Tag Archives: unlearning

Operators, Functions, and Properties – part 30

Posted on 2010/11/16 by Bert Speelpenning

In many of the posts in this series we’ve shown operators that work on a single number coming in and that produce a single number coming out. This is a hugely important subcategory of operators, but single-in single-out operators aren’t … Continue reading →

Posted in Uncategorized | Tagged extending patterns, models, unlearning, whole vs. parts | Leave a comment

Representations – Black Boxes – Equivalence 2

Posted on 2010/05/08 by Bert Speelpenning

We ended the previous post in this series by looking at this figure: To recap, a black box is something where we have access to the behavior but not the internal organization. We can propose a model for a black … Continue reading →

Posted in Uncategorized | Tagged black box, denominations, equivalence, extending patterns, models, representations, reverse engineering, unlearning | Leave a comment

Operators, Functions, and Properties – part 1

Posted on 2010/04/19 by Bert Speelpenning

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

Representations – Black Boxes – Equivalence

Posted on 2009/09/10 by Bert Speelpenning

I introduced the notion of a black box in an earlier post as some thing that has an internal organization that drives its behavior, and though we can see the behavior, we don’t have perfect knowledge of that internal organization. … Continue reading →

Posted in Uncategorized | Tagged black box, embedding, extending patterns, models, representations, reverse engineering, unlearning | 1 Comment

Representations – Number and Some Alternatives

Posted on 2009/08/25 by Bert Speelpenning

There are lots of ways to represent number – such as the number “ten”. As grown-ups, we’re so used to a particular way of representing “ten” that we don’t often stop to think about what we’re doing – we just … Continue reading →

Posted in Uncategorized | Tagged denominations, extending patterns, invariants, representations, unlearning | Leave a comment

Representations – Formulas and Some Alternatives

Posted on 2009/08/23 by Bert Speelpenning

There are systems of notation for mathematical expressions that are in wide use. One of them is so widely used and so well-known that we often think of it as the only one, the real one, the true one and … Continue reading →

Posted in Uncategorized | Tagged embedding, extending patterns, math class, models, representations, unlearning, whole vs. parts | Leave a comment

Key Math Ideas Not Taught In School – Invariants

Posted on 2009/07/27 by Bert Speelpenning

“Counting” involves a number of different mathematical ideas If you watch really young children count, you may notice that they aren’t all doing the same thing. For some children, counting “one-two-three” is done in very much the same way as … Continue reading →

Posted in Uncategorized | Tagged education, invariants, math class, models, reverse engineering, unlearning | 4 Comments

Key Math Ideas Not Taught In School

Posted on 2009/07/01 by Bert Speelpenning

There is a shape, a progression, to the typical school curriculum from Kindergarten through High School, at least in the United States, and this progression hasn’t changed much in the last 50 years or so. We’ve gotten used to this … Continue reading →

Posted in Uncategorized | Tagged education, extending patterns, invariants, math class, models, representations, reverse engineering, unlearning | 2 Comments

Quantity – Different Kinds of Numbers: Notations

Posted on 2009/06/13 by Bert Speelpenning

When you think of operations as having a front office component and a back office component, where the front office component provides the public face and the back office component provides the implementation, as we first introduced in the post … Continue reading →

Posted in Uncategorized | Tagged denominations, extending patterns, models, naming, representations, reverse engineering, unlearning | 1 Comment

Quantity – Different Kinds of Numbers: Classes

Posted on 2009/06/12 by Bert Speelpenning

Let me recap what this series of blog posts has been about. I’ve been looking at different kinds of quantities, different kinds of numbers. I started with observations like: it’s meaningless to add 1951 AD to 2009 AD but completely … Continue reading →

Posted in Uncategorized | Tagged denominations, embedding, invariants, models, naming, representations, unlearning | 3 Comments