Editing 3001: Temperature Scales

{{comic
| number    = 3001
| date      = October 21, 2024
| title     = Temperature Scales
| image     = temperature_scales_2x.png
| imagesize = 740x535px
| noexpand  = true
| titletext = In my new scale, °X, 0 is Earths' record lowest surface temperature, 50 is the global average, and 100 is the record highest, with a linear scale between each point and adjustment every year as needed.
}}

==Explanation==
{{incomplete|Created by an EXPONENTIAL TEMPERATURE SYSTEM. Do NOT delete this tag too soon.}}

Since the invention of the thermometer, a number of different temperature scales have been proposed. In modern times, most of the world uses {{w|Celsius}} for everyday temperature measurements, as it is part of the {{w|metric system}} that has been widely adopted for official uses. A small number of countries (namely Liberia, the USA and its three associated free states in the Pacific) retain the US customary (or 'imperial') system, which uses the ''slightly'' older {{w|Fahrenheit}} scale (°F was initially defined in 1724, the general current form of °C was created in 1743). The other widely used temperature scale is {{w|Kelvin}}, which uses the same scale as Celsius, but is rooted at {{w|absolute zero}}, making it both useful in scientific calculations and easy to convert to and from Celsius. Even in countries that use Fahrenheit regularly, scientific measurements are typically done in Celsius and/or Kelvin.

The strip proceeds to compare these scales, and a number of others, on a scaled of "cursed"-ness. The joke is highlighting how strange and generally difficult to use many older proposed systems were. All of the listed scales are real, but may be considered obsolete to varying degrees. Please see also [[1923: Felsius]], a combination of  Fahrenheit and Celsius.

{| class=wikitable
! scope="col" | Unit
! scope="col" | Water Freezes
! scope="col" | Water Boils
! scope="col" | Notes
! scope="col" | Cursedness
! scope="col" | Explanation
|-
| {{w|Celsius}} || 0 || 100 || Used in most of the world || 2/10 || Celsius is defined (indirectly, these days, by way of comparison to Kelvin) so that the freezing and boiling points of pure water at standard atmospheric pressure are 0 and 100 degrees respectively. This (along with Kelvin) is considered the least cursed temperature system (at least from those where the ranking values make any sense), likely due to Randall's background. Notably it is still considered a 2/10, implying an inherent degree of cursedness for all systems.
|-
| {{w|Kelvin}} || 273.15 || 373.15 || 0K is absolute zero || 2/10 || Kelvin is a scientific unit of measure invented by {{w|Lord Kelvin}} that intends to use the same scale as degrees Celsius, but is offset by 273.15, in order to set the zero point at absolute zero (by way of using the {{w|Boltzmann constant}}, as of 2019). This is very practical for the math of thermodynamics, but unintuitive for non-expert users. Kelvin and Celsius are, by far, the most common units used in scientific measurements and calculations. Their utility and inherent logic is likely what makes them the least "cursed".
|-
| {{w|Fahrenheit}} || 32 || 212 || Outdoors in most places is between 0–100 || 3/10 || Fahrenheit is officially used in several countries across the globe, and unofficially in several others. It was derived in an era where factors of 360 were more popular in science than powers of ten, so water freezing and water boiling were calibrated to be 180° apart. In addition, Daniel Fahrenheit believed that pure water freezing was not worthy of the 0° benchmark and resolved to set 0° to the coldest possible temperature he could create: the freezing point of ammonium chloride brine. While modern scholars find these benchmarks arbitrary and outdated, it gained usage, primarily in Anglophone countries, likely due to the scale being considered intuitively useful for some common functions (the range roughly matches the typical span of weather conditions, for various ranges of climate, and the 100 point is quite near normal human body temperature, even though 90 was initially presumed to be this). While it was largely displaced by the Celsius scale, the US (Randall's home country) continues to typically use it. It is ranked as slightly more cursed than Celsius.
|-
| {{w|Réaumur scale|Réaumur}} || 0 || 80 || Like Celsius, but with 80 instead of 100 || 3/8 || A historical French system used in some places until the early 20th century. In modern times mostly used in cheesemaking. The rating (3/8) is a joke on the boiling point of water in standard atmosphere being 80 instead of 100 as it is in Celsius; converting this to an out-of-ten scale would give 3.75/10, labelling it as more cursed than Fahrenheit but less so than Rømer.
|-
| {{w|Rømer scale|Rømer}} || 7.5 || 60 || Fahrenheit precursor with similarly random design || 4/10 || Created by the Danish astronomer Ole Christensen Rømer in around 1702, while the Fahrenheit scale was proposed in 1724. Much like Fahrenheit, it uses the freezing point of ammonium chloride brine as the benchmark for 0°, and the scale is built with factors of 360 in mind with the boiling point of pure water at 60°. Like the Fahrenheit scale, the freezing point of pure water was not originally considered significant by Ole Rømer, but the scale was later updated to fix it to 7.5.  The scale is also the last common ancestor of Celsius and Fahrenheit, as Reuamur was inspired by it, and Celsius by Reamur, and Fahrenheit specifically wanted a Rømer scale with more steps to avoid using decimals.
|-
| {{w|Rankine scale|Rankine}} || 491.7 || 671.7 || Fahrenheit, but with 0°F set to absolute zero  || 6/10 || As the chart mentions, Rankine is to Fahrenheit what Kelvin is to Celsius, an absolute scale rather than a relative one. The scale is mostly obsolete, but is still occasionally used in legacy industrial operations where absolute temperature scales are required.
For unclear reasons, Randall uses "0°F" to describe absolute zero on the Rankine scale, when the actual measurement would be written as 0°R. Both reference points are also rounded to one decimal place (from .67 to .7).

