Can you solve Seth Godin's math problem?(sethgodin.typepad.com)
sethgodin.typepad.com
Can you solve Seth Godin's math problem?
http://sethgodin.typepad.com/seths_blog/2009/08/not-so-good-at-math.html
10 comments
I live in Canada where we typically get both mpg and liter/100 km. I've found that, almost universally, my friends that report mpg have less fuel efficient cars than the ones that quote liters per 100 km when asked about a vehicle's fuel efficiency.
I tend to think that one of the reasons that Americans tend to have less fuel efficient cars is that when they are evaluating alternatives 9 mpg and 10 mpg are "closer" or more equivalent than 47 mpg and 50 mpg. For example, if I go out and buy a Truck in Canada I could either compare
Ford F150: 15.7 liters/100km (15 mpg) city, 11.2 liters/100km (21 mpg) highway.
GMC Sierra 2500 4WD: 14.7 liters/100km (16 mpg) city, 11.76 liters/100km (20 mpg) highway.
With the Sierra, you are using a full liter less of gas during city driving at the cost of only half a liter of highway driving, so unless I'm doing more than 66% of my driving on highway like conditions, I should go with the Sierra, but that information does not come across to gas conscious buyers that use mpg.
I tend to think that one of the reasons that Americans tend to have less fuel efficient cars is that when they are evaluating alternatives 9 mpg and 10 mpg are "closer" or more equivalent than 47 mpg and 50 mpg. For example, if I go out and buy a Truck in Canada I could either compare
Ford F150: 15.7 liters/100km (15 mpg) city, 11.2 liters/100km (21 mpg) highway.
GMC Sierra 2500 4WD: 14.7 liters/100km (16 mpg) city, 11.76 liters/100km (20 mpg) highway.
With the Sierra, you are using a full liter less of gas during city driving at the cost of only half a liter of highway driving, so unless I'm doing more than 66% of my driving on highway like conditions, I should go with the Sierra, but that information does not come across to gas conscious buyers that use mpg.
The root of the problem is that we shouldn't be thinking in miles per gallon - we should be thinking in gallons per mile.
The follow-up problem is that average person think miles per gallon is linear (as they would phrase it, "the difference between 1MPG and 2MPG is the same as the difference between 60MPG and 61MPG") because they don't know any better, whereas it's really an inverse/reciprocal relationship.
I wrote a more though explanation of this - http://www.daniellanger.com/blog/2009/08/miles-per-gallon-vs... - the last time MPG came up in discussion, when there was some minor outrage over the Volt claiming 230MPG.
The follow-up problem is that average person think miles per gallon is linear (as they would phrase it, "the difference between 1MPG and 2MPG is the same as the difference between 60MPG and 61MPG") because they don't know any better, whereas it's really an inverse/reciprocal relationship.
I wrote a more though explanation of this - http://www.daniellanger.com/blog/2009/08/miles-per-gallon-vs... - the last time MPG came up in discussion, when there was some minor outrage over the Volt claiming 230MPG.
I'm going to agree with another commenter, however, that the "saving fuel" premise is flawed.
Personally, I like MPG because it makes the range-on-a-tank-of-fuel calculation much easier, and I care much more about range than about fuel economy.
I was sad when it turned out the original Honda Insight didn't get 70MPG, because, otherwise, it would have been interesting due to the 700 mile range.
Personally, I like MPG because it makes the range-on-a-tank-of-fuel calculation much easier, and I care much more about range than about fuel economy.
I was sad when it turned out the original Honda Insight didn't get 70MPG, because, otherwise, it would have been interesting due to the 700 mile range.
I'm curious - why the fixation on range of a tank of gas?
If we're talking about serious off-road vehicles, then I can see why you'd want to max out your range to make trip planning easier. But thinking of the majority of drivers doing the majority of their driving (especially in cars like a Honda Insight), they'd be hard-pressed to end up going somewhere that didn't have a gas station at least every 200 miles.
If we're talking about serious off-road vehicles, then I can see why you'd want to max out your range to make trip planning easier. But thinking of the majority of drivers doing the majority of their driving (especially in cars like a Honda Insight), they'd be hard-pressed to end up going somewhere that didn't have a gas station at least every 200 miles.
Time and money, depending on which two types of longer trips I'm considering.
The first is commuting. Filling up takes an extra 5-10 minutes above and beyond the fuel dispensing time (assuming that's linear, which, with my CNG car, it isn't, but that's another topic). A car with a 450 mile range over one with a 225 mile range would save me 4-8 hours per year.
The second is pleasure travel. Sure, the nearest fueling facility may be under 50 miles away, but it may easily be 10-30% more expensive than a farther one, especially across a tax jurisdiction border (especially Canada/US). At $3/G and 60G for a 2000 mile round trip, I'd prefer to keep the Andy Jackson or Uly Grant (Common Loon or Snowy Owl on the reverse if North of the border) or spend the money on an unplanned couple hundred miles' detour.
