This is a collection of our best essays from 2018, as determined by our 2018 Review . It contains over 40 redesigned graphs, packaged into a beautiful set of 5 books with each book small enough to fit in your pocket.
If you’re anything like me, you probably find that the effort to get by in life takes up most of your time and energy. You spend your life working, commuting, going to the grocery store, doing the laundry, and all the other sundry tasks required to stay afloat in our modern world. But it’s hard to live a happy and fulfilled life if all you do is what you must do to survive. You’ve got to carve out opportunities to invest in yourself as well. One of the ways I do that is a life practice I think of as “Forever Projects.”
Last year I spent six months working on map borders, and I got a few questioning comments about spending so much time on that topic. That’s a perfectly understandable reaction from someone who looks at what I’m doing through the lens of limited time, and wonders why I would spend so much effort on a minor aspect of map creation. But I’m not “building a map app”; I’m doing a Forever Project about procedural generation, computer art and many other things. I’ve always had an interest in Celtic knots, so I spent a couple of months learning how they were drawn and how to implement them in Dragons Abound. I learned something new (to me), and that bit of personal growth is the reward - regardless of whether or not I ever “finish” Dragons Abound.
here my hypothesis: Adam was a very good optimization algorithm for the neural networks architectures we had few years ago and people kept evolving new architectures on which Adam works.
This book brings new mathematical rigour to the ongoing vigorous debate on how to quantify biological diversity. The question “what is diversity?” has surprising mathematical depth, and breadth too: this book involves parts of mathematics ranging from information theory, functional equations and probability theory to category theory, geometric measure theory and number theory. It applies the power of the axiomatic method to a biological problem of pressing concern, but the new concepts and theorems are also motivated from a purely mathematical perspective.
Here is a takeaway for you:
Associativity is Euclidean
Vector addition makes sense in absolute geometry but it only gives an abelian group in the Euclidean case. In the hyperbolic case, it gives a nonassociative Bruck loop!
Bruck loops are related to many other mathematical structures, including quandles and symmetric spaces. More generally, quasigroups and loops show up in many places in mathematics. I hope to touch upon these in future threads.