Furkan Semih Dündar's Personal Website PhD. in Physics

A Monadic Interpretation of Wolfram Model

In my article published in the journal Foundations of Physics I investigated Leibnizian ideas in the context of Wolfram Model. It is found that the hypergraph ontology of Wolfram Model is very apt to model a monadic universe in Leibnizian terms. The main idea is that monads are defined in their relation to one another and hypergraph ontology is very appropriate to model them.

The main tenet from Wolfram Model that is a game-changer in terms of modelling (a possible) dynamics of Leibniz’s monads is the concept of a re-write rule. Because monads are defined in their relation to one another, a dynamics defined on monads should only pay attention to their connection structure, which is given by the hypergraph ontology. If you would like to have a single take-away message from this study, it would be that re-write rules would be highly important in terms of defining a (possible) dynamics on monads.

Similar to the study mentioned below, I studied the concept of variety defined in Barbour and Smolin (1992) which is named as BSD Variety in the present study, as an acronym of Barbour-Smolin-Deutsch. In the multiway system of Wolfram Model, physical paths are singled out as the paths where all hypergraphs are Leibnizian. Among the physical paths, there are maximal variety paths as defined by extremizing an action defined as the sum of variety of each hypergraph on the path. It might be that these paths have a similar role of singling out an ontological basis in The Cellular Automaton Interpretation of Quantum Mechanics of ’t Hooft. However as of now, this is unknown.

A few speculative comments regarding the status of non-Leibnizian hypergraphs are made in the paper. One is that even though a hypergraph is non-Leibnizian, through a re-write rule, it may produce a sequence of Leibnizian hypergraphs. This observation is likened to a big bang event, where the initial ‘singularity’ is not physical but it nevertheless gives rise to the observed universe. For more information, please refer to the original article.

The code that is used to calculate various quantities in the study is available on my GitHub repo, under the GPL3 License. There are two main files, one is a C++ code that uses OpenMP parallelization and another is a Mathematica package.

Leibniz's Philosophy and String Variety

I am quite happy to share my latest research, which through a paper by Barbour and Smolin (1992) , connects with the ideas of Leibniz. Leibniz famously said that we live in the best of all possible worlds as an attempt to solve the "problem of evil" (which is also called as "Theodicy"). The idea behind the Barbour and Smolin paper is that the universe attains a state with the highest variety and as a toy model they considered a character string universe with cyclic boundary conditions where each place can have two values, such as "X" and "-" or zero and one.

In my article I have given a possible time evolution model for this type of universe. The basic idea is that a universe with highest variety (of string length N) hops to another configuration with highest variety (of string length N+1). Which configuration hops to which configuration is solved by the "best matching" technique of Barbour. The idea is that a string hops to another string which is "closest" to the previous string. I used the (cyclic) Levenshtein distance to measure the closeness between strings. Because there could be more than one match, the time evolution is not linear and in general is a directed graph. The most obvious interpretation of this toy model is by the Everett's Many Worlds interpretation of quantum mechanics. It may be interesting to see where this interpretation in terms of Many Worlds would lead us. This is also important because the main motivation behind the Barbour and Smolin paper was to put forward a theory for quantum cosmology. As part of my presentation in a conference (28th--30th June 2022 in İstanbul) I have calculated maximum variety of longer strings and listed all distinct (modulo symmetries) Leibnizian maximal variety strings for N < 36. You can reach the details of the paper and the conference through my GitHub link that I share in the next paragraph.

For more information and to reach the computer codes (under the GPL3 License) I have written (which are in Haskell and C: Haskell code is good for experimenting with configurations with small strings where as the C code is highly optimiezed and runs on parallel using OpenMP) please visit my GitHub repo.