R Packette - Fraction Matrix Operations

Open up any linear algebra textbook and have a look at the matrix entries. Are there all integers? Are they all written as decimals? There's probably at least some that are fractions. Matrices in computer programs are almost always in decimal form. The exception is symbolic mathematics programs like Maple and Mathematica. That's because computers store non-whole numbers as floating-point values instead.

Floating-points are fine most of the time, but they're often not exact. What happens if we work the fractions directly?

Reading questions: Struck by Lightning

The book Struck by Lightning, by Jeffery Rosenthal hits that balance of scientific correctness and approachability just right for a general audience book on probability. It’s been in print for 14 years now, and was a Canadian bestseller, so there’s nothing new that would come from a traditional review and therefore I won’t write one.

Instead, two points:

1.      It should be required K-12 or 100-level math/stats reading.

Degrees of Freedom, Explained

You can interpret degrees of freedom, or DF as the number of (new) pieces of information that go into a statistic. Using examples from this video [https://www.youtube.com/watch?v=rATNoxKg1yA , James Gilbert, “What are degrees of freedom”]

I personally prefer to think of DF as a kind of statistical currency. You earn it by taking independent sample units, and you spend it on estimating population parameters or on information required to get compute test statistics.

In this article, degrees of freedom are explained through these lenses through some common hypothesis tests, with some selected topics like saturation, fractional DF, and mixed effect models at the end.

Freakazoid, a Repetition-Robust Symmetric Cipher.

This post describes the mathematical principles behind the Freakazoid cipher such that someone could recreate it with software if they wished. For a targeted guide to some of the terminology used here, please see my previous post discussing some fundamentals of encryption.

It is not meant to be a serious attempt at a cipher, and is presented as food for thought only. It was originally developed more than ten years ago as part of a semester of research as a math undergrad.

Freakazoid is a cipher based on DES, an old cipher that was used as an industry standard for a time, but with the added step that a new key is generated each block of data to be encrypted. The generation of this key is governed by a master key. For clarity, we call a key applied to a particular block of data the block key.

Some Timely Fundamentals of Encryption

This post is in response to some questions about the mechanics of encryption that have been getting more frequent as cryptocurrency and related technologies become more well-known.