I guess you shower in liquid lead
lol I see how this shower-thought can seem obvious.
What lead to the shower-thought was thinking about dimensions in linear algebra. If you want to represent a function with more parameters, you need more dimensions.
For example, two parameters could be represented by
ax + by = c
wherea
,b
, andc
are constants andx
andy
are real numbers. Note that this equation describes a 2-D plane. Three parameters would require an additional variable and an associated constant:ax + by + cz = d
, whered
is an additional constant andz
is an additional real number. Note that this equation describes a 3-D space.Can you see how if you wanted to represent four parameters, you would need four dimensions?
However, facet plots seem to override this need for more dimensions in a particular way: splitting up axes, like cutting up a cake. If you have four parameters (in which two of them can only take up discrete values), instead of requiring four dimensions, you can split up two dimensions in discrete chunks, like a cake, and represent four parameters in two dimensions. That was interesting for me to realize.
I guess for cake-cutters, this post is silly and trivial. But for someone trained to think “more parameters = more dimensions in the sense of going from
ax + by = c
toax + by + cz = d
”, it was surprising to realize facet plots break that rule.