6 ms·

Consistency is not the only value of a system of units. Convenience is also of importance. And that is where the metric system shines. Having all measures of a

Consistency is not the only value of a system of units. Convenience is also of importance. And that is where the metric system shines. Having all measures of a unit in multiples 10 combines perfectly with our decimal calculations. Having as few as possible magical numbers to convert and combine between units makes making mistakes harder. How many calories in kinetic energy has a pound going 10 miles per hour ? I know a kilo going 10 meters per second has 50 joules of kinetic energy without looking up anything and doing the calculation in my head.

mulmen 6y ago
If working with simple units of ten is beneficial then every mission should redefine units in terms of expected velocities and vehicle size so they are optimized for the actual calculations at hand. That's not realistic, obviously, so we just pick one. The units in the system are arbitrary, really. In reality regardless of the system you choose every calculation is going to end up with fractions of something. You aren't just going to do it in your head.
- heisenzombie 6y ago
  Physicists are quite fond of redefining units so that the constants they care about are all just 1. (https://en.wikipedia.org/wiki/Natural_units https://en.wikipedia.org/wiki/Natural_units). For example, you could define mars units where the gravitational acceleration on mars is 1. Now your velocity in freefall is just equal to the time you've been freefalling! You don't even have to do a calculation! (note: Don't actually do this. Gravitational acceleration isn't a constant when you're doing orbital mechanics.)
  - mulmen 6y ago
    Honestly I would expect something like that to be happening at a hardware level. The number of bits in a memory address for the ground sensing radar is very interesting. Or the algorithm to determine vehicle acceleration given the voltage reading of a solid-state sensor vs the baseline. The metric system vs the imperial system is not an interesting distinction in these contexts.
  - MereInterest 6y ago
    The main convenience of it is when deriving formulas, rather than when applying them. With all the constants set to 1, they don't need to be tracked throughout the formula, and can be put back in at the very end by looking at the units. Sprinkle the appropriate (hbar*c) or (mu0*epsilon0) at the end, and then you get your constants back.
killjoywashere 6y ago
Can’t talk to the statute mile, but the nautical mile is sublime: one minute of latitude. The amount of math you can do in your head with a system with so many factors of 2, 3, and 5 is truly amazing.
- mulmen 6y ago
  I'm not aware of any tricks to make mile calculations easier but the fractional scale common with the inch is very useful for real-world mental calculation and practical exchange. Effectively everything is powers of two. Got something between 1/4 and 1/2 inch? Great, use 1/8ths. It's three. Not close enough? How about five 16ths? It infinitely scales to provide another unit that is suited to the measurement at hand. In some contexts you might just say you pick the closest 1/8th. In others you might use 32nds. You can use the same measuring devices to agree on an ad-hoc standard that everyone understands. But with the metric system you only really get cm (too coarse) and mm (too fine) but you don't get something like 9/16 so you can't "work in 16ths" and have everything be whole units again. Adjusting HVAC in degrees-C is infuriating to my Fahrenheit sensibilities. 20C is cold, 22C is hot. 21C is probably ok but really I want something like 20.5C. The comfortable range for a room is 3-5 whole units of F, but requires a bunch of fractions in C that you may not even have available on your thermostat. Sure, converting between units is easy in the metric system. That doesn't make it the best thing to use all the time. Hell, the idea of thousandths of an inch is used commonly, so even the imperial system is base 1000 in some cases. But I've never seen anyone utilize the fractional scale with metric units, probably because the units are the wrong size for that to be useful.
  - onion2k 6y ago
    But with the metric system you only really get cm (too coarse) and mm (too fine) but you don't get something like 9/16 so you can't "work in 16ths" and have everything be whole units again. People who use metric units are perfectly happy rounding to the nearest 0.5cm or 0.25cm if that's what's needed, exactly as people do with inches. Why on earth would you imagine people use mm if something doesn't call for them?
sojournerc 6y ago
As an occasional woodworker and carpenter, I can tell you having evenly divisable (inch) measurements makes mental division a whole lot easier. It's just a case of using the right tool for the job.
- deleted 6y ago
  [deleted]
- mulmen 6y ago
  It’s unfortunate that fractional measurements and the base size of units get conflated. Maybe metric users do use fractions and I just don’t hear about it. Is that table one and a quarter meters high?
  - spaetzleesser 6y ago
    People often say something is 1 and a half meters long. I don't understand how people can work with inch measurements. How do you divide 7"3/8 by 5? This seems a major pain.
    - mulmen 6y ago
      One and a half seems natural. What about something like a quarter meter? I guess that just becomes some number of centimeters? > How do you divide 7"3/8 by 5? Same way I divide 4.7625 cm by 5. With a calculator.
      - flemhans 6y ago
        > I guess that just becomes some number of centimeters? 25, yes. It's not too hard to do the math. > Same way I divide 4.7625 cm by 5. With a calculator. That's roughly 0.95 right by intuition, but (7"3/8) / 5 doesn't come easy to me.
    - chordalkeyboard 6y ago
      You multiply 7* 8 then add 3 and put that number over 8* 5, resulting in 59/40, roughly 1.5”.

