That strange number 0

[Steven G]

Ever since I got my first car I noticed something about 0 that was unique to any other number.
I was hoping to hear your comments about what I wrote below--especially any consequences of what I am writing as well as other strange properties that 0 may have.

Suppose you and I get the same exact gas mileage while driving at exactly 50 mph. In that case if we both drove our car exactly 50 mph for a fixed time, then we would have used the same amount of gasoline. Same true if my car and a different car (or the same car) got the same mpg at a speed of say 11 mph.
Now 0 is strange in this situation. Suppose I have a small 4 cylinder can and you have an 8 cyl muscle car. If we both sat at idle, ie we traveled at 0 mph, then the 8 cyl car would have used more gas than my 4 cyl even though we both are getting the same mpg, namely 0 mpg! Well this sounded correct when I thought that the muscle car always got less mpg at any speed than my small 4 cyl car. Then I consider two cars that are exactly the same in every way, in particular they got the same mpg at any speed. Well, if I lower the idle speed on one car, it will have the same mpg as mine if the car is moving since their rpms will be equal. But this is not true at 0 mph. The car with the lower engine speed (lower idle) will use gasoline at a slower rate then the other identical car. It seems that 0 mpg [math]\neq[/math] 0 mpg.

I do not think that this is a paradox at all but none the less it is strange/unique.

 

[tkhunny]

Not all metrics are applicable in all situations. My favorite example, what is the percent error when the expected value is zero (0)?

 

[LCKurtz]

[MATH]\text{mpg} = \frac{\text{miles}}{\text{gallons}}[/MATH] is certainly [MATH]0[/MATH] for any vehicle with engine running and not moving. No problem there. But that says nothing about how many gallons are consumed because the calculation

[MATH]\displaystyle \text{gallons} = \frac {\text{gallons}}{\text{miles}}\cdot \text{miles}[/MATH]
is undefined. Does that take away some of the "weirdness"?

 

[Steven G]

[MATH]\text{mpg} = \frac{\text{miles}}{\text{gallons}}[/MATH] is certainly [MATH]0[/MATH] for any vehicle with engine running and not moving. No problem there. But that says nothing about how many gallons are consumed because the calculation

[MATH]\displaystyle \text{gallons} = \frac {\text{gallons}}{\text{miles}}\cdot \text{miles}[/MATH]
is undefined. Does that take away some of the "weirdness"?

Ah, I was looking for a 0/0 situation somewhere. Thanks

 

[Deleted member 4993]

Calculation of MPG - with "idling" factored in - is very similar to the inclusion of "fixed cost" (like factory rental, administrative cost, etc.) into the calculation of "manufacturing cost" of products in business. The fixed cost is added for each part produced - and it is "spent" whether or not a single item was produced in the factory.

 

[Steven G]

Calculation of MPG - with "idling" factored in - is very similar to the inclusion of "fixed cost" (like factory rental, administrative cost, etc.) into the calculation of "manufacturing cost" of products in business. The fixed cost is added for each part produced - and it is "spent" whether or not a single item was produced in the factory.

Nice logic!