Rhizomes

Introduction to Lean for Programmers

Tue, 19 May 2026 17:43:51 +0000

The syntax and semantics of mathematics

Infinite chessboard. Image generated by Grok (xAI)

Intro to proof assistants

I’m a software engineer who transitioned into data science, and I work daily with machine learning algorithms. I’m fascinated both by their apparent magic and by the mathematics that underlies them. Pry open any machine learning library and you’ll find mathematical tricks involving matrix decompositions, convolutions, Gaussian curves, and more. These, in turn, are built on even more fundamental axioms and rules, such as function application and logic.

Can You Become a 10x Developer by Writing a Tech Blog?

Wed, 03 May 2023 12:08:29 +0000

Swiss Hermes Baby Typewriter that I use for coding

People believe that experts are built differently, that 10x developers, like Harry Potter, are born wizards. However, a study has shown that masters are made from a “life-long period of deliberate effort to improve their performance in a specific domain.” (Ericsson, Krampe & Tesch-Romer, 1993).

Take driving as an analogy: you won’t achieve mastery by driving back and forth from work. You need practice and challenges on racetracks and dirt roads. So how can you expect to be a master programmer in your 9-to-5? You will need to step outside your comfort zone, and deliberately study and practice your field.

The Thirteen-Factor Team

Wed, 02 Mar 2022 12:26:19 +0000

Effective Practices for Motivated Deployments

Three years ago I joined the AT&T R&D center as a full-stack developer. I was welcomed directly into a brand new project, where I coincidentally witnessed a restructuring of the company’s engineering practices. As I was getting my photo id and laptop, seating arrangements changed, the department rebranded, QAs were being trained as developers, and developers started assuming operational tasks.

During these three years we moved fast and morale was high, even though we had to assume new responsibilities and learn new skills, often within a short time period. We grew professionally while witnessing rewarding metrics from almost 18 million devices in production.

How Nix-Shell Saved Our Team's Sanity

Wed, 27 Oct 2021 09:37:22 +0000

Shared developer environments across macOS and Linux systems for consistent builds.

Photo by Tim van der Kuip on Unsplash

We’re developing a large React Native app which relies heavily on native components already written in Java, C++, and Objective-C. This means that we needed to develop, build, and test many different platforms on complex developer environments and build tools, that change often with platform updates.

What Does the Event Loop Sound Like?

Mon, 12 Jul 2021 07:50:42 +0000

A musical journey inside Node internals

Node’s Libuv’s logo over a Max for Live Connection Kit

There’s a notion that coding and debugging are purely intellectual tasks. Car mechanics can determine engine issues by listening to the engine, scrutinizing its starting sound and reverberations like a physician might with their stethoscope. Meanwhile, developers are stuck with the Terminal Bell — ASCII code 7 — a relic from electronic typewriters. There’s much more than meets the eye.

How I Switched from TypeScript to ReScript

Wed, 20 Jan 2021 11:12:20 +0000

A glimpse into a more civilized (yet challenging) tool in the JavaScript ecosystem

Art for ReScript Blog, credit to Bettina Steinbrecher

This is not evangelism of ReScript or a one-to-one comparison with TypeScript. I love TypeScript. I decided to rewrite a small TypeScript+React+Jest side project into ReScript.

ReScript is not new. In a way it’s as old as JavaScript itself. ReScript is a rebranding of ReasonML (Facebook) and BuckleScript (Bloomberg), which wrap OCaml on both ends. The former is an interface of the OCaml syntax, while the latter makes sure to compile the AST into JavaScript. ReasonML was created by Jordan Walke, the creator of React. ReasonML still exists as a parallel project to ReScript, with a slightly different syntax and mission.

