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I don't understand the hate for this post. If you're shopping for a car, you're trying to balance factors like comfort, carrying capacity, impressing coworkers,

I don't understand the hate for this post. If you're shopping for a car, you're trying to balance factors like comfort, carrying capacity, impressing coworkers, purchase cost, resale value, maintenance costs, and of course, fuel costs. Using a MPG measure would lead one to think that 20 mpg and 30 mpg are equidistant from 25 mpg, when in fact, going from 20 mpg to 25 mpg saves you $4,000 over 100,000 miles at $4/gal, while going from 25 mpg to 30 mpg only saves you an additional $3,667. This has political implications as well, since CAFE standards are based on this non-linear value, a car company with a barbell of an extremely inefficient car and an extremely efficient car can have a better average than a company with a moderately efficient car even though the barbell uses more gas and pollutes more. (We'll ignore the irrational averaging by models rather than by sales -- that's another issue.) I recently started looking at whether it would be worth it to replace my current gas guzzler and this was part of the calculation. You can see my numbers here: https://docs.google.com/spreadsheet/ccc?key=0AkSgUqAZJOp-dEJENjFUYXpqRHNBMkk2c0RPbXp6eGc https://docs.google.com/spreadsheet/ccc?key=0AkSgUqAZJOp-dEJ...

ta12121 14y ago
The hate comes from OP's description of MPGs as clearly inferior to L/100km when in reality he's just engaging in a Holy War between two things that are nearly equivalent. The non-linearity argument is not as strong and you and OP think, because many people naturally think in ratios. In fact, in some anthropological studies hunter gatherers that don't know arithmetic mostly said that the value halfway between one and nine is three.
- JumpCrisscross 14y ago
  Fascinating on the anthropological perspective - would you happen to have a source?
  - ta12121 14y ago
    http://www.freakonomics.com/2011/11/29/addition-is-useless-multiplication-is-king-channeling-our-inner-logarithm/ http://www.freakonomics.com/2011/11/29/addition-is-useless-m... http://www.unicog.org/biblio/Year/2008.complete.html#Dehaene2008 http://www.unicog.org/biblio/Year/2008.complete.html#Dehaene... Abstract from the original paper: The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education
- orangecat 14y ago
  In fact, in some anthropological studies hunter gatherers that don't know arithmetic mostly said that the value halfway between one and nine is three. Which still doesn't produce the right answer; you save three times as much gas going from 10MPG to 30 compared to going from 30 to 90. (More generally, going from k to kn MPG saves n times as much as going from kn to k*n^2).
  - ta12121 14y ago
    I don't think the emphasis on saving is correct. You're picking an arbitrary origin which is not zero. If you go from 10 MPG to 30 MPG you are now using 1/3 as much gas. If you go from 30 MPG to 90 MPG you are once again using 1/3 as much gas.
schiffern 14y ago
In computing CAFE numbers, the inverse of mpg is used in the average. They are also weighted by sales, so both your points are specious.
- usaar333 14y ago
  Correct. Indeed, they are taking the average of the mpg directly, just the harmonic average (http://en.wikipedia.org/wiki/Harmonic_mean http://en.wikipedia.org/wiki/Harmonic_mean) rather than the arithmetic one we are more familiar with.
- Drbble 14y ago
  They should be weighting by miles, not sales, though that is harder to measure.
- kevinpet 14y ago
  Thank you for the correction. I suspect I must have read a simplified explanation once and missed that it was simplified.
damoncali 14y ago
I don't understand the hate for this post. It's because it's much writing and reasoning about comparing two ways to describe exactly the same thing, and comes to the conclusion that there is somehow a meaningful difference between them. No matter how you slice it, you have to do some third grade math to figure out the economic impact of fuel economy. This is not a big deal. It's the same faulty logic behind the supposed superiority of the metric system. Big whoop. You can multiply by 10. It's literally two sides of the same ruler.
- lotharbot 14y ago
  > "It's the same faulty logic behind the supposed superiority of the metric system." In grad school (applied math) it was always good for a laugh when we heard someone make a big deal out of metric. We always scaled out as much as possible to get nice dimensionless equations with the minimum number of parameters. That said, sometimes one choice of units or basic quantities is more convenient than another for a particular application. Not right or superior in a general sense, just better suited to some specific context.
  - damoncali 14y ago
    This is great point. For metalworking, inches are great for length because the tolerance limits of a typical machine are around .001". You can use cm, but it's awkward. I've also found that with complex calculations, the metric system's ease can be frustrating - it hides "off by a power of 10" unit errors.
- masklinn 14y ago
  > It's because it's much writing and reasoning about comparing two ways to describe exactly the same thing, and comes to the conclusion that there is somehow a meaningful difference between them. This difference has been empirically demonstrated: people have a much harder time comparing comparisons in MPG than in L/100: they over-estimate efficiency changes in high-MPG and underestimate efficiency changes in low-MPG (e.g. 10 to 11 MPG and 30 to 45 MPG are roughly the same efficiency improvement of 1 gal per 100 miles but most people will eyeball the second case as being a significantly better improvement than the first) > No matter how you slice it, you have to do some third grade math to figure out the economic impact of fuel economy. No, L/100 (or gal/MI) is linearly related to fuel economy, there's no math to perform (you can do it if you want precise figures, but it's optional). > Big whoop. You can multiply by 10. Yeah, who cares if bytes are 4, 6, 8 or 9 bits after all?

