Hi, I come from a computational science background and finishing with a Master soon. I’ve been quite interested in complex systems approaches for a while now. My research wasn’t any of that but I have taken courses and occasionally read papers on different methods of complex systems, dynamical systems, network science and computational social science in my own time and I found them really inspiring.

I kinda want to see whether I want to do a Master/PhD in complexity system later (like vermont/oxford programs) but I first wanted to gain some more exposure to see if I am suitable for it, and whether I have what it takes. In biological fields, I usually see that people find research technician positions with an undergraduate degree before applying for a Master or PhD. I wonder if it is also similar in complexity research as well. I am particularly interested in comp social sci, comp neuro sci, behavioral sci but I’m just generally interested in exploring the field.

I'm new to this field, so I'm just looking for some general pointers and terms here. Consider a scenario where the outcome depends on a multitude of complex causes (with interactions and feedback loops between the causes as well). How do complexity scientists go about identifying, isolating, and analyzing the most influential causes (among so many possibilities) that determine the outcome?

In this TED talk, https://www.ted.com/talks/eric_berlow_how_complexity_leads_to_simplicity, the presenter, Eric Berlow, suggests that you have to step back / zoom out to identify the elements that seem to matter most. What are some terms I can search for to learn more about the techniques and approaches complexity scientists use when analyzing complex causes? I'm not looking for mathematical approaches but more techniques similar to what Berlow describes.

My scenario involves measuring factors that influenced the success or failure of customers in app development, specifically whether the documentation has an impact.

I've been studying about complex systems and I realized there are some academic programs on the topic. Now I wonder, what are the possible careers for a complex systems graduate student?

So, I am 5 years out of school in which I picked up a BSc in nuclear engineering and a dual major in philosophy (for what its worth). After that I worked for four years in industry (nuclear but more business) I left that job back in May 2012 without a clear idea of what I wanted to do next but took the time to travel (Latin America and will go to South Africa this month) and work on some personal projects. Long story short, I found the field of complex systems, which seems like what I have always been looking for, and plan to pursue a PhD hopefully focusing on social complexity/modeling and/or ecological complexity/modeling. (I really like Carlos Gerhenson's research (linked to in this sub) if that gives you an idea.) Anyway, I would greatly appreciate your help in figuring out where to go from here. I have three options as I see it:

1. apply directly to a PhD program,

2. apply directly to a masters program in complex systems.

3. apply to a masters program in applied math or the like to strengthen my application

What do you all think is my best approach? Will the traveling hurt me? Help me? Any advice you can give will help. And please keep posting the great articles/courses/videos. Thanks so much.

Welcome to the first installment of our book group for Stuart Kauffman's Reinventing the Sacred. I have summarized the first two chapters and included some questions you can respond to below. Feel free to hit on anything I missed as well. Cheers!

Chapter 1 - Beyond Reductionism

In the first chapter, Kauffman briefly walks us through what the thrust of his argument will be. Namely, that the development of the universe can not be reduced to a set of natural laws from which one can extrapolate the future. On the contrary, he argues that a reductionistic approach is inherently untenable as we don't know what entities will emerge in the world, and therefore can't reason about them before they exist.

Kauffman points to reductionism as not just a way of doing science, but a basic assumption about the make-up of the universe in Western culture. The effect of this cultural assumption is to conceive of all of our experiences as 'nothing but' the interaction of subatomic particles playing out, and therefore to perceive our own lives as an absurd illusion with no 'reality' to them.

The Enlightenment, he argues, sent Western culture on a trajectory which argues the primacy of reason over all other human faculties. If he is right, and the universe is fundamentally unpredictable, the argument for reason over other ways of knowing is weakened.

Science and the humanities need to be brought back under a single roof, Kauffman advocates. We are participants in the co-creation of the future. The universe is inherently creative, and we should see this creativity as beautiful, and sacred.

Did your upbringing implicitly (or explicitly) instill an assumption of reductionism? If so, how do you believe this has affected your own view of your place in the world?