The first is commuting. Filling up takes an extra 5-10 minutes above and beyond the fuel dispensing time (assuming that's linear, which, with my CNG car, it isn't, but that's another topic). A car with a 450 mile range over one with a 225 mile range would save me 4-8 hours per year.
The second is pleasure travel. Sure, the nearest fueling facility may be under 50 miles away, but it may easily be 10-30% more expensive than a farther one, especially across a tax jurisdiction border (especially Canada/US). At $3/G and 60G for a 2000 mile round trip, I'd prefer to keep the Andy Jackson or Uly Grant (Common Loon or Snowy Owl on the reverse if North of the border) or spend the money on an unplanned couple hundred miles' detour.
I think its more useful for a lot of people. If you drive to work and back every day, then you know how many miles you drive. So you can say "I need to fill up my tank every week" or something, and you can figure out how much money you need to spend each week. Its not about wondering if you can fill up during a trip, but about how much you need to spend on gas.
Interesting - I would never have thought of doing my budgeting that way.
The way I do it is that I know my work commute is about 30KM, so about 150KM per week, and that my Mazda has an average combined fuel efficiency of about 7L/100KM - meaning that my commute uses about 42L of fuel per month. I know that gas costs around $0.96/L in this area at this time of year, so my commuting costs about $40 per month in fuel.
I use this line in my budget, and hence pay less attention to exactly when I refill my tank - and know that any amounts I spend on gas above this number are somewhat discretionary.
The way I do it is that I know my work commute is about 30KM, so about 150KM per week, and that my Mazda has an average combined fuel efficiency of about 7L/100KM - meaning that my commute uses about 42L of fuel per month. I know that gas costs around $0.96/L in this area at this time of year, so my commuting costs about $40 per month in fuel.
I use this line in my budget, and hence pay less attention to exactly when I refill my tank - and know that any amounts I spend on gas above this number are somewhat discretionary.
we should be thinking in gallons per mile
The average person is pretty bad at dealing with fractions, too. Are they going to get the difference between 0.05 gpm and 0.04 gpm? Seems pretty small, it's just 0.01!
The average person is pretty bad at dealing with fractions, too. Are they going to get the difference between 0.05 gpm and 0.04 gpm? Seems pretty small, it's just 0.01!
Valid - gallons/100mi would probably be a more user-friendly measure.
Another interesting argument, although I can't find a source offhand, was to force manufacturers to display a gallons/10,000mi - on the basis that since the average American drives something like 10Kmi per year, this would convey much more concretely the longer-term difference between fuel consumption.
Another interesting argument, although I can't find a source offhand, was to force manufacturers to display a gallons/10,000mi - on the basis that since the average American drives something like 10Kmi per year, this would convey much more concretely the longer-term difference between fuel consumption.
The premise is flawed. We start with: Let's say your goal is to reduce gasoline consumption.
And then we start talking about fuel efficiency. IIRC, though, it's pretty well established in the economics literature that increasing fuel efficiency doesn't reduce gas consumption much, if at all. Increased fuel efficiency means lower effective gas prices, which people respond to by driving more.
The net effect is about the same level of fuel consumption, with more cars on the road (i.e. more traffic and more accidents).
If you want to reduce gas consumption, you have to increase the price. Good ways of doing this include taxing it, increasing demand for other stuff made from petroleum, or reducing supply.
And then we start talking about fuel efficiency. IIRC, though, it's pretty well established in the economics literature that increasing fuel efficiency doesn't reduce gas consumption much, if at all. Increased fuel efficiency means lower effective gas prices, which people respond to by driving more.
The net effect is about the same level of fuel consumption, with more cars on the road (i.e. more traffic and more accidents).
If you want to reduce gas consumption, you have to increase the price. Good ways of doing this include taxing it, increasing demand for other stuff made from petroleum, or reducing supply.
The problem with increasing the price of gas is you hurt the poor most of all. Honestly, jacking up the price of gas isn't going to change my driving habits at all, but doubling the cost of gas (for example) will absolutely impact the budget of a lower income person who is commuting to work in an older car. They can't afford a newer car, they can't afford to move closer into the city, and there isn't public transportation available. They have no options other than to cut back on things like food and braces for their kids, etc... (sure some folks blow lots of money on cigs, big screen tvs, beer, etc... - but honestly the majority of people who are just scraping by, are doing their best).
Figure out how to make it affordable (while being safe) for people to live closer into major cities, and you'll have a real impact on gasoline usage.
Figure out how to make it affordable (while being safe) for people to live closer into major cities, and you'll have a real impact on gasoline usage.
Two things come to mind that might work:
1) Gas credits for the poor... but this might be hard to get right.
