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A mathematician's way of converting miles to kilometers

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Re: A mathematician's way of converting miles to kilometers

#91

Post by rocqua »

Moru wrote: post #81
rocqua wrote: post #74

Earlier quoted context omitted.

I like arguing for arcane standards, and there are aspects of the imperial system I like. Specifically, I tend to advocate for a base 12 system based arround the inch. Base 12 because the very structured multiplication table, which also makes for easy dividing. The inch because I find my lengtg estimation accuracy to be better captured by inches.

Your length estimation accuracy is dependent on what you used more.

I have never used inches outside screen diagonals. Yet I still feel inches better match my accuracy. My actual accuracy in inches is horrible though, because I never get into contact with them.

Re: A mathematician's way of converting miles to kilometers

#92

Post by ciceryadam »

ghaff wrote: post #49
jedberg wrote: post #46

Earlier quoted context omitted.

> which miles vs. kilometers doesn't really in day-to-day life Standard units are much more useful in carpentry. It's a lot easier when you can divide by 2,3,4, and 6.

Yep. Factoring is useful in a lot of cases. Also, although not strictly a debate around metric, the Fahrenheit scale gives you more granularity without going to decimals and requires less use of negative numbers on a day to day basis. And, if one is really concerned about a scientifically relevant temperature scale, we'd be using Kelvin, not Celsius.

Kelvin IS Celsius, only starts at absolute zero. 0 C is 273 Kelvin, and 0 Kelvin is -273 Celsius. You add 273 to any Celsius measurement, and voila, it's Kelvin.

Re: A mathematician's way of converting miles to kilometers

#93

Post by zonidjan »

jedberg wrote: post #46
ghaff wrote: post #14

Earlier quoted context omitted.

There are a fair number of people who seem to take personal offense that the US (and to some degree the UK) don't use SI for everyday types of things and add it to their laundry list of grievances about the US generally. Never mind the fact that SI is generally used for engineering and other areas where it has legitimate advantages (which miles vs. kilometers doesn't really in day-to-day life).

> which miles vs. kilometers doesn't really in day-to-day life Standard units are much more useful in carpentry. It's a lot easier when you can divide by 2,3,4, and 6.

It's a lot easier to do things when you don't have to go "okay, what's the conversion between these two units again?". The problem isn't base 10 vs base 12, it's the fact that in SI, every unit scales in the same way (the prefixes). With imperial units, every unit scales differently. How many fl.oz to a tablespoon? No idea. How many teaspoons to a tablespoon? No idea.

Re: A mathematician's way of converting miles to kilometers

#94

Post by sgentle »

magoon wrote: post #73

I use a similar method of easy-to-remember numbers in conversion between celsius to Fahrenheit: 0 = 32 10 = 50 20 = 68 30 = 86 Then roughly, subtract/add two F for every extra C. It’s easy to remember 32 and 50, while 68 and 86 are reversed.

I use "double and add 30" (or "minus 30 and halve" for F->C). The accuracy isn't that great, but it's within single digits between freezing and boiling. More than good enough to parse "oh my god it was like 40 degrees outside" as being a meaningful statement about the weather.

Re: A mathematician's way of converting miles to kilometers

#95

Post by ghaff »

ciceryadam wrote: post #92
ghaff wrote: post #49

Earlier quoted context omitted.

Yep. Factoring is useful in a lot of cases. Also, although not strictly a debate around metric, the Fahrenheit scale gives you more granularity without going to decimals and requires less use of negative numbers on a day to day basis. And, if one is really concerned about a scientifically relevant temperature scale, we'd be using Kelvin, not Celsius.

Kelvin IS Celsius, only starts at absolute zero. 0 C is 273 Kelvin, and 0 Kelvin is -273 Celsius. You add 273 to any Celsius measurement, and voila, it's Kelvin.

No. That's actually not quite correct. You add 273.15... The size of the degree is the same of course.

My point is that if you want to use a "correct" scientific measurement on a day to day basis you'd use Kelvin. As soon as you're converting, you're converting whether from Celsius or Fahrenheit.

ADDED: There's an argument for Celsius vs. Fahrenheit of course in so far as the size of the degree is baked into some other SI measurements. But there's no particular other reason that Celsius is superior on a day to day basis other than familiarity for some. There's some logic to basing easy to remember numerical points around water properties but it's not clear that actually has a lot of advantages for day-to-day questions about how hot or how cold it is.

Re: A mathematician's way of converting miles to kilometers

#96

Post by Phenomenit »

aerophilic wrote: post #77

Since we are talking about “useful approximations”, one I have always found useful in robotics is doubling m/s to get miles per hour. While a bit “rough” usually “good enough” for when thinking about normal driving speeds. Here are some examples: 1 m/s ~ 2 mph (2.2 mph) 5 m/s ~ 10 mph (11.2 mph) 10 m/s ~ 20 mph (22.4 mph) 20 m/s ~ 40 mph (44.7 mph) 30 m/s ~ 60 mph (67.1 mph) You could argue that it is a very rough es…

In physics class we used 3,6*m/s to get km/h all the time. It's not superclean but it 3,6 is still pretty easy to multiply or divide with.

Re: A mathematician's way of converting miles to kilometers

#97

Post by iiv »

Phenomenit wrote: post #96
aerophilic wrote: post #77

Since we are talking about “useful approximations”, one I have always found useful in robotics is doubling m/s to get miles per hour. While a bit “rough” usually “good enough” for when thinking about normal driving speeds. Here are some examples: 1 m/s ~ 2 mph (2.2 mph) 5 m/s ~ 10 mph (11.2 mph) 10 m/s ~ 20 mph (22.4 mph) 20 m/s ~ 40 mph (44.7 mph) 30 m/s ~ 60 mph (67.1 mph) You could argue that it is a very rough es…

In physics class we used 3,6*m/s to get km/h all the time. It's not superclean but it 3,6 is still pretty easy to multiply or divide with.

Well, that is literally how to convert between them. It's not an approximation.

Re: A mathematician's way of converting miles to kilometers

#98

Post by gus_massa »

magoon wrote: post #73

I use a similar method of easy-to-remember numbers in conversion between celsius to Fahrenheit: 0 = 32 10 = 50 20 = 68 30 = 86 Then roughly, subtract/add two F for every extra C. It’s easy to remember 32 and 50, while 68 and 86 are reversed.

If you want to get fancy, you can call it the Taylor approximation.

I'm a bit lazy so I try to use the F(c)= 2 * c + 32 approximation described in a sibling comment, but for the range of human-friendly temperatures the error is too big. The problem is not the absolute difference, but how each temperature feels. So I have to resort to making the exact calculation or using Google for the conversion. I'll try your method in the future.

Re: A mathematician's way of converting miles to kilometers

#99

Post by jypepin »

sgentle wrote: post #94
magoon wrote: post #73

I use a similar method of easy-to-remember numbers in conversion between celsius to Fahrenheit: 0 = 32 10 = 50 20 = 68 30 = 86 Then roughly, subtract/add two F for every extra C. It’s easy to remember 32 and 50, while 68 and 86 are reversed.

I use "double and add 30" (or "minus 30 and halve" for F->C). The accuracy isn't that great, but it's within single digits between freezing and boiling. More than good enough to parse "oh my god it was like 40 degrees outside" as being a meaningful statement about the weather.

and it has never failed me! +1
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