mulmen 6y ago

If working with simple units of ten is beneficial then every mission should redefine units in terms of expected velocities and vehicle size so they are optimized for the actual calculations at hand. That's not realistic, obviously, so we just pick one. The units in the system are arbitrary, really. In reality regardless of the system you choose every calculation is going to end up with fractions of something. You aren't just going to do it in your head.

heisenzombie 6y ago
Physicists are quite fond of redefining units so that the constants they care about are all just 1. (https://en.wikipedia.org/wiki/Natural_units https://en.wikipedia.org/wiki/Natural_units). For example, you could define mars units where the gravitational acceleration on mars is 1. Now your velocity in freefall is just equal to the time you've been freefalling! You don't even have to do a calculation! (note: Don't actually do this. Gravitational acceleration isn't a constant when you're doing orbital mechanics.)
- mulmen 6y ago
  Honestly I would expect something like that to be happening at a hardware level. The number of bits in a memory address for the ground sensing radar is very interesting. Or the algorithm to determine vehicle acceleration given the voltage reading of a solid-state sensor vs the baseline. The metric system vs the imperial system is not an interesting distinction in these contexts.
- MereInterest 6y ago
  The main convenience of it is when deriving formulas, rather than when applying them. With all the constants set to 1, they don't need to be tracked throughout the formula, and can be put back in at the very end by looking at the units. Sprinkle the appropriate (hbar*c) or (mu0*epsilon0) at the end, and then you get your constants back.

killjoywashere 6y ago

Can’t talk to the statute mile, but the nautical mile is sublime: one minute of latitude. The amount of math you can do in your head with a system with so many factors of 2, 3, and 5 is truly amazing.

mulmen 6y ago
I'm not aware of any tricks to make mile calculations easier but the fractional scale common with the inch is very useful for real-world mental calculation and practical exchange. Effectively everything is powers of two. Got something between 1/4 and 1/2 inch? Great, use 1/8ths. It's three. Not close enough? How about five 16ths? It infinitely scales to provide another unit that is suited to the measurement at hand. In some contexts you might just say you pick the closest 1/8th. In others you might use 32nds. You can use the same measuring devices to agree on an ad-hoc standard that everyone understands. But with the metric system you only really get cm (too coarse) and mm (too fine) but you don't get something like 9/16 so you can't "work in 16ths" and have everything be whole units again. Adjusting HVAC in degrees-C is infuriating to my Fahrenheit sensibilities. 20C is cold, 22C is hot. 21C is probably ok but really I want something like 20.5C. The comfortable range for a room is 3-5 whole units of F, but requires a bunch of fractions in C that you may not even have available on your thermostat. Sure, converting between units is easy in the metric system. That doesn't make it the best thing to use all the time. Hell, the idea of thousandths of an inch is used commonly, so even the imperial system is base 1000 in some cases. But I've never seen anyone utilize the fractional scale with metric units, probably because the units are the wrong size for that to be useful.
- onion2k 6y ago
  But with the metric system you only really get cm (too coarse) and mm (too fine) but you don't get something like 9/16 so you can't "work in 16ths" and have everything be whole units again. People who use metric units are perfectly happy rounding to the nearest 0.5cm or 0.25cm if that's what's needed, exactly as people do with inches. Why on earth would you imagine people use mm if something doesn't call for them?

sojournerc 6y ago

As an occasional woodworker and carpenter, I can tell you having evenly divisable (inch) measurements makes mental division a whole lot easier. It's just a case of using the right tool for the job.

deleted 6y ago
[deleted]
mulmen 6y ago
It’s unfortunate that fractional measurements and the base size of units get conflated. Maybe metric users do use fractions and I just don’t hear about it. Is that table one and a quarter meters high?
- spaetzleesser 6y ago
  People often say something is 1 and a half meters long. I don't understand how people can work with inch measurements. How do you divide 7"3/8 by 5? This seems a major pain.
  - mulmen 6y ago
    One and a half seems natural. What about something like a quarter meter? I guess that just becomes some number of centimeters? > How do you divide 7"3/8 by 5? Same way I divide 4.7625 cm by 5. With a calculator.
    - flemhans 6y ago
      > I guess that just becomes some number of centimeters? 25, yes. It's not too hard to do the math. > Same way I divide 4.7625 cm by 5. With a calculator. That's roughly 0.95 right by intuition, but (7"3/8) / 5 doesn't come easy to me.
  - chordalkeyboard 6y ago
    You multiply 7* 8 then add 3 and put that number over 8* 5, resulting in 59/40, roughly 1.5”.