The hottest Computation Substack posts right now

And their main takeaways
Category
Top Science Topics

Natural Ordinal Addition

Infinitely More • 7 implied HN points • 15 Mar 26
🔬 Science Computation
  1. The natural sum and product (Hessenberg operations) make the ordinals into a commutative semiring, contrasting with standard ordinal arithmetic where addition and multiplication are not commutative.
  2. The natural ordinal operations match the operations on surreal numbers, so the ordinals under natural addition and multiplication form a subsemiring of the surreals.
  3. There are five independent, self-contained ways to define the natural sum and product—order-theoretic, computational, proof-theoretic, and others—and all five are equivalent, giving complementary perspectives and routes to generalization.

Unreal numbers

lcamtuf’s thing • 4489 implied HN points • 15 Feb 26
🔬 Science Computation
  1. Natural numbers can be built from a base element (zero) and a successor rule, and addition and multiplication follow from simple recursive definitions.
  2. Integers and rationals are formed by ordered pairs and equivalence classes so subtraction and division have in-system representations, and these extended sets remain countable.
  3. Computable numbers are those a Turing machine can approximate and are still countable, but the real numbers are uncountable (by diagonalization), so most reals cannot be computed.

How to turn a number into a rooted forest

A Piece of the Pi: mathematics explained • 90 implied HN points • 01 Mar 26
🔬 Science Computation
  1. Matula arborification is a recursive recipe that turns any positive integer into a rooted forest: 1 is the empty forest, 2 is a single node, primes become trees by attaching a new root to the forest of their index, and composites are represented by juxtaposing the trees of their prime factors.
  2. This correspondence is useful in number theory and combinatorics — it can help prove relationships between primes and encodes integer sequences (for example the primeth sequence appears as vertical chains of trees).
  3. The idea also has practical applications in chemistry for canonically labeling alkane structures (with valence limits ruling out some forests), and there are online tools that generate and visualize Matula trees for given integers.

What is Life?

Gonzo ML • 189 implied HN points • 19 Jan 26
🔬 Science Computation
  1. Life can be understood as self-modifying computronium: systems that compute and change themselves are favored because replication gives them dynamic stability and long-term persistence.
  2. Major evolutionary innovations come from symbiogenesis — the merging and hierarchical composition of simpler replicators — which produces reusable, repeated, code-like structures in genomes and bodies.
  3. Toy artificial-life models show replicators naturally emerge as dynamical attractors: after a chaotic start, self-replicating programs take off exponentially, increasing computational activity and leaving traces of nested sub-replicators.

Holding two thoughts

Sunday Letters • 139 implied HN points • 11 Aug 24
🕹 Technology Computation
  1. AI is a big change, and it's hard to label it just good or bad. We're still figuring out how to use it effectively, but it has a lot of potential.
  2. In everyday life, AI is starting to prove useful in small ways, like transcribing recipes quickly or helping create survey questions.
  3. Just like with e-commerce and search engines, AI will gradually become more integrated into our lives as people find ways to use it better.
Get a weekly roundup of the best Substack posts, by hacker news affinity:

What Interviews Should I Look For?

Computer Ads from the Past • 384 implied HN points • 11 Aug 25
🕹 Technology Computation
  1. The author is enjoying finding and sharing interesting interviews from old computer magazines. It's like digging for treasures from the past.
  2. The author is asking readers for suggestions on who they would like to see interviewed next. It’s a way to involve the audience in choosing future content.
  3. Readers are encouraged to share their thoughts in the comments. This helps create a community and shapes the direction of future posts.

☞ The Humanistic Computation Project

Cabinet of Wonders • 300 implied HN points • 07 Jan 25
🕹 Technology Computation
  1. Computation can help us understand many fields, not just programming. It can connect ideas from literature, biology, philosophy, and more.
  2. The study of computation involves looking at how we think and use language. It also explores the limits of mathematics and the nature of reality.
  3. Humanistic computation blends computer science with the humanities and social sciences. This new field encourages us to think deeply about how technology and culture interact.

10. On Emergence

Insight Axis • 79 implied HN points • 15 May 23
🔬 Science Computation
  1. Emergence occurs when an entity has properties that its individual parts do not possess, displaying behaviors that only emerge in interaction.
  2. Simple computational or geometric rules can lead to unpredictable and complex outputs, showcasing the beauty of emergence.
  3. Emergence, as seen in cybernetics with Braitenberg's Vehicles, demonstrates how simple structures can give rise to emergent, complex behavior, hinting at the potential for understanding the universe through simple rules.

Guinea Pigs are Fermions -- Part 2

Maximum Effort, Minimum Reward • 319 implied HN points • 28 May 23
🔬 Science Computation
  1. In this series, the quantum mechanics of guinea pigs are explored and analyzed.
  2. The Hamiltonian model for guinea pig dynamics in pigloos is simplified by eliminating uninteresting terms.
  3. Quantum computing with guinea pigs is proposed, including using pigspin as qubits and entanglement through interference.

The Bitter Lesson

Artificial Fintelligence • 20 implied HN points • 26 Jun 25
🕹 Technology Computation
  1. Over time, methods that use more computing power will usually do better than those that don't. It's important to think about how to use more compute in AI.
  2. In the short term, adding human knowledge can help achieve good results quickly, but it's often not a good long-term strategy. Relying too much on human input can stall advancement.
  3. Real success in AI comes from focusing on general improvements that can scale, rather than chasing quick wins with expert knowledge. This approach is harder but pays off in the long run.

Benchmarks for Poker 2-party computation

Bram’s Thoughts • 19 implied HN points • 18 Sep 23
🕹 Technology Computation
  1. Practical approach for Poker on blockchain involves playing out hands normally and cancelling any with duplicate cards.
  2. On-chain protocol for Poker involves multiple steps of committing to and revealing images for cards and calculations.
  3. Benchmarks for practical Poker protocol include computation time, round trips, and data transfer limits.

The Physics of Intelligence

Breaking Smart • 99 implied HN points • 07 Apr 23
🔬 Science Computation
  1. The physics of intelligence is not substrate dependent, similar to the physics of flight.
  2. The key questions in understanding the physics of intelligence relate to attention, memory, and the relationship between intelligence and information.
  3. Intelligence is not just about computation, but also about embodiment and specific interactions within the universe.

Algorithmic Dark Matter

Bzogramming • 15 implied HN points • 13 Feb 23
🔬 Science Computation
  1. In computer science, there are hidden structures and algorithms that go beyond our current understanding.
  2. New paradigms of computation may hold solutions to complex problems, such as optimization and error correction.
  3. Exploring fields like quantum computing and biochemical computation could lead to groundbreaking discoveries in algorithmic tools.