18 ms·

111,111.1 meters is reliably 1 degree of latitude

341 points by mholt 3y ago

delta_p_delta_x 3y ago
The metre was re-defined[0] in 1791 as one ten-millionth of the quarter-meridian, or ninety degrees of arc, through Paris. It then follows straightforwardly that 1° ≡ 1/90 × 10^7 m = 111 111.111... m. It also follows straightforwardly that the circumference of Earth is approximately forty million metres, or 40 000 km. [0]: Edit: the initial definition of the metre was the length of a seconds pendulum, i.e. the length of a pendulum with a period of two seconds. Given the formula T ≈ 2π√(L/g), letting T = 2 and L = 1, we have 1 = π√(1/g), and 1 = π²/g. This is also why g is so close to the value of π²—because the former is expressed in units that are defined that way. It's also not a coincidence that 1 cm³ of water is 1 g—for a long time, that was the definition of the gram.
- deleted 3y ago
  [deleted]
- aappleby 3y ago
  And a 32-bit integer can represent latitude or longitude to an accuracy of around 1 centimeter :D.
  - OscarCunningham 3y ago
    Call that a long long.
    - teaearlgraycold 3y ago
      long lon
      - linkjuice4all 3y ago
        At my last job we used lon long
    - dylan604 3y ago
      That’s up there with buffalo buffalo buffalo
    - isaacremuant 3y ago
      If you are serious, 32 bit is a more specific term, therefore better.
      - ronsor 3y ago
        Can't be serious, because long long is 64 bits on most platforms.
        OscarCunningham 3y ago
        Right, a 64 bit longitude would be a long long long.
        downvotetruth 3y ago
        ‘long long long’ is to long for GCC, but not for the Beatles who may be made to sing it a long long i; // = todo time
- purkka 3y ago
  Given that the second is an older unit [0] than the redefinition of the metre, and defined based on "nice" subdivisions of the day, it would seem that there's still a bit of a coincidence there. Since the metre was previously defined by the seconds pendulum, it was entirely defined by the definition of a second and the value of g. From the equations, 1 m = 1 s² × g / π². While this makes g ≈ π² straightforward, it seems coincidental that the Earth's circumference was close enough to 40 000 km that the redefinition of the metre was a nice power or 10 without too much change to the metre. [0]: Late 16th century, based on https://en.wikipedia.org/wiki/Second#Fraction_of_solar_day https://en.wikipedia.org/wiki/Second#Fraction_of_solar_day
  - marcosdumay 3y ago
    Well, it's not much of a coincidence. There are all kinds of constants around us, and one of them is prone to be close to a round number. If the Earth's circumference wasn't a nice number, people would have chosen another one.
    - deleted 3y ago
      [deleted]
  - Thorrez 3y ago
    Was the meter based on the length of the pendulum similar to the length of the meter today? This doesn't necessarily say they were similar: > In 1675, Tito Livio Burattini suggested the term metre for a unit of length based on a pendulum length, but then it was discovered that the length of a seconds pendulum varies from place to place. https://en.wikipedia.org/wiki/Metre#Pendulum_or_meridian https://en.wikipedia.org/wiki/Metre#Pendulum_or_meridian
    - petters 3y ago
      The period is also not independent of the amplitude. That is only the case of you approximate sin x ≈ x in the differential equation
      - 3y ago
- deleted 3y ago
  [deleted]
- ianburrell 3y ago
  I’m surprised that there isn’t GPS coordinate system which is just kilometers. Instead of 360 degrees uses 40,000 km. The real calculation would use the real distances but the approximation is close enough. This means don’t have to do any conversion to distances, at least for metric folks. One problem with degrees is that hard to convert to useful distances. This tricks help a lot, but it would be better to have no conversion.
  - dharmab 3y ago
    The perfect sphere approximation of Earth is not at all close enough for GIS applications. Geoid data (the actual ellipsoid-ish shape with height variance) is an important factor in accurate GIS software.
  - jonsen 3y ago
    > ...don’t have to do any conversion to distances... Are you advocating for the use of Manhattan distances for everything?
  - pezezin 3y ago
