3038: Uncanceled Units

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Uncanceled Units
Speed limit c arcminutes^2 per steradian
Title text: Speed limit c arcminutes^2 per steradian

Explanation[edit]

Another of Randall's pet peeves, this comic expresses disapproval of units that could be mathematically simplified (in other words, the 'uncanceled' of the title refers to mathematical cancellation, not cancellation by a body, like how SI supplanted the CGS system with MKS).

White Hat is presenting a refrigerator to Cueball, saying it uses 3 kWh per day. This is a common and useful way to report power usage. But mathematically, the units can be simplified because there are two time units that cancel each other:

3 kWh per day = 3 kW * 1 hour / 1 day = 3 kW * (1 hour / 24 hours) = 0.125 kW = 125 W

This gives the (average) power usage in watts (a unit for the rate of energy transfer, equal to 1 joule per second).

The reason people would use "kWh / day" without simplifying the unit is that kWh is a commonly used unit for energy, and it's often viewed as a base unit even though it's composite (1 kWh is the amount of energy consumed by one kilowatt of power usage over one hour, and is equal to 1 kJ/s * 1 h = 3600 kJ). It's the unit in which energy consumption is typically reported and in which bills are calculated, so it's more familiar to the average consumer, and giving the power usage in kWh / day makes it easier for the consumer to understand how much money it will cost them to run per day. Also, "per day" makes it clear that this is the average power usage rather than the maximum power usage (they are different because refrigerators cycle on and off throughout the day). But mathematically, "kWh / day" is inelegant, because it uses power (which is already a measure of energy per time) multiplied by a time unit then divided by another time unit.

Cueball (probably representing Randall) sardonically wonders whether the refrigerator would fit in his kitchen, since the ceiling is only 50 gallons per square foot high. This is clearly an abnormal and unhelpful way of reporting height. This unit turns a normal measurement of height (feet and inches in the US; meters and centimeters most other places) into a weird collection of uncancelled units. Gallons can be transformed to cubic feet (1 US gal = 231 in3), which can be divided by the square feet, yielding a ceiling height of around 6 feet 8 inches, or 203.7 cm. (Using imperial gallons [1 UK gal ≈ 277.42 in3], the height is roughly 8 feet, or approximately 244.7 cm.) This is intended to lampoon the use of both non-metric and uncancelled units by showing how odd things become if they're generally used.

The exact ceiling height in feet, assuming the US gallon is used, can be calculated as:

50 gallons per square foot = 50 gal * 231 in3/gal * (1/12 ft/in)3 / 1 ft2 = 6.68 ft = 6 ft 8 in

This can be understood as "the height such that every square foot of ceiling has 50 gallons under it." what if?: Droppings also covers strange instances of unit cancellation, including a measure of volume per distance converted to area; similar to Cueball's measure of volume per area representing a distance (the height of his ceiling).

A common source of unit drama occurs between lay people who are looking for everyday practicality and science/engineering types who are inclined towards formalized mathematical operations. For example U.S. customary units which support many divisibility rules (1 foot = 12 inches; 1 inch = 72 points = 1440 twips; 3 feet = 1 yard; 2 yards = 1 fathom; 22 yards = 1 chain; 10 chains = 1 furlong; 1 mile = 5280 feet; 1 league = 3 miles) versus metric units which prioritize base 10 scales. In this case, telling the average customer the energy use in joules per day or average consumption in watts would require them to perform more complicated conversions to get to the figure they actually care about — the actual cost per day. White Hat could just give this cost figure directly, but does not know what every customer pays for electricity (an explicit yearly cost estimate would be included on the government-required energy efficiency label).

In the title text, a speed limit is given as c arcminutes2 per steradian, where c is presumably the speed of light in a vacuum — 2.998×108 m/s (meters per second) or 186282 mi/s (miles per second). A steradian (sr) is the SI unit for solid angle, subtended by a section of a sphere (like a radian is a unit of angle subtended by a section of a circle). A square arcminute is also a unit of solid angle, equivalent to a section of a sphere of 1/60 of a degree by 1/60 of a degree. There are ((1/60)*(π/180))2 = 8.462×10-8 sr in a square arcminute. Then multiplying by c gives a speed of 56.75 mph (probably 55 mph, based upon the 'traditional' US speed limit, before rounding errors in the reverse direction), or 91.33 km/h, showing that you can combine an outrageously high speed with two unnecessary units that cancel each other to form a normal road speed.

