There is no conflict between Math and Magic. In any event where it seems there is a conflict between Math and Magic, Magic is wrong. Throw it overboard.
With that said, we find things in math which might seem to be a bit magical…
We sometimes get the answers to our calculations for things with curvature by using approximations that build structures out of small straight-line segments.
Going further with this “small straightness within curvature” magic, we speak of there being a small neighborhood around a point on a curvature and within that small neighborhood it’s all flat.
You should smile or even laugh when you find these crazy things. One way to stabilize your thinking–use the following incantation:
“When we said it was flat, it wasn’t. We really meant we could approach the correct answer using an approximation or approximations built out of “flat” or “straight”.
We might argue for a kind of “math apathy” that says if you have 5.99999 with lots of 9’s it’s okay to claim that 6 approximates the “five with lots of nines” that you are holding. That’s right, we flipped it around. We stopped calling 5.999 the approximation and we said that 6 was the approximation. Use your own magic and decide ultimately what is approximately what and maybe play the song “White Wing Dove” by Stevie Nicks.
A word like “continuous” has some magic in it? How else could you cast an infinite number of points between two points and also have it that between any two points there is an infinite number of points.
We might say the magic of the word “continuous” is similar to the magic we have with the word “induction”. As a brief review, induction is the magic where you declare something is true for 1 and then you also declare that if it is true for integer ‘n’ then it is also true for integer ‘n+1’.
True for ‘1’ gives us true for ‘2’ since we have n=1 and thereby also (n+1)=2…
True for ‘2’ gives us true for ‘3’ since we have n=2 and thereby also (n+1)=3…
What we did twice above keeps going and going and going…
There is a violent explosion and we suddenly have the whatever to be true for of the counting numbers. We might say we have the magic of the dot dot dot:
counting numbers: {1, 2, 3, …}
There is more magic. We might write sentences to describe things and as we put more words in (each word is its own incantation) it changes what we have.
For example, we started with the counting numbers above: {1, 2, 3, …}
If we add the adjective ‘even’ to the story we kill numbers like 1 and 3 and this leaves us with {2, 4, 6, …}
Vectoreverything 