Regarding questions, I believe that all good science is about asking the right questions. Entire academic careers are built on just one or two appropriately chosen questions. Of course we encourage all children to be curious scientists. But I feel we hold off too long on giving them a qualitative sense of what a good question is.
But today I am more intersted in estimation.
Estimation: Of course, Math is precise, and there tends to be only one 'correct' answer - however you may arrive at it.
But once you get around to using math in the real world, I feel that one of the most important skills is being able to tell whether you are headed in the right direction, or is your answer way off. (In my undergraduate civil engineering, the professor who taught us design of steel structures would not let us start a calculation until we had first estimated an answer. Your building doesn't collapse because you got a few decimal places wrong. They collapse when you are off by an order of magnitude.)
My own feeling is that in early education children pick up this feeling that math is about exact answers. As they grow older many of them then have difficulty accepting that magnitudes in the real world have uncertainity, and more importantly have trouble being able to determine what level of uncertainity is important in a particular situation.
I was in this frame of mind when I saw that the 3/31 issue of the NY Times Science section had an article/review by Natalie Angier on estimation, calling attention to this book - Guesstimation: Solving the world's problems on the back of a cocktail napkin (by Lawrence Weinstein.) For example, "What is the total volume of human blood on earth?"
I have always enjoyed such estimation problems (going so far as to say you should be able to do them in the shower, without access to paper or google). This interest got a further boost when I found books suggesting that Microsoft commonly used this in their interviews. (I am not that sure this is true anymore.) Going through some of those books/websites certainly made it easier to start rolling-my-own problems from everyday life around me.
Here is an example that popped out at me in yesterday's newspaper, which I think is more relevant to 'the world's problems' than the total volume of human blood.
Report Says Small-Car Buyers Sacrifice Safety for Fuel Economy ... If you crash a mini-size (i.e. fuel efficient) car into a mid-size sedan (head-on, each going at 40 mph), the mini car comes out much worse. The Insurance Institue of Highway Safety, quite rightly, recommends reducing the speed limit and horsepower of cars. (Both politically unpalatable.)
[I can't get blogger to display the graphic below correctly. I think if you click on it you will be able to see it better.]
Sadly there is not enough information in this graphic to extract what I am looking for. But let us just assume that if you drive a mini-sized car, you have a 81 in 1 million chance of dying each year, compared to a 62 in 1 million chance of dying if you drove a mid-size (a difference of about 20 per million registered vehicle years.)
Let us also assume that there about 100 million households in the US (300M population, divided by 3 people per household. I think it is 2.7). Multiply that by 2 cars per household (probably a bit on the high side) and you get something like 200 million cars on US roads. And from there about 70*200=14,000 car fatalities per year, with mini-size cars possibly contributing 4000 more deaths than mid-size cars.
[Sadly, I have no sense how close to the true number 14,000 is. If I am off by a factor of two, then maybe it is 28,000. I seriously doubt if it is more than 50,000.]
Now read on a few more pages in the same issue of the Times until you get to the The American Way in which Op-Ed columnist Bob Herbert said, "So what if eight kids are shot to death every day in America. So what if someone is killed by a gun every 17 minutes."
So how do these numbers stack up? Car-related deaths vs. gun-related deaths.
60 minutes divided by 17 deaths per minute is about 4. So about 4 gun related deaths per hour, or less than 96 per day, or about 36,000 a year (365*100). (Let's round that down to 30,000 to account for the earlier approximations). Since the population of the USA is about 300M. So we are looking at about 100 gun-related deaths per 1 million persons.
So far I have 30,000 gun-related deaths per year, compared to 14,000 car-related deaths per year (or maybe 28,000 for cars)
A Honda Fit likely costs $15,000. A Honda Accord maybe $20,000. Since 5-year costs are about twice the retail price, you are looking at maybe $10,000 more to drive an Accord compared to a Fit. If you chose the Accord over the Fit primarily for 'safety', then your premium is about $2000/year. This is what you are willing to pay to drop your chances of a fatality by 30%.
Since you are twice as likely to die from a gun-related injury, compared to a car, how much would you be willing to pay per year to lower that 30,000/year number for gun deaths?
Let's say my numbers are wrong, and you are only just as likely to die from a gun-related injury as a car-related one. Still, how much are you willing to spend to lower the death toll from guns?
I know that this discussion could quickly get very political, so I don't care for the exact answer. I am more interested in whether we can use simple powers of estimation to begin comparing such everyday numbers.
Here is another one related to mini-cars.
What does the relative cost of fuel to hourly-wages have to be before it becomes economical for everyone to slow down?
Remember how I said the IIHS recommends lowering the speed limit.... Everyone agrees that lowering the speed of a car improves it fuel efficiency. Lowering the speed of all cars also lowers their weight, since the shell does not have to be so strong to resist a high-speed impact. Right now cars tend to weigh 15-20 times the weight of the driver. So you are burning up a lot of fuel just to move around that protective cage. If you dropped the weight you could improve the fuel efficiency by a lot. [Just imagine what doubling car fuel efficiency would do for global warming?]
But if you mandated a 10% lower highway speed, that means you may spend upto 10% longer to get to your destination.
Of course, it all depends on what your hourly-wage is. But for a professional trucker I am guessing that it is an awfully close trade-off. Let's assume a trucker makes $60,000 per year, divided by 2000 hours worked, = $30 per hour. That sounds a bit too high. I would have expected about $20.
Let's assume a Semi gives a mileage of 6mpg. Which means at 60mph, you are using 10 gallons of diesel per hour, or about $20-$30 on fuel per hour. If slowing down to 54 mph could boost your mileage by 10%, then it seems to me that it just might be economical to do just that. [Of course there are other costs like the loan payments on the truck, the insurance, etc that are not related to mileage that I am not accounting for.]
I googled this a bit to see how close I was. You are definitely better off driving at 60mph compared to 70mph. 55mph vs 60mph was not so clear, although 54 is definitely cheaper than 60, I couldn't tell if it was 10% cheaper*. If gas was $4/gallon, and trucker wages did not go up, my calculation is you'd have more cash in your pocket by driving slower.
*When I searched a second time, I struck gold. Kenworth, the truck company, says "every mph increase above 50 mph reduces fuel mileage by 0.1 mpg" So a change in 6mph results in 0.6mpg, which is exactly 10% of 6mpg. Interestingly, Kenworth used the following numbers. $4.50/gallon for fuel. 100,000 miles per year. 6 mpg. 500-mile day. Engine running time 10 hours. Trip time 12 hours. A GPS unit more than pays for itself in terms of avoiding extra miles when you get lost.
Now that you see how much I like doing these number games, if anything strikes you as you watch the news or read the paper, do send them my way.
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