of value in economies: (Domestic) Production (GDP), where the measuring stick is units of currency or money.
Measuring an economy's GDP should follow the same principle as measuring an island or the Koch snowflake's perimeter; in this context, the only measuring tool is money or currency.
To go any further, do we need to clarify what money is? By definition, money should be - with the help of the circular flow of income model: Y=P=E - a liquid means of exchange, derived from income (Y), which comes from production (P), and will, in turn, be what expended or spent (E).
It follows that if the Product (the production) of the Koch snowflake is the triangle bits, then these bits represent money as a means of exchange.
As the fractal grows (as demonstrated in the fractal zoom below), the sides and bits get smaller and smaller while the perimeter gets larger and larger.
 |
| the Koch fractal zoom - growth |
If we were to stop the zoom at any time, we see the same 'snowflake' ahead, just like the shape as earlier in the zoom: that is to say, in our analogy, the money looks the same, only the numbers have changed. We still see an equilibrium shape.
With that, I conclude that inflation is natural and that growth, development, and inflation are now inextricably linked through the fractal mechanics.
However, it begs the question, what about printed or fiat money? Does it distort reality? Is there such a thing as unnatural inflation?
I think fiat money is another fractal. Suppose we print (more) money than our resources call for. In that case, we will shorten the measuring tool more than what is natural, distorting reality with an even longer perimeter or larger (misleading) GDP.
Also, for inflation to be fractal, it has to be a universal concept: I am interested to learn that hotels now have 6, 7, and 8 stars to rate their quality. Have hotels changed so much to deserve more numbers than the ‘5-star’? Of course, they have, but maybe the system is open to some distortion - 5 should be the ultimate. As the 'stars' increase or inflate above the original ‘5 star’, that 5 star loses value. Other examples exist academic grade inflation - where the school leaving qualification creeps up and up, from a Degree to a Master's to where you need a PhD to work behind a bar.
From experience and neoclassical economics, we know that price inflation fits the above 'rules': (nominal) prices rise for the same object; consumers get used to the new prices—there is a new equilibrium, and finally, money itself devalues in relation to its past value.
I also consider changes in models of cars (for example) without any innovation or evolution, just the colour or style, as inflation - design inflation. The new car devalues the old just because it has something different (not practical) - even if they are basically the same car.
I still think there is more to this: there could be something in the quantity of 'triangles' to explore.
2021: You can read my paper on this topic at Quantum Mechanics, Information and Knowledge, All Aspects of Fractal Geometry and Revealed in an Understanding of Marginal Economics.
With that, I conclude that inflation is natural and that growth, development, and inflation are now inextricably linked through the fractal mechanics.
However, it begs the question, what about printed or fiat money? Does it distort reality? Is there such a thing as unnatural inflation?
I think fiat money is another fractal. Suppose we print (more) money than our resources call for. In that case, we will shorten the measuring tool more than what is natural, distorting reality with an even longer perimeter or larger (misleading) GDP.
Also, for inflation to be fractal, it has to be a universal concept: I am interested to learn that hotels now have 6, 7, and 8 stars to rate their quality. Have hotels changed so much to deserve more numbers than the ‘5-star’? Of course, they have, but maybe the system is open to some distortion - 5 should be the ultimate. As the 'stars' increase or inflate above the original ‘5 star’, that 5 star loses value. Other examples exist academic grade inflation - where the school leaving qualification creeps up and up, from a Degree to a Master's to where you need a PhD to work behind a bar.
From experience and neoclassical economics, we know that price inflation fits the above 'rules': (nominal) prices rise for the same object; consumers get used to the new prices—there is a new equilibrium, and finally, money itself devalues in relation to its past value.
I also consider changes in models of cars (for example) without any innovation or evolution, just the colour or style, as inflation - design inflation. The new car devalues the old just because it has something different (not practical) - even if they are basically the same car.
An essential watch on measurement:
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