Tuesday, April 27, 2010

MAM Day 27: Optimization of space

Hey math fans! Following yesterday's topic of packaging, today's topic is the optimization of space, something I've been looking forward to the entire month. I'm not sure why I'm so fascinated with the optimization in general, but the optimization of space is something I see it quite a bit in my day-to-day.

Optimization generally refers to maximizing or minimizing a mathematical function and finding the max or min value of the function. Merriam-Webster defines it as: an act, process, or methodology of making something (as a design, system, or decision) as fully perfect, functional, or effective as possible. The optimization of space then means being able to spatially fit as much stuff into a defined space as possible, the optimization of volume in a way.

I have quite a few real world examples, but yesterday, my friend Sonal over at Science Club for Girls had a peculiar problem. We were on a fast food adventure with another friend and she had lots of Science Club stuff in her back seat. To make enough room for both of us in her car, we had to reorganize the boxes. By giving up her rear view, all three of us fit in the car and we had a successful adventure.

Some of us love optimizing space

Another example that helped me think up this topic is the public transportation system in Boston, the T. I'm sure lots of us have experienced a crowded T before, after work during rush hour, rainy days on the Silver Line, Sox game nights, Bruins game nights, weekend nights on the B Line, after big city-wide events like the 4th or the Boston Marathon. There are lots of cases when this happens, and most of us dread a packed T car. I tend to feel really uncomfortable being squished in with so many other people, trying my best not to fall over or push and shove some stranger.

Look familiar?

But it's an optimization problem when you're on the outside, trying to push your way into the T so you can get home. How many people CAN fit in one of those cars? It all depends on how efficiently people can maneuver themselves into the space, how much personal space they're willing to give up, and how much or little stuff people have with them, etc. There are a number of factors, but if everyone on the T can give up just a little more space, more people can pack onto the T car. It's about minimizing our personal space and minimizing our discomfort, in order to maximize how many people can get on the T. It amuses me for about 5 minutes before I intensely dislike feeling like cattle :(

In Japan they have subway workers who push people into the subway.

Optimization of space happens when you're packing for a trip, packing a suitcase, backpack, duffel bag, whatever. How do you fit all your clothes into the bag? Sometimes, it comes down to an optimization problem. If you need all your stuff to fit, but don't have enough room, sometimes reorganizing everything helps things fit better. Other times you have to leave something behind, take stuff out so that everything else can fit. Either way, it's an unconscious optimization problem.

My roommates and I were discussing how parking garages manage to fit so many cars into one area. We also reveled in the design of parking structures that allows cars to both go up and down at the same time. We guessed that they're structured like DNA helix or rotini pasta, there are two rotating levels that let people go up or down and sections in between that let people choose which way they want to go. But parking structures are optimizing how to store cars. Instead of having a parking lot, we can store literally tons more cars in the same space.

Not quite the same as a helix parking structure, but you get the idea right?

Speaking of the DNA helix, talk about optimization of space! Two or three meters of DNA fit into one single human cell!

How about living situations? People who live in apartments (a large majority of Boston residents) are literally living on top of one another. The optimization of residential space comes down to how comfortable people are living in small spaces. The City of Boston's population of 620,000 is spatially living in an area of about 50 square miles. My hometown has about 100,000 less people living in an area three and a half times larger than Boston's area. The population density of Boston is 12,800 people/square mile, while my hometown's population density is only 2,800 people/square mile. Lots of people live in apartment buildings in Boston, while more people live in houses in New Mexico.

These pictures are population density maps that show how many people are living in certain areas of the world or the United States.

A few months back, I also came across a photo series that is incredibly revealing about how Hong Kong residents have adapted to this optimization of human living spaces problem. It seems less space is a small living movement in minimization of stuff and space.

One of the most interesting photo series I've seen yet.


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