It's Time You Learn About Monads

Wed, 21 Oct 2020 13:55:34 +0000

You know what an Object is, why not learn about the Monad?

celebrate (seed 2568290493) by @noisemakerbot, Algorithmical/Generative artwork

Monads, with a name that originated in metaphysics and its roots in pure mathematics, is a concept that might seem esoteric at first. The “aha!” moment that builds our intuition for it is a Satori that many developers trying to understand functional programming want to reach, finally consummating in a blog post such as this one. In the book What I Wish I Knew When Learning Haskell, Stephen Diehl suggest an Eightfold Path, of which the first two are:

Mutants Against Bugs

Wed, 05 Aug 2020 14:08:22 +0000

Mutants Against Bugs: Implementing mutation testing in a niche language

Untitled, Computer Assisted Drawing, 1975, Paul Brown, written with FORTRAN punched cards on a ICL 1903A mainframe, plotted on a Calcomp Drum Plotter

Unit Tests and Coverage

Unit tests are the best way to determine the reliability of code. Tests assert that specific code behaves as intended by running it in isolation. This assures that we notice breakage as code evolves and grows.

Equihashについて

Fri, 12 Apr 2019 00:00:00 +0000

This is the Japanese translation of “Speaking of Equihash”, prepared for Beam Japan. The original Beam Japan Medium post is here.

一般化された誕生日のパラドックス

1つの部屋に2人だけが居合わせた場合、その2人の誕生日が同じになる確率は、1年における365日と2月29日（閏年）を合わせた366日、すなわち366分の1です。1つの部屋に367人が居合わせた場合、100%の確率で同じ誕生日の人が2人いるでしょう。なぜなら、想定しうる誕生日の日数より多くの人が集まっているからです。しかし、50%の確率で同じ誕生日の人が2人いるようにするためには何人必要なのでしょうか。驚くべきことに、たった23人しか必要ありません。というのも、1年のうち、どの日に生まれるかの確率は等しいにもかかわらず、30人の生徒が在籍する平均的な規模のクラスでは、その確率は70%に上がり、70人が居合わせた場合には、99.9%の確率で2人が同じ誕生日となるのです。

このパラドックスは、可変長である年数によって一般化することができます。1年が $d$ 日だとすると、ランダムに選ばれた $n$ 人の、$n$ がいくつなら、最低でも50％の確率で誕生日が重なるでしょうか。問題は、2つの側面（あるいは2つの分類）にも拡張され得る、2つのグループの人々、例えば、$m$ 人の男性と $n$ 人の女性がいるとき、少なくとも1人の男性と1人の女性が同じ誕生日になる確率（2人の男性または2人の女性が同じ誕生日となる確率は考慮しない。）はどのくらいでしょうか。David Wagner は $k$ 個の側面[1]を一般化し、複数の側面を持つタイプを加えました。「$n$ ビットの $k$ つのリストが価値を持つとすれば、ビット演算の結果が0となるように、それぞれの要素から何らかの方法で1つずつ選びなさい。」といった問いを設定したのです。彼はその複雑さを証明し、そのためのアルゴリズムを考案しました。そこには多大な時間と労力が費やされたでしょう。

最初の誕生日の問題では、組み合わせの矛盾が生じますが、後者の一般化された問題は、暗号化とハッシュの衝突の研究にとって重要となります。

以下で述べられている通り、この問題の要旨はPoWに援用でき、それはASICの収益に限界点を与えるトレードオフに繋がっています。

PoWにおける課題

Biryukov and Khovratovich

Equihashを発展させたBiryukovとKhovratovichは、調整可能なパラメーターによる非対称的なPoWに様々な課題が生じていることを示しました。こうした課題は計算複雑性理論のもとで形式化されます。それらは解決困難であり、理論上では解決できても、いずれの解決策もリソースを費やしすぎてしまうため、現実では有用性に欠けます。実現可能性は、多項式時間解として定義されます。つまり、問題が大きいほど、$k$ が正の定数の場合、$n^k$ のような多項式として計算が大きくなります。しかし、手に負えない問題は指数関数的に大きくなります。十分に大きな問題は、計算するために永久とも言える時間を要するでしょう。

ソース: BIGOCHEATSHEET.COM

これらの難しい問題の1つは、巡回セールスマン問題です。「都市のリストと各都市間の距離が与えられた時に、各都市を訪問して出発地の都市に戻る最短の経路はどれですか？」というものです。もう1つは、試験のスケジュール設定の問題です。「生徒が多くのクラスに登録している場合に、同じ時間に複数の試験が重ならない最短の試験スケジュールを見つけなさい。」という問題です。まだそのようなありふれた問題を解くための優れた方程式はありません。それでも、問いが小さなサイズであれば、力ずくのアプローチはまだ実行可能です。

