No Particular Place to Go

**lenny7** · 05-18-2010, 11:44 PM

with apologies to George Thorogood...

My daughter & I are planning a little road trip over memorial day weekend and while online researching possibilities, I found this forum. I love a good road trip. When we plan a vacation, I get just as excited about the drive as I do the destination. When our family of 5 took a 2 week vacation and drove from Minneapolis to Oregon, I was in heaven.

Only one other family member shares my love of road trips and that is my 14 year old daughter. My wife and 2 sons enjoy the trips, but they don't get excited about the drive. So, for the trip we're planning (or not planning, as I'll get to below) for Memorial day weekend, it's just my girl and me.

It all started when I shared with my daughter the story of how my mom & I would take walks when I was a kid. We'd come to an intersection and we'd take turns deciding which way to go next...left, right, or straight ahead. Eventually we'd make it back home. Then we thought we should do that sometime in the truck, just wander about and see where the road takes us. Finally we found a weekend to do it, and it will be on Memorial Day.

So far the only thing we've planned is that we'll take off on Friday, May 28th, sometime around noon, and hope to get back home on Monday, May 31st, sometime around 5pm. True to our plans, we have not decided where we'll be going, but we have talked about how the trip will play out. We may truly randomly decide every turn, or we'll get in the truck on that Friday morning and decide on a general direction, but be open to change along the way, or we may even look at the forecast for the weekend and make sure we avoid anyplace that will be rainy. Whatever we do, the choice will be hers.

I'm torn between the spontaneity of our original intent and my usual penchant for planning the trip with an engineer's precision. After all, planning is part of the fun. I've fed my craving for planning by checking out mapping websites and determining what we can reasonably do depending on our direction of travel. So if she tells me to drive south, I'm thinking Arkansas. If she tells me to go east, then I'm thinking Michigan's UP. If we don't make it that far, or get side tracked, so what.

Next Friday can't come soon enough!

**Midwest Michael** · 05-19-2010, 05:49 AM

Welcome to the RTA Forum!

That sounds like a great plan. Some of my favorite trips have been based on the decide which direction to go when we get to the next intersection. I'd even make sure to grab your passport in case one of your roads takes you north across the border!

Its been far too long since I've taken one of those trips, and I will say that I am very jealous of the opportunity you're about to have. Do a little planning and get a rough idea of what things you might pass by in every direction - but mostly just enjoy the time and see where the road takes you!

**AZBuck** · 05-19-2010, 11:42 AM

Welcome aboard the RoadTrip America Forums!

What you've described is known (appropriately) in the mathematics community as a 'random walk'. There is one problem with it though. Although you cannot know beforehand the exact path you will take, certain global properties of the process are known, and one of them is that you will never stray far from your original starting point. One thing I've done on occasion though is very similar. Say I wanted to go (as I often did) from New England to the Chesapeake Bay area. Well the general direction is southwest. So every road (numbered highway in my case, because I did want to get somewhere) I came to I would take either south or west as dictated by orientation of the road. I would do that until I either became hopelessly lost, the road dead-ended, or I ran out of time. In your case, the modification would be to divide up your time on the road into roughly five equal periods. For the first time step go, say, southeast, then southwest, then northwest, then northeast, completing a rough diamond and leaving yourselves the fifth time step to figure out where you ended up and to get home.

AZBuck

**lenny7** · 05-19-2010, 12:38 PM

I think you'd get along with my wife. She has her Master's degree in Mathematics and her dissertation had something to do with infinite space. I don't recall the title but I do recall telling her it was more like a paragraph than a title. :)

In my mind I'll be keeping tabs on how long it will take us to get home from where ever we're at. I'll pad a few hours to that and when the time comes to go back, we'll go back. Unless we're already there, of course.

Thanks for the welcome!