Mathematics takes us still further from what is human into the region of absolute necessity, to which not only the actual world, but every possible world must conform.
-Bertrand Russell
I have not had a lot of spare time recently but I can summarize what I have been doing fairly succinctly with a handy algorithm I came across that generalizes beyond mathematics.
1. Write down the problem
2. Think very hard
3. Write down the solution
Wednesday, March 24, 2010
Monday, March 22, 2010
Sunday, March 7, 2010
Sunset Snowshoe
We just had the two nicest days of March weather you could ever hope or dream of this weekend. One of the ways I decided to enjoy it was doing a couple trips around our local field which is about 4 square kilometers and a two minute bike ride from my house. I could not find any humans to accompany me on the trek but the Siberian Husky showed a lot of interest in the trip as soon as I reached for his harness. I was treated to a beautiful sunset Saturday and Sunday but preferred to leave my phone and hence camera at home.
Another treat for me this weekend was watching my roommate take off and land on his first flight at the Ottawa Flying Club on Saturday morning. Brodie accompanied me again but seemed to take a lot more interest in below ground as I gazed up at the sky. Other highlights were a trip to the Ottawa Bagelshop for hot bagels out of the wood burning oven. Also a trip to the World of Maps to order a custom map of the Quebec city area where a ski touring trip will happen over next Christmas holiday.
I mentioned a while back that I had a set back on my bicycle in the form of a flat tire. Well recently the roads have improved significantly and yet my bike has still been riding about 10 minutes slower on my commute to school than it normally would. Turns out I was riding a damaged rim and blown tire for the last month and blamed it on the poor conditions. Live and learn. The guys at Fresh Air Experience hooked me up with 30% off on a new rim and tire and a new tube for free, I attribute this to the good vibes I was giving out. So if anyone needs a bike go see Duncan at Fresh Air he knows his stuff!
I also felt very privileged to be able to attend a lecture called Painting With Parts given by my Uncle Pete at the National Art Gallery of Canada. Peter presented his life's work and I thought it was outstanding. The theme of the lecture was thinking of a building in terms of several main constituent components or parts. These parts can be designed very precisely by a computer and that allows greater competition among manufacturers to build each part. This simplifies construction and reduces manufacturing cost. In other woods....very cool. In terms of design one thing that stuck was the following. Turnover is very high amongst the brave souls that answer our 911 phone calls. My uncle designed an emergency response centre in Vancouver with a view of the North Shore mountains for the operators at their desks. The average length of employment tripled for these employees after this building opened. This shows me the power our surroundings have on us humans. This fact also serves as a perfect introduction into my next topic.
Before I begin I want to say my intention is not to be critical it is merely to present my own approach. I also do a lot of gross oversimplification partly for tractability and partly because of my own time contraints. One of the questions I get asked frequently is... Where do you see yourself in (insert number of years)? This comes up from friends, family members and in job interviews. It also comes up a lot at my house with my roommate Dan. Both of us have what seems like to us as a dramatically different perspective than the conventional view. I will define a few terms before I discuss my answer.
The lifecycle problem is a question that fascinates me and a lot of economists. In an abstract sense it means over your life how much and at what time do you consume, save and how much do you earn. The idea is to choose the level of consumption because that is what you control in order to maximize lifetime happiness. This could be for a person, a family or a country. For example the United States has accumulated 10 trillion in debt because it continually chooses to consume more than it earns. It can justify this by saying we are going to live a long time and we are going to make more money in the future. We have all seen what happens when people question these assumptions.
A conventional view to the lifecycle problem goes something like this. You begin your economic life at around 18 and your earning power will initially be very low. This is the perfect time to educate yourself in order to receive higher income later in life. The returns to education can easily justify the use of student loans. Next you enter the workforce and begin at a fairly low salary that will steadily increase until about age 55 or whenever you happen to reach the peak of your career. Over that period you typically accumulate a large amount of debt when buying a house. You then use the higher income you receive from increased workplace experience to build equity in your house and accumulate assets (savings) in preparation for retirement. At around 65 you hopefully have accumulated enough assets to receive investment income to support your desired level of consumption or you worked for a company that accumulated assets on your behalf (a pension). The key point in this analysis is that at any period you can use your income and credit or saving facilities to obtain some desired level of consumption and try to secure consumption in the future. Common sense but it is quite beautiful represented mathematically in an optimal control framework.
