# Perspective

It's all in how you look at it

## Analysis

A couple of weeks ago now, I was doing my laundry. When taking my clothes out of the washer to put them in the dryer, I noticed they were actually fairly warm - since the washer is supposed to rinse using cold water this isn't normal. Dad had been doing some repairs in the basement though, so I quickly decided he must have hooked up the hoses the wrong way - the one that should be hot to the cold faucet and vice versa.

When I got everything into the dryer and came upstairs, I told him my conclusion. When he asked why I thought so, I explained about the temperature of the clothes - and that's when the "fun" started. Seems like a week earlier Susan (my stepmom) had complained that the washer seemed to be overheating, and Dad had spent some time "fixing" it, based on the same observation.

I know a lot of people think Mathematics is all about numbers, or facts (like the sum of the angles of a triangle adding up to 180 degrees) or formulas (like how to solve a quadratic equation). That's not true at all - well for any math classes after elementary school. Math is really about solving problems. In lower-level math you use those facts and formulas to solve problems, in higher level maths you actually have to prove those facts and formulas are correct (the formula itself is the problem).

However, we very rarely teach problem solving itself as a skill, we sort of just expect people to absorb it by watching or some such - and many don't.

The first part of problem solving is identifying the problem. In the story above both Susan and I realized there was a problem, unfortunately she had identified what the problem was incorrectly. If you want to get technical about it ... if the washer had been overheating it would not have heated the clothes uniformly. Those nearer to the heat source (whichever part it might have been) would have been hotter, those further away cooler. Additionally - as warm as the clothes were, if something were overheating it would have to have been extremely hot, which usually produces some sort of smell in the air (ozone, rubber, melted insulation - several such smells depending on what overheated and how hot it got).

Additionally (as stated in the story) Dad had been working downstairs (refinishing the floor) and had moved the washer while doing so, hence it was quite likely he could have hooked the hoses up wrong. A washer that no one has disconnected and that suddenly starts getting warm like that - that would be different. But under the circumstances the hoses being hooked up wrong was the most likely cause.

(In more difficult problems you might actually have to do more tests to identify the problem - though that's not so much mathematics as science in general.)

Of course, once you have identified the problem - correctly - the solution may be pretty obvious. This being my dad's house I didn't really want to mess with the washer myself, though switching the hoses around is not a particularly difficult process. In other situations one might encounter, the process to arrive at a solution may be more difficult. There are some problems in Mathematics that have been around for hundreds of years without a real solution being found - though obviously you won't see most of those in high school.

Now of course in your day-to-day world problems may be easier or harder, sometimes identifying the problem is as much about how you believe as about actual facts ... you know, politics, economics, that kind of stuff. It's always a good idea to think seriously about the nature of the problem and make sure you know what you're trying to solve. In my case Dad is pretty handy with any type of machinery and so didn't have to call a repairman to "fix" the overheating "problem", for other people they might have had to pay to have someone come out when all that was really needed was to change the hoses. (Admittedly I'm sure he could have come up with better ways to spend his time, though.)
December 2013
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