    https://en.wikipedia.org/wiki/Earth-centered,_Earth-fixed_coordinate_system https://en.wikipedia.org/wiki/Earth-centered,_Earth-fixed_co... In a previous life I had to implement conversions between ECEF and WGS84. If you do it, make sure to use at least 64-bit floats, the Earth is so big that 32-bit arithmetic will introduce errors on the order of meters.
    - sgarland 3y ago
      You’ve brought memories of dealing with NAD83 (for local maps) and WGS84 (for everything else) crashing back. The error between those is tiny at the distances I was dealing with, but it was enough that it bothered me. “I’ll just automate this mapping task in Python, how bad could it be?” - A very-new-to-everything me, years ago.
  - bmacho 3y ago
    Do you have an example in mind? A problem that you may encounter, how do you calculate now, and how could you calculate with a GPS system that is just kilometers?
- lern_too_spel 3y ago
  The French also applied decimalization to angle measurements, so it's really 1 gon = 100 km, and 1 km is just 1 centigon.
- thomasahle 3y ago
  Why did they change the definition from the length of the pendulum to the circumference of the Earth?
  - Daz1 3y ago
    Couple reasons 1) why use seconds when you can just measure a segment of a known distance? 2) pendulums swing faster or slower depending on altitude, 3) Problems with accurate measurement of seconds, swing time etc.
    - thomasahle 3y ago
      I guess for (1) I would imagine it was easier for an independent group of scientists to accurately measure a pendulum, than to travel all the way to the north pole in a straight line through Paris. But I guess they were using the stars or something so maybe it's not as hard as I'd imagine. Also (2) and (3) are great points.
- saalweachter 3y ago
  Note that the meter is also basically 3 Paris feet, which comes out to about 0.97m (compared to 3 English feet, which is only around 0.91m). They weren't working in a vacuum to derive the most principled or cosmically beautiful unit length, just trying to find a way to define the unit they already used that wasn't "the length of this stick we have over here".
  - madcaptenor 3y ago
    But in practice the meter ended up being "the length of this special metal stick we keep in Paris".
    - saalweachter 3y ago
      Yeah, because measuring the mean equatorial and longitudinal circumference of the Earth on a line passing through Paris is a pain in the ass. The meter was also standardized at a weird golden period for units -- we had global trade and travel (and so it was getting inconvenient to have different standard unit length sticks in different countries, let alone cities), we had enough science to have the notion of basing it on physical constants instead of random sticks, but we also weren't yet in a world where precision mattered all that much. You could change the length of your units by 3% and it wouldn't really matter as much it would today, where every bolt and manufactured part would instantly become a nightmare. It's kind of a shame, because now we could pick so much cooler definitions for our units, because our science is so much better. Take restandardizing the foot as 1 ns * c -- so much more elegant than the mean circumference of the Earth, or an ugly number of wavelengths of a caesium atom. But changing the foot by 1.5% -- half as much as the difference between the meter and 3 Paris feet -- would be devastating today in a way that it wasn't in 1800. Hell, it'd probably be easier to change the definition of a second than the definition of a foot.
- japanuspus 3y ago
  The work to measure the meridian with the highest possible precision was in itself a fascinating multi-year ordeal: https://en.wikipedia.org/wiki/Arc_measurement_of_Delambre_and_M%C3%A9chain https://en.wikipedia.org/wiki/Arc_measurement_of_Delambre_an....
  - mrciacco 3y ago
    A nice novel about it is Denis Guedj's "La Méridienne". https://en.wikipedia.org/wiki/Denis_Guedj https://en.wikipedia.org/wiki/Denis_Guedj
- overengineer 3y ago
  > The metre was re-defined[0] in 1791 as one ten-millionth of the quarter-meridian Doesn't sound like a good idea. Circumference of earth around Paris is not unchangeable.
  - fsloth 3y ago
    Exact geographic measurements where the high technology of 18th century. Each society uses the highest precision measurements available to them. Also, plate tectonics were scifi fantasy until 1950's. The definition has been updated after that. https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_ba...
