# Cryptocurrency
### A Mistake
Yesterday, I suddenly realized a misconception I had in a dream. I used to thoughtlessly believe that in the case of Bitcoin, the number of users and the price were positively correlated, and both maintained exponential growth.
### Number of Users vs Price
Let's first look at the first half of the sentence, 'the number of users and the price are positively correlated.' This implies several logical simplifications:
1. The number of users ≈ Demand for Bitcoin. This can be considered fundamentally valid.
2. Price is positively correlated with demand. This assumption only holds under the condition of stable supply. The actual supply of Bitcoin is as follows:
(The blue line represents Bitcoin's supply, while the red line represents Bitcoin's inflation rate)
Bitcoin's supply first increased quickly and then slowed down, currently supplying 90%.
### How does the number of users grow
Next, let's look at the second half of this statement, 'the number of users and the price of cryptocurrency consistently maintain exponential growth.' First, about the number of users. The reason I have the impression that the number of users shows exponential growth is largely due to this chart:
This chart covers the period from 1990 to 2005, which was the early days of the internet. Clearly, the number of internet users could not have consistently shown exponential growth, and similarly, the number of Bitcoin adopters cannot either. The complete curve of internet users looks like this:
This is completely consistent with the model in [[The Bullish Case for Bitcoin]]:
It can be seen that we are still in the 'early stage.' As we enter the 'late stage,' the growth of Bitcoin users is bound to slow down. More importantly, this curve is not an 'exponential growth' curve but rather a [logistic function](https://en.wikipedia.org/wiki/Logistic_function) curve (this curve is commonly used to describe the population reached by new technologies). Only when the curve approaches the inflection point does it approximate exponential growth; the rest of the segments grow slower than exponential growth.
### How does the price of cryptocurrency change
Next, let’s examine [[Bitcoin Historical Prices]]. Before that, let's look at a chart to feel the power of the exponential curve.
(y=10^x; the left is conventional coordinates, and the right is semi-logarithmic coordinates)
We commonly see two types of Bitcoin price charts; typically, logarithmic coordinates are used when viewing long-term historical prices:
If converted to conventional coordinates, it would look like this:
![[Pasted image 20250105154130.png]]
(Due to the severe volatility of early Bitcoin, it is difficult to discern Bitcoin's alpha on conventional coordinates, which will be discussed later. Nevertheless, the pattern of exponential growth is still very evident, as the first half of the curve is nearly a horizontal line.)
The fitted curve of Bitcoin price over time given in [[Bitcoin Price Guide]] is:
$$price=10^{5.84\times log_{10}{time}-17.01} $$
This formula can be expressed as:
$$price=10^{-17.01} \cdot time^{5.84} $$
In other words, the price of cryptocurrency (in USD) shows exponential growth over time (in days since January 3, 2009).
![[Pasted image 20250105193649.png]]
(Standard coordinates, time converted to years)
![[Pasted image 20250105194004.png]]
(Logarithmic coordinates)
In summary: if we ignore volatility, the price of Bitcoin shows exponential growth over time.
### Discussion
Having examined both the number of users and the price, let's return to the discussion of their relationship.
From 2009 to 2024, Bitcoin's supply first increased quickly and then slowed down, currently supplying 90%. This means that the suppressive effect of supply on price is diminishing, and after 2028, it will be negligible.
On the other hand, the number of users increases at a rate lower than exponential (the first half of the logistic function), with the growth rate accelerating (in recent years, institutions have rushed in, and the number of whale wallets has rapidly increased; currently, wallets holding more than 10 BTC account for only 0.28% of the total wallets but hold 82% of Bitcoin). As mentioned in [[The Bullish Case for Bitcoin]], the transition of Bitcoin from a monetary good to a general medium of exchange may require the participation of nation-states. At that time, the inflection point of the logistic function curve, which is the segment with the highest growth rate, will arrive. Coincidentally, this year marks Trump's presidency, uh, well... never mind, anyway, we are definitely still in the 'early stage.'
As institutions gradually occupy the main market share, market volatility (Beta) will decrease. This is true. However, many people express a sorrowful demeanor of 'having missed the best years' when discussing Bitcoin's decreasing volatility, which I believe is incorrect. You have only missed 16 years, and you have not missed the most exciting movements.
- Supply suppression is increasingly weak;
- The number of users is growing increasingly faster;
- From 2009 to 2024, the fitted regression of the price still basically shows exponential growth;
- Market volatility is decreasing;
We seem to be able to draw a very bullish conclusion: **With decreasing volatility, the price of Bitcoin will grow increasingly faster, at least maintaining the current momentum of exponential growth!** The most exciting movements of Bitcoin may still be ahead. Of course, the above analysis simplifies many aspects, and many things could happen in this world, so let's wait and see.