2) Cheap public transportation. This won't work everywhere, but I suspect it would work in big cities and their suburbs.
I think you're basically right, but I wonder about the details.
For example, my own driving is not money-limited-- gas could double in price and I would drive just as much, because I drive so little already. Whether I pay $200/year or $400/year for gas doesn't make a difference.
I suspect that the vast majority of miles driven are driven by people who would find cheaper alternatives, like buses or bicycles or email, if prices went up even 20%. But that's just speculation. Empirically, when gas costs doubled briefly last year, it seemed to me that traffic was still almost as bad.
So, I mostly agree with you, but I'm not 100% convinced.
For example, my own driving is not money-limited-- gas could double in price and I would drive just as much, because I drive so little already. Whether I pay $200/year or $400/year for gas doesn't make a difference.
I suspect that the vast majority of miles driven are driven by people who would find cheaper alternatives, like buses or bicycles or email, if prices went up even 20%. But that's just speculation. Empirically, when gas costs doubled briefly last year, it seemed to me that traffic was still almost as bad.
So, I mostly agree with you, but I'm not 100% convinced.
my own driving is not money-limited...
Yes, but (I infer that) you're a well-paid, environmentally-conscious professional living in the center of a dense (and expensive) city. For everybody like you, there's a pizza delivery driver on the other side of the bell curve who covers 200 miles a night. If delivery-miles get cheaper, we have no reason to think the pizzeria wouldn't spend the savings on more drivers, so as to reduce the amount of time customers have to wait.
when gas costs doubled briefly last year...
We wouldn't expect to see much change so soon after the price shock. Filling up at $4.50/gallon is no fun, but in the short term it's something people are willing to put up with rather than buying a new Prius or moving into a new home with a shorter commute.
Yes, but (I infer that) you're a well-paid, environmentally-conscious professional living in the center of a dense (and expensive) city. For everybody like you, there's a pizza delivery driver on the other side of the bell curve who covers 200 miles a night. If delivery-miles get cheaper, we have no reason to think the pizzeria wouldn't spend the savings on more drivers, so as to reduce the amount of time customers have to wait.
when gas costs doubled briefly last year...
We wouldn't expect to see much change so soon after the price shock. Filling up at $4.50/gallon is no fun, but in the short term it's something people are willing to put up with rather than buying a new Prius or moving into a new home with a shorter commute.
I find the easiest thing to do is assume we drive some distance, then work out how much gas is used.
If we drive 1300 miles the numbers all work out easily (because it's divisible by 10, 50 100 and 13)
Suburbans get 10 mpg: 130 gallons
Priuses get 50 mpg: 26 gallons.
Suburbans @ 13 mpg: 100 gallons (30 gallons improvement)
New Prius @ 100 mpg: 13 gallons (13 gallons improvement)
So clearly the best thing to do is scrap all the Suburbans and replace each with a newer style Prius.
If we drive 1300 miles the numbers all work out easily (because it's divisible by 10, 50 100 and 13)
Suburbans get 10 mpg: 130 gallons
Priuses get 50 mpg: 26 gallons.
Suburbans @ 13 mpg: 100 gallons (30 gallons improvement)
New Prius @ 100 mpg: 13 gallons (13 gallons improvement)
So clearly the best thing to do is scrap all the Suburbans and replace each with a newer style Prius.
This is a solved problem. Seth actually linked to my explanation of it. http://charliepark.tumblr.com/post/169016492/in-seth-godins-...
That would only be a "math problem" if it came with enough numbers to do some calculations.
Oh, wait -- he's probably assuming that the only worthwhile metric in the problem is fuel usage. Well, with that requirement, it's easy. Hell, I've even done the calculations for determining how long it would take to recoup my losses if I bought a motorcycle and used that instead of a car with decent fuel efficiency, given some assumptions about future gas prices, a while ago:
http://sob.apotheon.org/?p=449
Oh, wait -- he's probably assuming that the only worthwhile metric in the problem is fuel usage. Well, with that requirement, it's easy. Hell, I've even done the calculations for determining how long it would take to recoup my losses if I bought a motorcycle and used that instead of a car with decent fuel efficiency, given some assumptions about future gas prices, a while ago:
http://sob.apotheon.org/?p=449
Here's a better solution: replace the suburbans with Priuses instead of buying into Godin's tired, second-hand false dichotomy. Some of us are wired for arithmetic, actually.
It may look unintuitive, but it's just an optimmization problem. When you optimize, you always begin with the most resource-intensive element, because that's where most of the gains are.
If the goal is to reduce gasoline consumption I'd suggest
* banning futures trading on oil world-wide.
* provide free public transportation.m/10 - m/13 > m/50 - m/100
I fixed his problem below:
(And you don't have to "go metric", just using gallons/1000miles would do fine.)