Equational

Today a friend's son asked me to help him with his math. The magic of internet meant that could read up the topic on wikipedia while listening to the request and accept in confidence. Here are a few hints on how to teach: Allow learning from mistakes : the young man's first request was to erase what he had done, as it was wrong. I stopped him and led him through the understanding of what he had done, building a knowledge of what "not to try again". This happened a few more times where I let him make his mistakes so that he could understand better how not to make these mistakes. Do not provide solutions but support the learning of decision making along the way : Learning is about associating together thoughts and methods and by doing so building a new way to do or understand something. In this case, I help him identify which of the mathematical tools he possessed already would help him for this type of problem. Help maintain a notion of goal at all times : The problem ...

What to say to C++ programmers about functional programming, especially now that many compilers have implemented C++0X features like lambda and auto. I am pretty good at C++, having started using it with the Zortech compiler V1 and the first versions of CFront (the orginal C++ to C translator). I have also written much fancy template code. Therefore thinking about this post leaves me in the dilemma that there is one part of me that likes the features of C++0X that "wrap up" loose ends, and another part of me, the functional programming part, that makes me want to rant! I will not rant today, but part of that reasons for being upset needs to be said, as is relevant. The "magic" of mature functional programming are: Statements, expressions, functions and types support each other Type inference and polymorphism automate the relation between statements, expressions, functions and types Monadic and other "advanced" types are available to define new executio...

Many years ago I implemented an augmented tree structure in C++. Inspired, I decided to implement the structure in F#. FYI by augmentation I mean storing extra data at each node of the tree that will accelerate the later operations on the tree. In DB terms, augmentations are typically used include secondary key conditions in your tree query. This is what I did: Take a balanced tree implementation off the web. I was thinking finger tree but then though better to start with a simpler implementation. I chose an AVL tree. (I may revert the code to a red and black tree to simplify). Add a node field to store the augmentation (a generic type) Refactor the code by replacing the call of the node constructor by a call to a function that will first build an augmentation and then call the node constructor Pass the generic augmentation "maker" function as argument to the function calls On this last point I wasted much time. Initialy, I tried to encapsulate the "augmentation...

An old friend asked me if the flash crash had been caused by "spoofing" of the exchanges with very large flows of order entry/order cancel commands. My feeling was that this was not the case and a quick search on google picked up a confirmation in this article: The Microstructure of the ‘Flash Crash’: Flow Toxicity, Liquidity Crashes and the Probability of Informed Trading ” This article supports the explanation that the main cause of the flash crash was simply the lack of liquidity because the market makers had become too edgy due to too much new information coming in to the market. It is an excellent article and brings back the notion that some systems are only sustainable with enough "friction", or said differently, by being under-optimal with regards to certain ways to look at them. When a group of people need to work together, they nominate a chief, or at least they give specific roles and ownerships to members of the group. These people get an "unfair...