Editing 3065: Square Units

{{comic
| number    = 3065
| date      = March 19, 2025
| title     = Square Units
| image     = square_units_2x.png
| imagesize = 545x678px
| noexpand  = true
| titletext = The biggest I've seen in a published source in the wild is an 80-fold error in a reported distance, which I think came from a series of at least three unit conversions and area/length misinterpretations.
}}

==Explanation==

In this comic, [[Megan]] is using her phone to read about an insect species that consumes (hyperbolically described as 'devours') one square inch of grass per day. As it is relayed through a chain of conversations, this measurement gets misinterpreted up to 12 times until [[Hairbun]] tells other people that it devours an area of grass equal to two times the land area of Australia per day, which is clearly impossible by one insect.{{citation needed}} This is similar to the premise of [[2585: Rounding]].

This gross error is the result of repeatedly misinterpreting the number of square units as the side length of a square, thus increasing the described area by the power of two. The chain also involves converting between {{w|imperial units}} and {{w|International System of Units|SI}} units, thus introducing smaller rounding errors, and frequently switching which measurement is "a single square with sides of a certain distance" and which is "the number of squares that are each of unit length". The upshot is that, while each statement has two (or more) roughly similar measurements of area, the chain of misunderstanding ends up escalating to ever larger relative expanses. The later participants in this chain also clearly forget to sanity-check their figures, blithely informing others that an individual insect is effectively consuming impossibly huge quantities of food, and traveling enormous linear distances every day to do so. In fact, assuming the insect could continuously eat a 1cm strip of grass, it would need to travel at (2,500 miles)<sup>2</sup> / 1cm / 24 hours = 1.87×10<sup>7</sup> km/s, which is about 62 times the speed of light.

In the final frame, [[Blondie]] further misinterprets the comparative 'area of Australia' to mean the ''actual'' land mass of Australia, with the notional insect entirely defoliating the country twice a day, presumably of whatever had managed to grow within each 12 hour cycle. This would quickly kill off a large proportion of the vegetation, leading to a decreasing food supply for the insect.

The title text tells us that [[Randall]] once found an 80-fold error in a reported distance in a published source. However, it is left as an exercise for the reader to figure out which one. In imperial units, a mile is equal to 80 {{w|chain (unit)|chain}}s, but the 80-fold error was likely due to a different chain of at least three unit conversions and area/length misinterpretations.

===Table of conversions===
{{incomplete|Explain the meanings behind the different colors.}}