Randall has shown disdain for this scale before, like in [[2292: Thermometer]].  This is slightly odd, given that it makes ''more'' logical sense than Fahrenheit, as its zero point is somewhere logical rather than being arbitrarily defined.
|-
| {{w|Newton scale|Newton}} || 0 || 33-ish || Poorly defined, with reference points like "the hottest water you can hold your hand in" || 7-ish/10 || Created by Isaac Newton, measuring "degrees of heat". The rating (7-ish/10) is a joke about the vagueness of the scale's definition.
|-
| {{w|Wedgwood scale|Wedgwood}} || –8 || –6.7 || Intended for comparing the melting points of metals, all of which it was very wrong about || 9/10 || Created by potter Josiah Wedgwood in the 18th century. The measurement was based on the shrinking of clay when heated above red heat, but was found to be very inaccurate. Randall has a typo, as the scale is called Wedgwood (''without the e''). 
|-
| Galen || –4? || 4?? || Runs from –4 (cold) to 4 (hot). 0 is "normal"(?) || 4/–4 || {{w|Galen}}, in his medical writings, is said to have proposed a standard "neutral" temperature made up of equal quantities of boiling water and ice; on either side of this temperature were four degrees of heat and four degrees of cold, respectively. The rating (4/–4) is a joke about the scale being defined between positive and negative 4, and could be interpreted as –100% cursedness, though it's not clear what negative cursedness would mean. Of course it is not actually clear what "cursedness" means, so maybe that is not an issue.
|-
| {{w|Celsius#History|''Real'' Celsius}} || 100 || 0 || In Anders Celsius's original specification, bigger numbers are ''colder''; others later flipped it || 10/0 || Most scales' temperatures can be indefinitely large, but have an absolute minimum temperature. By starting at a maximum value and counting down, this scale is indeed cursed, as nearly all possible temperatures (an indefinite range of them) will be negative. The rating (10/0) is a joke on the scale "flipping" the fixed points of modern Celsius. This might be interpreted as "infinitely cursed", or else just {{w|NaN|Not a Number}}.
The original logic was that zero could be easily calibrated to the height of a column of mercury at the temperature of boiling water, and further measurements then made of the amount it ''reduced'' in height under cooler conditions. This direction 'survives' in the historic {{w|Delisle scale}}, which predates (and arguably helped greatly inspire, though with a different factor) the classic version of °C. The version originally used by Anders was only 'corrected' posthumously, but nobody seemed bothered enough to do the same with Delisle's scale.
|-
| [https://physics.stackexchange.com/questions/459851/john-daltons-temperature-scale#459863 Dalton] || 0 || 100 || A nonlinear scale; 0°C and 100°C are 0 and 100 Dalton, but 50°C is 53.9 Dalton || 53.9/50 || {{w|John Dalton}} proposed a logarithmic temperature scale. The scale is defined so that absolute zero is at negative infinity, with the exponent chosen to match Celsius at 0 and 100. While Dalton temperature is defined for all positive and negative numbers, the nonlinear scale is difficult to work with since the amount of heat represented by a change of one degree Dalton is not constant. Degrees Dalton differs from Celsius by as much as 3.9 degrees between 0 and 100, but diverges much more for more extreme temperatures.

The rating (53.9/50) is a joke about the unit, as 53.9 Dalton would be 50 degrees Celsius — i.e. the cursedness could be understood as 50/50 (or 10/10, entirely cursed), but perhaps instead as 107.8% (even more than entirely cursed).
|-
| °X ([[Randall]]'s new temperature scale as defined in the title text) || 41.9 || 154.4 || Title text: "In my new scale, °X, 0 is Earths' [sic] record lowest surface temperature, 50 is the global average, and 100 is the record highest, with a linear scale between each point and adjustment every year as needed." || N/A (but likely ''very'') || Usually temperature records are measured 1 m above ground as surface temperatures can be much higher. It is uncertain if Randall actually meant surface or just usual temperature records like the ones mentioned here.

The record lowest temperature on Earth is –89.2°C (–128.6°F), recorded at the {{w|Vostok Station|Vostok Research Station}} in Antarctica on July 21, 1983. On the X scale, 0° would be set to this (unless it is surface temperature instead). This would be adjusted if a new lowest temperature were recorded.