  - delta_p_delta_x 3y ago
    > Doesn't sound like a good idea Which is why the CGPM changed the definition of the metre to: - the length of the International Metre (a 9:1 platinum-iridium bar) in 1889; - and then to 1650763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum in 1960; - and finally to the modern definition, the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second in 1983. This means the realisation of the metre depends on the definition of the second.
- ragebol 3y ago
  This stuff why the SI units system really is a system. Rather than the collection of unrelated units that was used before.
gp 3y ago
1 nautical mile (~6076 ft) is exactly one minute of arc at the Earth's equator. As a sailor, I wish that all miles were nautical miles because they have a real meaning. What good is 5280 feet?
- delta_p_delta_x 3y ago
  Most other 'mile's are derivatives of the Roman mile which developed somewhat independently of the English units (foot, yard, inch, barleycorn, etc), ergo the weird conversion factors. The original Roman mile was 5000 Roman feet. In fact, 1 nmi ≡ 1.852 km exactly. Also from the original definition of the metre: 1/60 × 1/90 × 10^7 = 1851.85185185... m. Inter-convertability was a defining trait of SI (or more precisely, its predecessors, MKS and CGS) from the very outset, which is why we have 1 m ≡ 1 s ≡ 1 kg ≡ 1 N ≡ 1 Pa ≡ 1 J ≡ 1 A ≡ 1 C ≡ 1 V ≡ 1 Ω ≡ 1 F ≡ 1 W ≡ 1 Wb ≡ 1 T ≡ 1 H ≡ 1 Hz (I use '≡' loosely here to suggest conversion factors, rather than its usual meaning of equivalence). The only outliers in the SI are the kelvin, the mole, and the candela (and derived units from these). The former two are dealt with straightforwardly with the Boltzmann and Avogadro constants. I have issues with the presence of the candela in the SI.
  - skissane 3y ago
    > Most other 'mile's are derivatives of the Roman mile which developed somewhat independently of the English units (foot, yard, inch, barleycorn, etc), ergo the weird conversion factors. The original Roman mile was 5000 Roman feet. Pre-metric Europe was full of units with weird conversion factors, based on a shared heritage (mixture of Roman and Germanic), but with lots of divergent evolution subsequently. England didn't really stand out; France, Spain, Italy, Germany, etc, were really no different. Then the Continent did away with most of that complexity by adopting metric, and for whatever reason the English dragged their feet on doing that, and their American offshoots even more so. But the fact that people have forgotten that the French/Germans/etc used to have feet/inches/miles/pounds/etc too, [0] albeit with somewhat different definitions, makes people think English units were somehow unique. They never were. The uniqueness is in the slowness in replacing them with metric, not the units themselves. [0] They still have some of these units for certain purposes. In France and Germany, the pound is still used, albeit redefined to be exactly 500 g. Nautical miles are used in maritime and aviation applications; American influence (and to a lesser degree British) led to the adoption of the Anglo-American foot as the unit of altitude in aviation – the foot French pilots use to measure altitudes is the English foot not the old French foot; etc
HPsquared 3y ago
And 1 nanosecond at light speed ≈ 1 foot
- chungy 3y ago
  That's remarkably close to reality. I'm impressed :) $ units c ft/ns * 0.98357106
  - maxmcd 3y ago
    Admiral Grace Hopper Explains the Nanosecond: https://youtu.be/9eyFDBPk4Yw https://youtu.be/9eyFDBPk4Yw
    - dylan604 3y ago
      The first time I saw one of her demonstrations of a nanosecond, I was confused when she pulled out a length of wire. I don’t remember what class it was in or what context the video was being used, but this was 6th grade
      - Mountain_Skies 3y ago
        Possibly an urban legend but there's a story about a company in India that ordered a Soviet made computer system that has an sloppy spool of wire attached to the main board. They contacted the Soviet institute that built the computer system and it was explained that the computer needed a timing delay between two components but didn't have the proper ICs on hand so they used a precise length of wire to introduce the needed delay to make the timing correct.