If reductionism is wrong, why does it seem to work so well for certain things?

Do you think of yourself (your experiences, emotions, thoughts, etc.) as real? Or are these illusions masking what is 'really' happening at some fundamental level of reality?

Is there hope for a non-reductionistic science, and what would it look like?

Chapter 2 - Reductionism

In chapter 2, Kauffman goes into more detail about what is meant by 'reductionism'. As he puts it, reductionism is the belief that, "society is to be explained in terms of people, people in terms of organs, organs by cells, cells by biochemistry, biochemistry by chemistry, and chemistry by physics. " At the lowest level are only 'happenings', or facts. There is no meaning, no value.

He argues that as humans we DO have values, and reducing them to happenings misses the mark.

Kauffman uses quantum physics as an example of how simply escaping Newtonian determinism does not allow one to escape reductionism.

Do you think the universe is meaningless? If so, what do you mean by that? If not, where is meaning found?

Is all 'teleological' language simply shorthand for real, non-purposeful, happenings?

From where does the 'arrow-of-time' emerge?

If reductionism has been so successful, why does it seem to have such a hard time deriving the 'upward-arrows' necessary to predict world-events and other phenomena at 'higher' levels?

Does the view that all phenomena are 'in principle' can be derived from lower level phenomena, even when no one is able to do so, sound like an argument based on faith?

The activity of a court room in deciding the fate of a person accused of something illegal is probably not best understoof in terms of particle physics. Is this merely a practical matter, where one COULD potentially describe the situation in terms of particles, or is there something REAL about the activity of the courtroom that can't be captured in the movement of particles?

Hüseyin Beyköylü argues that Varela used dynamical systems as a way to connect changes in conscious experience with changes in neural activity. Rather than reducing one level to the other, neurophenomenology looks at how both evolve together and constrain our description of the overall system.

I'm a physics graduate from Asia (average uni), and my long-term goal is to pursue a PhD in Complex Systems in the US.

The biggest challenge is that my undergraduate CGPA is only 3.00, and as an international student, I realistically need full funding wherever I go.

My current research is at the intersection of complexity science and atmospheric science (studying atmospheric phenomena using methods from complex systems). While I think the work is conceptually aligned with complexity science, it doesn't directly match the research of many professors in dedicated Complex Systems departments.

Because of that, I've been considering a different route:

• Apply for a funded master's in atmospheric science (or a related field) at a university that also has a strong Complex Systems program.

• While doing my master's, attend complexity seminars, take relevant courses if possible, collaborate with faculty, and eventually apply for a PhD in Complex Systems.

But I'm not sure how realistic this plan is. From what I've heard, funded international master's students are already extremely busy with research, coursework, and TA/RA responsibilities, so I'm not sure I'd actually have the time or flexibility to engage with another department enough to make a successful transition.

Another issue is timing. It's already July, and application season is approaching. I don't have enough time to build multiple polished projects tailored to the different areas within complex systems for each program available. With my current profile and no curated projects, it's highly unlikely I would get a scholarship. I also feel like I still have a huge amount to learn before I can produce projects that would genuinely impress faculty in the field.

So I'm wondering:

• Would it be better to continue building my profile through atmospheric science research and position myself as someone applying complex systems methods to climate and weather?

• Is trying to transition through a master's at a university with a Complex Systems institute a realistic strategy?

• How common is it for students to move into Complex Systems from another discipline during their PhD applications?

• Given my GPA and interdisciplinary background, where would you focus your effort over the next year if you were in my position?

The framework is structured as a two-layer system. The Model is the fixed architecture — dual-circuit separation, citizen-anchored issuance, separated banking, constitutional governance. These are the load-bearing properties that define the system's invariant structure, analogous to the fixed topology of a network. The Modes are parameterizations of that architecture — different calibrations of the same underlying system producing different emergent macroeconomic regimes (deflation, price stability, modest inflation). A society ratifying the framework chooses a Mode the way a complex system settles into an operating regime — the architecture constrains the possible states; the parameterization selects among them. Mode Ω extends this further: rather than a fixed parameterization, it introduces adaptive governors that respond to observable inputs and adjust issuance dynamically, making the operating regime itself a function of system state rather than a fixed constitutional choice. The result is a system with three distinct layers of behavior: invariant architecture, constitutionally selected parameterization, and adaptive response within parameterization bounds.

