Difference between revisions of "3065: Square Units"

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{{incomplete|Created by a SQUARE AREA DEFOLIATION BOT - Do NOT delete this tag too soon.}}
 
{{incomplete|Created by a SQUARE AREA DEFOLIATION BOT - Do NOT delete this tag too soon.}}
  
−
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. This unit gets misinterpreted 11 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]].
+
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 unit gets misinterpreted 11 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 an imperial unit and a metric unit, alternating, thus introducing smaller rounding errors even while 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 roughly similar measurements of area, the chain of misunderstanding ends up claiming 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 travelling enormous linear distances every day to do so.
 
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 an imperial unit and a metric unit, alternating, thus introducing smaller rounding errors even while 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 roughly similar measurements of area, the chain of misunderstanding ends up claiming 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 travelling enormous linear distances every day to do so.

Revision as of 10:19, 20 March 2025

Square Units
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.
Title text: 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

    Ambox notice.png This explanation is incomplete:
    Created by a SQUARE AREA DEFOLIATION BOT - Do NOT delete this tag too soon. If you can fix this issue, edit the page!

    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 unit gets misinterpreted 11 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 an imperial unit and a metric unit, alternating, thus introducing smaller rounding errors even while 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 roughly similar measurements of area, the chain of misunderstanding ends up claiming 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 travelling enormous linear distances every day to do so.

    The title text tells us that Randall once found an 80-fold error in a reported distance in a published source.

    Table of conversions

    step percentage gain total percentage gain square inch square cm square foot acre square meters square kilometers square miles
    1 N/A N/A 1 6.4516 0.00694444444 1.5942251e-7 0.00064516 6.4516e-10 2.4909767e-10
    2 -7% -7% 0.93 6 0.00645835 1.4826e-7 0.0006 6e-10 2.3166e-10
    3 +600% +558% 5.58001 36 (6x6) 0.0387501 8.8958e-7 0.0036 3.6e-9 1.39e-9
    4 +3,600% +20,000.9% 200.8804 1,296 (36x36) 1.395003 3.20249e-5 0.1296 1.296e-7 5.00388e-8
    5 -28.3% +14,400% 144 929.03 1 2.2957e-5 0.092903 9.2903e-8 3.587e-8
    6 +87,188% +125,550.25% 125,550.251 810,000 (900x900) 871.876744 0.0200155359 81 8.1e-5 3.1274275e-5
    7 +103.22% +12,960,000% 129,600 836,127 900 (30x30) 0.0206612 83.6127 8.3613e-5 3.2283e-5
    8 +90,000% +11,664,000,000% 116,640,000 752,514,624 810,000 (900x900) 18.5950413 75,251.4624 0.0752514624 0.0290547521
    9 +107.55% +12,545,275,491% 1.255e+8 8.094e+8 871,200 20 80,937.1 0.0809371 0.03125
    10 +7,907,375% +992,001,984,003,868% 9,920,019,840,040 6.4e+13 68,889,026,666.94 1,581,474.44139 6,400,000,000 (80,000x80,000) 6,400 2,471.053814672
    11 +0% +992,001,984,003,868% 9,920,019,840,040 6.4e+13 68,889,026,666.94 1,581,474.44139 6,400,000,000 6,400 (80x80) 2,471.053814672
    12 +252,928% +2,509,056,048,112,096,000% 2.509056e+16 1.6187426e+17 1.7424e+14 4,000,000,000 1.6187426e+13 16,187,425.69 6,250,000 (2,500x2,500)

    The land area of Australia is 7,688,287 square km or 2,968,464 sq mi, making it the 6th largest country on Earth by area. A 2,500 mile square would actually be 2.1 times greater than the land area of Australia, once again having a rounding error.

    Transcript

    Ambox notice.png This transcript is incomplete:
    Do NOT delete this tag too soon. If you can fix this issue, edit the page!
    [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...