It is worth noting that, although some of these examples are ridiculous, there are cases where uncancelled units can be helpful to understanding the concept. For example, while the Hubble Parameter can be expressed as 2.17132212 × 10-18 Hz, expressing it as 67 km/s/Mpc directly relates the quantity to how it is measured and its natural interpretation. Another example would be fuel efficiency in cars, where mi/gal and km/l technically simplify to 1/area, but expressing it in volume and distance allows easy estimations of range and travel cost, while mm-2 or in-2 would require significant unit conversions. Another example might be the units of the gravitational constant G, ~6.674 × 10-11 m3/(kg×s2), which might be written as (m/s2)/(kg/m2), although this only involves unjumbling rather than uncancelling units.

Transcript[edit]

[White Hat and Cueball are standing to either side of a refrigerator. White Hat is lifting one hand up to touch the side of the fridge. The fridge has two compartments, with two doors that open to the top compartment and one bottom compartment, a drawer. The top left compartment has a tall handle on its right, the top right compartment has a tall handle on its left, and the bottom compartment has a long handle on its top. The top left compartment has an oval shape on the top and a paper attached, both with unreadable text. There is also a small square note in the top right corner and an oval shape on the side of the fridge above White Hat. These also have unreadable text.]
White Hat: This fridge uses only 3 kWh per day!
Cueball: But will it fit in my kitchen? The ceiling there is only 50 gallons per square foot.
[Caption below the panel:]
Pet peeve: Uncanceled units


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Discussion

DUDE I'M STILL IN SCHOOL RN, WHAT? (also, the joke is that energy is power*time, so kWh is kJ/s... in an hour Caliban (talk) 13:27, 15 January 2025 (UTC)

I guess not every comic can be a winner. Talking about an appliance using a certain amount of kWH per day is clear and normal. Power gets billed by the kWh, not the Joule. While technically not wrong, wanting "cancel" a sub-part of the commonly-used energy unit kWh and leaving it in deliberately-obscured units most people are less familiar with is the sort of insanity I'd more expect from White Hat than Cueball. 172.70.35.171 13:39, 15 January 2025 (UTC)

Maybe that is a meta-joke? To frame kWh/day as something crazy by giving that line to whitehat --Lupo (talk) 13:52, 15 January 2025 (UTC)
Even if the consumer is technically more familiar with the watt, for example from lightbulbs, they absolutely have no idea how much a watt costs on their monthly bill, so the salesperson is unquestionably correct to quote the use in kwh/time. 172.70.210.130 05:11, 19 January 2025 (UTC)
There's a difference between instantaneous power draw, and the total "volume"(/area, really) of power over time. Though a fridge is "always on", it is still only irregularly at full-draw. But, to the power company (or to the gas company, who will generally give a kWh measure of 'energy taken from the network'), they don't (generally) care whether you used twice as many kW over half the time or half as many over twice the time, within any given total billing period, even if it affects what you think. 172.70.163.46 14:39, 15 January 2025 (UTC)
Using joule as if it was an everyday unit of energy would be weird but I don't agree that watt is crazy. It's a normal unit of energy consumption that does mean something to people, e.g. 1000W microwave, 100W (incandescent) light bulb. Don't get me wrong kWh/day is also useful to translate it to your energy bill, but I do feel slightly uncomfortable every time I see that time divided by time :-) Mtcv (talk) 14:40, 15 January 2025 (UTC)
I don't think the complaint is that it's unclear, it's that Cueball/Randall instinctively wants units simplified - as they would be in a science context rather than a useful-for-normal-people's-everyday-needs context. 108.162.238.183 02:40, 16 January 2025 (UTC)
Yes, it is normal, but to people who know what it means it hurts to look at. kWh are a measure of energy that is technically SI-friendly and at a useful scale, but from an scientific perspective there isn't a great reason (to my knowledge) other than convention to not just use megajoules (1 kWh is 3.6 MJ). That on its own bothers me, and probably Randal based on a lot of his other comics. The added complaint here is that by making them per/day it is back to a measure of power (which kW measure) Stardragon (talk) 23:34, 16 January 2025 (UTC)

