Posted on February 7, 2020

Here is a list of some of the links that I saved during January

### Discovering a formula for the cubic

In the UK you learn the formula for the roots of a quadratic equation in high school. At my school we were also taught the “completing the square” method for solving a quadratic equation which can also be used to derive the quadratic formula.

At university I learned that formulae also existed for the roots of cubic, quartic and quintic equations and I remember proving in a group theory course that no such formula can exist for polynomials of a higher degree than this. But I never learned what the formula for solving a cubic (or anything else) was.

This post shows that you can easily derive the quadratic formula if you assume a certain form of the results (which is kind of obvious because you know the two roots are equidistant from the min/max point on the parabola). Then it shows how to go through a similar process for the cubic. It isn’t quite so easy because it is not as obvious what form the roots should take.

### How a cabal of romance writers cashed in on Amazon Kindle Unlimited

A fascinating look into a world I had no idea existed. Amazon share royalties from the Kindle unlimited platform based on pages read so authors optimise their works accordingly. There is also “cockygate” but I think this has just been included to add a bit of slightly rude colour.

### human psycholinguists: a critical appraisal

I’ve discussed GPT-2 and BERT and other instances of the Transformer architecture a lot on this blog. As you can probably tell, I find them very interesting and exciting. But not everyone has the reaction I do, including some people who I think ought to have that reaction.

Whatever else GPT-2 and friends may or may not be, I think they are clearly a source of fascinating and novel scientific evidence about language and the mind. That much, I think, should be uncontroversial. But it isn’t.

GTP-2 and BERT can write some pretty realistic looking simulated text. Some linguists say this is only because of the huge amounts of training data used so this can’t tell us very much about language and how human brains process it. The nostalgebraist (the author) argues that we probably should be able to learn something about it because GPT-2 isn’t just any network; it has a specific architecture that works better than other networks that have been tried in the past.

### The economics of all-you-can-eat buffets

I love an all you can eat buffet (although I don’t go as crazy with them as I did when I was younger) and, like anyone who has ever eaten a lot at one I’ve wondered “are they losing money on me?”. This link doesn’t fully answer that question (for which the answer is definitely “it depends”!) but it does go into a few of the factors that make a buffet profitable or not.

### Normalization of deviance

I first heard about normalisation of deviance in one of Feynmans’s essays on the Challenger disaster. IIRC there were some components with a built in safety margin (maybe the o-rings?) and although these weren’t failing the safety margin was being used up. Technicians dismissed this as “within the margin of safety” but if the component had been designed correctly and was being used under the conditions it was designed for then the safety margin would never be reached. Instead the deviance was normalised and people stopped worrying about it with disasterous results.

In this link Dan Luu has many examples from tech.

### DCGANs — Generating Dog Images with Tensorflow and Keras

I found this while working on my Cat Engine Optimisation post, thinking that this might be another technique to explore one day.