Size Comparisons
If you shrank the Solar System to the size of Texas, the Houston metro area would be smaller than a grasshopper in Dallas.
If you shrank the Solar System to the size of Texas, the Houston metro area would be smaller than a grasshopper in Dallas.
Another comic in the My Hobby series.
Cueball attempts to emphasize to Ponytail the size of Texas (the largest state in the contiguous United States, and the second largest US state overall), by making a size comparison. He states that with Texas expanded to the size of the Solar System, the ants in Texas will be as large as Rhode Island (the smallest US state). However, Cueball on purpose (according to the caption) just proves how small Texas actually is compared to the Solar System (which is a lot larger).[citation needed] Additionally, the deeper truth of the original statement is inverted; if a much smaller state (Rhode Island, Delaware, etc.) were scaled up to the size of the solar system, its ants would be the size of Texas itself, over 200 times as large as the scaled up Texan ants, so the relative smallness of the Texan ants shows how big Texas is.
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 flea could jump the equivalent height of the Eiffel Tower (if jumping ability scaled with animal size; which it does not). 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 likely 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.
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 Neptune's aphelion (the farthest point from Sun of the outermost planet). Using the circle area equation, we might say that the 'area' of the solar system is 6.49×1019 square kilometers (2.506×1019 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 9.32×1013 (not a 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. Houston (a city in Texas) has a 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 Dallas, another city in Texas. This is doubly confusing as the comparison made is between a shrunk object (something in Houston) and an unaltered object (something in Dallas) in the same reference frame (Texas). 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 quoted in some places, but is significantly smaller than notably large species. Whether the Dallas grasshopper is any particular variety (or even a native, rather than an exotic pet) is not expounded upon and thus it's actually irrelevant if the grasshopper is from Dallas - which adds to the confusion mentioned before.
On the other hand, the comparison would be meaningful the other way around: "The Solar System is so big that if you shrink it to the size of Texas, (the shrunken) Rhode Island would now be as small as (unshrunken) ants".