This is especially funny with US units. My car needs about 5l/100km, or 0.05mm². Now I am wondering how many ft^(-2) my car does... --Lupo (talk) 13:49, 15 January 2025 (UTC)

You make a good point about the units (at least in one instance). Shouldn't the reduced units for fuel economy be inverse area? Effectively, it is a measure of the distance the vehicle could travel while consuming a column of fuel with a specific height and specific top (or bottom) surface area. Or, The better the fuel economy, the less the surface area that is necessary to move a specific distance. SammyChips (talk) 20:41, 15 January 2025 (UTC)
It depends on what the original unit is. In my country (Germany) we measure it in volume/distance, which would reduce to area. North American convention is in distance/volume which would reduce to inverse area. Good thing about distance/volume is that "high number = good". However I think outside of escaping from a nuclear disaster or in a zombie apocalypse it isn't a really helpful thing to know. Because how often do you know "I got x amount of fuel. Wonder how far I can get." But you will likely be in the situation where you quickly want to see "How much fuel do I need to get to place x which is y distance from here". --Lupo (talk) 21:57, 15 January 2025 (UTC)
how often do you know "I got x amount of fuel. Wonder how far I can get." Quite often, because the question I'm really asking is whether I can get where I'm going with some margin built in before I need to refuel my car. When I do refuel or recharge the car, I'll go to 100% of capacity. I just want to know whether I have to do that now or if I can wait and do it later because later would be more convenient. The only time I want the number the other way is when I'm buying a car and want to make it as efficient as possible. Once I have it, the amount of fuel I need isn't going to change.Yttrium (talk) 09:02, 16 January 2025 (UTC)
Mhh... probably a question of what one is used to. If I need to go 400 km, and I know my car uses 5l/100km, I just multiply 4*5 to see that I need 20l, and will know if what I have is enough or not. But I guess with mpg you can do a just as easy calc: If my car gets 50mpg (roughly 5l/100km) and I have 5 gallons (roughly 20l), I can go 50*5=250 miles, which is roughly 400km. My nitpick is: My car, and I think all cars I ever drove just shows me a dial from empty to full. Knowing how much "full" is, I can estimate how much gas I have, while my GPS will tell me a pretty exact number of km I need to go. So if I am fuelling up on a monday morning (where gas tends to be more expensive in my area than on other times), or fuel up right before I get my next salary, I might just put in as much as I need right now. But yes, maybe/probably it is mostly a thing about habits and what you are used to. And might be more of an European issue, since fuel is basically free in North America in comparison. So I guess everyone just fuels up fully all the time, but has to be cautious to reach the next gas station when travelling through the more sparely-populated areas...--Lupo (talk) 10:19, 16 January 2025 (UTC)
More usefully imagined as the front (or back) end of a horizontal column (or, twisting as it may, a pipeline) that traverses the journey made by the vehicle. As if (instantaneous variations excepted) you consume precisely the fuel that your vehicle passes 'through/around'. 141.101.76.92 20:45, 15 January 2025 (UTC)
Yeah. Maybe we should express fuel consumption in terms of the speed fuel needs to be drawn through a standard fuel line. SammyChips (talk) 21:01, 15 January 2025 (UTC)

fridge 172.70.126.147 14:22, 15 January 2025 (UTC)

The late Sir David MacKay wrote an excellent book, Sustainable Energy – without the hot air (which is available free online). On this page he talks about the units he uses in the book: kWh for energy ("one unit") and kWh/day for power - becuase it's simple for lay-people to understand - how many units does this appliance use per day. It's a good book if any of you are interested in sustainable energy (although it was written in 2008, so some bits might be out of date by now) 172.70.85.33 (talk) 14:33, 15 January 2025 (please sign your comments with ~~~~)

If anyone's curious, I found an online gallons per square foot calculator: https://www.omnicalculator.com/construction/gallons-per-square-foot 172.71.223.6 15:54, 15 January 2025 (UTC)

The answer to Cueball's question is likely NO in the US and YES in the UK, due not just to gallon size but also fridge size (a model like that is a particularly large fridge, when I bought one 10 years ago going for the smallest available I had to modify my cabinet above the fridge as there wasn't one less than 6'8"- the fridge hole was 6' previous).Seebert (talk) 16:02, 15 January 2025 (UTC)