        defrost 3y ago
        As a stone cold fact physical mediums with known delay timings were once used as memory storage for computers and as "echo removal" filters in radar installations. Although a mathematician, Turing took quite an interest in the engineering side of computer design. There was some discussion in 1947 as to whether a cheaper substance than mercury could not be found for use as an ultrasonic delay medium. Turing's contribution to this discussion was to advocate the use of gin, which he said contained alcohol and water in just the right proportions to give a zero temperature coefficient of propagation velocity at room temperature. ~ MAURICE V. WILKES 1967 A CM Turing Lecture https://sci-hub.ru/10.1145/321439.321440 https://sci-hub.ru/10.1145/321439.321440 https://en.wikipedia.org/wiki/Delay-line_memory https://en.wikipedia.org/wiki/Delay-line_memory https://www.theregister.com/2013/06/28/wilkes_centenary_mercury_memory/ https://www.theregister.com/2013/06/28/wilkes_centenary_merc...
NelsonMinar 3y ago
This post also has a nice rule of thumb that 111,111 * cos(latitude) meters is 1 degree of longitude. I like the correction! In practice you can use some simple constants; 25° is about 100,000 meters. 44° is about 80,000 meters. 57° is about 60,000 meters.
Waterluvian 3y ago
But given the Earth is an oblate spheroid won’t the actual arc length of 1 degree of latitude be variable? Or does “reliably” just mean “close enough to be useful”? Gah. I’ve been doing non-geography work for far too long. I used to know this stuff.
- mholt 3y ago
  Reliably means close enough to be useful, but the estimation is also quite precise where most populations live. My use case which led me to discover this fact is sort of documented here: https://twitter.com/mholt6/status/1695685022710477043 https://twitter.com/mholt6/status/1695685022710477043 -- even if my use case did have whole kilometers of displacement, it wouldn't likely be near the poles, and if it was, the answer would be, "Meh, we get it, you're at the pole."
- ragazzina 3y ago
  The Earth diameter at the equator is 43 km larger than at the poles. It's like the Earth orbit: we learn in school that it's an ellipse, but we are never actually given a sense of the shape, and most of the drawings give a completely wrong idea.
- hanche 3y ago
  The title of the post could make you think that a degree of latitude varies by less than a decimeter, but that is of course not true. But close enough for many practical purposes, definitely.
andreygrehov 3y ago
rant: I live in the US for more than 10 years and I still can't get used to the imperial system. I never will. It just doesn't make any sense to me. The metric system is pure gold: 1cm = 10mm 1m = 100cm 1km = 1000m 1kg = 1000g 1ton = 1000kg The imperial system is like, hold my beer: 1in = ??? 1ft = 12in 1yd = 3ft 1mile = 5280ft 1lb = 16oz Jesus Christ, who the hell came up with this madness?
- cj 3y ago
  I think there’s even a lot of people who grew up in America that don’t fully get our system. I would be surprised if more than 50% of the population knows how many ounces are in a cup of water. Same for feet per mile, etc. Thank goodness even in the US the metric system is used as standard within the science community.
  - fanf2 3y ago
    In US customary units, a fluid ounce of water does not weigh an ounce avoirdupois, because US volume measures are not Imperial units: they are based on the pre-Imperial Queen Anne wine gallon. The British fluid ounce was defined to be the volume of an ounce of water, and the Imperial gallon was defined to be the volume of 10lb of water. This vague nod towards decimalization happened to match the pre-Imperial beer gallon fairly well, and it’s also why the Imperial pint has 20 fl oz instead of 16.
- invalidator 3y ago
  > 1in = ??? 25.4 mm, ever since 1959 when we redefined it.
  - rmu09 3y ago
    I believe an opportunity was missed some time ago in the past to define one inch to 25.6mm, which would make for much nicer conversions IMO, especially with the convention to use fractions of powers of two in the inch world (e.g. 15/16" would be 24mm exactly vs. 23.8125mm).
nixass 3y ago
How many football fields is that?

