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    Model S VIN P01536 Robert.Boston's Avatar
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    Units

    For those who don't read XKCD, you're missing a treat. Here's a segment from this week's "What If?" segment:
    In the US, we measure fuel economy in miles/gallon—which could just as easily be written as gallons/mile. (This reciprocal form has some advantages. It’s popular in Europe, where it’s expressed as liters per 100 kilometers.)

    But regardless of which units you use, there’s something strange going on here. Miles are units of length, and gallons are volume—which is length3. So gallons/mile is length3/length. That’s just length2.

    Gas mileage is measured in square meters.

    You can even plug it into Wolfram|Alpha, and it’ll tell you that 20 MPG is about 0.1 square millimeters (roughly the area of two pixels on a computer screen).
    Unit cancellation is weird.

    Ok, so what’s the physical interpretation of that number? Is there one?

    It turns out there is! If you took all the gas you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube.

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    mod squad bonnie's Avatar
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    that just made my evening.
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    Sig X#1100 and X#1618 Discoducky's Avatar
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    Reminds me of calculus paradoxes:

    Zeno of Elea was a pupil and friend of the philosopher Parmenides, and lived between 490 BC to about 425 BC. Zeno’s philosophy, known as monism, centers around the theory that “all is one.” That is, the many things that appear to exist individually are merely a single reality. Zeno proposed a number of paradoxes to support his argument against the idea that the world contains more than one thing. These paradoxes are derived from the assumption that if a magnitude can be divided then it can be divided infinitely often. One of these paradoxes, known as The Dichotomy, is described by Aristotle in his work Physics:
    “There is no motion because that which is moved must arrive at the middle of its course before it arrives at the end.”

    The idea behind the paradox is this: Suppose you would like to shoot an arrow at a target:

    In order to reach its destination, the arrow must first travel half the distance to the target. Once there, half the distance still remains. From this position, the arrow must now travel half the remaining distance, and so on. Clearly, there is always some small amount of distance remaining between the tip of the arrow and the target. So, the arrow must always travel half that remaining distance first, thereby leaving the other half still to go. This argument compels us to conclude that the arrow cannot EVER reach the target. Of course, experience tells us that the arrow DOES reach the target! (All who disagree are welcome to stand in front of the target.) Hence we arrive at the paradox.

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    Roadster 919, S 2006 Doug_G's Avatar
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    Zeno didn't know about calculus. It travels half the distance in half the time. In the limit we end up with a finite time for transit.
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    EU Model S P-37 VolkerP's Avatar
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    I still admire the fact that the ancient Greek arrived at the idea that something like atoms must exist - just by thinking! ἄτομος (atomos) -- uncut, indivisible. from 1 /A "not" and 5114 /tomṓteros, "to cut".

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    Model X #1417
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    Quote Originally Posted by Robert.Boston View Post
    For those who don't read XKCD, you're missing a treat. Here's a segment from this week's "What If?" segment:
    ...
    Ok, so what’s the physical interpretation of that number? Is there one?

    It turns out there is! If you took all the gas you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube.
    That reminded me of an exercise we did in an engineering class involving estimating the tread wear lifetime of a tire and the decrease in radius. It came out to the tire leaving a somewhat patchy stripe of rubber one molecule thick behind it on the road.

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    Leeroy Jenkins sublimaze1's Avatar
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    I have a headache

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    Model X #1417
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    Quote Originally Posted by sublimaze1 View Post
    I have a headache
    Another example of something the Ancient Greeks knew about long before calculus and modern physics!

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    ERIC VFX vfx's Avatar
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    Quote Originally Posted by Robert.Boston View Post
    ... Here's a segment from this week's "What If?" segment:
    It turns out there is! If you took all the gas you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube.
    So is there an electron unit equivalent for an EV?
    The world loves to be deceived.

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