The goal is for you to read some things that Alice said at the beginning of the story and to get a “feeling” that Alice might enjoy the study of tensors.
“How can one possibly pay attention to a book with no pictures in it?”
“In my world the books would be nothing but pictures.”
“If I had a world of my own, everything would be nonsense.”
“Nothing would be what it is, because everything would be what it isn’t.”
And, contrariwise, what it is, it wouldn’t be.”
“And what it wouldn’t be, it would.”
***
“What if I should fall through the earth and come out through the other side where people walk upside down?
Appendix A
Alice lived in a world that had developed counting numbers.
She would be happy to be transported to our world and learn about zero.
Yes, we can have a quantity where the something is nothing.
But that isn’t enough, we have numbers that are negative. Our number three is attacked by negative three and after the violent fight we have nothing, that “evil” zero.
And what of a number like 1/x where as x gets larger, the number gets smaller?
Shall I go on? (we haven’t mentioned irrational numbers or imaginary numbers…)
Or how about we tell Alice that after she reads an entire book about Algebra (with lots of pictures in it–the pictures are next to examples), she read another book about an Algebra that is based on true and false.
Appendix B
“After tangling a bit on the Wikipedia’s article talk page I’ve discovered that the regulars there have the following agenda/beliefs: (1) tensors are never defined over infinite-dimensional vector spaces and (2) tensors are never defined over different vector spaces (even if finite). As I don’t have the time/stamina to battle people with a weird agenda and who are willing to spend most of their waking hours pushing it over there (despite the literature)… my note might be gone soon enough. Which is why reading Wikipedia on any topic is fraught with hazards… even on something as tame as math.”
The writer of the paragraph set enough or meet you a caution flag. Sadly, everything said makes sense. Wikipedia was supposed to be such that things could always improve because things are always being evaluated and perfected. However someone who has control could stymie the process when it tries to go past a certain point
Vectoreverything 