Space

If you search for information about space, in the context of math, you will find articles written about specific types of space, and often the choice is Vector Space. It is as if it is not possible to talk about a general Space.

We will take a stab at it in Appendix B, but please don’t use our answer on a test.

We have found some hints about what the answer might look like:

“A space is a set with some added structure.”

The best article we found on structure explained that there is not a consensus on what general answer we should give if a student asks “what is structure?” We are limited to discussions of specific examples of structure.

When we study a Vector space, with its list of rules, we get the impression that these rules are a fence to keep out all kinds of “weird possibility” creatures that we don’t want walking around on our front lawn.

A rule that a value must be real protects us from creatures such as complex numbers.

We define structure as fencing that declares what is true in a way to exclude all other possibilities as being false.

Appendix B

An artist’s conception of space..

We started with nothing, then we have some mathematical constructions in a set and a rule or rules about what you can do with them. In the moment that we have the set of constructions and the rules together, there is a flash of light and a loud boom, and the space comes into existence.