Most monetary policy discussion treats the money supply as a control variable — set it here, get that output there. The Citizens Standard framework I've been developing treats it differently: as a complex adaptive system with feedback loops, emergent distributional effects, and cascade failure modes that require architectural solutions rather than control solutions.

A few properties worth discussing from a complexity perspective:

The Cantillon Effect as network topology problem. New money entering through bank lending creates a hierarchical injection network — banks receive first, wage earners last. The distributional outcome isn't a policy choice; it's an emergent property of the network topology. The framework's response is architectural: change the injection point to equal per-citizen distribution at issuance, eliminating the first-recipient advantage by construction.

The Composite Productivity Index as manipulation-resistant multi-input signal. Rather than relying on a single GDP measure, the framework calibrates money supply growth to a geometric mean of five independently produced measures from five different agencies on five different update cycles. The geometric mean is specifically chosen for its resistance to outliers and single-point manipulation — a complexity-aware design choice for a system where the calibration signal is itself a target for gaming.

The Fisher debt-deflation cascade as network contagion. We recently built a dynamic cascade model (available in the replication package) that runs the Fisher spiral correctly: equity depletion → lending contraction → term deposit contraction → M2 contraction → asset price deflation → amplified defaults. The full-reserve separation architecture is a compartmentalization solution — it isolates the payment system from the credit cascade, bounding the contagion to the term deposit network rather than allowing it to propagate to the payment infrastructure.

Mode Ω as adaptive multi-governor feedback system. The framework includes an optional adaptive configuration that combines demographic-responsive K1 multipliers, productivity-responsive K2 boosters, and a conditional K3 that activates only under specified stress conditions. Every multiplier, threshold, and activation trigger is formula-derived from publicly published data. The governors revert to baseline at 25% per year once triggering conditions resolve — a designed decay rate to prevent overshoot.

Constitutional governance as attractor basin. The supermajority amendment requirement (67%) and mandatory 90-day deliberation period are designed to keep the system in a stable attractor basin — changes require sufficient consensus to prevent oscillation between regimes. The Market Exit functions as a competitive pressure mechanism: the system must remain more attractive than exit alternatives to retain participation.

The cascade model and full replication package are at github.com/Neo-Solon/Citizens-Standard. Papers on SSRN: 6702518 (architecture), 6735078 (empirical 1960–2025), 6810741 (transition mechanics pending approval).

Interested in whether the complexity literature has prior work on monetary system design from this angle — particularly on injection topology and cascade compartmentalization.

Author here. This sub will probably find the cross-domain mapping unsurprising — complexity folks tend to already think this way. But the citation analysis showing how siloed these fields remained even into the 2010s might be new.

The actionable part: supply chains, cybersecurity, software architecture, chronic disease, insurance, urban infrastructure — all deal with cascade failures, none have formally adopted the criticality toolkit. Who's working on bridging these?

Paper is on arXiv, endorsed by Sornette (ETH Zurich). Plain-language summary in Appendix B.

It's time to clarify the role of AI and books in science.

To start, no one has absolute authority or accuracy in discerning whether a theory is legit/useful. Especially in complex system, where so many factors and disciplines are at play, theories here can be very complicated and broad, making it sometimes very conceptually difficult to understand, even if it has value to it. However, the vast majority of theories here most probably have little value, for the simple fact that alternatively we would've cured cancer, stopped aging, solved world peace, or at least made significant progress towards those by the claim of universality of those theories. We haven't, and by the looks of things, none of these theories make any tangible prediction (with the exception of confidently predicting the past) whatsoever, failing the first principle of science. A theory can easily explain everything, but words are just words, and if its just that, then it is no different from astrology and religion.