I disagree with this comic, and I think the final paragraph in the explanation about Hubble's constant best explains why. Beanie talk 15:57, 15 January 2025 (UTC)

It doesn't make any sense to 'disagree' with an observation.141.101.98.245 09:36, 16 January 2025 (UTC)
"[My] Pet peeve" so the comic is expressing an opinion 172.68.3.36 03:38, 18 January 2025 (UTC)

Hubble's constant can be expressed in reciprocal seconds, but it should not be expressed in Hz. Hz are reserved for repeating phenomenon. There is insufficient evidence of a cyclic universe. Using Hz could be an attempt to insert an unwarranted assumption into cosmology. This type of subtle "propaganda through choice of units" happens fairly often. Changing units can give a different perspective. Usually this will be through simplification because there is no algorithmic method to choose useful complex units.172.71.167.69 18:32, 17 January 2025 (UTC)

So you think we should represent it with becquerels? guess who (if you desire conversing | what i have done) 02:06, 22 January 2025 (UTC)

Technically, kWh should be written as kW⋅h or kW h, because it literally means "kilowatts multiplied by one hour", not "kilowatts per hour" as many people assume. However, almost nobody writes it correctly. (kW/h is sometimes also seen, but egregiously incorrect.) Also, particularly now that electric vehicles are becoming more popular, people often get confused between kW and kW h. The car can charge at a peak or average rate expressed in kW, but energy billed by a charging service provider is expressed in kWh. People frequently either add or remove the "h" incorrectly because they don't understand the difference. In some places like India, a kilowatt-hour is simply referred to as a "unit" to avoid confusion. In my opinion, it was an enormous mistake to use kWh when we could be using mJ instead, which I think is probably something close to the point Randall may have been trying to make. Anyway, I wasn't sure if there was a place for any of this random trivia in the article itself, but feel free to use it. Equites (talk) 17:11, 15 January 2025 (UTC)

No!. TF?. ms is meter times seconds, m/s is meter per second. There is NOTHING wrong with kWh, it literally means kW times hours, and CANNOT mean anything else. kW per hour would be kW/h.. 172.71.160.34 12:41, 16 January 2025 (UTC)
Technically, the SI would have you write m s for meter-seconds and ms for milliseconds. Thus, similarly, it should be kW h for kilowatt-hours, not kWh. It is unambiguous either way, but the standard is the standard. But that is a totally bizarre thing to get hung up on. Also, Equites's suggestion to use millijoules instead was maybe not well thought-out. 172.68.15.234 17:45, 16 January 2025 (UTC)

Relevant XKCD… I mean relevant YouTube video: "Cursed units" 1 and 2: https://www.youtube.com/watch?v=kkfIXUjkYqE https://www.youtube.com/watch?v=Zg7xe8MkJHs Fabian42 (talk) 17:31, 15 January 2025 (UTC)

Highly relevant, in fact. The first video referred to the kilowatt-hour as "cursed", which became a highly polarizing issue in the comments, something that was addressed at the beginning of part 2. Assuming these responses weren't cherry-picked, I get the impression that there are a lot of people on both sides of this. It seems like the same kind of thing we're seeing in this very comment section. ISaveXKCDpapers (talk) 18:10, 15 January 2025 (UTC)

I always wonder why people here prefer liter/m^2 for the amount of rain. Where the same number as mm is way easier to imagine. 172.68.50.99 18:14, 15 January 2025 (UTC)

