2733: Size Comparisons

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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.
Title text: 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, 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 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, 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 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.

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".


[Cueball speaking to Ponytail.]
Cueball: Texas is so big that if you expanded it to the size of the Solar System, the ants there would be as big as Rhode Island.
Ponytail: Wow!
Ponytail: ...Wait.
[Caption below the panel:]
My hobby: Unhelpful size comparisons

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But Texas isn't even the largest US State. It's the second largest state, behind Alaska. Mind you, if you took Alaska and divided it into two then Texas would no longer be in second place... It would now be third! 02:11, 4 February 2023 (UTC)

LOL, poor Texans. I'm from Australia. We only have 6 states, and 4 of them are bigger than Texas. So Texas would be in the smallest 50% of states if it was part of Australia Boatster (talk) 14:01, 4 February 2023 (UTC)

I started an explanation. My first, so I hope it's OK. Notice how I resisted [Citation needed]. Nitpicking (talk) 03:20, 4 February 2023 (UTC)

... and ninjaed. Nitpicking (talk) 03:21, 4 February 2023 (UTC)

Fixed the beginning, now it says Texas is the second-largest state. WhatDoWeDoNow (talk) 03:29, 4 February 2023 (UTC)

Alaska isn't usually considered part of the "contiguous US", so Texas is indeed first there. Barmar (talk) 03:39, 4 February 2023 (UTC)
Whoops, didn't see that. Sorry! WhatDoWeDoNow (talk) 19:09, 4 February 2023 (UTC)
2082:_Mercator_Projection: If you drive north from the Pacific northwest you actually cross directly into Alaska 20:46, 7 February 2023 (UTC)

Note that if you scale Rhode Island up to the size of the Solar System, the ants would be even larger. Jordan Brown (talk) 06:46, 4 February 2023 (UTC)

Trivia: In Germany we like to compare big things to the size of the Saarland, the smallest federal state that is not a city state. But since it is also the state with the least people living in it almost noone really knows how big the Saarland really is (and of the rest noone really cares to find out). This reminds me a lot of this Texas vs. Alaska discussion and I wonder if every country has something like this...? -- 07:44, 4 February 2023 (UTC)

In the UK, at a certain range of scale our general comparison standard is (half/three times /etc) "the size of Wales". e.g. the quantity of rainforest that is doomed, at any particular time. There are a lot of people there (often, according to the Welsh themselves, too many English incomers) and it is usefully easy to identify (I think of it as the "head of the pig that the gnome is riding", but that might just be me), given its prominant appearance in the outline of Great Britain itself. Usually! 08:51, 4 February 2023 (UTC)
In Australia we seem compelled to use Sydney Harbour as the unit of measurement for any large amount of waterBoatster (talk) 13:57, 4 February 2023 (UTC)
And when we don't compare to the size of states, we usually use sports fields. "football fields" is a frequent unit of measurement in the media. Barmar (talk) 15:13, 4 February 2023 (UTC)
Oh, yes, football fields (association football, aka. soccer) are popular here, too, but less controversial as they are always roughly 100 by 50 meters in size. -- 05:46, 5 February 2023 (UTC)
I just started a similar conversation, where we started discussing comparing the size of something with the size of an Olympic Swimming Pool, which is 25x50 meters, but never spoken like that in the US, because, metric. :) The volume can vary, since it might be somewhere between 2 and 3 meters deep, but is also often used for a tangible volume of things. RandalSchwartz (talk) 22:40, 5 February 2023 (UTC)
Although I suspect a good number of people don't really have a firm grasp of the size of Wales - I think there's often a tendency to picture it as everything west of a straight line running from somewhere around the Mersey down to around Gloucester, thus making it about 1/4 - 1/3 bigger by lumping in chunks of Cheshire, Shropshire, and Gloucestershire, and most of Herefordshire. 10:37, 8 February 2023 (UTC)
Bear in mind that much more of Britain was 'Welsh' before the Saxons barged in, so you could cut them some slack. The faithful following of the current subnational boundary is one option, but you could imagine many other abstractions that don't vastly change things. I'm sure some people would Offa a completely different line for your consideration... 17:52, 8 February 2023 (UTC)

Notably, the larger the state you scale up the smaller the ants will be, as you would have to scale it by a smaller factor. The comparison would be more accurate if it read: "Texas is so big that if you expanded it to the size of the Solar System, the ants there would "only* be as big as Rhode Island." Svízel přítula (talk) 10:31, 4 February 2023 (UTC)

Wait, Jordan Brown already said that. Svízel přítula (talk) 10:32, 4 February 2023 (UTC)

I just barely resisted changing the "Dallas" wikipedia link to point to the page for the TV show. Barmar (talk) 15:11, 4 February 2023 (UTC)

A note that, in an edit I just made, amongst other things I went through and (hopefully) clarified the style of the area measurements. (Though only assuming that they were numerically correct... Didn't check!) If you say "N kilometres squared", this can be so easily taken/meant as "(N km)²", rather than "N square kilometres", which is "N (km²)". Both areas, but different. Just like the volume described as "10 centimetres cubed" would also be "1000 cubic centimetres". (In both cases being 1 litre).
The easy confusion coming from the "km²" unit which you will read straight as "kilometres squared". And a single one is a "kilometre squared", before being given a number as some multiple of "kilometre squared"s, but that generally aint the same as a "multiple of kilometres" squared. So it is instead best to word it (if you do that at all) as "(a multiple of) square kilometres".
((Next up, I shall probably go on to explain the technical difference between "degrees Kelvin", °K (or alternately as required for the scales Centigrade, Fahrenheit, Rankine, Delisle, whatever), and "Kelvin degrees", K°... ;) ))
Oh and, don't worry. Though I used the international version of "litre", etc, above, I tried to make sure I use the American-type spelling in the article itself, despite all my British instincts and natural preference... Just that here I couldn't.conscuously stand to write it 'wrongly' in my own far more personalised bit of prose. :P 17:06, 4 February 2023 (UTC)

If Texas were expanded to the size of the solar system, the size of an ant would not change. The size of objects is not affected by changes in scale of the surrounding environment. An ant would still be the same size relative to Texas as it would be relative to the solar system.chatgpt

It is clearly assumed in the comic that the ants of Texas would be scaled proportionally to Texas. So where these scaled ants would gave the same relative size to the scaled Texas, they would now be as large as Rhode Island compared to the not scaled Texas! --Kynde (talk) 13:47, 6 February 2023 (UTC)

Hey, couldn't the joke also be that ant sizes don't really change around states, and so it would be a bad comparison because it doesn't tell you about the size of Texas at all? ||10:33, February 4 2023 (PST)

No. If you scaled any other state of the contiguous US up to the size of the solar system, the ants would be even bigger since the other states are smaller than Texas and thus the scaling factor would be larger --Kynde (talk) 13:47, 6 February 2023 (UTC)
Texas is 733 miles across. The solar system is 3.88 billion miles across. A black ant is about 1/3 cm long. This means an ant scammed up by the same factor would be a little less than half the size of Rhode Island. 17:25, 7 May 2023 (UTC)
Neptune's orbital radius is a tad under 3 billion miles, meaning the diameter of it, alone, is 6ish billion miles in size (then add Kuiper, to taste, before even considering the Oort cloud). Even on your figures, though, there are many sizes of ant, including ones roughly twice the size of your example. 18:32, 7 May 2023 (UTC)