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    Discussion

    I like this one :) reminds me of trying to use recipes in imperial units with metric equipment 162.158.108.29 19:48, 19 March 2025 (UTC)

    I so want to stand outside Randall's office holding up {{citation needed}} for not giving an actual citation on the title text. 162.158.175.159 20:07, 19 March 2025 (UTC)

    We should start using ares as a common unit of measure. https://www.britannica.com/science/are 172.69.135.15 20:09, 19 March 2025 (UTC)

    We have done, some still do: Hectare#Are 172.70.163.70 21:20, 19 March 2025 (UTC)
    I really hate when people use "metric ton" instead of the correct megagram (Mg). SDSpivey (talk) 12:28, 20 March 2025 (UTC)

    The area of eaten vegetation is all well and good, but we really need to know the total volume consumed. In barn-megaparsecs, ideally. 172.71.241.89 21:26, 19 March 2025 (UTC)

    I just got the mail notification for this and the previous comic at the same time. I would say that Randall forgot to send out the previous one before, but surely this is automated, so I guess something went wrong with that setup. Fabian42 (talk) 00:01, 20 March 2025 (UTC)

    Percentages? Could we not? Can't we use multiplication factors instead? 172.70.230.38 21:30, 20 March 2025 (UTC)

    I really want to know what the 80-fold error was now Thief (talk) 10:54, 20 March 2025 (UTC)

    Here's an error in chemical names instead--Diphenhydramine (Benadryl) occasionally appears as diphenhydrazine, which (if it existed) might be a rocket fuel. Google for it, just for scientific fun. Rocket flight to Australia, now in your local pharmacy! 172.69.71.207 11:38, 20 March 2025 (UTC)
    There's a dangerous point of confusion between diphenhydramine and dimenhydrinate (Gravol). In medical contexts, the two are often given differing capitalizations to emphasize the differences between the words, to reduce the risk of patients being given the wrong one (e.g. dimenhyDRINATE vs. diphenhydrAMINE). BunsenH (talk) 14:51, 20 March 2025 (UTC)
    Realistically, if "diphenhydrazine" is diphenylhydrazine, it would be a much poorer rocket fuel than hydrazine. It's a known substance, used in chemical manufacture, melting point a bit above the boiling point of water, moderately nasty in terms of health risks. Flammable, yes, but not particularly exciting. BunsenH (talk) 15:05, 20 March 2025 (UTC)
    A particularly vexing origami issue.172.71.178.156 14:42, 20 March 2025 (UTC)
    80-fold error is nothing. I regularly see news articles wrong by factor of 1000, as a result from incorrect translation between languages using long and short scales.

    The land area of Australia really depends on when it last rained. There are very large areas that will be completely dry prior to rain that will be flooded after. SDSpivey (talk) 12:28, 20 March 2025 (UTC)

    I used the area from the CIA world factbook that included both land and water area. TomtheBuilder (talk) 18:26, 20 March 2025 (UTC)

    You should never write `square cm`, etc. but always `cm²`. Same for seemingly standard abbreviations: Don't write `ccm` for "cubic centimeter", but `cm³`. Even though, in spoken language "square centimeter" is correct. Another confusion can sometimes arise from not knowing that squaring or cubing binds less than the centi-/kilo-/... prefix. I.e., `cm³` is `(0.01m)³` not `0.01(m³)`. A liter (`l`) is `0.001m³` or `1dm³ = (0.1m)³`. A milliliter is `0.001l = 0.000001m³ = (0.01m)³ = 1cm³` --172.69.109.92 12:48, 20 March 2025 (UTC)

    All you need to remember is:
    "X units square" = a square of X units = (X units)² = X² (units²)
    "X square units" = X times a square unit = X (units²) = (√X units)²
    "X prefixunits" is (X × prefix) units, for the sake of preserving the units so "7 decagrammes" is "70 grammes" (or 0.07 kg, if you need that, for whatever reason) [though not to be confused with "grammage", which is "grammes per square metre"!] and "450 nanometres" is "450×10-9 metres" or "4.5×10-7 metres" 172.69.195.62 14:26, 20 March 2025 (UTC)
    Getting a bit off-topic, but is "grammage" really a unit or rather a quantity? I.e., "Grammage measured in gram(mes) per square meter", same as "mass in kilogram". Or would you say "Standard office paper has 80 grammage(s)?" (Disclaimer: I'm not a native English speaker, so honest question). --172.69.109.89 15:33, 21 March 2025 (UTC)
    More on-topic: I would never say "X units square" ("5 meter(s) square"), mostly because it sounds weird and unclear. But YKMV (your kilometrage may vary) --172.69.109.87 15:43, 21 March 2025 (UTC)