Dark red to light red shows a decrease in size due to inaccurate conversion, dark green to light green shows an increase in size.
{| class="wikitable sortable"
! Step !! Multiplier !! Total multiplier !! Square inch !! Square cm !! Square foot !! Acre !! Square meters !! Square kilometers !! Square miles
|-
! 1
| N/A || 100% ||style="background-color:lightgreen;"| 1||style="background-color:red;"| 6.4516 || 0.006945 || 1.594e-7 || 0.0006451 || 6.451e-10 || 2.490e-10
|-
! 2
| 0.93 || 0.93 || 0.93 ||style="background-color:pink;"| 6 || 0.006458 || 1.482e-7 || 0.0006 || 6e-10 || 2.316e-10
|-
! 3
| 6.00 || 5.58 || 5.58 ||style="background-color:lightgreen;"| 36 (6<sup>2</sup>)||0.03875 ||  8.895e-7 || 0.0036 || 3.6e-9 || 1.39e-9
|-
! 4
| 36.00 || 200.90 || 200.9 ||style="background-color:lightgreen;"|1,296 (36<sup>2</sup>) || style="background-color:red;"|1.395 || 3.202e-5 || 0.1296 || 1.296e-7 || 5.004e-8
|-
! 5
| 0.72 || 144.00 || 144 || style="background-color:red;"|929.03 || style="background-color:pink;"|1 || 2.296e-5 || 0.09290 || 9.290e-8 || 3.587e-8
|-
! 6
| 0.97 || 139.50 || 139.5 || style="background-color:pink;"|900|| 0.9688 || 2.224e-5 || 0.09 ||9e-8 || 3.475e-8
|-
! 7
| 90,000.00 || 125,550.25 || 125,550.25 || style="background-color:lightgreen;"|810,000 (900<sup>2</sup>)|| style="background-color:green;"|871.9||0.02002 ||  81||8.1e-5 || 3.127e-5
|-
! 8
| 1.032 || 129,600 || 129,600 || 836,127||style="background-color:lightgreen;"| 900 (30<sup>2</sup>) ||0.02066||  83.61||8.361e-5 || 3.228e-5
|-
! 9
| 90,000.00 || 1.1,66e+8 || 1.166e+8 || 7.525e+8 ||style="background-color:lightgreen;"| 810,000 (900<sup>2</sup>) || style="background-color:green;"|18.59|| 7.525e+4 || 0.07525 || 0.02905
|-
! 10
| 1.076 || 1.255e+8 || 1.255e+8 || 8.094e+8|| 871,200||style="background-color:lightgreen;"| 20|| style="background-color:green;"|8.093e+4 || 0.08093 || 0.03125
|-
! 11
| 7,91e+6 || 9.920e+12 || 9.920e+12 || 6.4e+13|| 6.889e+13 || 1.581e+6 || style="background-color:lightgreen;"| 6.4e+9 (80,000<sup>2</sup>) || 6,400 ||2,471
|-
! 12
| 1.00 || 9.920e+12 || 9.920e+12 || 6.4e+13|| 6.889e+13 || 1.581e+6 || 6.4e+9 || style="background-color:lightgreen;"|6,400 (80<sup>2</sup>) ||style="background-color:green;"|2,471
|-
! 13
| 253,128 || 2.509e+16 || 2.509e+16|| 1.618e+17 || 1.7424e+14|| 4.000e12 || 1.619e+13 || 1.618e+7 || style="background-color:lightgreen;"|6.250e+6 (2,500<sup>2</sup>)
|-
|}
The total area of Australia is 7,688,287 km² or 2,968,464 mi², making it the 6th largest country on Earth by area. A 2,500-mile square would actually be about 2.1 times greater than the land area of Australia, once again having a rounding error.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[Arrows point to each consecutive panel.]

:[Megan is looking at her phone, with Cueball standing next to her.]
:Megan: This newly-described insect can devour up to a square inch of grass per day.
:Cueball: Oh, neat.

:[Cueball is speaking to Ponytail.]
:Cueball: ...it eats a square inch, or 6 cm², of grass per day...

:[Ponytail is speaking to Hairy.]
:Ponytail: ...a 6-centimeter (2½ inch) square of grass, or 36 cm²...

:[Arrows now point to each consecutive conversion.]
:Written out of panel: ...a 36 centimeter square, or over a square foot...
:Written out of panel: ...a square foot, or 900 cm²...
:Written out of panel: ...a 900 cm (30 foot) square...
:Written out of panel: ...a 30 foot square of grass (900 square feet)...
:Written out of panel: ...a 900 foot square, or almost 20 acres...
:Written out of panel: ...20 acres (8 hectares, or 80,000 square meters)...
:Written out of panel: ...an 80,000 meter (80 km) square...
:Written out of panel: ...a square 80 km wide, or roughly 2,500 square miles...
:Written out of panel: ...a 2,500-mile square, or twice the land area of Australia, per day...

:[An arrow points from the last conversion to the last panel.]
:[Hairbun is looking at her phone, with White Hat, Danish and Blondie standing next to her.]
:Hairbun: Did you hear about this insect that defoliates the entire land area of Australia twice a day?
:White Hat: Gosh!
:Danish: Wow.
:Blondie: I hope at least it's contained there...

{{comic discussion}}
[[Category:Animals]]
[[Category:Math]]
[[Category:Comics featuring Megan]]
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Ponytail]]
[[Category:Comics featuring Hairy]]
[[Category:Comics featuring Hairbun]]
[[Category:Comics featuring White Hat]]
[[Category:Comics featuring Danish]]
[[Category:Comics featuring Blondie]]