One of the greatest revelations I had was when this blog was still a trading-oriented format. I was intrigued by Bill Williams’ fractals and oscillator. I had no idea how they worked but I recognized the beautiful simplicity behind the concept of man-made capital markets somehow resembling patters found naturally in our Universe. For those unfamiliar, Bill Williams’ was a master trader in the 80s and 90s, dubbed the ‘Bond King’ for his success in the bond market. He has a small hour and some change long seminar speaking to traders about the power of fractal patterns in capital markets. I won’t explain the specifics but the main wonder behind Bill’s love of fractals was the following. Mandelbrot, the father of fractals, measured the fractal dimension of the Mississippi River, it turned out to be 1.2610. He then was asked to make his financing his experiments to study something with greater profit potential. This led to a few things but namely it led to his studying of corn and cotton prices and found it was the same exact fractal dimension to 4 significant figures, 1.2610. This struck me as extremely profound and immediately resounded the idea Williams mentions, man-made markets are naturally occurring. That seems paradoxical but it makes sense, what is a market except the meeting place of people’s wants and desires, it may be translated into corn or cotton commodity prices, or the price of a Tesla stock, or the price of rice in a bazaar in Sudan. The fact that it is a converging place of people’s desires, one man desires a stock of Tesla at X price and another woman desires the same X amount of money. A rice and spices salesman in the bazaar is willing to trade his time in order to receive his patrons’ payments. Markets, when put on a chart on studied, apparently tend to replicate natural mathematical phenomena.
Physics and mathematics seem to be zooming ahead of engineering capabilities and have been for the last three decades. Cryptocurrencies were a recent breakthrough in the internet that have been slowly growing in efficiency but much slower than advances in other technologies. It seems as tho in order to catch up it would be wise to harness this intrinsic feature of markets to replicate nature to boost the capabilities of cryptocurrencies to benefit humans in the best way possible.
Stephen Wolfram is a world-renowned physicist who is currently working on a unifying ‘theory of everything’ in physics. For those readers who are not familiar, physics has long had the goal of being the science to explain the universe on a fundamental level, and since the early 20th century the goal has been specifically to have one concise theory which can describe everything in the universe on its own. This has been attempted by many, including Stephen Hawking, and has yet to be manifested into a reality, but we may not be so far away anymore.
In order to begin to explain the Wolfram Model (WM) it is necessary to lay out a few ideas. The WM assumes that space is a discrete thing made up of very small discrete ‘particles’ like atoms of space. This may seem like a small thing, but consider the fact that we experience at our level a continuous reality, similar to how water seems continuous yet it is made up of many disparate particles. Secondly it is best to be familiar with the idea of a graph before beginning which is better known as a network. It consists of various nodes, with edges between them symbolizing some sort of connection between the two. A hyper graph then is something which allows points to have connections between more than just two entities. This should be familiar to many crypto enthusiast as this is the typical way crypto networks are visualized, a large hyper graph of many interconnected nodes, where each node could be connected to several other nodes. Thirdly, the WM is ‘interested in finding the simple computational rule that describes our whole universe.’ This rule is of the following structure: when you see this pattern of space atoms, transform it into this other pattern*. It turns out this simple format can be used to derive how Einstein’s equations work, explain quantum entanglement, and much more. That is to say, from this model which looks nothing like anything else in physics, the greatest theories in physics are emerging, a great indicator that Wolfram is on the right path. The universe may be a big bag of space atoms, growing infinitely in size, constantly undergoing transformations in the underlying hyper graph of reality.
*Consider the string ‘BBAABABAAB’ and the rule ‘every time you see ‘BA’ switch it to ‘AB’.' After a few applications of the rule, the list will be sorted to: ‘AAAAABBBBB’*
The last thing that needs to be understood is a mathematical concept which is extremely powerful, casual invariance. Remember your elementary math days, you likely learned of order of operations, which stated the sequence in which you were to perform the actions of a math equation. If this is done improperly it will result in an incorrect answer. Take for example 2 + 5 * 8, if you were to add 2 to 5 first then multiply by 8 you would get 56, whereas the correct order would be to multiply first, resulting in 42. Causal invariance is a characteristic of a set of operations which does not matter in what order you apply these operations, it will always result in the same thing. A mathematical example. If you have a long list of polynomials, it does not matter in what order you multiply them, it will always be the same answer*.
*Think about the above string, apply that rule randomly in different orders to the same string and it will always become sorted to the same answer*
This is by no means a comprehensive view of the WM. However it will suffice so long as one understands the concept of causal invariance. That Is the key concept one needs to wrap their head around to understand where the fundamental flaw currently is in cryptocurrencies. It is trivial to see the parallels between the concept of the universe being a hyper graph of disparate nodes with connections between them to a cryptocurrency system. The nodes are miners and users, connections transactions, and the events are the transactions themselves occurring between parties. What is profound and novel is the idea of a causally invariant consensus mechanism.
There are quite a few things from the WM which are being left out due to the very technical nature they have in order to rigorously describe the nature of reality, a bit of overkill for these purposes. Therefore anyone familiar with WM will notice I mention the characteristics of certain properties yet refer to them by other names, that is simply because I am attempting to translate the ideas of how to universe operates to the way cryptocurrency systems operate.
Causal invariance has its greatest impact on the structure of consensus algorithms. In the current logical structure of most consensus systems, there is a large amount of effort put towards constraining the possible actions that take place within the system and the order in which they are allowed to occur. In other words this system currently has a many-to-one mapping from its possible variations in inputs, and the way those inputs are verified. This creates a bottle-neck constraining all systems to impose unnatural locks and mutexes forcing the system into one possible, valid order. A rule which would enforce consensus and also have the characteristic of causal invariance would create a system in which the order of operations did not effect the outcome. A consensus algorithm which can be applied asynchronously anywhere in the network, and still achieve consensus would also be causally invariant.
Replace the idea of a transaction in a network with an event. This event can only occur if the input to the event is also available. In the case of the WM physics model, that is the structure of the space atoms, in a crypto currency network the input is two or more wallet addresses/node entities and the outcome is a valid transaction. This model would be Asynchronous Byzantine Fault Tolerant (ABFT), the highest cryptography industry security standard.
Current systems exist with nodes forcefully restricting the possible order of transactions on the network, deciding validity upon an agreed set of rules in the network’s protocol. Instead, a causally invariant system would shift the burden of transaction verification back onto the wallet owners. This provides an increase in security for a tradeoff on local memory storage, a tradeoff made in crypto a long time ago when it was decided to have different classes of nodes in the network, some of whom process the transaction validity and maintain network consensus. Instead in this network, every node becomes its own dedicated network validator. In this causally invariant system the wallets themselves are now required to keep their own honest, verifiable log of transactions to submit to the event in order to allow the event to occur. Again, this is simply a shift of memory from being stored on special nodes to being locally stored. It would result in a more secure network as well as increase transaction verification time. That second benefit has second order effects in the block propagation time, in turn increasing the efficiency of the network’s ability to reach consensus.
A causally invariant crypto currency system would create instantaneous transactions and consistent network consensus applied asynchronously across a network. This article has laid out a simple idea, it is by no means comprehensive. Throughout the future I will continue to progress this idea forward. I would like to begin to envision a mathematical framework which can bring this idea into a more tangible reality. Any help would be greatly appreciated and if any of this has resonated as more than simply gibberish, please do not hesitate to reach out to me. My email is firstname.lastname@example.org and I am more than open to new ideas and discussion.
Anyone interested in the Wolfram Physics model, here is the main page, and here is a great interview with one of my favorite podcasters, Lex Fridman.