    I don't see that the table is too wide to display (on a "normal" full-hd screen). But I agree that more than ~3 significant digits are kind of useless. We could even add a column with the unit "area of Australia" --172.71.160.61 16:19, 20 March 2025 (UTC)

    Another point: The percentage "gain" column is mostly wrong, e.g. from 1 to 144 you have a "gain" of 143 or 14300% not 14400% (I'd rather show a gain factor though). --172.71.160.60 16:18, 20 March 2025 (UTC)

    There are other mistakes being made in communicating the factoid. One is called out by the comic itself (namely the defoliation of Australia in particular rather than a nondescript Australia-sized area of land), but there are others too. For example, it has become more ambiguous whether the factoid is about a single insect or the insect as a species. It'd be somewhat believable if you're talking about an entire species eating that much per day. The other miscommunication is that it's gone from talking about grass to foliage in general, but foliage in general can vary in density a lot more than a patch of grass, creating additional inaccuracies. 172.70.47.53 17:57, 20 March 2025 (UTC)

    "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." Isn't that what explainxkcd is for? 162.158.154.5 15:41, 21 March 2025 (UTC)

    Yes! That is the ENTIRE reason I came to this page! 172.68.164.68 06:36, 29 March 2025 (UTC)

    I was playing, originally with the following, but gave it up when the current table was inserted. Given the complaints about explaining the colours, etc, and a few problems with the one we see (no way of differentiating when it becomes a "square of side BLAH" instead of "BLAH square units", etc), I thought maybe someone might want to give it a revamp. - Note that I took inspiration from the "Template:Diagonal split header" that exists on actual Wikipedia, but flipped it (unfortunately, flipped it so that one defines Bottom Right colour then Top Left colour, but still gives Top Left text before Bottom Right text, which was the next thing on my list of editing to do). And in the Key I had intended to also demonstrate a value taken from the Bottom Right (X units²) of one row being misused as a Top Left (X x X unit square) 'feed'. One could still apply the colours for how much of an increase (or, occasionally, mild-decrease) of each step (here, based upon the definitive value of that step, vis-a-vis the prior one(s), not the conversion, which is mostly a fairly accurate and consistant-to-the-statement conversion) there was, but the general trend of a rise in cumulative factor can basically be read easily enough. Oh, and check the figures, maybe. I hand-copied them, for reasons best known to my past self, rather than autogenerated the entire table lines from the same thing that I used to organise the figures I had calculated. Other, non-numeric errors in transcribing/non-consistent formattings may also have slipped in.

    For what it's worth...
    Step Source
    Tells     		From
    To     		Step
    factor     		Cumulative
    factor     		Centimetre Inch Foot Metre Acre Hectare Kilometre Mile Australia
    X cm
    side

    X cm²
    X in
    side
    X ft
    side
    X m
    side

    X m²
    X km
    side
    X mi
    side

    1 Megan
    Cueball     		sq. of in or in²
    either     		1 1
    2.54

    6.45
    1
    8.33×10-2

    6.94×10-3
    2.54×10-2

    6.45×10-4
    		 1.59×10-7 6.45×10-8
    2.54×10-5

    6.45×10-10
    1.58×10-5

    2.49×10-10
    		 8.39×10-17
    2 Cueball
    Ponytail     		in²
    cm²     		0.930 0.930
    2.45*

    6
    (6.45)
    1
    8.33×10-2

    6.94×10-3
    2.54×10-2

    6.45×10-4
    		 1.59×10-7 6.45×10-8
    2.54×10-5

    6.45×10-10
    1.58×10-5

    2.49×10-10
    		 8.39×10-17
    3 Ponytail
    Hairy     		sq. of cm
    (sq. of in)
    cm²     		6 5.58
    6

    36
    2.5
    (2.36)

    6.25*
    0.197

    3.88×10-2
    6×10-2

    36×10-3
    		 8.90×10-7 3.60×10-7
    6×10-5

    3.6×10-9
    3.73×10-5

    1.39×10-9
    		 4.68×10-16
    4 Hairy
    unknown     		sq of cm
    ft²     		36 201
    36

