Tag Archives: embedding

Operators, Functions, and Properties – part 13

In this series, we have been looking at little machines that do things like “add 2”, and we’ve been chaining such machines together by connecting the output of one to the input of the next.  We’ve been exploring the behavior … Continue reading

Posted in Uncategorized | Tagged , , , , , , | 1 Comment

Representations – Black Boxes – Equivalence

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 , , , , , , | 1 Comment

Representations – Formulas and Some Alternatives

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 , , , , , , | Leave a comment

Quantity – Different Kinds of Numbers: Classes

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 , , , , , , | 3 Comments

Quantity – Different Kinds of Numbers: Vectors

Sometimes, when you assign a number to a quantity, a single number really isn’t enough.  Take blue jeans sizes, as a simple example.  Jeans sizes aren’t expressed with a single number, from small to large, like shoes.  Since at least … Continue reading

Posted in Uncategorized | Tagged , , , , | 2 Comments

Quantity – Different Kinds of Numbers: Keys

I introduced this series by noting that there are different kinds of numbers – more precisely, different kinds of quantities represented by numbers – and that each allows you to draw different kinds of conclusions. The most basic kind of … Continue reading

Posted in Uncategorized | Tagged , , , , , | 3 Comments

Quantity – Different Kinds of Numbers

We’re very used to representing quantities by numbers.   The cash register will tell us how much we have to pay, and the pump at the gas station will tell us how much gasoline we poured into our tank, and the … Continue reading

Posted in Uncategorized | Tagged , , , | 2 Comments