Suppose we conveniently extended the standard concept of cellular automaton to include
graphs and state-spaces Q of any cardinality and that the transition function F belonged to a certain adequate notion of "(hyper)computable function". We call this a hyper-cellular automaton HCA.
Consider the postulate: the universe can be described by a HCA with transition function F.
We cannot escape the problem of the initial condition Q_0. In the Wolfram Classification random initial conditions are considered. Hence the expediency for some topology or measure on Q.
Q will include for instance the usual sheaves (principle bundles and connections) considered in the standard model. It will also include other aspects to account for quantum gravity, consciousness, emergent biological complexity, etc.
It is an empirical fact that this HCA must be WC4 "complex patterns of localised structures" in the Wolfram Classification.
A major problem is the goal of reverse engineering F is that we do not have evolutions for other initial conditions at our disposal neither for the universe nor for subsystems of the universe. For physics at least a lot of locality and invariance hypotheses come in to play to justify the universality of experimental conclusions. The chemistry we observe on earth must also be that of the most distant star.
For biology the situation is drastically different. My question is: how can biology go beyond being a merely descriptive science as contrasted with fundamental physics ?
Biology seems to be mainly a "reverse engineering" affair. But it is also important
to have detailed, mathematically precise models - perhaps using HCAs - that can be used to test hypotheses and perform simulations.
Molecular biology suggests a new paradigm for software-hardware, a fluid mobile computer with essentially interconnected parts. A key characteristic is that information operations are tied to material and energetic constraints.
Also we must focus on ecosystems (the analogue of the cell ? ) rather than individual species. What about the idea of a "natural internet" (via horizontal gene transfer, etc.) ?
Dear Clarence Lewis Protin , thank you for posting your question. Assuming that I understood your question, for which I am not sure, I like to share my thoughts with you. Let us examine your question: how can biology go beyond being a merely descriptive science as contrasted with fundamental physics ? My reaction is: Why do you think that Biology is merely a descriptive science contrasted with fundamental physics? I think this is not the case. Every scientic endevour starts with describing what we see, perceive, feel and so on. The key question is what do we want to understand so we can learn i.e. model a transformation function F which should be computable (i.e. decidable) which result we can interprete and give meaning to it. Your axiom: Consider the postulate: the universe can be described by a HCA with transition function F is needed to understand that there are complexities which could be classified in WC4 "complex patterns of localised structures" in the Wolfram Classification. This ontology might help us to understand systembehavior but in itself it does not predict systembehavior unless a (hyper)computable function" exist. Here lies the problem. So I suggest to change your question which might be of some help to make a change in the nature of scientic enquery in biology (or any other science like economics, sociology, medicine .......) . Kind regards Rob
Rob Christiaanse Thank you for your reply and observations. I think I should clarify a few points.
I introduced HCAs and "hypercomputable functions" in order to be neutral with regards to fundamental physics (for Quantum Loop Gravity ordinary cellular automata might be ok, but not for String Theory).
Feynman wrote: It always bothers me that according to the laws of physics as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space and no matter how tiny a region of time.
The function F is supposed to be an abstraction of the fundamental laws of physics. And in practice F will not only be an abstraction but an approximation.
Consider the Navier-Stokes equations. In themselves these PDEs do not allow us to predict much about the behaviour of fluids. But thanks to numerical analysis applied to these equations the behaviour of a fluid can be approximated by a cellular automaton with a given transition function F. This function F can be seen indeed as an abstraction of the laws of physics. And we can study and predict many aspects of fluid behaviour (such as turbulence, laminar flow, etc).
My question was: why can't we do something similar for evolutionary biology ?
Find a cellular automaton which abstracts and approximates basic laws of physics and chemistry and perform simulations to see if any complex self-regulating and self-replicating structures similar to life emerge ?
Or perhaps prove a result about the radical insufficiency of our current fundamental physics and chemistry to account for life-like structures ?
I agree that biology in general is not merely descriptive any more than chemistry is. It is only merely descriptive on a more fundamental evolutionary and theoretical level.
My proposal is that CA models and simulations might be a way of developing an "experimental evolutionary biology".
Dear Clarence Lewis Protin , many thanks for your clarification. I fully agree with your proposal. Do you work on this proposal and if yes did you publish on the subject? Analogous your position the logic implies that there are theories like Feynman lectured. KR Rob
Dear Rob Christiaanse , I have not published on this subject but I have unpublished material on general systems theory that explores the analogy between computer engineering concepts (operating systems, networking, hardware, compilers, programing languages, simulation, video games) on one hand and biochemistry, neuroscience and cognitive science/linguistics on the other.
Regards,
Clarence
Your question is touching a very deep problem of biology. It goes beyond genes, as we know that biology is operating on quite a few emergent-levels above genes. Each next emergent-level has its own unique operational rules.
After giving myself a similar question [2], extensions of the Conway's 'Game of Life' started to be explored. Extensions can be of two kinds: rule and neighborhood.
