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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

#181

Post by robocat »

Jedd wrote: post #134
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.

> ... while 68 and 86 are reversed. Just had a flashback - my mum giving me a comparably helpful mnemonic about four decades ago: 16 (c) ~= 61 (f). That, along with human body temperature (38C ~= 98F) have stuck, and between them I can guesstimate most numbers in between on the foreign (F) scale.

37°C (not 38): 37 is a prime, and a centered hexagonal number, if you need some facts to hang your memory on. It's only approximate (same for °F where 98.6 is now seen as "normal"). "Normal" temperature depends on where on the body you measure anyway.

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

#182

Post by fgonzag »

yyyk wrote: post #61

While 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…

I'd say we're way past MK1 units... 7 million years of evolution.

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

#183

Post by JoBrad »

coldtea wrote: post #180
rdiddly wrote: post #165

I basically just use 6. 1.6 is the factor everyone talks about (approximation of 1.609), but it has 2 significant figures. To make mental calculations easier/quicker I use its reciprocal, 0.621, which I approximate with 0.6, which has only one significant figure, 6. Instead of multiplying by 1.6 you would divide by 0.6, which basically amounts to dividing by 6 and then moving the decimal point to someplace plausible.…

> 1.6 is the factor everyone talks about (approximation of 1.609), but it has 2 significant figures. To make mental calculations easier/quicker I use its reciprocal, 0.621, which I approximate with 0.6, which has only one significant figure, 6. How about just 1.5 + 0.1? I.e. the same amount plus half, plus a tenth? So, 55 mi -> 55 + (25 + 2.5) + 5.5 -> 88km And inversely, 0.5 + 0.1, so half plus a tenth: 80km -> 40 +…

This is exactly the way I do math in my head.

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

#185

Post by idlemind »

youeseh wrote: post #19

Come on guys, multiplying by 8 and dividing by 5 shouldn't be that difficult. Worst case scenario, you use your phones to punch it in.

Was hoping someone would say this. Times by 8 divide by 5 is super easy. And easy to reverse when you’re doing km to miles.

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

#186

Post by palimpsests »

RcouF1uZ4gsC wrote: post #148

As a programmer, I am much more facile with powers of 2, than Fibonacci. My way is to double the number 4 times (multiplying by 16) and divide by 10. So for example 55 mph, double 4 times: 110, 220, 440, 880 divide by 10: 88 So 55 mph is approximately 88 km/h

so in other words, you multiply by 1.6. How is having facility with powers of 2 helping you here other than knowing that 2^4 = 16?

I mean, I get what you're saying in that doubling a value several times is relatively easy mental math, and at the same time, this whole thread strikes me as overcomplicating something that doesn't need this much complexity and abstraction.

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

#187

Post by alexanderdmitri »

FabHK wrote: post #137
smcameron wrote: post #109

Earlier quoted context omitted.

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).

There's an argument against intelligent design right there (4 or 6 fingers per hand are obviously better).

Eh, evolution is a pretty nifty mix of oo class extensions, recursion, brute-force and bias weightings.

I'd wager Gawsh made the best system S/He could given product constraints (completely unfocused if you ask me [which I know no one did]) and the real need to deliver (take it easy over there Leibniz, the world is still crap as evidenced everywhere).

Anyway, can't knock it 'til you've built it.

This is an interesting article: https://www.scientificamerican.com/article/why-do-most-speci...

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

#188

Post by busyant »

Stratoscope wrote: post #173
wallace_f wrote: post #102

Earlier quoted context omitted.

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…

You are correct that "10" is a very special number, as long as you don't assume that it can only mean "ten". In fact, every number base is base "10" when you interpret the "10" in that base . Try it: 10 binary is two. 10 octal is eight. 10 hexadecimal is sixteen. This is the very definition of a number base: it is the multiplier that you represent by appending "0" to a string of numeric characters in that base. So th…

This illustrates the idea well: https://i.imgur.com/II5W6Pl.png

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

#189

Post by greggyb »

anamexis wrote: post #163
greggyb wrote: post #87

Earlier quoted context omitted.

I find it helpful to do similar, but mine is fuzzier and tied to day-to-day activities. I am a gross farenheit user, so this is my mental table for cross reference -42|-42: 9th layer of hell 0|32: freezing point 10-15: maybe think about a jacket 20-25: room temp 37|98: body temp 50: death valley 100|212: boiling It's not precise, except for some intersection points, but it sticks well for me and allows me to be conve…

Note: the 9th layer of hell intersection point is -40.

Whoops!

I did say I was imprecise, though (;

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

#190

Post by BeetleB »

rdiddly wrote: post #165

I basically just use 6. 1.6 is the factor everyone talks about (approximation of 1.609), but it has 2 significant figures. To make mental calculations easier/quicker I use its reciprocal, 0.621, which I approximate with 0.6, which has only one significant figure, 6. Instead of multiplying by 1.6 you would divide by 0.6, which basically amounts to dividing by 6 and then moving the decimal point to someplace plausible.…

I had a Canadian car in the US. My rule was simple. I knew the first few multiples of 16 up to 80. And I knew half of 16 is 8. So to convert 35 miles an hour it's just 48+8. And it's very convenient to know that 50 mi is 80km. Beyond that it's just adding 8s or 16s.

For going the other way is just find the nearest multiple of 5 in miles and do a quick approximation. So 70 km. I know that 40 mi is 64 km. Thus 45 mi is 72km. So I'll guess a little lower than 44mi

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