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| The title text furthers the joke by taking the imprecise rounding literally, implying that this increase could actually be used/abused as a novel form of propulsion, but it isn't clarified for what type of vehicle. It could be an engine for ground or air travel, but contains the implication that it is trying to 'trick physics' similar to the {{w|Alcubierre drive|theoretical 'warp drive'}} conceived to propel interstellar spacecraft at otherwise impossible speeds. One interpretation of the supposed chain of conversions is that it has somehow created a great deal of energy from nothing. Suppose there existed a device or system that could magically accelerate an object from 17 mph to 45 mph without any energy input. The sped-up object could be harnessed to a generator or engine in such a way that the object was slowed back down to 17 mph, with the difference in energy being output in a useful way, and the object fed back into the device. The result would be an engine that could create both free energy and non-conserved changes in momentum. | | The title text furthers the joke by taking the imprecise rounding literally, implying that this increase could actually be used/abused as a novel form of propulsion, but it isn't clarified for what type of vehicle. It could be an engine for ground or air travel, but contains the implication that it is trying to 'trick physics' similar to the {{w|Alcubierre drive|theoretical 'warp drive'}} conceived to propel interstellar spacecraft at otherwise impossible speeds. One interpretation of the supposed chain of conversions is that it has somehow created a great deal of energy from nothing. Suppose there existed a device or system that could magically accelerate an object from 17 mph to 45 mph without any energy input. The sped-up object could be harnessed to a generator or engine in such a way that the object was slowed back down to 17 mph, with the difference in energy being output in a useful way, and the object fed back into the device. The result would be an engine that could create both free energy and non-conserved changes in momentum. |
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− | At the demonstrated rate of about 4% median rounding gain, it would just take 73 more steps of rounding-acceleration to reach supersonic speed from the starting speed of 45 mph. If the speed of light could be approached without relativistic effects, another 349 steps would go from supersonic speed to the speed of light. (More efficient approaches may exist.)
| + | The problem of whether such a rounding process can reach arbitrary heights actually (perhaps surprisingly to some) has a negative answer, as can be seen in this math overflow post: [https://mathoverflow.net/questions/416965/how-far-away-can-we-get-by-multiple-rounding-and-unit-change/417018#417018 How far away can we get by multiple rounding and unit change?] |
− | | |
− | ===Table of rounding===
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− | {| class="wikitable"
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− | ! step !! percentage gain from rounding !! mph !! {{w|Metre per second|m/s}} !! {{w|Knot (unit)|knots}} !! {{w|fathom}}s/sec !! {{w|furlong}}s/min !! {{w|Kilometres per hour|km/h}} !! furlongs/hour !! {{w|yard}}s/sec
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− | |-
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− | ! 1
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− | | N/A ||style="background-color:lightgreen;"| 17 ||style="background-color:green;"| 7.599680 || 14.77260 || 4.155<span style="text-decoration:overline;">55</span> || 2.266<span style="text-decoration:overline;">66</span> || 27.35885 || 136|| 8.311<span style="text-decoration:overline;">11</span>
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− | |-
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− | ! 2
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− | | +5.27% || 17.89549 ||style="background-color:lightgreen;"| 8 ||style="background-color:green;"| 15.55076 || 4.37445 || 2.38607 || 28.8 || 143.16392 || 8.74891
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− | |-
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− | ! 3
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− | | +2.89% || 18.41247 || 8.2311<span style="text-decoration:overline;">11</span> ||style="background-color:lightgreen;"| 16 ||style="background-color:green;"| 4.50083 || 2.45500 || 29.63200 || 147.29977 || 9.00165
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− | |-
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− | ! 4
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− | | +11.09% || 20.454<span style="text-decoration:overline;">54</span>|| 9.144000 || 17.77451 ||style="background-color:lightgreen;"| 5 ||style="background-color:green;"| 2.727<span style="text-decoration:overline;">27</span>|| 32.91840 || 163.636<span style="text-decoration:overline;">36</span> || 10
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− | |-
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− | ! 5
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− | | +10.00% || 22.5 || 10.05840 || 19.55197 ||style="background-color:green;"| 5.50000 ||style="background-color:lightgreen;"| 3 || 36.21024 || 180|| 11
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− | |-
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− | ! 6
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− | | +9.09% || 24.545<span style="text-decoration:overline;">45</span> || 10.97280|| 21.32942||style="background-color:lightgreen;"| 6 || 3.272<span style="text-decoration:overline;">72</span>||style="background-color:green;"| 39.50208 || 196.363<span style="text-decoration:overline;">63</span>|| 12
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− | |-
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− | ! 7
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− | | +1.26% || 24.85485 || 11.111<span style="text-decoration:overline;">11</span>||style="background-color:green;"| 21.59827 || 6.07563|| 3.31398||style="background-color:lightgreen;"| 40 || 198.83878|| 12.15126
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− | |-
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− | ! 8
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− | | +1.86% || 25.31715 || 11.31778||style="background-color:lightgreen;"| 22 || 6.18864|| 3.37562||style="background-color:green;"| 40.74400 || 202.53718|| 12.37727
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− | |-
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− | ! 9
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− | | +0.63% || 25.47622 || 11.388<span style="text-decoration:overline;">88</span>|| 22.13823|| 6.22752|| 3.39683||style="background-color:lightgreen;"| 41 ||style="background-color:green;"| 203.80975 || 12.45504
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− | |-
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− | ! 10
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− | | +0.09% ||style="background-color:green;"| 25.50000 || 11.39952|| 22.15889 || 6.233<span style="text-decoration:overline;">33</span> || 3.40000 || 41.03827 ||style="background-color:lightgreen;"| 204 || 12.466<span style="text-decoration:overline;">66</span>