    1300
    14.2

    201
    >1*

    >1
    (1.40)
    0.36
    0.13
    		 3.20×10-5 1.30×10-5
    3.6×10-4

    1.30×10-7
    2.24×10-4

    5.00×10-8
    		 1.69×10-14
    5 unknown
    unknown     		sq. of ft or ft²
    cm²     		0.719 144
    30*

    900
    (929)
    12

    144
    1
    0.305

    9.29×10-2
    		 2.30×10-5 9.29×10-6
    3.05×10-4

    9.29×10-8
    1.89×10-4

    3.59×10-8
    		 1.21×10-14
    6 unknown
    unknown     		cm²
    ft²     		872 1.26×105
    900

    8.1×105
    354

    1.26×105
    30
    (29.5)

    900*
    9

    81
    		 0.02 8.10×10-3
    9×10-3

    8.1×10-5
    5.59×10-3

    3.13×10-5
    		 1.05×10-11
    7 unknown
    unknown     		sq. of ft
    ft²     		1.03 1.30×105
    914

    8.36×105
    360

    1.30×105
    30

    900
    9.14

    83.6
    		 2.06×10-2 8.36×10-3
    9.14×10-3

    8.36×10-5
    5.68×10-3

    3.23×10-5
    		 1.09×10-11
    8 unknown
    unknown     		sq. of ft
    acres     		900 1.17×108
    2.74×104

    7.53×108
    1.08×104

    1.17×108
    900

    8.10×10-5
    274

    7.53×104
    		 18.6 7.53
    0.274

    7.53×10-2
    0.170

    2.91×10-2
    		 9.79×10-9
    9 unknown
    unknown     		acres
    (via hectares)
    m²     		1.08 1.25×108
    2.84×104

    8.09×108
    1.12×104

    1.25×84
    933

    8.71×105
    283*

    8.00×104
    (8.09×104)
    		 20 8
    (8.09)
    0.284

    8.09×10-2
    0.176

    3.13×10-2
    		 1.05×10-8
    10 unknown
    unknown     		sq. of m
    sq. of km     		79,000 9.92×1012
    8.00×106

    6.40×1013
    3.15×106

    9.92×1012
    2.62×105

    6.89×1010
    8.00×104

    6.40×109
    		 1.58×106 6.40×105
    80

    6.40×103
    49.7

    2.47×103
    		 8.32×10-4
    11 unknown
    unknown     		sq. of km
    mi²     		1 9.92×1012
    8.00×106

    6.40×1013
    3.15×106

    9.92×1012
    2.62×105

    6.89×1010
    8.00×104

    6.40×109
    		 1.58×106 6.40×105
    80

    49.7
    6.40×103

    2.47×103
    		 8.32×10-4
    12 unknown
    Hairbun     		sq. of mi
    Australia     		2530 2.51×1016
    4.02×108

    1.62×1017
    1.58×108

    2.51×1016
    1.32×107

    1.74×1014
    4.02×106

    1.62×1013
    		 4.00×109 1.62×109
    4.02×103

    1.62×107
    2.50×103

    6.25×106
    		 2
    (2.11)
    13 Hairbun
    White Hat
    Danish
    Blondie     		Australia
    n/a     		0.950 2.38×1016
    3.92×108

    1.54×1017
    1.54×108

    2.38×1016
    1.29×107

    1.66×1014
    3.92×106

    1.54×1013
    		 3.80×109 1.54×109
    3.92×103

    1.54×107
    2.44×103

    5.94×106
    		 2
    Key to cell hues
    Spoken Values Unspoken
    Values
    'Fact' value (Additional) Conversion
    Exact Exact Exact Calculated
    (3SF)
    * = from Rough
    Rough
    (Better?)     		Rough
    (Better?)     		Rough
    (Better?)
    I more or less left it at the stage where I was considering adding and removing a few of the enforced line-breaks to make the rows of equal height (thus consistent with the diagonals), and also refine the positions of the align-left/align-right texts a bit better. But I'm not sure I'd want it, as it is now, actually replacing the current version. Maybe could act just as inspiration for the corrections necessary to the one we have noe, instead.... 172.70.58.46 00:19, 25 March 2025 (UTC)
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