The Curse of Dimensionality in Everyday Life

How many decisions do you make per day? It’s not a rhetorical questions, I am seriously asking! Can you even count the number of decisions you take per day? What time do I need to wake up? What am I going to wear? When do I need to leave for work (or wherever)? What road should I take? Do I need to pick up anything before work? When am I going to the gym? Am I picking up the kids this afternoon? Did I send that report? How am I going to catch up on news, my blog, and eat lunch in 1 hour? And the list goes on, and on. You get the idea. We are making an uncountable amount of decisions everyday regarding our life, health, work, family, and everything else. And some of us manage to somewhat optimize all of this!

The curse of dimensional is a term coined by Richard E. Bellman when he was working on solving optimization problems using dynamic programming.  It basically means that the amount of data you need to keep track off and compute for solving a certain problem grows too large that the machine crunching the numbers is unable to handle it. To more explain this with a nice example, let me introduce the Travelling Salesman Problem which states: Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?  Pretty straight forward right? So if we had 3 cities, by using all the available routes for a car we can solve this problem in acceptable time since the dimensions are acceptable. But think of this, how about solving the same problem for all the cities in the United States, or Europe, can you even imagine doing that for Asia, better yet let’s say the entire world. Solving the Travelling Salesman problem for the entire world would probably lead us to a very high dimensional problem, enter the curse of dimensionality.

So why am I telling you all of this? Well, today I was just thinking about the dimension of the problems we (our brains) solve on daily basis. Think about how many decisions we make that are interdependent, and how complicated one day looks like if we viewed it as an optimization problem. Better yet, think about your entire week! So the questions that are on my mind today, do our brains suffer from the curse of  dimensionality? If they do, what does that look/feel like? Would we even know it? Do the people with great organizational and time management skills suffer from it less? I do not really have any answers to these questions, but I think they make a great research topic. All I know is that today, more than any other day, I am awed by the computational powers of our brains!

The feature image is courtesy of Thomas Schultz. Brain dataset courtesy of Gordon Kindlmann at the Scientific Computing and Imaging Institute, University of Utah, and Andrew Alexander, W. M. Keck Laboratory for Functional Brain Imaging and Behavior, University of Wisconsin-Madison. It is publicly available here.

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