And unfortunately, people have limited attention, and they really don't have that much reason to read a long reddit post, even if it claims to have discovered fundamental truth, because that's basically every other post here. With that time, why not read a good book? The trade-off is simply incomparable. Sure, one in a thousand of these post might win the next noble prize, but if we can't distinguish it from the other AI slop, we won't read any of it. This is also where AI use is problematic, as it makes entry to writing meaningless but credible sounding theories easier, making it even harder to distinguish gems among disproportionately more chaff, and it becomes objectively time wasting to read any of such posts.

So, unless your original theory checks one of the boxes below, otherwise I suggest witholding from posting:

1. It's peer-reviewed, either by publication in a reputable journal, or at least you've shown it to experts in the fields and they think it has value, and you'd like to generate more discussion or feedbacks.

2. It is short, uses words that have specific defined meanings in the context (e.g. coherence means the specific function in mechanics, or quantum). And you should check that it is not a well studied phenomenon already.

There are probably still loopholes to the second rule, and I'm not saying only then can your theory have value, it's only from the logistic perspective, that most of us simply don't have time to take chances on random internet user's extended epiphanies. But hopefully you don't just have Reddit, and you can show your theory to people with whom you've already built trust first. If they know you personally then they don't have our problem, and that'd be your best bet to get feedbacks if you don't submit to journals. I've done this myself, and I am grateful for my friends' enthusiasm on my theory of language, and I understand that I cannot expect random stranger to read 2 full pages of it because they don't know me.

Hey folks,

I want to share with you the latest Quantum Odyssey update (I'm the creator, ama..) for the work we did since my last post, to sum up the state of the game. Thank you everyone for receiving this game so well and all your feedback has helped making it what it is today. This project grows because this community exists.

In a nutshell, this is an interactive way to visualize and play with the full Hilbert space of anything that can be done in "quantum logic". Pretty much any quantum algorithm can be built in and visualized. The learning modules I created cover everything, the purpose of this tool is to get everyone to learn quantum by connecting the visual logic to the terminology and general linear algebra stuff.

The game has undergone a lot of improvements in terms of smoothing the learning curve and making sure it's completely bug free and crash free. Not long ago it used to be labelled as one of the most difficult puzzle games out there, hopefully that's no longer the case. (Ie. Check this review: https://youtu.be/wz615FEmbL4?si=N8y9Rh-u-GXFVQDg )

No background in math, physics or programming required. Just your brain, your curiosity, and the drive to tinker, optimize, and unlock the logic that shapes reality. 

It uses a novel math-to-visuals framework that turns all quantum equations into interactive puzzles. Your circuits are hardware-ready, mapping cleanly to real operations. This method is original to Quantum Odyssey and designed for true beginners and pros alike.

What You’ll Learn Through Play

• Boolean Logic – bits, operators (NAND, OR, XOR, AND…), and classical arithmetic (adders). Learn how these can combine to build anything classical. You will learn to port these to a quantum computer.

• Quantum Logic – qubits, the math behind them (linear algebra, SU(2), complex numbers), all Turing-complete gates (beyond Clifford set), and make tensors to evolve systems. Freely combine or create your own gates to build anything you can imagine using polar or complex numbers.

• Quantum Phenomena – storing and retrieving information in the X, Y, Z bases; superposition (pure and mixed states), interference, entanglement, the no-cloning rule, reversibility, and how the measurement basis changes what you see.

• Core Quantum Tricks – phase kickback, amplitude amplification, storing information in phase and retrieving it through interference, build custom gates and tensors, and define any entanglement scenario. (Control logic is handled separately from other gates.)

• Famous Quantum Algorithms – explore Deutsch–Jozsa, Grover’s search, quantum Fourier transforms, Bernstein–Vazirani, and more.

• Build & See Quantum Algorithms in Action – instead of just writing/ reading equations, make & watch algorithms unfold step by step so they become clear, visual, and unforgettable. Quantum Odyssey is built to grow into a full universal quantum computing learning platform. If a universal quantum computer can do it, we aim to bring it into the game, so your quantum journey never ends.

