Re: [Phys-L] treating force as a vector ... consistently

[David Craig <craigda@lemoyne.edu>]

On 09/13/2016 11:57 AM, John Denker wrote:

> Yes, but first things first.  When the audience doesn't have a
> firm grasp of what a vector is, or how a vector field differs
> from a vector space, you can't start with tangent bundles.
>
> In fact a tangent bundle is defined in terms of tangent spaces,
> so it makes sense to do tangent spaces before tangent bundles.
>
> There is a rather general pedagogical principle that says "concept
> before name".  You can teach people pretty much everything they
> need to know about tangent bundles without ever using the word.

Settle down, John.  I was just giving it the proper name for those who care about such things.   I didn’t bring it up — you did.

> > One is free to dismiss it if you like, but when you are doing things like GR it really is a useful idea.
>
> That's ambiguous, due to a dangling antecedent.  Does "it” refer to rooted vectors, or to fiber bundles?

Seriously?   You definitely have too much time on your hands ;-)

All in good fun.   I always enjoy reading your posts, even if I haven’t the time to engage them.

David Craig


<http://web.lemoyne.edu/~craigda>