                                              |
o-------------------------------------------------o
|  (x_1, ..., x_k, ())   =         x_1 ... x_k    |
o-------------------------------------------------o

Laying out the arrows on the augmented venn diagram,
one gets a picture of a &quot;differential vector field&quot;.

o-------------------------------------------------o
|                                                 |
|                        o                        |
|                        |        