Fisher's famous formula, which describes the relationship between money and commodity prices, has obvious problems.

What's wrong?

The formula:

Quantity of goods * Price of goods = Velocity of money * Money

In this formula, we have a description of a linear scalar process that never exists in real life, and we have a measurement that can only be applied when we calculate the average velocity over an indefinite period of time.

Figure 1.

We can describe this process in physical terms of “Work” and “Speed”.

Work = Velocity * money.

Y =  m * S/T  =   m * V

In practice and in all statistical data, we always encounter ongoing nonlinear processes that can only be described using a power function.

Figure 2.

Y =  m * S1/T1 * S2/T2 =   m * V1 * V2  = m * V ^ 2

For example, we measure our household appliances in watts, not in joules, because power shows constant, current energy at a given moment, not energy spent over the indefinite period.

So it makes sense to rewrite Fischer's formula this way:

Quantity of goods * Inflation  =  Acceleration  of money * Money

Or with more mathematic form:

Quantity of goods * (Price Index+X/ Price Index) / T(=1)  =    (money supply + Y/ money supply)  / T(=1)   *  Money