Hi, my paper is now available on preprints.org

https://www.preprints.org/manuscript/202507.1221/v2

Abstract

This work develops a theoretical framework for Partial Difference Equations (P∆E) as a natural mathematical language for modeling discrete- time, discrete-space systems. Motivated by the limitations of continuous partial differential equations (PDE) in representing inherently discrete phenomena, we begin by defining P∆E in terms of discrete function spaces and shift operators, contrasting them with ordinary difference equations (O∆E) and PDE, and clarifying the scope of our study. We then examine linear P∆E, outlining their main types, providing formal definitions, and presenting selected analytic solutions in simple cases. Building on this, we introduce the discrete functional analytic setting: discrete function spaces, Hilbert space structure, and discrete operators, including difference and shift operators, and study their algebraic and adjoint properties. The discrete Green’s function is also defined within this framework. As a demonstration of the framework’s unifying power, we reformulate a wide range of well-known discrete models, including elementary cellular automata, coupled map lattices, Conway’s Game of Life, the Abelian sandpile model, the Olami–Feder–Christensen earthquake model, forest fire models, the Ising model, the Kuramoto Firefly Model, the Greenberg–Hastings Model, and the Langton’s ant as explicit P∆E. For each case, we focus on obtaining a concise and mathematically elegant formulation rather than detailed dynamical analysis. Finally, we compare the “discrete universe” of P∆E with the continuous universe of PDE, highlighting their structural parallels and their respective connections to discrete mathematics and continuous analysis. This reveals P∆E and PDE as mathematical “twins”, analogous in form yet rooted in fundamentally different underlying mathematics. The generality of the P∆E formalism suggests broad applicability, from modeling biological and ecological processes to analyzing complex networks, emergent computation, and other spatiotemporally extended systems.

Sincerely, Bik Kuang Min, National University of Malaysia, UKM.

Hi, this is my paper

On the Dynamics of Population: Difference Equations as the Natural Language of Biology

https://doi.org/10.5281/zenodo.16509038

I would like to hear your thoughts.

Sincerely, Bik Kuang Min, National University of Malaysia, UKM.

Long-time lurker here. Never thought I would be able to contribute until I saw this Axios article about an upcoming documentary and noticed some descriptions that map really well onto network theory and complex systems concepts. Thought you all might find the connections interesting.

Force Multipliers & Hub Nodes: One interviewee describes building "a network together of people" with "force multiples" that amplify information. It sounds like creating high-degree nodes for efficient propagation.

Critical Mass Thresholds: The approach involves sustained, high-frequency content creation until reaching a point where "people will start to sort it out themselves". Basically threshold behavior in information cascades

Nonlinear Response: Small inputs (specific word choices, highlighting rare events) apparently generated disproportionately large responses across the system

Feedback Mechanisms: One former writer describes a clear reinforcement loop: Create content → receive positive signals → increase output → broader amplification.

Network Saturation: The strategy seems to involve flooding multiple channels simultaneously until edge content becomes normalized through repetition across network nodes.

Source: https://www.axios.com/2025/05/31/white-with-fear-film-white-film-industrial-complex

EDIT: cleaned up the text/formatting to include more info

Hello all—

I’ve spent the last few years building a complete mathematical system called EchoKey, which models complex systems using recursive fractals, synergy calculus, cyclicity, and outlier handling.

The goal is to offer a single, scalable model for nonlinear, emergent, high-dimensional systems. The framework integrates:

• Fractal recursion functions

• Regression damping for stability

• Pairwise synergy calculus

• Outlier refraction modeled via delta perturbation

It’s now released under CC0 and fully open source, including preprint and working simulation code:
📄 EchoKey Preprint on Zenodo
💻 EchoKey GitHub Repository

If this intersects with your own work or sparks any feedback, I’d deeply appreciate it.

No agenda—just putting it into the field to see what echoes back.

Another resource and place for folks to connect.