• The Space of Triangles


    Plus: How do you generate a random sample of triangles? and: How can you measure the distance between two triangles

    Whenever you want to model something, say a physical system like the tumbler and pins in a door lock or a robotic arm, it's helpful to think of each possible …

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  • Practical One-Time Pad


    One-time pads are well known for their ability to provide unbreakable encryption, but they do not see very widespread use. This is understandable: they are limited in the amount of information they can practically convey, and generating them properly is tedius and slow1. And while there are some guides …

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  • Getting a Broad View of History


    For a long time I've felt that my grasp of history was very weak. My understanding of when significant chunks of history (even as big as the Roman empire) occurred relative to others has been murky at best. I think this has really stunted parts of my education because I …

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  • Order-of-Magnitude Probabilities


    Representing Probabilities

    Order-of-Magnitude values are excellent for representing both low probabilities and high probabilities, and make several common types of calculations easily workable in the head alone.

    For representing low probabilities, we can just directly use the value. For a one-in-a-million chance, that probability is just \(E^-6\). Using this …

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  • Order-Of-Magnitude Mental Arithmetic: Basics


    In "Order-of-Magnitude Mental Arithmetic: Motivation", I talked about how working with order-of-magnitude values might help with internalizing a rough sort of the numerical mental models that experts develop over the course of extensive experience. The mechanics of this are simple, but are worth going over deliberately.

    The first thing we …

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  • OOM Summation


    How do you sum a set of order-of-magnitude values? For example, if my personal library contains E0 dieting books, E0 classical literature volumes, E1 textbooks, and E2 fantasy books, then how many books do I have total? Clearly the fantasy books dominate and I have E2 total books. So to …

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  • Conceptual Maps For Clearer Writing


    Steven Pinker gave an interesting talk on effective writing which focused on the 'classical' style. The talk is worth watching, but there is one particular component of it I would like to look at.

    In one section of the talk, he describes writing as essentially taking a non-linear mental map …

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  • Why PowerShell? Responses


    Scoop is a package manager for windows that is written in PowerShell. In their documentation they list some well-thought-through reservations for using PowerShell and their reasons for using it anyway. These are my responses to their reservations.

    • The Verb-Noun verbosity, commands that were seemingly not designed to be typed

      • I …
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