Thread

Is MoE the 2nd or 3rd order derivative of SoV?

First order. I see SoV as a constant and MoE as a time depended change of that constant. Like position and velocity. Coincidentally, in economics one talks about the velocity of money, which is the speed of which one unit moves through the economy (changes hands), so this may be quite fitting.

Is it just this, or is there more to this? Using a chatbot (sorry) Let’s use the same mathematical framework to explain Bitcoin's roles as a store of value and a medium of exchange, using the analogy of position and velocity. ### Mathematical Analogy 1. **Position (Store of Value)**: - Think of Bitcoin as a **position** on a number line, representing its value over time. When you hold Bitcoin as a store of value, you are essentially "holding" a certain amount of value at a specific point in time. - For example, if you buy Bitcoin and hold it, your position might be represented as \( p(t) \), where \( p \) is the value of Bitcoin at time \( t \). This value can increase or decrease, but you are focused on the amount you have at that moment. 2. **Velocity (Medium of Exchange)**: - Now, consider the **velocity** as the rate at which you use Bitcoin to make transactions. This is like how quickly you are moving from one position to another. - Mathematically, velocity can be represented as the derivative of position with respect to time: \[ v(t) = \frac{dp(t)}{dt} \] - In this context, \( v(t) \) represents how quickly you are spending or using Bitcoin as a medium of exchange. If you are frequently using Bitcoin to buy goods and services, your velocity is high. If you are holding onto it without spending, your velocity is low. ### Summary - **Store of Value (Position)**: Holding Bitcoin as a store of value is like having a fixed position on a number line. You are focused on the value you have at that moment, represented by \( p(t) \). - **Medium of Exchange (Velocity)**: Using Bitcoin as a medium of exchange is like the velocity that describes how quickly you are changing your position. The more you spend Bitcoin, the higher the velocity \( v(t) \) becomes, indicating active use in transactions. In this analogy, the static position represents the value you hold (store of value), while the velocity represents how actively you are using that value (medium of exchange).