On Sun, Mar 2, 2014 at 3:13 PM, Joe Niederberger <email@example.com>wrote:
> > Kirby: > >I'd say the mathematical concept of "a function" plays a similar > integrating role in helping us think more reliably in mathematical terms. > > Well, yes, but I'd say the arguments about side-effects are more than just > religion -- the "side effects" issue is precisely about how one reasons > about a program. > > Cheers, > Joe N >
In terms of connecting the math.function concept to STEM more generally, I'm wanting students to contemplate LaPlace's notion that "now" is the domain, while "a moment from now" is the range, and "the function" is basically "the rules stuff follows".
His view was deterministic: given now: Verb(now) -> now (a moment later).
As we've already talked about, the math.function concept is only loosely connected with causality i.e. random pairings of set members with set members may be "without rhyme or reason".
I'm not seeking to hijack that mathematical concept. On the contrary, we need it for contrast, as it were, versus a machine-like causal take, reinforced by those function-as-machine metaphors.
On paper, this stuff is notational, sure, like music is notational, but really we're talking about "lived experience" in some dimension.
I go there because I want to reattach these abstruse concepts to an everyday reverie one could call "philosophical" but which is really "mnemonically rich" i.e. your daydreams will feed your technical knowledge base and vice-versa.
Now that concurrent programming is in vogue, I see even more convergence, of multi-process programming with multi-track media editing and composition. And given version control e.g. Github, software development is already more concurrent (multi-track) than it ever used to be.