I love language. I recently heard this sentence uttered by a co-worker, though he was not talking about work. He was talking to another guy about a scheduling challenge the guy's wife was having. The fellow's wife was setting up a schedule for first-year residents in the ER.
He said,
"This is a linear constraint-based optimization problem isomorphic to a constraint knapsack (or box pack)"
The scary thing is, he was being serious.
I had to look it up.
The word "isomorphism" applies when two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other structure, where "corresponding" means that the two parts play similar roles in their respective structures.
If there exists an isomorphism between two structures, we call the two structures isomorphic. Isomorphic structures are "the same" at some level of abstraction; ignoring the specific identities of the elements in the underlying sets, and focusing just on the structures themselves, the two structures are identical.
I looked up knapsack constraint problem.
Input description: A set of items 
, where item i has size 
and value 
. A knapsack capacity C.
Problem description: Find the subset 
that maximizes the value of 
given that 
; i.e. all the items fit in a knapsack of size C.
So, in short, he was saying ... it is an optimization problem, because you are making one schedule while taking everyone's schedule conflicts into consideration. Since everyone's schedules have the same vertices (all of them are calendars), it is isomorphic.
Now, how many pastors get to hear a juicy sentence like this everyday? You can see why I enjoy scientific apologetics so much. God gives me the privilege of sharing Christ with people like my friend. And I wouldn't trade it for the world. :-)
I'm not sure what makes me more of a geek - the fact that I knew what that sentence meant or the fact that I'm wondering how you put those formulas on your blog.
Posted by: Macht | July 15, 2005 at 17:14
I think both of those things qualify you as an official geek ;-)
I thank God for geeks ... they make excellent engineers ... and I enjoy the fruit of their labors :-)
I cut and pasted those forumulas into my blog ... I was surprised it worked, myself.
Your assignment is to work homeomorphic naturally into a sentence this next week ;-) That will be impressive.
Posted by: Dawn Treader | July 15, 2005 at 18:39
I am surprised they still put these schedules together by hand. It would not be hard to enter the people to schedule with some parameters and rules and you would have it all solved in a fraction of the time it takes to do by hand.
Posted by: Brian | July 16, 2005 at 00:28
I came to the same conclusion, Brian. This sounded like a fun assignment ... writing a rules based optimization engine with dynamic plug-and-play rules.
What impressed me more was that this guy used the word isomorphic in a lunch time conversation ;-)
I am still trying to figure out how to work in homeomorphic naturally into a conversation with someone. I'll keep you posted ;-)
Posted by: Dawn Treader | July 18, 2005 at 17:18