The hottest Complexity Theory Substack posts right now

The horse-enclosure puzzle can be encoded as an integer program using binary variables for walls and for whether a tile can escape, with linear constraints that enforce adjacency and boundaries, so solvers can quickly find and certify optimal enclosures.
Integer programming is a hugely practical and powerful tool for discrete optimization: even though it’s NP-hard in theory, modern solvers solve many real-world instances very fast and reliably.
Whether a combinatorial problem is fun depends on legibility and the right level of difficulty, and many NP-complete problems can be made engaging with a good interface; it’s not obvious whether this specific puzzle is provably NP-complete.

We are currently facing a 'meta-crisis' with multiple interconnected challenges, presenting both overwhelming circumstances and opportunities for transformation.
To thrive in today's world, we need to develop a new relationship with complexity, encompassing not just external systems but also our inner worlds.
The online course 'New Ways of Knowing' offers live tuition, small group interactions, and personal growth practices to help navigate complexity, gain new perspectives, and respond to the meta-crisis.

Complexity theory measures how much time and memory algorithms need so we can tell which problems scale feasibly and which become intractable. It separates problems that are merely computable from those that are practically solvable before resources run out.
P contains problems solvable in polynomial time, while NP contains problems whose solutions can be verified quickly even if they seem hard to find. NP-Complete problems are the hardest in NP because every NP problem can be reduced to them, and NP-Hard problems are at least that hard but not necessarily verifiable quickly.
If P = NP, many cryptographic systems would break because one-way functions would no longer exist. At the same time, P = NP would let us solve huge optimization and AI problems exactly and efficiently, radically changing many fields.

Complex problems require moving away from linear thinking and embracing complexity thinking that involves understanding interconnections and dependencies.
Leverage points in a system are areas where small changes can cause significant overall impact. These include adjusting parameters, dealing with stock buffers, considering system structures, managing feedback loops, controlling information flows, setting incentives and rules, enabling self-organization, and aligning with system goals and paradigms.
Differentiating between complicated and complex systems is crucial in problem-solving. In complex interconnected systems, problem statements often fall into categories such as coupled, causal, or standalone.

Bringing different people together in a fun way can help create new connections and ideas. It's important for everyone to share their unique perspectives.
Sometimes it's better to wait and see what happens instead of jumping into action right away. This allows space for good ideas to emerge naturally.
You can simplify complex issues to help understand them, but always remember to keep the messy details nearby so you don't lose important context.

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Complex systems, like software teams, are made up of many parts that interact with each other and change over time. Understanding these interactions can help improve how we manage and work within these systems.
Donella Meadows' framework shows that not all changes in a system will have the same impact. Some changes, like adjusting goals or encouraging new mindsets, can lead to much bigger improvements than simply tweaking numbers or rules.
To create a successful and adaptable environment, it's important to give teams the freedom to self-organize, share information openly, and align their goals with the overall mission of the organization.

Auerbach explores the concept of meganets, networks of humans and machines that have become semi-autonomous and out of our control.
These networks are causing economic instability, disinformation, and political/social polarization, requiring changes like slowing down growth and injecting diverse opinions.
Concerns about AI taking over the world may be eclipsed by the threat of meganet-driven systems that lack human control and have significant influence over society.