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Levels of Understanding

This is going to be a story of how I learn new things and come to understand them well enough to put that knowledge into practice. I imagine these levels of understanding are similar for everyone, but I can't be sure. I'm just going off of my own experience. It's possible that for any given person or any given skill, learning could stop at any point where they've gleaned enough usefulness and the desire to continue learning has been exhausted.

However, if that desire to learn is strong, learning can develop through three main levels of understanding. The first level is the basic what to do to accomplish a task. The second level delves deeper into how things work in context to solve problems in the domain. The third and final level explores why things work the way they do. The answers to those three simple questions: what, how, and why encompass all of the understanding that can be gained from any skill, subject, or domain. To ground this discussion we'll focus on programming to make things more concrete. What is involved in each of these levels of understanding when learning how to program?

Tech Book Face Off: Introduction to Algorithms Vs. Linear Algebra and Differential Equations

This Tech Book Face Off has been a significant undertaking, more so than I originally imagined. It took over ten months to get through these two books, slowly chipping away at them in my free time during the evenings until I had finally read all of the material and worked all (well, nearly all) of the problems. As a result it's been nearly a year since my last book review, and working through these books was quite the experience. The goal at the outset of this project was to revisit a couple of textbooks from college, things that I felt I should brush up on. I wanted to see how much I retained of these subjects and how much I had forgotten that may still be useful. I chose Linear Algebra and Differential Equations by Charles G. Cullen because I remember having breezed through this subject in college without giving it my full attention. It was easy at the time, and I coasted through the course without, I thought, giving it the effort it deserved. Then I picked up Introduction to Algorithms by the famed group of professors known throughout the programming world as CLRS. I love algorithms, and I have fond memories of this course and working through this book, so I wanted to go through it again in its entirety, picking up the subjects that we had skipped in the course as well. What follows is the perspective of one programmer rereading a couple of old textbooks fifteen or so years later.

Linear Algebra and Differential Equations front coverVS.Introduction to Algorithms front cover

For the Love of Books

I currently have seven books in flight—a few that I'm actively reading, a couple that I'm trying to juggle for learning new skills, and a couple more that I started a while back but had to put aside for the time being. What they are doesn't really matter. It seems I'm always in the middle of at least a few books at a time. Please understand this is not bragging; it's love. I love starting a new book, with all of its promises of knowledge or adventure or perspective. I love progressing through the middle of a good book, absorbing enough introductory material to understand more difficult concepts or following the intricate plot twists as a story builds to its conclusion. And I love finishing a great book, reflecting on the knowledge learned and the experiences had through the written word mixed with imagination. Books are still a major source of enjoyment and fulfillment for me, and I don't see that ever changing.

Are Computers Still a Bicycle for the Mind?

Steve Jobs had an enormous appreciation for the computer, believing it was the greatest human invention, and he commonly likened it to a bicycle for our minds. Here he is in one such explanation of this analogy:

He refined his delivery over the years, but the underlying analogy was always the same. The bicycle dramatically increases the efficiency of human locomotion, and likewise the computer dramatically increases the efficiency of human thought. While that is still the case when computers, the Internet, and increasingly Artificial Intelligence and Machine Learning are used as tools to leverage our innate abilities to solve huge, complex problems, they can also become other things for the mind that are not so useful. We are seeing it happen more and more that as computers proliferate, shrink in size, and become more convenient and ubiquitous, they stop being treated as a tool and start being treated as a toy or simply as a distraction. Maybe computers are becoming less like a bicycle for the mind and more like something else.

Explore Simple Game Algorithms with Color Walk: Part 12

We've now been exploring and discussing game algorithms using the simple game Color Walk for months over the course of 11 posts. We started out extremely simple with random and round-robin algorithms, advanced to some obvious greedy algorithms, and wound up discussing a number of graph algorithms. We've discovered a ton of stuff along the way, so it would be nice to step back and review the ground we've covered to see the big picture in all of the experimentation and details of the various algorithms we found along the way.