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− | |-
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− | ! 11
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− | | +1.96% ||style="background-color:lightgreen;"| 26 ||style="background-color:green;"| 11.62304 || 22.59338 || 6.355<span style="text-decoration:overline;">55</span> || 3.466<span style="text-decoration:overline;">66</span> || 41.84294 || 208 || 12.711<span style="text-decoration:overline;">11</span>
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− | |-
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− | ! 12
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− | | +3.24% || 26.84324||style="background-color:lightgreen;"| 12 || 23.32617|| 6.56168||style="background-color:green;"| 3.57910 || 43.200<span style="text-decoration:overline;">00</span> || 214.74588 || 13.12336
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− | |-
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− | ! 13
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− | | +11.76% || 30|| 13.41120|| 26.06929|| 7.333<span style="text-decoration:overline;">33</span> ||style="background-color:lightgreen;"| 4 || 48.28038|| 240||style="background-color:green;"| 14.666<span style="text-decoration:overline;">66</span>
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− | |-
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− | ! 14
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− | | +2.27% || 30.68182|| 13.71600|| 26.66177||style="background-color:green;"| 7.5 || 4.090<span style="text-decoration:overline;">90</span>|| 49.37760|| 245.454<span style="text-decoration:overline;">54</span>||style="background-color:lightgreen;"| 15
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− | |-
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− | ! 15
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− | | +6.67% || 32.727<span style="text-decoration:overline;">27</span>||style="background-color:green;"| 14.63040 || 28.43922||style="background-color:lightgreen;"| 8 || 4.363<span style="text-decoration:overline;">63</span>|| 52.66944 || 261.818<span style="text-decoration:overline;">18</span> || 16
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− | |-
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− | ! 16
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− | | +2.53% ||style="background-color:green;"| 33.55404 ||style="background-color:lightgreen;"| 15 || 29.15767 || 8.20210 || 4.47387 || 54|| 268.43236 || 16.40420
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− | |-
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− | ! 17
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− | | +1.33% ||style="background-color:lightgreen;"| 34 || 15.19936 || 29.54519 || 8.311<span style="text-decoration:overline;">11</span>||style="background-color:green;"| 4.533<span style="text-decoration:overline;">33</span> || 54.71770 || 272|| 16.622<span style="text-decoration:overline;">22</span>
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− | |-
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− | ! 18
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− | | +10.29% || 37.50000|| 16.76400||style="background-color:green;"| 32.58661 || 9.166<span style="text-decoration:overline;">66</span>||style="background-color:lightgreen;"| 5 || 60.35040|| 300|| 18.333<span style="text-decoration:overline;">33</span>
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− | |-
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− | ! 19
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− | | +1.27% || 37.97572|| 16.976<span style="text-decoration:overline;">66</span>||style="background-color:lightgreen;"| 33 || 9.28295|| 5.06343|| 61.11603|| 303.80577||style="background-color:green;"| 18.56591
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− | |-
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− | ! 20
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− | | +2.34% || 38.86364|| 17.37360|| 33.77158||style="background-color:green;"| 9.5 || 5.181<span style="text-decoration:overline;">81</span>|| 62.54496|| 310.909<span style="text-decoration:overline;">09</span>||style="background-color:lightgreen;"| 19
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− | |-
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− | ! 21
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− | | +5.26% || 40.909<span style="text-decoration:overline;">09</span>|| 18.28800||style="background-color:green;"| 35.54903 ||style="background-color:lightgreen;"| 10 || 5.45455|| 65.83680|| 327.272<span style="text-decoration:overline;">72</span>|| 20
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− | |-
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− | ! 22
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− | | +1.27% || 41.42806|| 18.52000||style="background-color:lightgreen;"| 36 || 10.12686||style="background-color:green;"| 5.52374 || 66.67200|| 331.42448|| 20.25372
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− | |-
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− | ! 23
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− | | +8.62% ||style="background-color:green;"| 45 || 20.11680 || 39.10393 || 11||style="background-color:lightgreen;"| 6 || 72.42048 || 360|| 22
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− | |-
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− | ! 24
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− | | +0.00% ||style="background-color:lightgreen;"| 45 || 20.11680|| 39.10393|| 11|| 6|| 72.42048|| 360|| 22
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− | |}
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| ==Transcript== | | ==Transcript== |
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| :Cueball: If you round. | | :Cueball: If you round. |
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− | :[To their right is a large number with unit, with an arrow going straight down to a normal sized similar number. From there and proceeding all the way down to the bottom, in alternating leftward and rightward rows, the rest of the comic shows arrows connecting conversions from one measured unit into another unit. Straight arrows show the direction of the sequence on each line, the end of each line curving down to start the next line in the opposite direction. The last of these lines ends close to the middle of the panel, with a straight arrow down to another large number with unit, like the first.] | + | :[To their right is a large number with unit, with an arrow going straight down to a normal sized similar number. From there and proceeding all the way down to the bottom, in alternating leftward and rightward rows, the rest of the comic shows arrows connecting conversions from one measured unit into another unit. Straight arrows show the direction of the sequence on each line, the end of each line curveing down to start the next line in the opposite direction. The last of these lines ends close to the middle of the panel, with a straight arrow down to another large number with unit, like the first.] |
| :<big>'''17 MPH'''</big> | | :<big>'''17 MPH'''</big> |
| :8 meters/sec | | :8 meters/sec |