The book prints the finished table. These three build it in front of you, one target word at a time, counting from the text on screen rather than from a stored table. Every one has a step button, so you can stop anywhere and check a number by hand before moving on.
Two sentences that mean opposite things, dropped word by word into a bag. Both bags come out identical.
A ramped ten-word window fills two matrices. The left pass and the right pass disagree, and that asymmetry is the point.
A symmetric four-word window fills one matrix, which is step one of the three that make a COALS vector.
All three belong to Count Vectors, PPMI, and SVD, the chapter where a word stops being a symbol and becomes a row of numbers. Read the chapter for the arithmetic, run hal.py and coals.py to reproduce the tables, and use these when you want to see the counts land.
There are four more interactive demos on the course home page: a live BPE tokenizer, Zipf and Heaps fitted to a real corpus, word vector arithmetic, and an n-gram generator.