At first, I was wondering if you would have rather had it in microliters/mm^2, but you meant the column height of the rain, like inches are used in the US. Along the line of L/m^2, something like mL/cm^2 might be nice considering the density of water, although the value also would be different by a factor. SammyChips (talk) 20:51, 15 January 2025 (UTC)
That's the neat thing about the metric system, they are trivially simple to convert. 1l/m² is exactly 1mm. The fact that the meteorology uses the former just stems from the fact that that's how they measure it. The catch the rain on an area of 1m² into a beaker that contains some volume which is measured in liters. What annoys me though, is that noone seems to be talking about how terribly inefficient the fridge in the comic is. Mine only needs a tenth of the one that Whitehat tries to sell, and that's not even particularly good. -- 162.158.203.28 (talk) (please sign your comments with ~~~~) 21:21, 15 January 2025 (UTC)
UK measurements, once it gets to weather reports/forecasts, tend to be in millimetres (or centimetres, where more for the layperson who don't need mm-resulution; or occasionally recast as 'old money' inches, with really bad rain events summarised in relation to whole feet), which is implicitly the depth to which any area would be filled (in a case where large catchment + funnelling valley situation is concerned, suffering from the run-off, might be reported as "equivalent to N feet of rain", down where the bad effects get concentrated, but this is not a meteorological measure as such).
Not sure I've ever seen volume/area as an end-result figure (might be relevent as an intermediate for measurement/calculation, especially when discussing the funelling effects of the given local geography), but of course it's trivially relatable.
Density of water would only figure in from replacing litres with kilogrammes (litres are 1/1000th of metres³ and any m² is 10,000 times the cm² (or millilitre), so a factor of 10 between L/m² and mL/cm²; divide L to mL by 1000, times m² to cm² by 10,000, => 10x) but I always find it useful to know that three 2L bottles of pop are (very close to, going by the nominal water content alone) 6kg... makes me feel better about lugging the weekly shopping home, where these might be the single most significant part of the weight. More usefully than cross-converting into length-cubed measure. ;) 141.101.98.69 21:42, 15 January 2025 (UTC)

Isn't the point that KwH/day can be simplified to Watts (an average perhaps, but still) 162.158.41.72 (talk) 21:24, 15 January 2025 (please sign your comments with ~~~~)

Yes, the joke seems pretty clearly about watts or kilowatts, not megajoules. Using megajoules doesn't result in any units being canceled; the denominator remains "/day". BatmanAoD (talk) 23:52, 15 January 2025 (UTC)

If the argument for kWh/day is that it's easy for the consumer to understand how it will affect their electricity bill – then kWh/month would be the right choice, because I doubt anyone receives an electricity bill every day. But the salesman prefers 3 kWh/day because it sounds like a smaller number than 90 kWh/month. And of course, if electricity bills were written in joules instead of illogical watt-hours, then MJ/month would be the easiest for the consumer. 162.158.134.90 (talk) 22:31, 15 January 2025 (please sign your comments with ~~~~)

Per-month is tricky. You seem to assume month=30 days, when it can be 28-31 and is only 30 days a third of the time. Per quarter(-year) is a bit more consistent, less fractionally variant and closer to most utility bill frequencies as well, if you're looking for something not as eye-wateringly frightening as an annual estimate (which 'only' varies every 4.1237... years, on average). 172.70.163.47 00:21, 16 January 2025 (UTC)
"Per-month is tricky. You seem to assume month=30 days, when it can be 28-31..." My electric bill for December 2024 is 33 days. The company closes the book when it is convenient, not per some calendar. --PRR (talk) 05:22, 16 January 2025 (UTC)
Which is why electric consumption per month is even more tricky. --Lupo (talk) 06:33, 16 January 2025 (UTC)
It's still per some calendar. Just a calendar

of the electric company, that you're not privy to.141.101.98.245 09:36, 16 January 2025 (UTC)

facepalm and yes you are right, if you include that the meter reader may be a week late because of healing from pet related off work time from reading an electric meter in a back yard. And usually the person who turns the reading into a bill isn't sick. ... Pretty sure my electric company really loves the "phones home every 83 seconds" new meter they installed a few yag. The old and new meters are pretty much a wall wart with a screw on shield. I was surprised by no dead spiders in the socket on the replace.172.70.34.72 00:23, 18 January 2025 (UTC)
It's an average. We're not talking specifically about February. You could multiply by 365.24/12 and get 91.31 kWh/month on average – but there's only one significant figure in 3 kWh/day. White Hat doesn't say 3.000 kWh/day. You have to round 91.31 to 90 to avoid false precision.
The stated average is an estimate based on assumptions about how much you'll fill the fridge, how often you'll open the door, how long you'll leave the door open, the room temperature in your kitchen, how much surrounding cabinets will restrict air flow across the condenser, et cetera. The combined uncertainties make it meaningless to state a highly precise power consumption. The length of the month is just one of many sources of variation. 162.158.134.90 10:40, 16 January 2025 (UTC)
Ahem... "multiply by 365.2425/12". As anyone with a fridge at least 125-years-old would appreciate... ;) 141.101.98.178 12:23, 16 January 2025 (UTC)