In [2], it was demonstrated that there exist robust, injected errors resistant rules exactly as is observed in the biology. The software [1] is enabling to change neighborhood within 5 times 5 radii, and select one of the possible hundreds of thousands neighborhoods.
By just playing with [1], it was found that gliders can propagate by the speed of one cell per one step. To my surprise, some neighborhood combinations of eight cells are displaying remarkable features and behaviors. Those working in neuroscience might find striking similarities between such simple cellular automata with relaxed neighborhood and rule and their observed of neuronal activities.
Just one example from the paper [2], see the relevant animations linked there, emergents displaying periodically located active cells in 2D having period of two were found.
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See one software and introductory research paper showing the complexity of cellular automata modeling of functioning of biological systems at their lowest level with links to python programs & animations in PNG format (information lossless).
https://www.researchgate.net/publication/365477118_Python_program_GoL-N24_simulating_the_'Game_of_Life'_with_variable_neighborhood_using_eight_neighbors_from_24_possible
https://www.researchgate.net/publication/361818826_Robust_massive_parallel_information_processing_environments_in_biology_and_medicine_case_study
Dear @Clarence-Protin,
Finally, the video demonstration is prepared. Check it, visual info is way more expresdive! It demonstrates quite interesting behaviors observed in some extended neighborhoods of GoL, see
The John H. Conway's 'Game of Life' (GoL) Cellular Automaton:
https://m.youtube.com/watch?v=gc42D2sdL8I
Dear Jiří Kroc
Thank you for the interesting video of your program.
One thing that intrigues me is the question of scale and level of approximation. Supposes we ran GoL-type rules on a massive scale,
let us say on a 10^9 x 10^9 grid. Could there be any interesting "macropatterns" that emerge and which could not be detected on smaller simulations ?
Dear @Clarence-Protin,
This a great question. A short answer is: "Yes. Everything computable can be simulated in the GoL because it was already proven to be Turing machine equivalent!", see the paper citation in the paper [1].
A partial answer to your question can be found in the simulation of AND logic gate, see my publications list. For examples of the development of the whole computer processor in GoL, see again the links in the paper [1].
The core message of this paper is to define the initial steps on the path of emergent, self-assembling, error-resilient computers. The paper demonstrated a way to search for error-proof computation means. The end result should be computers, which after destroying their substantial part will have the capability to reconfigure themselves to the original functions, possibly just a bit slower in delivering of outputs.
Back to your question from the previous comment, large-scale simulations can reveal some very interesting types of behaviors. I do see how to tackle this problem on a large and sufficiently powerful computer, cooperation on this project is open.
[1] Jiri Kroc: "Robust massive parallel information processing environments in biology and medicine: case study", Problems of Information Society 13:2 (2022) 12-22.
https://www.researchgate.net/publication/361818826_Robust_massive_parallel_information_processing_environments_in_biology_and_medicine_case_study
So, what do you think is the tool for describing the laws of complex science? Simple science, like physics, uses mathematical equations, but what about complex science?
I am very interested in complex science, and I think it is a revolution in science, a revolution in methodology
I don't think cellular automata can describe the laws of biology very well, and the tool to describe the laws of complex science is something like a computer program: a program. The biological DNA is programs.
I read several books on the complex science, and by summarizing them, I found that they actually proposed a tool to describe the complex science: the program. Of course, the method these books are computer program simulation, but I think here they are wrong, not computer program simulation, but the law of complex science is "program," just is program, not a computer program. Biology and economics are both complex sciences, so their laws should be described by "program".
Clarence Lewis Protin
I think this approach is in the opposite direction. We should not study the whole from the micro parts, but should study the part from the whole.
Dear Colleagues,
It might be interesting to observe one of the simulations of GoL-N24 software, which is expressing the second-order emergence.
https://www.researchgate.net/publication/368635079_Emergent_Computations_Emergents_are_Breeding_Emergens_As_Demonstrated_on_Ships_Breeding_Trains_of_Oscilattors_Occuring_in_Modified_GoL_Using_Program_GoL-N24
Feel free to share your understanding of those simulations. The version of the software is getting tested and final improvements prior releasing its beta-testing version. Everyone is welcomed to test the software once it will be released.
Personally, I really like to observe the rise of multi-level complexity from simplicity.
The link to the Python software, which is going to be released:
https://www.researchgate.net/publication/365477118_Exploring_emergence_Python_program_GoL-N24_simulating_the_'Game_of_Life'_using_8_neighbors_from_24_possible
The current online version is simple and old.
Jiří Kroc
Why do you all think it's possible to simulate with "computer programs"? I don't think we can simulate the evolution of organisms with "computer programs," because creatures are not computers. We can use a "program" as a tool to describe patterns, but not with a computer program.
