Git is a complicated beast. The Git index, if you’re coming from other VCS’s, is a new concept. Yesterday I described how I use the Git index in my workflow:

These pictures illustrate the multiple locations, or “data stores”, that host a copy of the source tree. These stores are: the working directory, local and remote repositories, and the index. In order to show more of the whole development process, the second picture also includes a “distribution directory”, for code that is being distributed outside of Git. (The distribution directory could be the deployment directory of a web site, or a compiled artifact, such as a binary, that is placed in firmware or on a DVD.)  read more »

Git‘s great! But it’s difficult to learn (it was for me, anyway) — especially the index, which unlike the power-user features, comes up in day-to-day operation.

Here’s my path to enlightment, and how I ended up using the index in my particular workflow. There are other workflows, but this one is mine.

What this isn’t: a Git tutorial. It doesn’t tell you how to set up git, or use it. I don’t cover branches, or merging, or tags, or blobs. There are dozens of really great articles about Git on the web; here are some. What’s here are just some pictures that aren’t about branches or blobs, that I wished I’d been able to look at six months ago when I was trying to figure this stuff out; I still haven’t seen them elsewhere, so here they are now.  read more »

(Or, a Cobordism of Carbon.)

Here’s my understanding of this (with the energy cost dip greatly exaggerated).

Oops! It takes a village (down) to raise an (American) child.

Anyone want to make one of these with real numbers?

This is an ambigram by Scott Kim, vectorized by Miles Steele, cleaned up by Dan Lewis, and put inside an OpenLaszlo application. (If you don't see it, click here.)

Uh oh! I overthought fizzbuzz:

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Full size (pdf, png).

Update: This is what I call an entry-level metaphor — it’s a rough sketch of the relation between the concepts, not a productive metaphor that can be used to reason about them beyond this. It doesn’t support analytic microeconomic analysis, and it’s not even consistent at the level of the supply chain. (For example, the unit cost needs to include the component cost, whereas the illustration shows these as complementary; this is because the metaphor leaves out profit.) Nonetheless, I find it a helpful starting point before going more analytic.  read more »

Update: (1) There’s a discussion (at the moment) on reddit. (2) Thanks to FusionGyro for suggesting the name change to “revising”.

Here’s a picture I drew to explain addition and subtraction of fractions to the sixth-grader:

We also ended up using a variant on Euclid’s algorithm for finding the GCD. It uses subtraction instead of division and remainder; it’s in general less efficient, but it’s easier to explain and can be easier to do in your head, when the numbers are small.

Construct a series whose first two terms are the inputs, and then continue as follows: each successive term is the absolute value of the difference between the preceding two terms —- that is, simply subtract the smaller from the larger. If you reach one, the GCD is one; if you reach zero, the GCD is the previous term. (Or, you could also let the series peter out to zero, but the way I’ve stated it is simpler in practice.)  read more »

I posed a second-grader the question of what nine squared was. She reasoned that ten squared is 100, and nine times ten is ten less then that, and nine times nine is nine less than that, so the answer is 81. Then I asked her what eight squared was, and she was flummoxed. She saw that it was a similar problem to the one she’d just solved, but wasn’t sure how to apply the analogy.

Here are the pictures that showed her how to figure out the answer. We drew the location of the squares on a multiplication grid:

and I introduced the idea of a “solution structure”. A solution structure is a graphical representation of the steps of a solution. This is the section that represents the relation between 9² and 10².  read more »

Dot numbers are a new notation for numbers, that make integer addition look like rational multiplication. They may be useful in primary school math education. The idea is that once you understand integers and addition, you can learn another way to look at it that sets you up to understand fractions and multiplication.

I made up dot numbers a few years ago to try to explain negative numbers to my then-four-year-old son.

Basics

A dot number is a way of writing a number. A dot number is represented as a number of dots above a line. This is the number 3, as a dot number:
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