The 50°X point would be set to the "global average", but it's unspecified what timespan this average is taken over. Since adjustments are made yearly, most likely the yearly average is meant; the most recent yearly average temperature, for 2023, was 14.98°C (58.96°F), which happened to be the highest ever by some margin.[https://climate.copernicus.eu/global-climate-highlights-2023]

The {{w|Highest temperature recorded on Earth|record highest temperature}} is 56.7°C (134.1°F), recorded on July 10, 1913 at {{w|Furnace Creek, California|Furnace Creek Ranch}} in Death Valley, California. This record is disputed, however, and a more reasonable record is 54.0°C (129.2°F), which has been recorded several times {{w|Highest temperature recorded on Earth|at Furnace Creek and elsewhere}} in recent years. [https://what-if.xkcd.com/152/] The X scale would set this temperature to 100° (unless the X scale uses surface temperature; surface temperatures on the ground of 94°C (201°F) have been recorded at Furnace Creek). The 100°X point would also be adjusted if a new highest temperature were measured.

{{cot|Derivation}}
To break the scale into two linear parts (below and above 17.16°C), we define two separate equations for each range:

1. Below 17.16°C (from –89.2°C to 17.16°C):
* 0 °X corresponds to –89.2°C
* 50 °X corresponds to 17.16°C

We calculate the slope m₁:

<center>m₁ = (50 – 0) / (17.16 – (–89.2)) = 50 / (17.16 + 89.2) = 50 / 106.36 ≈ 0.47</center>

Now, using the point (17.16°C, 50 °X), we calculate the intercept b₁:

<center>50 = 0.47 × 17.16 + b₁</center>

<center>50 = 8.06 + b₁</center>

<center>b₁ = 50 – 8.06 = 41.94</center>

Thus, the equation for temperatures '''below 17.16°C''' is:

<center>'''X = 0.47 × C + 41.94'''</center>

2. Above 17.16°C (from 17.16°C to 56.7°C):
* 50 °X corresponds to 17.16°C
* 100 °X corresponds to 56.7°C

We calculate the slope m₂:

<center>m₂ = (100 – 50) / (56.7 – 17.16) = 50 / 39.54 ≈ 1.26</center>

Now, using the point (17.16°C, 50 °X), we calculate the intercept b₂:

<center>50 = 1.26 × 17.16 + b₂</center>

<center>50 = 21.63 + b₂</center>

<center>b₂ = 50 – 21.63 = 28.37</center>

Thus, the equation for temperatures '''above 17.16°C''' is:

<center>'''X = 1.26 × C + 28.37'''</center>

;Freezing and Boiling Points

Freezing point of water (0°C): Since 0°C is below 17.16°C, we use the equation X = 0.47 × C + 41.94:

<center>X = 0.47 × 0 + 41.94 = 41.94</center>

So, the freezing point is 41.9 °X.

Boiling point of water (100°C): Since 100°C is above 17.16°C, we use the equation X = 1.26 × C + 28.37:

<center>X = 1.26 × 100 + 28.37 = 126 + 28.37 = 154.37</center>

So, the boiling point is 154.4 °X.
{{cob}}
See also [[2701: Change in Slope]].

Since extreme temperature records are being broken frequently due to {{w|climate change}}, this scale will need to be recalibrated regularly.

Randall also fails to specify what happens with temperatures beyond the record extreme surface temperatures. The simplest approach would appear to be to extend the slope of the two defined areas beyond the boundaries, but given the awkwardness of what is specified, there is no reason to assume that simplicity is a design consideration here.

See [[1061: EST]] for another example of an overly complicated system of measurement. As part of the title text, a cursedness scale isn't given.
|}

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:Temperature Scales

:[A table with five columns, labelled: Unit, water freezing point, water boiling point, notes, cursedness. There are eleven rows below the labels.]

:[Row 1:] Celsius, 0, 100, Used in most of the world, 2/10
:[Row 2:] Kelvin, 273.15, 373.15, 0K is absolute zero, 2/10
:[Row 3:] Fahrenheit, 32, 212, Outdoors in most places is between 0–100, 3/10
:[Row 4:] Réaumur, 0, 80, Like Celsius, but with 80 instead of 100, 3/8
:[Row 5:] Rømer, 7.5, 60, Fahrenheit precursor with similarly random design, 4/10,
:[Row 6:] Rankine, 491.7, 671.7, Fahrenheit, but with 0°F set to absolute zero, 6/10
:[Row 7:] Newton, 0, 33-ish, Poorly defined, with reference points like "the hottest water you can hold your hand in", 7-ish/10
:[Row 8:] Wedgewood, –8, –6.7, Intended for comparing the melting points of metals, all of which it was very wrong about, 9/10
:[Row 9:] Galen, –4?, 4??, Runs from –4 (cold) to 4 (hot). 0 is "normal"(?), 4/–4
:[Row 10:] ''Real'' Celsius, 100, 0, In Anders Celsius's original specification, bigger numbers are ''colder''; others later flipped it, 10/0
:[Row 11:] Dalton, 0, 100, A nonlinear scale; 0°C and 100°C are 0 and 100 Dalton, but 50°C is 53.9 Dalton, 53.9/50

{{comic discussion}}

[[Category:Charts]]
[[Category:Science]]