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2048 Bit RSA and the Year 2030
Update: NIST released a draft that modified their recommendations (Oct 2024) 1) . RSA 2048 is to be only considered “deprecated” after 2030. The draft states:
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 221 posts.
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Circles do not exist
Many logos, drawings and other graphical designs have the following shape in it. What is this shape? If you thought: "Ah-ha! I'm smart and r...
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How far can you jump from a swing?
In this post I derive the physics of pumping a swing and the physics of jumping from a swing. Then, using both pieces I compute the optimal strategy of jumping from a swing to maximize the traveled distance. I propose this game as a new Olympic sport.
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A tutorial quantum interpreter in 150 lines of Lisp
a personal blog
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Cargo Cult Quantum Factoring
Just days after we celebrated my wife’s 40th birthday, she came down with COVID, meaning she’s been isolating and I’ve been spending almost all my time dealing with our kids. But …
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Is the reversal curse in LLMs real?
A recent paper The Reversal Curse points out an apparent failure in large large language models like GPT-4. From the abstract: We expose a surprising failure of generalization in auto-regressive large language models (LLMs). If a model is
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Category Theory Illustrated – Sets
Ready, set , begin… (you don’t know how hard I tried to resist to making that pun). We begin our inquiry with the theory of sets. Set theory and category theory share many similarities. We can view category theory as a generalization of set theory. That is, it’s meant to describe the same thing as set theory…
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Symmetry in Chaos
The following is based upon systems of equations found in "Symmetry in Chaos, A Search for Pattern in Mathematics, Art, and Nature" (the second edition) by Michael Field and Martin Golubitsky. They ask the question whether there are aperiodic chaotic attractors that generate symmetric patterns? Can there be order…
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The unreasonable effectiveness of conditional probabilities
I have been steeping myself in probabilistic exercises recently, because it’s an area where I feel like I could benefit from building better intuition. I have found a recurring key to solving many of them: conditioning on an intermediary state, and then computing the value of that intermediary state separately. This…
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Bayesians moving from defense to offense
Erik van Zwet, Sander Greenland, Guido Imbens, Simon Schwab, Steve Goodman, and I write :
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How random is xkcd? (2015)
Apparently Randall Munroe gets a lot of messages saying that the “random” button on xkcd is biased.
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The Sell ∀ ∃ as ∃ ∀ Scam
Artificial intelligence, like machine learning before it, is making big money off what I call the “sell ∀ ∃ as ∃ ∀ scam.” The scam works as follows. Build a sy…
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The infamous coin toss
In 2011 I gave a 15-minute talk to a lay audience in London. The topic I had chosen was ergodicity breaking, and the challenge was clear: how do you get this across? I invented a coin-toss gamble, which has since become a go-to illustration of ergodicity break
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Matrices and Graph
The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices
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Data diffs: Algorithms for explaining what changed in a dataset (2022)
tl;dr: part 1 explains what an explanation algorithm is, and part 2 describes an open source SQL data differ.
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A Mechanistic Interpretability Analysis of Grokking
Neel Nanda reverse engineers neural networks that have "grokked" modular addition, showing that they operate using Discrete Fourier Transforms and tr…
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The Irish Logarithm
From the highly eclectic blog of Mark Dominus
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GPT-4 gets a B on my quantum computing final exam
Update (April 14): On the suggestion of my TA Justin Yirka, I gave GPT-4 problem 2 from the final exam, along with its own answers and my and Justin’s grading comments, and asked it whether i…
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Finally getting two's complement
A different view on two's complement math.
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When gradient descent is a kernel method
Suppose that we sample a large number N N N of independent random functions f i : R → R f_i \colon \R \to \R f i : R → R from a certain distribution F \Fc F and propose to solve a regression problem by choosing a linear combination f ˉ = ∑ i λ i f i . \bar{f} = \sum_i \lambda_i f_i. f ˉ = i ∑ λ i f i . For…
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Introduction to the Fourier transform for image processing (2001)
The definitons of the transform (to expansion coefficients) and the inverse transform are given below:
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The New XOR Problem
In 1969, Marvin Minsky and Seymour Papert published Perceptrons: An Introduction to Computational Geometry. In it, they showed that a single-layer perceptron cannot compute the XOR function. The main argument relies on linear separability: Perceptrons are linear classifiers, which essentially means drawing a line to…