3038: Uncanceled Units - Revision history

Grabadora304 at 01:43, 8 June 2025

2025-06-08T01:43:36Z

CalibansCreations: /* Explanation */ forgot to italicise

2025-02-25T09:39:30Z

‎Explanation: forgot to italicise

CalibansCreations: /* Explanation */

2025-02-25T09:37:22Z

‎Explanation

Xurkitree10: /* Explanation */

2025-01-26T14:41:16Z

‎Explanation

Frob: Updated the value of G to ~6.674 × 10<^-11 (m/s^2)/(kg/m^2).

2025-01-22T22:49:29Z

Updated the value of G to ~6.674 × 10<^-11 (m/s^2)/(kg/m^2).

Frob at 22:20, 22 January 2025

2025-01-22T22:20:00Z

172.71.146.216: every day -> everyday

2025-01-22T14:00:02Z

every day -> everyday

Frob at 19:15, 21 January 2025

2025-01-21T19:15:10Z

172.71.26.37: /* Explanation */

2025-01-20T16:28:37Z

‎Explanation

172.69.0.164: /* Explanation */

2025-01-19T08:05:18Z

‎Explanation

@@ Line 26: / Line 26: @@
 : 50 gallons per square foot = 50 gal * 231 in<sup>3</sup>/gal * (1/12 ft/in)<sup>3</sup> / 1 ft<sup>2</sup> = 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." The ''[[what if? (blog)|what if?]]'' article ''{{what if|11|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).<!-- This may not be relevant enough to keep -->
+This can be understood as "the height such that every square foot of ceiling has 50 gallons under it." The ''[[what if? (blog)|what if?]]'' article ''{{what if|11|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). In [[2327: Oily House Index]], volume is also divided by area to get house height.<!-- This may not be relevant enough to keep -->
 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).

@@ Line 26: / Line 26: @@
 : 50 gallons per square foot = 50 gal * 231 in<sup>3</sup>/gal * (1/12 ft/in)<sup>3</sup> / 1 ft<sup>2</sup> = 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." The ''[[what if? (blog)|what if?]]'' article {{what if|11|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).<!-- This may not be relevant enough to keep -->
+This can be understood as "the height such that every square foot of ceiling has 50 gallons under it." The ''[[what if? (blog)|what if?]]'' article ''{{what if|11|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).<!-- This may not be relevant enough to keep -->
 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).

@@ Line 26: / Line 26: @@
 : 50 gallons per square foot = 50 gal * 231 in<sup>3</sup>/gal * (1/12 ft/in)<sup>3</sup> / 1 ft<sup>2</sup> = 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? (blog)|what if?]]'': [https://what-if.xkcd.com/11/ 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).<!-- This may not be relevant enough to keep -->
+This can be understood as "the height such that every square foot of ceiling has 50 gallons under it." The ''[[what if? (blog)|what if?]]'' article {{what if|11|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).<!-- This may not be relevant enough to keep -->
 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).

@@ Line 10: / Line 10: @@
 ==Explanation==
 Another of [[Randall]]'s [[:Category:Pet Peeves|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).
@@ Line 34: / Line 32: @@
 In the title text, a speed limit is given as c arcminutes<sup>2</sup> per steradian, where c is presumably the speed of light in a vacuum — 2.998×10<sup>8</sup> 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))<sup>2</sup> = 8.462×10<sup>-8</sup> sr in a square arcminute. Then multiplying by c gives a speed of 56.75 mph (probably 55 mph, based upon the {{w|National Maximum Speed Law|'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 {{w|Hubble's law|Hubble Parameter}} can be expressed as 2.17132212 × 10<sup>-18</sup> {{w|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<sup>-2</sup> or in<sup>-2</sup> would require significant unit conversions. Another example might be the units of the gravitational constant G, ~6.674 × 10<sup>-11</sup> m<sup>3</sup>/(kg×s<sup>2</sup>), which might be written as (m/s<sup>2</sup>)/(kg/m<sup>2</sup>), although this only involves unjumbling rather than uncancelling units.
 ==Transcript==

@@ Line 34: / Line 34: @@
 In the title text, a speed limit is given as c arcminutes<sup>2</sup> per steradian, where c is presumably the speed of light in a vacuum — 2.998×10<sup>8</sup> 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))<sup>2</sup> = 8.462×10<sup>-8</sup> sr in a square arcminute. Then multiplying by c gives a speed of 56.75 mph (probably 55 mph, based upon the {{w|National Maximum Speed Law|'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 {{w|Hubble's law|Hubble Parameter}} can be expressed as 2.17132212 × 10<sup>-18</sup> {{w|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<sup>-2</sup> or in<sup>-2</sup> would require significant unit conversions. Another example might be the units of the gravitational constant G, 6.6720 × 10<sup>-11</sup> m<sup>3</sup>/(kg×s<sup>2</sup>), which might be written as (m/s<sup>2</sup>)/(kg/m<sup>2</sup>), although this only involves unjumbling rather than uncancelling units.
+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 {{w|Hubble's law|Hubble Parameter}} can be expressed as 2.17132212 × 10<sup>-18</sup> {{w|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<sup>-2</sup> or in<sup>-2</sup> would require significant unit conversions. Another example might be the units of the gravitational constant G, ~6.674 × 10<sup>-11</sup> m<sup>3</sup>/(kg×s<sup>2</sup>), which might be written as (m/s<sup>2</sup>)/(kg/m<sup>2</sup>), although this only involves unjumbling rather than uncancelling units.
 ==Transcript==

@@ Line 30: / Line 30: @@
 This can be understood as "the height such that every square foot of ceiling has 50 gallons under it." ''[[what if? (blog)|what if?]]'': [https://what-if.xkcd.com/11/ 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).<!-- This may not be relevant enough to keep -->
-A common source of unit drama occurs between lay people who are looking for every day 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).
+A common source of unit drama occurs between lay people who are looking for every day 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 arcminutes<sup>2</sup> per steradian, where c is presumably the speed of light in a vacuum — 2.998×10<sup>8</sup> 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))<sup>2</sup> = 8.462×10<sup>-8</sup> sr in a square arcminute. Then multiplying by c gives a speed of 56.75 mph (probably 55 mph, based upon the {{w|National Maximum Speed Law|'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.