Tuesday, July 6, 2010

A Packing and Random Walk Problem

Day 0 -- Home

Google Earth Measurements (straight line between locations)
Distance from Vancouver: 0 km
Distance from Kingston: 3540 km

My house to our new apartment
 
Introduction

Laura and I are moving from our homes in Richmond, BC to Kingston, ON for me to do my MSc in Astronomy at Queen's University. Our move-in date is 1 August 2010, and we are going to move by car. It will be a vacation to see most of Canada as well as moving!

We plan to take video and make a video blog (link available soon) but putting together video could take awhile so I thought a text and pictures blog would let our friends and family get updates in a much more timely fashion.

Being a physics student, there will be some math/physics (e.g. see below) in this blog. We apologize in advance for our non-physics readers :)

We hope you will join us in our adventure!

A Packing Problem

We've packed all the stuff we want to take in many boxes of various sizes, all numbered from 1 to 19, one number per category. There are even multiple boxes for some categories (e.g. Kitchen). We have a master spreadsheet that allows us to translate numbers to list of contents. We hope we don't lose it (it's backed up in several location and we have several print copies). Yeah organization!

Our boxes. Only the items on and in front of the coffee
table will be packed into our car.

Boxes packed into trunk! Our suitcases, duffel bags, and
backpacks go in the back seat and are the only items visible.

We will be driving some of our boxes over in the next 3 weeks. My parents thought driving across Canada is a cool idea so they will be copying us -- they will drive out in early August as well with the rest of our stuff. They will visit us and other family out in Ontario.

A Random Walk Problem

Our total driving distance is estimated at around 5200km including all the detours we will be making, but not including driving within cities. But, "as the bird flies", it's only 3540km. For fun, if we were traveling by random walk (assuming our vehicle can float), we would have to travel a total distance of 12 531 600 km to end up 3540km from home. With a standard highway speed of 120km/hr, this is 104 430 hours, or 11.91 years. However, that does not determine the direction! The urban area of Kingston (from Lake Ontario to the 401) is about 8km at the largest separation. A circle centred at home with a radius of 3540km would have a circumference of 22 242 km. So the probability of ending up in urban Kingston is 0.04%, which means we need to make 2500 trips, on average, to end up in urban Kingston. Assuming we magically teleport back home every time we end up in the wrong location, it could take up to 29 775 years to make this trip by random walk! Good thing we have our GPS device!

What's Next

Penticton, BC is our next stop! Estimated Arrival Date: 6 July 2010.

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