341 points by mholt 3y ago

The metre was re-defined[0] in 1791 as one ten-millionth of the quarter-meridian, or ninety degrees of arc, through Paris. It then follows straightforwardly that 1° ≡ 1/90 × 10^7 m = 111 111.111... m. It also follows straightforwardly that the circumference of Earth is approximately forty million metres, or 40 000 km. [0]: Edit: the initial definition of the metre was the length of a seconds pendulum, i.e. the length of a pendulum with a period of two seconds. Given the formula T ≈ 2π√(L/g), letting T = 2 and L = 1, we have 1 = π√(1/g), and 1 = π²/g. This is also why g is so close to the value of π²—because the former is expressed in units that are defined that way. It's also not a coincidence that 1 cm³ of water is 1 g—for a long time, that was the definition of the gram.

deleted 3y ago
[deleted]
aappleby 3y ago
And a 32-bit integer can represent latitude or longitude to an accuracy of around 1 centimeter :D.
- OscarCunningham 3y ago
  Call that a long long.
  - teaearlgraycold 3y ago
    long lon
    - linkjuice4all 3y ago
      At my last job we used lon long
  - dylan604 3y ago
    That’s up there with buffalo buffalo buffalo
  - isaacremuant 3y ago
    If you are serious, 32 bit is a more specific term, therefore better.
    - ronsor 3y ago
      Can't be serious, because long long is 64 bits on most platforms.
      - OscarCunningham 3y ago
        Right, a 64 bit longitude would be a long long long.
        downvotetruth 3y ago
        ‘long long long’ is to long for GCC, but not for the Beatles who may be made to sing it a long long i; // = todo time
purkka 3y ago
Given that the second is an older unit [0] than the redefinition of the metre, and defined based on "nice" subdivisions of the day, it would seem that there's still a bit of a coincidence there. Since the metre was previously defined by the seconds pendulum, it was entirely defined by the definition of a second and the value of g. From the equations, 1 m = 1 s² × g / π². While this makes g ≈ π² straightforward, it seems coincidental that the Earth's circumference was close enough to 40 000 km that the redefinition of the metre was a nice power or 10 without too much change to the metre. [0]: Late 16th century, based on https://en.wikipedia.org/wiki/Second#Fraction_of_solar_day https://en.wikipedia.org/wiki/Second#Fraction_of_solar_day
- marcosdumay 3y ago
  Well, it's not much of a coincidence. There are all kinds of constants around us, and one of them is prone to be close to a round number. If the Earth's circumference wasn't a nice number, people would have chosen another one.
  - deleted 3y ago
    [deleted]
- Thorrez 3y ago
  Was the meter based on the length of the pendulum similar to the length of the meter today? This doesn't necessarily say they were similar: > In 1675, Tito Livio Burattini suggested the term metre for a unit of length based on a pendulum length, but then it was discovered that the length of a seconds pendulum varies from place to place. https://en.wikipedia.org/wiki/Metre#Pendulum_or_meridian https://en.wikipedia.org/wiki/Metre#Pendulum_or_meridian
  - petters 3y ago
    The period is also not independent of the amplitude. That is only the case of you approximate sin x ≈ x in the differential equation
    - 3y ago
deleted 3y ago
[deleted]
ianburrell 3y ago
I’m surprised that there isn’t GPS coordinate system which is just kilometers. Instead of 360 degrees uses 40,000 km. The real calculation would use the real distances but the approximation is close enough. This means don’t have to do any conversion to distances, at least for metric folks. One problem with degrees is that hard to convert to useful distances. This tricks help a lot, but it would be better to have no conversion.
- dharmab 3y ago
  The perfect sphere approximation of Earth is not at all close enough for GIS applications. Geoid data (the actual ellipsoid-ish shape with height variance) is an important factor in accurate GIS software.
- jonsen 3y ago
  > ...don’t have to do any conversion to distances... Are you advocating for the use of Manhattan distances for everything?
- pezezin 3y ago
  https://en.wikipedia.org/wiki/Earth-centered,_Earth-fixed_coordinate_system https://en.wikipedia.org/wiki/Earth-centered,_Earth-fixed_co... In a previous life I had to implement conversions between ECEF and WGS84. If you do it, make sure to use at least 64-bit floats, the Earth is so big that 32-bit arithmetic will introduce errors on the order of meters.
  - sgarland 3y ago
