One of my favorite shows as a kid in the 90s was Batman: The Animated Series. A wonderful show that went all out to show why Batman is one of the most interesting (though I’d argue least effective) superheroes.
The episode “Baby-Doll” plays with the themes of illusions and mirrors and even today has great emotional weight to it. The episode concerns a washed-up actress who suffers from hypopituitarism and thus has not been able to grow up in size despite being a “full-grown” adult.
The actress is jealous of her former co-stars success and decides to kidnap them, when Batman comes in to rescue them, with the help of Robin. While Robin is trying to get the co-stars out from a trap, Batman is led into a fun house with mirrors and illusions.
Below we have a particularly effective emotional scene that says a lot about Baby-Doll as a character without saying anything at all. And it’s all done through the use of mirrors and illusion!
With programs like Concorde TSP Solver we have ways to make the Traveling Salesman Problem irrelevant to our everyday lives. Maps like Google maps can already handle multiple locations and trying to give you the best route. Not to mention you can use any number of alternative map services.
In the larger context however, TSP still lives on as a big problem for mathematicians, to the extent to have considered what it would mean to truly solve the problem in the 2012 movje Traveling Salesman.
Meanwhile, although the problem has been made much easier, truckers delivery drivers still have to deal with the problem from day to day. And given how much it can drive a person crazy we should be thankful we have modern technology to help guide us through the easier version.
That said, if you want to truly kill the TSP then answer P vs. NP and collect your million dollars, here.
I was curious about graph theory and what prominent topics are involved in it. Perhaps one of the most interesting and practical problem I found in the Wikipedia entry for graph theory is the art gallery problem (also see here).
To sum it up: The problem asks us to consider how many security guards we’d need to carefully monitor an art gallery. This depends on many variables such as the size and shape of the art gallery.
Marianne Freiberger for Plus Magazine, summarizes the mathematician S. Fisk’s answer to this conundrum as:
..[Y]ou never need more than n/3 guards (so that’s 9/3 = 3 guards in the example in the figure). That’s true for any simple polygon with n vertices, no matter how complicated and irregular it looks.”
Which is pretty amazing.
So next time you’re watching your favorite heist movie or thinking about starting a heist campaign in D&D, consider the art gallery problem!
I just want to briefly go over why I think the Copeland method is the best method (as opposed to Boarda, Plurality and Elimination/Runoff). As a recap, Copeland meets the most criteria of any method. The one who wins through the Copeland method is often going to be Condorcet, since the methods are similar. Majority is also a guarantee because when one wins through the Copeland method often has a majority as well. And if you are placed higher in the Copeland preference schedule then you’d just do better in it, so the monotonicity method is satisfied as well.
The only problem with the Copeland method is the Independence of Irrelevant Alternatives (IIA) criterion. However, I don’t think this criterion is very important and in fact, I’d probably vote IIA as the least important criterion to meet. What should matter in a given preference schedule is who or what is actually in the schedule, not what would happen if some hypothetical candidate wasn’t there.
So the fact that the Copeland method doesn’t meet this criterion isn’t very important. And in fact no method of the four previously mentioned does, so it’s not like you can do better besides Approval voting. Speaking of, I’m interested to see if anyone has any ideas about Approval Voting vs. Copeland.
Trivia: Wikimedia, which is related to Wikipedia, uses the Copeland method, and we all know Wikipedia is one of the best things to happen to the Internet since memes.