What is a Logarithmic Function, Is Bitcoin a Logarithmic Functio

Simply looking at this BTC chart on a LOG scale and plotting havings on the dotted yellow lines, I see a clear logarithmic function in the price movement of Bitcoin. What am I missing? It can't be this straight forward, (programmed scarcity) I don't believe that I am smart enough to see such an obvious price movement?

I had a conversation with ChatGPT about this, and I recommend anyone who might read this to do the same. Ask it "what is a Logarithmic function", "what are characteristics of a logarithmic function". The answer I got was as follows -

"A logarithmic function is a mathematical function that is the inverse of an exponential function. It helps to solve for the exponent in equations where the variable is in the exponent position. For example, in the logarithmic function f(x)=log⁡b(x)f(x)=logb​(x), bb is the base of the logarithm, and xx is the argument. The logarithm answers the question: "To what power must the base bb be raised to produce xx?"

For example, if log⁡2(8)=3log2​(8)=3, it means 22 raised to the power of 33 equals 88.

I followed up with, “So could we apply this principle to computational sciences to program scarcity, such as programming electronic gold?”, from my experience you need to use ChatGPT like a hunter baiting a trap, to get the most out of it before tying it back into your topic of choice. Like manipulating a child, don't ask your question straight forward, let them wander till they get where you want them.

It answers as follows-

Absolutely! In computational sciences, logarithms are used in various applications, including programming systems that simulate scarcity, like digital currencies. For example, in cryptocurrencies such as Bitcoin, logarithmic functions can help manage and simulate the scarcity of the digital asset by controlling the rate at which new coins are generated. This ensures that the total supply of the currency remains limited, much like how physical gold is finite. Logarithmic functions can also be used in algorithms that ensure the system's growth and supply constraints are maintained efficiently.

Right where I wanted it to step, boom, "So is Bitcoin a logarithmic function?” I ask

Not exactly. Bitcoin itself isn't a logarithmic function, but logarithmic functions are used in the underlying algorithms and economics of cryptocurrencies.

Bitcoin uses a process called "mining" to generate new coins, and this process involves complex mathematical algorithms. The total supply of Bitcoin is capped at 21 million coins, and the rate at which new coins are created decreases over time in a manner that can be described using exponential decay functions.

Logarithms come into play in various aspects of computing and cryptography, such as in calculating the difficulty of

Now if any is still reading, hold on your pants this is where it gets interesting “So could somebody simply look at the scarcity of gold throughout history, copy that scarcity logarithmic function, and apply that to programmed cryptocurrencies such as Bitcoin, and then just re-emulate history's past performance through a logarithmic function using technologies like cryptocurrencies?” I asked. If this is true... I am not sure, you could re-create history ?

I'll not include the Google-able info it said about the BTC having protocol to save on length, but this was the 'kill shot' for my hunt.

"Now here's where logarithms come in:
In computer science and cryptography, logarithms are often used in the algorithms that estimate how difficult a given task is, especially when the task involves exponential growth or decay. For example, calculating the logarithmic growth of the hash rate over time can help in modelling or predicting future difficulty levels. Similarly, some of the cryptographic protocols underlying Bitcoin (like Elliptic Curve Digital Signature Algorithm or ECDSA) involve operations with logarithmic complexity.

To break it down:

- Mining difficulty increases as the network grows more powerful — and the adjustments are made to maintain a consistent block time.
- Logarithmic and exponential functions are useful to describe these kinds of non-linear relationships — like how small changes in hash rate can have large impacts on mining performance or difficulty.
- In cryptography, discrete logarithms are a fundamental part of the security assumptions underlying public-key cryptographic systems.

So while Bitcoin itself isn't based on a logarithmic function, logarithmic thinking is absolutely baked into the mathematics that keep the network secure, balanced, and scarce by design.
Want to dive deeper into how the actual difficulty adjustment formula works or how ECDSA uses logarithms?"

These last 2 Sentences are the back straps, programmed scarcity.

I now go down the mathematical rabbit whole of the ECDSA of various different cryptocurrencies and the models they have implemented, some aiming to replicate Trad Fi economic models and some that create their own independent models of scarcity. I do believe that the BTC having protocol is the best implementation and bulletproof (brick dumb) way of implementing a model that it is the most obvious to society. These models, similar to AI models, are a canvas technology and what you get out of the end result is the sum of all things that are put into building that model.

- LLS