    You’ve brought memories of dealing with NAD83 (for local maps) and WGS84 (for everything else) crashing back. The error between those is tiny at the distances I was dealing with, but it was enough that it bothered me. “I’ll just automate this mapping task in Python, how bad could it be?” - A very-new-to-everything me, years ago.
- bmacho 3y ago
  Do you have an example in mind? A problem that you may encounter, how do you calculate now, and how could you calculate with a GPS system that is just kilometers?
lern_too_spel 3y ago
The French also applied decimalization to angle measurements, so it's really 1 gon = 100 km, and 1 km is just 1 centigon.
thomasahle 3y ago
Why did they change the definition from the length of the pendulum to the circumference of the Earth?
- Daz1 3y ago
  Couple reasons 1) why use seconds when you can just measure a segment of a known distance? 2) pendulums swing faster or slower depending on altitude, 3) Problems with accurate measurement of seconds, swing time etc.
  - thomasahle 3y ago
    I guess for (1) I would imagine it was easier for an independent group of scientists to accurately measure a pendulum, than to travel all the way to the north pole in a straight line through Paris. But I guess they were using the stars or something so maybe it's not as hard as I'd imagine. Also (2) and (3) are great points.
saalweachter 3y ago
Note that the meter is also basically 3 Paris feet, which comes out to about 0.97m (compared to 3 English feet, which is only around 0.91m). They weren't working in a vacuum to derive the most principled or cosmically beautiful unit length, just trying to find a way to define the unit they already used that wasn't "the length of this stick we have over here".
- madcaptenor 3y ago
  But in practice the meter ended up being "the length of this special metal stick we keep in Paris".
  - saalweachter 3y ago
    Yeah, because measuring the mean equatorial and longitudinal circumference of the Earth on a line passing through Paris is a pain in the ass. The meter was also standardized at a weird golden period for units -- we had global trade and travel (and so it was getting inconvenient to have different standard unit length sticks in different countries, let alone cities), we had enough science to have the notion of basing it on physical constants instead of random sticks, but we also weren't yet in a world where precision mattered all that much. You could change the length of your units by 3% and it wouldn't really matter as much it would today, where every bolt and manufactured part would instantly become a nightmare. It's kind of a shame, because now we could pick so much cooler definitions for our units, because our science is so much better. Take restandardizing the foot as 1 ns * c -- so much more elegant than the mean circumference of the Earth, or an ugly number of wavelengths of a caesium atom. But changing the foot by 1.5% -- half as much as the difference between the meter and 3 Paris feet -- would be devastating today in a way that it wasn't in 1800. Hell, it'd probably be easier to change the definition of a second than the definition of a foot.
japanuspus 3y ago
The work to measure the meridian with the highest possible precision was in itself a fascinating multi-year ordeal: https://en.wikipedia.org/wiki/Arc_measurement_of_Delambre_and_M%C3%A9chain https://en.wikipedia.org/wiki/Arc_measurement_of_Delambre_an....
- mrciacco 3y ago
  A nice novel about it is Denis Guedj's "La Méridienne". https://en.wikipedia.org/wiki/Denis_Guedj https://en.wikipedia.org/wiki/Denis_Guedj
overengineer 3y ago
> The metre was re-defined[0] in 1791 as one ten-millionth of the quarter-meridian Doesn't sound like a good idea. Circumference of earth around Paris is not unchangeable.
- fsloth 3y ago
  Exact geographic measurements where the high technology of 18th century. Each society uses the highest precision measurements available to them. Also, plate tectonics were scifi fantasy until 1950's. The definition has been updated after that. https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_ba...
- delta_p_delta_x 3y ago
  > Doesn't sound like a good idea Which is why the CGPM changed the definition of the metre to: - the length of the International Metre (a 9:1 platinum-iridium bar) in 1889; - and then to 1650763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum in 1960; - and finally to the modern definition, the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second in 1983. This means the realisation of the metre depends on the definition of the second.
ragebol 3y ago
This stuff why the SI units system really is a system. Rather than the collection of unrelated units that was used before.