Explore Simple Game Algorithms with Color Walk: Part 11

In this installment of exploring game algorithms using the simple game Color Walk, we're going to do something a little different. Last time we explored a number of variations and hybrids of Dijkstra's algorithm—the classic, efficient graph algorithm for finding shortest paths—and found that pairing it with a pre-run of Greedy Look-Ahead (GLA) performed better than any other algorithm we've seen so far. This time we're not going to explore any new algorithms. Instead, we're going to look into what makes Dijkstra's algorithm tick: the priority queue. Save for this variant of a standard queue, Dijkstra's algorithm is conceptually the same as Breadth-First Search (BFS), so we want to see what makes this priority queue so special and how we can implement one efficiently with a binary heap.

Explore Simple Game Algorithms with Color Walk: Part 10

We're back for another round of exploring game algorithms using the simple game Color Walk. We finally reached the point of evaluating Dijkstra's algorithm—the classic, efficient graph algorithm for finding shortest paths—in the last post. It performed pretty well against the top dogs: Greedy Look-Ahead (GLA) and the GLA-BFS hybrid, especially when it came to consistently finding the best moves. However, it failed to find the best moves when a board could be solved in under 29 moves, so we're going to see if we can squeeze out any more performance by modifying Dijkstra's algorithm further. To do that, we're going to try combining Dijkstra's algorithm with GLA, running Dijkstra's algorithm in more than one pass, and changing the heuristic we use to guide the search.

Explore Simple Game Algorithms with Color Walk: Part 9

Welcome back for more exploration of game algorithms using the simple game Color Walk. In the last post we covered the other fundamental graph search algorithm, depth-first search (DFS), the counterpart to the previously discussed breadth-first search (BFS). These graph algorithms do a full search of the graph of a color walk game, the full set of board positions resulting from each move at each point in the game. We found that running either of these algorithms to completion is extremely prohibitive due to the graph size being exponential in the number of moves. In order to deal with that exponential growth, we need to look at other graph algorithms, and we have quite a few to choose from. We'll explore some categories of graph algorithms and look at one in more detail, Dijkstra's algorithm.

Explore Simple Game Algorithms with Color Walk: Part 8

We're continuing this ongoing saga of different game algorithms using the simple game Color Walk. In the last post we started exploring the fundamental graph search algorithms with breadth-first search (BFS), because after all, the full set of move choices and resulting board positions of any game can be arranged as a graph. After looking at BFS and finding that we can nominally improve the search for shortest number of moves, on average, it's time we look at the close sibling of BFS: depth-first search (DFS). We'll quickly run into performance issues just like we did for BFS, but let's see if we can come up with a reasonable way to limit DFS so that it can be a useful algorithm.

Explore Simple Game Algorithms with Color Walk: Part 7

We're continuing to explore different game algorithms using the simple game Color Walk. In the last post we took a deep dive into other heuristics that could be used instead of the obvious maximize-the-number-of-blocks-removed approach and found that the obvious choice is actually hard to beat. After looking at various heuristics, it's time we fill in some gaps in our exploration of algorithms by looking at a couple of fundamental graph algorithms: breadth-first search (BFS) and depth-first search (DFS). These algorithms are the two basic ways to search for something in a graph of nodes (or vertices) connected by edges, and a graph is exactly what we have when we draw out all possible move choices with each node representing a move and edges connecting sequential moves. We'll focus on BFS for this post.

Explore Simple Game Algorithms with Color Walk: Part 6

What's next with exploring different game algorithms using the simple game Color Walk? We've come a long way so far with building out the game's interface to support looking at different algorithms, looking at trivial round-robin and random algorithms, and designing a greedy algorithm that picked each move based on the most blocks removed. The last post showed how far we could push the greedy algorithm to look ahead and try to pick a better move that would result in more blocks removed up to five moves ahead, but even after improving the data structure for the board, we hit diminishing returns in looking more moves ahead. It's time to expand our search for algorithms by looking at other heuristics we can use to pick the best move. The greedy algorithm used a heuristic of "the most blocks removed" for any given move, but there are others that we can use.