I suspect this comic is inspired by the much more common pet peeve of incorrect/nonsensical units, frequently encountered in similar contexts. I'm so used to hearing kWh mistakenly written simply as kW, that I initially misread and assumed that's what the comic is about. That's a particularly common example, where you'll hear battery capacities listed in kW, or instantaneous power described in watt-hours. PotatoGod (talk) 09:53, 16 January 2025 (UTC)

Calories vs. calories, also... ;) 141.101.98.178 12:23, 16 January 2025 (UTC)
Yeah, get it straight people! Instantaneous battery discharge rate should be in some scale of watt-hours per second :P All this hassle because apparently nobody likes Joules or Coulombs as a unit. Besides the obvious unit cancelation thing, why would kilowatt-hours be more of a thing than watt-seconds anyway, since they are the same general order of magnitude? -- SammyChips (talk) (please sign your comments with ~~~~) SammyChips 16:05, 17 January 2025 (UTC)

It could be worse.. I keep seeing TVs marked in kWh per 1000 hours... That is just insanity pure and simple.. It is in fact Watts!!!172.71.160.34 12:38, 16 January 2025 (UTC)

This is even some kind of a "standard", officially. See first image in here: https://ec.europa.eu/commission/presscorner/detail/en/ip_21_4484
Also, world power consumption is almost exclusively represented in TWh per year, because TW is obviously not a thing. 172.68.50.6 13:42, 16 January 2025 (UTC)
That whole kerfluffle is mentioned in the "Cursed Units 2" video linked above. Admiral Memo (talk) 01:58, 17 January 2025 (UTC)

Can I be the obnoxious arse that points out that a 125W fridge will NOT be pulling 3kWh (or 3 units?) per day? Fridges run a compressor which makes the cold happen (via science and magic) and when there's enough cold in the box, it'll click off until cold is lacking. The durations will depend on ambient temperature, however observing my (oldish) fridge, it seems to run for about fifty seconds every four or five minutes. 141.101.69.92 18:45, 16 January 2025 (UTC)

Fridge is actually heating device: it heats up your kitchen by pumping the heat from inside to outside. -- Hkmaly (talk) 22:32, 16 January 2025 (UTC)
It's actually a heat pump, moving heat from one location to another. Whether a heat pump is a heating device or a cooling device depends entirely on your perspective. 172.69.246.148 23:17, 17 January 2025 (UTC)
It heats your kitchen more than it cools the inside. QED. -- Hkmaly (talk) 09:13, 30 January 2025 (UTC)

There is actually a good reason to differentiate between Wh/h (energy over time) and W (power): Non-constant consumption. If the fridge consumes 3kWh/d, its compressor will be rated in the 300-400W nominal range (the thermostatic controller will cycle the compressor on and off; for a modern fridge-freezer combination, a typical duty cycle would be in the 25-30% range). The unit nameplate will say "400W" because that's the rated power the electrical installation will have to be designed for (how many of these fridges can you put on a 20A breaker etc.). This is only determined by the physical properties of the compressor motor. The energy consumption additionally depends on insulation, internal space of the cabinet etc. etc. and only makes sense as a time average (due to the intermittent operation of the compressor). Not sure about US rules, but here in Europe, there's a standard energy class label for fridges which specifies kWh/a as a primary means of comparison. (Averaging over a year has the advantage that you can test against a standardized profile of ambient temperature change between summer and winter). Ogehrke (talk) 21:28, 16 January 2025 (UTC)

Instead of overcomplexificationing the units, all you need to do is write "average power consumption" on the label. Also, none of that is an argument against using joules per year instead of joules per second times hour per year.