これらの問題のサブセットであるNP完全問題は、Proof of Workの為の最良の候補です。なぜなら、それらにとって最良なアルゴリズムとは、指数時間で実行され、多項式時間で検証され、それが容易であることだからです。

Super Mario Coin — Nintendo

About Bird Box

Thu, 03 Jan 2019 16:19:17 +0000

Sometimes works of fiction hit the nail in the head when it comes to expressing deep fears and emotions with the right metaphors. In such cases, the meaning reveals itself in their lasting impression, in the feelings and moods the work aroused in us. The right analysis takes the work as an intense dream after we are awaken, in which the premise only serves to bind together the medley of deep REM-stage emotions, and the plot are our coping mechanisms.

Buterin Unveils Ethereum 2.0 at Devcon 4

Thu, 13 Dec 2018 15:50:06 +0000

Vitalik Buterin presented the new Ethereum roadmap at the opening of Devcon 4 in Prague this week. The first iteration of this conference took place in 2014 in Berlin and it was where the first visions of Ethereum were presented to core developers. Four years later, Devcon has become one of the most anticipated gathering for blockchain developers.

The Secure Bulletin Board System (SBBS) implementation in Beam

Thu, 13 Dec 2018 14:29:16 +0000

Beam is built on Mimblewimble protocol¹, a wonderful piece of technology that achieves confidentiality while significantly improving blockchain scalability. However, this comes with a significant caveat. In Mimblewimble there are no addresses, and transactions need to be built interactively by the participating parties.

That poses a challenge: if Alice wants to send money to Bob, both their wallets have to connect and perform the necessary actions. Creating a direct socket connection every time is not really practical (most people sit behind NATs). Also, what if Bob’s computer is offline at the moment Alice wants to send funds?

Speaking of Equihash

Wed, 14 Nov 2018 00:00:00 +0000

The generalized birthday problem

If there are two people alone in a room, they have a chance of 1 in 366 to have the same birthday, one for every day of the year, plus February 29. If there are 367 people in a room, you can be 100% sure that two of them will have the same birthday, since there are more people than possible birth dates. However, how many people you need to have a probability of 50%? The answer might be surprising since we only need 23 people for that. For an average classroom of 30 students, the probability goes up to 70%, and with only 70 people we have a 99.9% chance of a double birthday, assuming that each day of the year is equally probable for a birthday.

Ibn Ezra and Astrology in Judaism

Sat, 04 Aug 2018 00:00:00 +0000

Abraham Ibn Ezra was a Jewish philosopher and sage from the Middle Ages. Lived in Spain under Moorish rule before escaping persecution from the Almohads. He then became a wanderer and a destitute poet. Full of satirical wit, he had brilliant correspondences with sages such as Rabbi Yehuda Halevi, wrote concise biblical commentary, and above all, looked at the stars for guidance.

This is a free translation of a treatise from his commentary on the Book of Names (Exodus). I’ve translated השם literally as “the name” where others have translated it as “God.” The purpose of this translation is artistic, and I hope to review this draft in the future for stylistic improvements.

The underlying mission of AlphaGo and DeepMind

Thu, 10 Mar 2016 00:00:00 +0000

In an interview with Nature magazine, Demis Hassabis -Google’s DeepMind’s prodigious CEO- said that the big challenge for society over the next decade or two is dealing with the large amounts of data being collected -meteorological, healthcare, economic, etc.- and make sense of that data by finding its underlying structure and make insights on it. For that reason DeepMind has developed an algorithm that can play Go, and recently it did so well that it beat the current world champion Lee Sedol in the first of five projected games.

The Most Important Tech Case in a Decade

Wed, 24 Feb 2016 00:00:00 +0000

In the wake of the Apple-FBI case and the importance of privacy issues in the digital age, I gathered together pieces of relevant articles for those who want to better understand the case which Edward Snowden called on Twitter “the most important tech case in a decade.” Most notably, the official order compelling Apple to assist agents of search, and Apple’s official letter to customers rejecting the request.