ta12121 14y ago

The hate comes from OP's description of MPGs as clearly inferior to L/100km when in reality he's just engaging in a Holy War between two things that are nearly equivalent. The non-linearity argument is not as strong and you and OP think, because many people naturally think in ratios. In fact, in some anthropological studies hunter gatherers that don't know arithmetic mostly said that the value halfway between one and nine is three.

JumpCrisscross 14y ago
Fascinating on the anthropological perspective - would you happen to have a source?
- ta12121 14y ago
  http://www.freakonomics.com/2011/11/29/addition-is-useless-multiplication-is-king-channeling-our-inner-logarithm/ http://www.freakonomics.com/2011/11/29/addition-is-useless-m... http://www.unicog.org/biblio/Year/2008.complete.html#Dehaene2008 http://www.unicog.org/biblio/Year/2008.complete.html#Dehaene... Abstract from the original paper: The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education
orangecat 14y ago
In fact, in some anthropological studies hunter gatherers that don't know arithmetic mostly said that the value halfway between one and nine is three. Which still doesn't produce the right answer; you save three times as much gas going from 10MPG to 30 compared to going from 30 to 90. (More generally, going from k to kn MPG saves n times as much as going from kn to k*n^2).
- ta12121 14y ago
  I don't think the emphasis on saving is correct. You're picking an arbitrary origin which is not zero. If you go from 10 MPG to 30 MPG you are now using 1/3 as much gas. If you go from 30 MPG to 90 MPG you are once again using 1/3 as much gas.

schiffern 14y ago

In computing CAFE numbers, the inverse of mpg is used in the average. They are also weighted by sales, so both your points are specious.

usaar333 14y ago
Correct. Indeed, they are taking the average of the mpg directly, just the harmonic average (http://en.wikipedia.org/wiki/Harmonic_mean http://en.wikipedia.org/wiki/Harmonic_mean) rather than the arithmetic one we are more familiar with.
Drbble 14y ago
They should be weighting by miles, not sales, though that is harder to measure.
kevinpet 14y ago
Thank you for the correction. I suspect I must have read a simplified explanation once and missed that it was simplified.

damoncali 14y ago

I don't understand the hate for this post. It's because it's much writing and reasoning about comparing two ways to describe exactly the same thing, and comes to the conclusion that there is somehow a meaningful difference between them. No matter how you slice it, you have to do some third grade math to figure out the economic impact of fuel economy. This is not a big deal. It's the same faulty logic behind the supposed superiority of the metric system. Big whoop. You can multiply by 10. It's literally two sides of the same ruler.

lotharbot 14y ago
> "It's the same faulty logic behind the supposed superiority of the metric system." In grad school (applied math) it was always good for a laugh when we heard someone make a big deal out of metric. We always scaled out as much as possible to get nice dimensionless equations with the minimum number of parameters. That said, sometimes one choice of units or basic quantities is more convenient than another for a particular application. Not right or superior in a general sense, just better suited to some specific context.
- damoncali 14y ago
  This is great point. For metalworking, inches are great for length because the tolerance limits of a typical machine are around .001". You can use cm, but it's awkward. I've also found that with complex calculations, the metric system's ease can be frustrating - it hides "off by a power of 10" unit errors.
masklinn 14y ago
> It's because it's much writing and reasoning about comparing two ways to describe exactly the same thing, and comes to the conclusion that there is somehow a meaningful difference between them. This difference has been empirically demonstrated: people have a much harder time comparing comparisons in MPG than in L/100: they over-estimate efficiency changes in high-MPG and underestimate efficiency changes in low-MPG (e.g. 10 to 11 MPG and 30 to 45 MPG are roughly the same efficiency improvement of 1 gal per 100 miles but most people will eyeball the second case as being a significantly better improvement than the first) > No matter how you slice it, you have to do some third grade math to figure out the economic impact of fuel economy. No, L/100 (or gal/MI) is linearly related to fuel economy, there's no math to perform (you can do it if you want precise figures, but it's optional). > Big whoop. You can multiply by 10. Yeah, who cares if bytes are 4, 6, 8 or 9 bits after all?