gp 3y ago

1 nautical mile (~6076 ft) is exactly one minute of arc at the Earth's equator. As a sailor, I wish that all miles were nautical miles because they have a real meaning. What good is 5280 feet?

delta_p_delta_x 3y ago
Most other 'mile's are derivatives of the Roman mile which developed somewhat independently of the English units (foot, yard, inch, barleycorn, etc), ergo the weird conversion factors. The original Roman mile was 5000 Roman feet. In fact, 1 nmi ≡ 1.852 km exactly. Also from the original definition of the metre: 1/60 × 1/90 × 10^7 = 1851.85185185... m. Inter-convertability was a defining trait of SI (or more precisely, its predecessors, MKS and CGS) from the very outset, which is why we have 1 m ≡ 1 s ≡ 1 kg ≡ 1 N ≡ 1 Pa ≡ 1 J ≡ 1 A ≡ 1 C ≡ 1 V ≡ 1 Ω ≡ 1 F ≡ 1 W ≡ 1 Wb ≡ 1 T ≡ 1 H ≡ 1 Hz (I use '≡' loosely here to suggest conversion factors, rather than its usual meaning of equivalence). The only outliers in the SI are the kelvin, the mole, and the candela (and derived units from these). The former two are dealt with straightforwardly with the Boltzmann and Avogadro constants. I have issues with the presence of the candela in the SI.
- skissane 3y ago
  > Most other 'mile's are derivatives of the Roman mile which developed somewhat independently of the English units (foot, yard, inch, barleycorn, etc), ergo the weird conversion factors. The original Roman mile was 5000 Roman feet. Pre-metric Europe was full of units with weird conversion factors, based on a shared heritage (mixture of Roman and Germanic), but with lots of divergent evolution subsequently. England didn't really stand out; France, Spain, Italy, Germany, etc, were really no different. Then the Continent did away with most of that complexity by adopting metric, and for whatever reason the English dragged their feet on doing that, and their American offshoots even more so. But the fact that people have forgotten that the French/Germans/etc used to have feet/inches/miles/pounds/etc too, [0] albeit with somewhat different definitions, makes people think English units were somehow unique. They never were. The uniqueness is in the slowness in replacing them with metric, not the units themselves. [0] They still have some of these units for certain purposes. In France and Germany, the pound is still used, albeit redefined to be exactly 500 g. Nautical miles are used in maritime and aviation applications; American influence (and to a lesser degree British) led to the adoption of the Anglo-American foot as the unit of altitude in aviation – the foot French pilots use to measure altitudes is the English foot not the old French foot; etc

