Top Posts
 What is Multiplication  the Series
 Operators, Functions, and Properties  part 41
 Notes on Representation  Tally Marks
 Notes on Operations  Unary Minus
 Groupings, Shopping Lists, Vectors: part 12
 Series  Another way to navigate this site
 Notes on Deferred Computation  the Pythagorean Spiral
 Quantity  Different Kinds of Numbers: Vectors
 Mathematical Notation and Schools  10
 What is Multiplication  part III

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Tag Archives: state
Operators, Functions, and Properties – part 41
In this series, we’ve pictured operators as black boxes with inputs and outputs. In the previous post we looked at rather ordinary addition from a less ordinary perspective: we imagined the number line arranged as a cylindrical spiral, like a … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, representations, state
1 Comment
Operators, Functions, and Properties – part 5
In earlier parts of this series, we have talked about devices that change their state when you press some button. Such devices are both very normal and very common. A very simple example of this is a counter, where the … Continue reading
Operators, Functions, and Properties – part 4
In the two previous posts in this series, we looked at decidedly different models that each could explain the same simple external behavior. To recap, we have been looking at internal models for a device that looks like this: and … Continue reading
Posted in Uncategorized
Tagged black box, extending patterns, models, representations, reverse engineering, state
1 Comment
Operators, Functions, and Properties – part 2
In the previous post I introduced the idea of a device like the one pictured below: where the single digit on the little screen was observed to cycle through a repeating pattern every time the red button is pushed, as … Continue reading
Posted in Uncategorized
Tagged extending patterns, models, representations, reverse engineering, state
3 Comments
Operators, Functions, and Properties – part 1
I intend to write some things on operators in mathematics, beginning in this post. Functions and properties will be brought in as appropriate. The idea of operators is absolutely basic and central to computers and computing; they are also important … Continue reading
Posted in Uncategorized
Tagged deferred computation, extending patterns, models, naming, representations, state, unlearning
7 Comments