God must love bees.

Some folks over in the UK decided they wanted to know how the Bombus terristrus (a bumble bee) figured out and remembered the path along which it visited flowers for nectar.  What they did was pretty clever.  They first developed these computer controlled flowers that they could activate how they saw fit.  Then the introduced one flower to the bees at a time (over the course of about two days).  If the bees continued to visit these sucrose dispensaries in the order they were introduced they would be traveling along the least optimal path (i.e. flying over a far greater distance than they had to). 

Instead the researchers found that over the course of just a few days the bees most often favored an optimal path to visit the flowers (213 times versus 110 trips along the discovery route).  Additionally, after two days the optimal route was traveled over 30 times as often as the discovery route.

Essentially the bees had solved the traveling salesman problem (visiting each "house" once in an optimal way) which is an NP-Hard problem.  In fact, for n houses the direct algorithm should take something on the order of O(n!) time to run.   This means that for 2 flowers there are 2 "checks" needed to solve the problem, but for 3 flowers there are 6 checks and for 4 there are 24! Indeed, it would only take 5 flowers to require over 100 checks (120!!).  This problem with the bee flight is even more complex because the bee is also weighing in the decision to spend energy along the trip (see this for more details) which makes the problem something like F raised to the NP-Hard.  Ouch!  Humans have been tested doing this too.  I'm afraid we didn't do as well as the bees.

AC vs. Window?

So I wanted to pitch an experiment to get this problem resolved: Should I just unroll my window or turn on the AC?  Slate has a pretty good article that covers some of the basics but I don't think all the data is really there.  There are a few concerns that need to be addressed:

1. Physiological Response (Comfort)
2. Economy (When is it worth it?)
3. Actual Performance.

Regardless of the method employed the passengers in the car must be within some ambient temperature that they perceive as comfortable.  This will vary within a car depending on whether or not this air is moving (I find I can stand 90 degree air if it is moving much easier than if it is still).  Thus the first thing to consider is the physiological response to temperature under various "wind" regimes.  We may do this with a series of tests within cars in a wind tunnel where the vehicle is brought to certain internal temperatures and the subject is exposed to various speeds of wind.  Various biometrics (e.g. blood pressure, pupil dilation, etc.) may be measured and paired with their personal testimony of comfort to quantify the physiological response.

1. Physiological Response (Comfort)
   
2. Economy (When is it worth it?)
3. Actual Performance.

The next part is yet again a sociological component.  Now that we know how a person's comfort is affected by temperature and wind speed we may now attempt to assess how they value this comfort.  There needs to be devised some sort of menial task that the subject must perform while under the various heat regimes in the first section.  Before entering the subject is given say $20.00 and told that after each round of performing the task they may attempt to buy their way out (they may be refused).  The amount the subject offers after each round may be used as some sort of valuation on comfort.  Thus, we've assigned a $$ amount to comfort.

1. Physiological Response (Comfort)
   
2. Economy (When is it worth it?)
3. Actual Performance.

The final step is now the true-blue wind tunnel experiment.  Essentially there should be devised a series of partial open window regimes (i.e. driver and front passenger 1/2, all 1/4, driver fully open, etc...) and then the car is operated on rollers under various driving regimes (i.e. city, highway, constant speed, etc...).  The fuel economy of all these situations may be assessed and then compared to all windows closed and the AC running (the AC too may be put under specific regimes of full on, set to a specific temp, only slightly on, etc...).  In the end, the cost to achieve comfort (window vs. AC) may be compared to the socio-economic data for true recommendations to be made.

That's the way I'd do it.

When Penguins Pooh...

Figured that the inaugural post here be something with some substance as well an Ig Noble Prize winner.  These two guys did some crazy kookie modeling of the fluid dynamics problem of a penguin pooping.  Still not interested?  Watch this.  I've done a little bit of homework and found that these guys are actually accomplished scientists, not just bored stoners who can do math.  I'm fairly certain I'm not allowed to post the article here but this link will take you to the original text and this image brings tears of joy to my eyes.