Okay back to my original question. The times in my life where I can remember being the happiest and can picture myself being the happiest are at a cottage or in the woods. I also perceive that everyone else around me is at their best as well. This could my grandparents cottage on Lake Temagami which my Mom and stepfather Paul have taken over. My Aunt Trudy and Uncle Mike's cottage in Calabogie. Going for a ski or summer hike and swim at Mont Tremblant. Fishing with my Dad and brothers in Northern Quebec. Hiking for turns, and winter camping with Dan. And more recently lying on the white sandy beach on the shores of Lake Huron at my girlfriends parents cottage. The point is this is what I love to do. Which now begs the question how does that fit in with my own lifecycle problem?
Well I am very fortunate to be blessed with a gift in life that I call enjoying math homework. Why that is such a blessing is that it can be done in essentially any location on the planet equally well. A friend from school recently told she performed most of her summer work for the math department outside on her deck. Taking a break at her leisure to go for a long jog. This is the type of lifestyle I anticipate being able to obtain with my education.
Another thing I encountered recently was having a bit of fun searching for property in Quebec city with Dan. The properties were listed as ideal locations to build a second "vacation home." Our view is why leave the vacation behind and go back to a non-vacation home. It looks like Dan is going to have the opportunity to own a nice sized chunk of Canadian playground in the next few years.
So my own lifecycle problem solution goes something like this. Spend as much time as possible in the next few years to receive the best quality education possible. I am not sure exactly form that will take but my guess right now is an MSc in Applied Mathematics and another MSc in Computer Science. Then obtain a job performing operations research and spend roughly 10 years building a reputation and developing contacts. Once I have enough money saved pick-up a large property and build a small house with the ability to have my own bike trail, and skijoring circuit. Ideally there would be water access as well. I would then be permanently on vacation and work on a consulting basis to support my outdoor recreation addiction. I never would plan to retire because the concept would have no meaning for me.
What is working in my favor? The Canadian population is continually becoming more urbanized putting pressure on house prices in cities and depressing house prices in rural areas. Canada has no shortage of the terrain I am interested in, quite the opposite actually. I also plan on working in a technical area that does not require me to be physically present in an office to do my work. So that pretty much answers the question where do I see myself in ...(insert number of years)? Too long of an answer for a job interview though.
Another treat for me this weekend was watching my roommate take off and land on his first flight at the Ottawa Flying Club on Saturday morning. Brodie accompanied me again but seemed to take a lot more interest in below ground as I gazed up at the sky. Other highlights were a trip to the Ottawa Bagelshop for hot bagels out of the wood burning oven. Also a trip to the World of Maps to order a custom map of the Quebec city area where a ski touring trip will happen over next Christmas holiday.
I mentioned a while back that I had a set back on my bicycle in the form of a flat tire. Well recently the roads have improved significantly and yet my bike has still been riding about 10 minutes slower on my commute to school than it normally would. Turns out I was riding a damaged rim and blown tire for the last month and blamed it on the poor conditions. Live and learn. The guys at Fresh Air Experience hooked me up with 30% off on a new rim and tire and a new tube for free, I attribute this to the good vibes I was giving out. So if anyone needs a bike go see Duncan at Fresh Air he knows his stuff!
I also felt very privileged to be able to attend a lecture called Painting With Parts given by my Uncle Pete at the National Art Gallery of Canada. Peter presented his life's work and I thought it was outstanding. The theme of the lecture was thinking of a building in terms of several main constituent components or parts. These parts can be designed very precisely by a computer and that allows greater competition among manufacturers to build each part. This simplifies construction and reduces manufacturing cost. In other woods....very cool. In terms of design one thing that stuck was the following. Turnover is very high amongst the brave souls that answer our 911 phone calls. My uncle designed an emergency response centre in Vancouver with a view of the North Shore mountains for the operators at their desks. The average length of employment tripled for these employees after this building opened. This shows me the power our surroundings have on us humans. This fact also serves as a perfect introduction into my next topic.
