Editing 2733: Size Comparisons
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A common analogy for expressing a statistic (such as area/volume/population size/population density) of unfamiliar things is to compare that thing to some other reference that people are likely to already have an understanding of, if only through past comparisons. For instance, it is said that a human-sized {{w|flea}} could jump the equivalent height of the {{w|Eiffel Tower}} (if jumping ability scaled with animal size; which it does not, due to how some of the different numbers involved will scale to the square or cube of the linear factor, so such aspects as power-to-weight ratios and sheer biomechanical strengths cannot be maintained). In this case, Randall is comparing objects that are extremely different in scale (the state of Texas and a small insect), but then blowing Texas up to yet another size many orders of magnitude larger, and then comparing it with something else his addressee has no comprehension of, with the result that the comparison is of no value in understanding how big Texas is (which could be supposed to be Cueball's intended impartation), or what ants have to do with anything in the first place. The only message you get in the end is that "Texas is much bigger than an ant!"{{Citation needed}} | A common analogy for expressing a statistic (such as area/volume/population size/population density) of unfamiliar things is to compare that thing to some other reference that people are likely to already have an understanding of, if only through past comparisons. For instance, it is said that a human-sized {{w|flea}} could jump the equivalent height of the {{w|Eiffel Tower}} (if jumping ability scaled with animal size; which it does not, due to how some of the different numbers involved will scale to the square or cube of the linear factor, so such aspects as power-to-weight ratios and sheer biomechanical strengths cannot be maintained). In this case, Randall is comparing objects that are extremely different in scale (the state of Texas and a small insect), but then blowing Texas up to yet another size many orders of magnitude larger, and then comparing it with something else his addressee has no comprehension of, with the result that the comparison is of no value in understanding how big Texas is (which could be supposed to be Cueball's intended impartation), or what ants have to do with anything in the first place. The only message you get in the end is that "Texas is much bigger than an ant!"{{Citation needed}} | ||
| − | There are a lot of definitions for how large the Solar System is, but one that is used (and easily agreed upon) is based upon {{w|Neptune}}'s {{w|Apsis#Perihelion and aphelion|aphelion}} (the farthest point from Sun of the outermost planet). Using the {{w|Area of a circle|circle area equation}}, we might say that the 'area' of the solar system is 6.49×10<sup>19</sup> square kilometers (2.506×10<sup>19</sup> square miles), which is a lot, with Texas's area being in turn measured as 696,241 km² (268,820 mi²). The difference in size is the huge factor of 9. | + | There are a lot of definitions for how large the Solar System is, but one that is used (and easily agreed upon) is based upon {{w|Neptune}}'s {{w|Apsis#Perihelion and aphelion|aphelion}} (the farthest point from Sun of the outermost planet). Using the {{w|Area of a circle|circle area equation}}, we might say that the 'area' of the solar system is 6.49×10<sup>19</sup> square kilometers (2.506×10<sup>19</sup> square miles), which is a lot, with Texas's area being in turn measured as 696,241 km² (268,820 mi²). The difference in size is the huge factor of 9.32x10<sup>13</sup> (not a [[2707: Astronomy Numbers|simple number]]). Ants, unfortunately for the calculations, vary vastly in size, but Rhode Island's area is known to be 3,144 km² (1,214 mi²). We can therefore back-calculate that Randall's average "ant" would occupy 33.73 square millimeters. Roughly measured, an ant has an "aspect ratio" of 1:2 (width to length), and such an assumption leads to a length of 8.21mm, which falls easily into the range of 2–25mm for various possible species and types of ants. Therefore, Randall's calculated comparison indeed holds up as valid. |
The title text refers to the opposite, with the entire Solar system being scaled down to the size of Texas. {{w|Houston}} (a city in Texas) has a {{w|Greater Houston|metropolitan area}} (an area extending a bit beyond the city itself) that, if ''shrunk'' by the same factor as before, would be smaller than a grasshopper in {{w|Dallas}}, another city in Texas. (This, of course, only works if Houston's environs are part of what is shrunk, yet the grasshopper – and perhaps at least part of its apparent hometown of Dallas – remains unchanged.) The calculations to verify this hinge upon Houston's metro area normally being considered to be 26,061 km² (10,062 mi²), and hence becoming 279.6 square millimeters. A grasshopper may be considered thinner than an ant, so we shall use the aspect ratio of 1:3 instead, to give a length of 28.96 mm, or almost 3 centimeters and approximately an inch. This falls within the range of 1–7cm range, that may be found [https://animalcorner.org/animals/grasshopper/ quoted in some places], but is significantly smaller than [https://a-z-animals.com/blog/the-10-largest-grasshoppers-in-the-world/ notably large species]. Whether the Dallas grasshopper is any particular variety (or even a native, rather than an exotic pet) is not expounded upon. | The title text refers to the opposite, with the entire Solar system being scaled down to the size of Texas. {{w|Houston}} (a city in Texas) has a {{w|Greater Houston|metropolitan area}} (an area extending a bit beyond the city itself) that, if ''shrunk'' by the same factor as before, would be smaller than a grasshopper in {{w|Dallas}}, another city in Texas. (This, of course, only works if Houston's environs are part of what is shrunk, yet the grasshopper – and perhaps at least part of its apparent hometown of Dallas – remains unchanged.) The calculations to verify this hinge upon Houston's metro area normally being considered to be 26,061 km² (10,062 mi²), and hence becoming 279.6 square millimeters. A grasshopper may be considered thinner than an ant, so we shall use the aspect ratio of 1:3 instead, to give a length of 28.96 mm, or almost 3 centimeters and approximately an inch. This falls within the range of 1–7cm range, that may be found [https://animalcorner.org/animals/grasshopper/ quoted in some places], but is significantly smaller than [https://a-z-animals.com/blog/the-10-largest-grasshoppers-in-the-world/ notably large species]. Whether the Dallas grasshopper is any particular variety (or even a native, rather than an exotic pet) is not expounded upon. | ||