Dear @Duan Xian Xiang,
Thank you for your very clever question. The spoiler is: "The emergent massive-parallel problem-solving (computations) is not computation in the classical sense!" The reality is more convoluted than one can imagine. My current research is based on a 30 years old idea of mine that we can uncover, understand, and build emergent solving of problems. I am often using the term emergent computing, but the more appropriate term should be functioning.
The software update that I am currently finalizing in its beta version is computing at the level between the computer's processor unit and the backend, simulating a massive parallel computer. The word backend is important. Basically, a massive-parallel 'computer' is simulated withing standard von Neumann computer design! Keep this in the mind in the following.
Any massive-parallel computational environment (computer) is solving problems using a very disparate vocabulary and techniques from what we understand as computation.
I have quite a few publications explaining the very workings of cellular automata, their design, and open-source software to dive into the subject quickly and efficiently. Read the introduction of the last paper on emergent computations from 2022, there are listed essential resources.
My answer is: "We are standing at the edge of the paradigm change in problem-solving which is utilized by all living systems and quite a few non-living ones in the sense of emergent massive-parallel interactive environments." Please, feel free to give your take on my explanation, it helps me to estimate the clarity of my explanation. 🙏
Jiří Kroc
I also believe that: “We are standing at the edge of the paradigm change in problem-solving which is utilized by all living systems” The natural science paradigm of reductionism is shifting towards the complex science paradigm, and the social sciences and life sciences are suitable for description by complex science methods.
Jiří Kroc
Have you read John E.Mayfield's book The Complex Engine? In the first half of the book, he actually proposed a tool to describe the complex laws of the science: computing (which I call "program"), But the second half of his book is about using computers to simulate the laws of biological evolution, which I think is a mistake. The law of biology can be described by "program", but this "program" is not a computer program, computer program is only one of it, "program" or "calculation" includes psychological program, economic activity program, political activity program, gene program of organism, etc. I mean, the laws of complex science can use "programs" as a tool to describe them, but it has nothing to do with the computer. The laws of complex science are "programs" rather than mathematical equations. For example, the economist Quesaay's economic chart is a program, but this table can not be simulated by computer or cellular automata.
Jiří Kroc
I said a computer including what you call a "parallel computer" or "cellular automata," or any computer with a silicon-based chip.
Clarence Lewis Protin
"I have not published on this subject but I have unpublished material on general systems theory that explores the analogy between computer engineering concepts (operating systems, networking, hardware, compilers, programing languages, simulation, video games) on one hand and biochemistry, neuroscience and cognitive science/linguistics on the other."
.......
Therefore, the law of these disciplines can be compared with computer, the law of computer is "program", then the law of these disciplines can be described by something similar to "program"?
Preprint Analysis of Financial Crisis Causes and Complex Systems Scie...
Clarence Lewis Protin
In biology, we can look for programs of biological change, and DNA is said to be programs, to study these programs, and see how these programs work.
Dear Duan Xian Xiang,
Your words "The law of biology can be described by "program", but this "program" is not a computer program, computer program is only one of it, "program" or "calculation" includes psychological program, economic activity program, political activity program, gene program of organism, etc." are consistent with my review paper where are explained examples and methodologies used in biology and medicine to describe, simulate, and predict the behavior of biological systems.
The book you mentioned sounds interesting, but I do not know it.
According to my understanding, emergents and their mutual interactions are the best current methodological description of biological and many physical phenomena observed. In many cases, there exists no alternative to such descriptions, as demonstrated on medical applications in my review.
The review describing the basic principles of complex systems descriptions in biology:
"Complex Systems and Their Use in Medicine: Concepts, Methods and Bio-Medical Applications"
https://www.researchgate.net/publication/330546521
We could generalize the definition of cellular automata to any kind of partial order. In this way even a system described by a partial (or integral) differential equation could be seen as a cellular automata.
Dear Clarence Lewis Protin,
Cellular automata rule can be designed according to discretizatiin scheme of partial differential equations. This is shown in the work in works of Toffoli and Vichniac published in Physica D sometime around 1980.
Those issues are discussed in my latest review paper on emergent information processing.
The exact citations are here:
Toffoli, T (1984) “Cellular automata as an alternative to (rather than an approximation of) differential equations in modeling physics” , Physica D, 10, 117-127.
Vichniac's paper is in the same issue.
But consider any ordinal omega. To each ordinal alpha in omega let us attach an automaton A_alpha. Then if alpha is a successor ordinal alpha = beta + 1 the transition function of A_alpha is determined as usual via the states of the 'neighbours' of alpha which are beta and alpha + 1. But what if alpha is a limit ordinal ? Then the transition function will involve a limit process much like in calculus. This is what I was thinking about regarding a generalization of cellular automata that comes closer to differential equations (of course we always obtain CAs via standard numerical methods !).
Regarding this topic I think it is important to start transposing the concepts of theoretical computer science to hyper-computational or non-standard models of computation. That is, machines with countably infinite memory which can do countably infinite discrete operations in finite physical time. Maybe also be a semantics for infinitary logic.
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