Before I begin I want to say my intention is not to be critical it is merely to present my own approach. I also do a lot of gross oversimplification partly for tractability and partly because of my own time contraints. One of the questions I get asked frequently is... Where do you see yourself in (insert number of years)? This comes up from friends, family members and in job interviews. It also comes up a lot at my house with my roommate Dan. Both of us have what seems like to us as a dramatically different perspective than the conventional view. I will define a few terms before I discuss my answer.
The lifecycle problem is a question that fascinates me and a lot of economists. In an abstract sense it means over your life how much and at what time do you consume, save and how much do you earn. The idea is to choose the level of consumption because that is what you control in order to maximize lifetime happiness. This could be for a person, a family or a country. For example the United States has accumulated 10 trillion in debt because it continually chooses to consume more than it earns. It can justify this by saying we are going to live a long time and we are going to make more money in the future. We have all seen what happens when people question these assumptions.
A conventional view to the lifecycle problem goes something like this. You begin your economic life at around 18 and your earning power will initially be very low. This is the perfect time to educate yourself in order to receive higher income later in life. The returns to education can easily justify the use of student loans. Next you enter the workforce and begin at a fairly low salary that will steadily increase until about age 55 or whenever you happen to reach the peak of your career. Over that period you typically accumulate a large amount of debt when buying a house. You then use the higher income you receive from increased workplace experience to build equity in your house and accumulate assets (savings) in preparation for retirement. At around 65 you hopefully have accumulated enough assets to receive investment income to support your desired level of consumption or you worked for a company that accumulated assets on your behalf (a pension). The key point in this analysis is that at any period you can use your income and credit or saving facilities to obtain some desired level of consumption and try to secure consumption in the future. Common sense but it is quite beautiful represented mathematically in an optimal control framework.
Okay back to my original question. The times in my life where I can remember being the happiest and can picture myself being the happiest are at a cottage or in the woods. I also perceive that everyone else around me is at their best as well. This could my grandparents cottage on Lake Temagami which my Mom and stepfather Paul have taken over. My Aunt Trudy and Uncle Mike's cottage in Calabogie. Going for a ski or summer hike and swim at Mont Tremblant. Fishing with my Dad and brothers in Northern Quebec. Hiking for turns, and winter camping with Dan. And more recently lying on the white sandy beach on the shores of Lake Huron at my girlfriends parents cottage. The point is this is what I love to do. Which now begs the question how does that fit in with my own lifecycle problem?
Well I am very fortunate to be blessed with a gift in life that I call enjoying math homework. Why that is such a blessing is that it can be done in essentially any location on the planet equally well. A friend from school recently told she performed most of her summer work for the math department outside on her deck. Taking a break at her leisure to go for a long jog. This is the type of lifestyle I anticipate being able to obtain with my education.
Another thing I encountered recently was having a bit of fun searching for property in Quebec city with Dan. The properties were listed as ideal locations to build a second "vacation home." Our view is why leave the vacation behind and go back to a non-vacation home. It looks like Dan is going to have the opportunity to own a nice sized chunk of Canadian playground in the next few years.
So my own lifecycle problem solution goes something like this. Spend as much time as possible in the next few years to receive the best quality education possible. I am not sure exactly form that will take but my guess right now is an MSc in Applied Mathematics and another MSc in Computer Science. Then obtain a job performing operations research and spend roughly 10 years building a reputation and developing contacts. Once I have enough money saved pick-up a large property and build a small house with the ability to have my own bike trail, and skijoring circuit. Ideally there would be water access as well. I would then be permanently on vacation and work on a consulting basis to support my outdoor recreation addiction. I never would plan to retire because the concept would have no meaning for me.
What is working in my favor? The Canadian population is continually becoming more urbanized putting pressure on house prices in cities and depressing house prices in rural areas. Canada has no shortage of the terrain I am interested in, quite the opposite actually. I also plan on working in a technical area that does not require me to be physically present in an office to do my work. So that pretty much answers the question where do I see myself in ...(insert number of years)? Too long of an answer for a job interview though.
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