The explanation incorrectly states that fuel efficiency in the metric system is measured in km/l. It's not. It's measured in l/km, so it reduces to area, not 1/area.172.71.182.77 22:40, 16 January 2025 (UTC)

I recall seeing a book in my youth about "understanding units" that included great things like viscosity and explanations for why E=mc² cancels units properly. But they got to gasoline consumption, and used the analogy that the "area" represented here is the equivalent of the area of an adjacent trough of gas that would have to be scooped up by your car to keep it running. Very interesting way of illustrating unit cancellation. RandalSchwartz (talk) 23:05, 16 January 2025 (UTC)

Am I the only one bothered by the low ceiling? I hate rooms where I can't stretch without bumping. I had to come here to make sure I hadn't miscalculated the ceiling height. DougM (talk) 00:21, 17 January 2025 (UTC)

Just assume that Cueball is using british gallons to further mess with the units. As the explanation that makes the room 2.44m which is a pretty standard - although still not very high - room height. --Lupo (talk) 06:29, 17 January 2025 (UTC)

Isn't there a joke about the salesman as well? Maybe I'm thinking too european, but kWh x 365 days = 1095 kWh/year seems ridiculously high to me. 172.70.247.41 (talk) 12:10, 17 January 2025 (please sign your comments with ~~~~)

German weather forecasts report rain as liters per square meter instead of millimeters. --172.69.109.87 12:55, 17 January 2025 (UTC)

re "there are cases where uncancelled units can be helpful to understanding the concept", something about mixing ratios could be added. E.g. 10g/kg and 10mL/L are both 1% ratios, but expressing them as uncancelled makes it clear that one is a ratio by mass and one is a ratio by volume. 172.70.208.76 21:12, 17 January 2025 (UTC)

also dosages for medicine. At least for pets it is often mg/kg. --Lupo (talk) 13:07, 18 January 2025 (UTC)
If a railroad company wants to build track across my farm, I want to know how many ACRES of good arable farmland I will lose PER MILE of track they build. Oh sure, you could tell me how many millimeters, or how many fathoms, furlongs, or light years, but doing so would only force me to convert it to something useful: how many acres per mile. 172.70.215.42 23:02, 25 January 2025 (UTC)
Sounds like you know how many miles "across your farm" is. If you've got a square/rectangular plot and you know the angle the track will go, edge to opposite edge (not clipping corners, not twisting or turning), then the result of the "acres per mile" of any given cut-across (more for a multilane highway, less(+temporary?) for digging a pipeline in, somewhere in-between for railway, depending upon any spread from the rail-bed for how much of a cutting/embankment they might need to add).
I think I'd rather work it out from the other direction. Tell me the effective (mean) width of the intrusive works, and then look at what path they're proposing to go over (what may be more important, even than the pure quantified footprint, is it it requires demolishing some or all of a building/utility feature - and what, if any, plans they have for bridges/underpasses/on-grade-crossings to unsever each side's now separate areas) and total area derives at least as easily as from a width*length calculation as for an (area/length)*length.
Being very near to a (first proposed, then vastly realigned, now totally cancelled) new railway project, myself, I studied the early/later proposals a lot (initially, it impacted some urban and rural bits of land quite near me, the revamped version went through other bits that I knew well and went so close to some new-build housing that some residents had their places compulsarily purchased with a view to having to be demolished, with neighbours and even others on the furthest edges finding their effective house-prices plunging to more than 50% loss in just the teo or three years since they'd been built as premium housing). Apart from just the total fuss of having a railway (intended to be) built across one's land, and the attendant construction-disruption, it seemed that both farmer and homeowner mostly had to concern themselves with the spread (temporary, during construction, and permanent once the true boundaries had been eventually been established) as the biggest factor, once the path was known to either cross or straddle your personal land-boundaries.
Or maybe I don't appreciate your own personal priorities. Perhaps you're thinking area/length ≈ compensation_factor, and you don't care how long/if it crosses, so long as the return from surrendering is commensurate against alternative schemes' compensating factors? But even that seems like it's be better discussed using $/acre, or similar measures. 172.70.85.116 01:03, 26 January 2025 (UTC)

I used to tell people I work 7.5 hours per day, but after reading this comic I'm going to switch to saying I work 0.3125 with no units. 172.70.162.36 22:48, 17 January 2025 (UTC)

Go the other way and add combinable units... 0.3125 Hertz-seconds. Or go really wild with the ratio. I'm sure you could work out how many "lumen per hectare-luxes" it would be (3125?)... 162.158.74.119 23:22, 17 January 2025 (UTC)