In related news - pounds to kilos is "divide by 2, less 10%". Very precise too. 160lbs = 80 - 8 = 72kg
Any similar shortcut for feet inches to cm? I find this conversion to be slower to compute than miles to km or lbs to kg.
A mathematician's way of converting miles to kilometers
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Re: A mathematician's way of converting miles to kilometers
#102While using only additions and shifts (if we generalize) without floating point or multiplication should appeal to HN, this method uses a lookup table and calculating values needs a lot of memory accesses e.g. f(7) => f(4) + f(3) => (f(3) + f(5)) >> 2 + f(3) . The Human Mk1 processing units are also capable of small multiplication/divisions, especially on bases 2 and 10, but bad at lookups - who thought manufacturing…
What if we had just 4 digits on each limb or even 6 perhaps. How does those numbers look in base 8 or 12.
I never bought this argument, but I'm not confident about it. Isn't base 10 inherently intuitive because of the obvious reasons? IE an order of magnitude is just another 0?
Since I learned about base 2, etc, long ago, I always thought there was something magically elegant about base10 and never understood this? The explanation I've always heard, being 10 fingere, doesn't seem to explain all the elegance with base 10 being easy to work with?..?
Re: A mathematician's way of converting miles to kilometers
#103It's both easier and more accurate to multiply by 1.6
Yeah times 1.6 isn't too hard right? Just add 50% and 10% in succession, very easy to do in your head. The other way around is trickier. I tend to divide by 8 (or /2/2/2) and multiply by 5, which is harder but still consists only of steps that are clearly defined in my head.
Yeah, converting via the 5/8 ratio is how I've always done it. I traveled to Florida a number of times as a kid, and for whatever reason I have a permanent memory of the speed limit signs showing "55 MPH / 88 KMH". It's weird what one's brain seems to fixate on sometimes...
Re: A mathematician's way of converting miles to kilometers
#104In related news - pounds to kilos is "divide by 2, less 10%". Very precise too. 160lbs = 80 - 8 = 72kg
Any similar shortcut for feet inches to cm? I find this conversion to be slower to compute than miles to km or lbs to kg.
@sigfpe in a reply to the tweet mentioned
Fₙ in ≈ Fₙ₊₂ cm
Re: A mathematician's way of converting miles to kilometers
#105Earlier quoted context omitted.
don't they still use pounds per square inch ? Now, in Europe (excluding the UK) they also still use some weird units from the past. Calories for example, and horse (!!) power.
A calorie was originally defined as as the amount of heat required at a pressure of 1 standard atmosphere to raise the temperature of 1 gram of water 1° Celsius. But you're right that is sort of a weird unit from the past insofar as it's related to the SI system but isn't formally part of it. (It's basically now defined by its ratio to joules.)
Adding: There are a number of measurements that aren't necessarily obviously related but are actually the same thing in terms of units. Heat, work, and energy are all newton meters or kg m^2/sec^2 in SI units.
Re: A mathematician's way of converting miles to kilometers
#106Does not seem to be very convenient for figures which are not the product of one of the first few members of the Fibonacci sequence and a power of 10, at least compared to multiplying by 1.6.
Re: A mathematician's way of converting miles to kilometers
#107Since 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.
It's not an approximation...
To convert from m/s to km/h you need to divide by 1000 (there are 1000 meters in 1 km) and multiply by 3600 (there are 3600 seconds in 1 hour).
So 3600/1000 = 3.6
Re: A mathematician's way of converting miles to kilometers
#108Re: A mathematician's way of converting miles to kilometers
#109Earlier quoted context omitted.
What if we had just 4 digits on each limb or even 6 perhaps. How does those numbers look in base 8 or 12.
I never bought this argument, but I'm not confident about it. Isn't base 10 inherently intuitive because of the obvious reasons? IE an order of magnitude is just another 0? Since I learned about base 2, etc, long ago, I always thought there was something magically elegant about base10 and never understood this? The explanation I've always heard, being 10 fingere, doesn't seem to explain all the elegance with base 10…
In base 8 (if we'd had 8 fingers), an "order of magnitude" would have been defined as "times 8" instead of "times 10", so it would also be adding another 0. Same with base 12. Base 16 would have the further advantage that we could easily halve, quarter, eighth, or 16th any number ending in 0 to a whole integer (in base 10, we can only halve, fifth, or tenth).
Re: A mathematician's way of converting miles to kilometers
#110Earlier quoted context omitted.
What if we had just 4 digits on each limb or even 6 perhaps. How does those numbers look in base 8 or 12.
I never bought this argument, but I'm not confident about it. Isn't base 10 inherently intuitive because of the obvious reasons? IE an order of magnitude is just another 0? Since I learned about base 2, etc, long ago, I always thought there was something magically elegant about base10 and never understood this? The explanation I've always heard, being 10 fingere, doesn't seem to explain all the elegance with base 10…
Base 10 is intuitive because we are taught to work in base 10. If we worked in base 7, then multiplication by seven would be just another 0. (And if we worked in base 7, we would probably have defined “an order of magnitude” to be a multiplication by 7, rather than 10).