HPsquared 3y ago

And 1 nanosecond at light speed ≈ 1 foot

chungy 3y ago
That's remarkably close to reality. I'm impressed :) $ units c ft/ns * 0.98357106
- maxmcd 3y ago
  Admiral Grace Hopper Explains the Nanosecond: https://youtu.be/9eyFDBPk4Yw https://youtu.be/9eyFDBPk4Yw
  - dylan604 3y ago
    The first time I saw one of her demonstrations of a nanosecond, I was confused when she pulled out a length of wire. I don’t remember what class it was in or what context the video was being used, but this was 6th grade
    - Mountain_Skies 3y ago
      Possibly an urban legend but there's a story about a company in India that ordered a Soviet made computer system that has an sloppy spool of wire attached to the main board. They contacted the Soviet institute that built the computer system and it was explained that the computer needed a timing delay between two components but didn't have the proper ICs on hand so they used a precise length of wire to introduce the needed delay to make the timing correct.
      - defrost 3y ago
        As a stone cold fact physical mediums with known delay timings were once used as memory storage for computers and as "echo removal" filters in radar installations. Although a mathematician, Turing took quite an interest in the engineering side of computer design. There was some discussion in 1947 as to whether a cheaper substance than mercury could not be found for use as an ultrasonic delay medium. Turing's contribution to this discussion was to advocate the use of gin, which he said contained alcohol and water in just the right proportions to give a zero temperature coefficient of propagation velocity at room temperature. ~ MAURICE V. WILKES 1967 A CM Turing Lecture https://sci-hub.ru/10.1145/321439.321440 https://sci-hub.ru/10.1145/321439.321440 https://en.wikipedia.org/wiki/Delay-line_memory https://en.wikipedia.org/wiki/Delay-line_memory https://www.theregister.com/2013/06/28/wilkes_centenary_mercury_memory/ https://www.theregister.com/2013/06/28/wilkes_centenary_merc...

NelsonMinar 3y ago

This post also has a nice rule of thumb that 111,111 * cos(latitude) meters is 1 degree of longitude. I like the correction! In practice you can use some simple constants; 25° is about 100,000 meters. 44° is about 80,000 meters. 57° is about 60,000 meters.

Waterluvian 3y ago

But given the Earth is an oblate spheroid won’t the actual arc length of 1 degree of latitude be variable? Or does “reliably” just mean “close enough to be useful”? Gah. I’ve been doing non-geography work for far too long. I used to know this stuff.

mholt 3y ago
Reliably means close enough to be useful, but the estimation is also quite precise where most populations live. My use case which led me to discover this fact is sort of documented here: https://twitter.com/mholt6/status/1695685022710477043 https://twitter.com/mholt6/status/1695685022710477043 -- even if my use case did have whole kilometers of displacement, it wouldn't likely be near the poles, and if it was, the answer would be, "Meh, we get it, you're at the pole."
ragazzina 3y ago
The Earth diameter at the equator is 43 km larger than at the poles. It's like the Earth orbit: we learn in school that it's an ellipse, but we are never actually given a sense of the shape, and most of the drawings give a completely wrong idea.
hanche 3y ago
The title of the post could make you think that a degree of latitude varies by less than a decimeter, but that is of course not true. But close enough for many practical purposes, definitely.

andreygrehov 3y ago

rant: I live in the US for more than 10 years and I still can't get used to the imperial system. I never will. It just doesn't make any sense to me. The metric system is pure gold: 1cm = 10mm 1m = 100cm 1km = 1000m 1kg = 1000g 1ton = 1000kg The imperial system is like, hold my beer: 1in = ??? 1ft = 12in 1yd = 3ft 1mile = 5280ft 1lb = 16oz Jesus Christ, who the hell came up with this madness?

cj 3y ago
I think there’s even a lot of people who grew up in America that don’t fully get our system. I would be surprised if more than 50% of the population knows how many ounces are in a cup of water. Same for feet per mile, etc. Thank goodness even in the US the metric system is used as standard within the science community.
- fanf2 3y ago
  In US customary units, a fluid ounce of water does not weigh an ounce avoirdupois, because US volume measures are not Imperial units: they are based on the pre-Imperial Queen Anne wine gallon. The British fluid ounce was defined to be the volume of an ounce of water, and the Imperial gallon was defined to be the volume of 10lb of water. This vague nod towards decimalization happened to match the pre-Imperial beer gallon fairly well, and it’s also why the Imperial pint has 20 fl oz instead of 16.
invalidator 3y ago
> 1in = ??? 25.4 mm, ever since 1959 when we redefined it.
- rmu09 3y ago
  I believe an opportunity was missed some time ago in the past to define one inch to 25.6mm, which would make for much nicer conversions IMO, especially with the convention to use fractions of powers of two in the inch world (e.g. 15/16" would be 24mm exactly vs. 23.8125mm).

nixass 3y ago

How many football fields is that?