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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

#191

Post by wallace_f »

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…

That is nice of you to provide such a well-written answer, and a human response at the end.

Your reasoning seems quite obvious now with hindsight after having given it some thought; and yet, even still I have such a strong inclination that ".........." is a special number? Why? I guess it really is entirely my cognitive bias, because I can't find a reason for it.

But I should have known better as I've--probably obviously being a user here--encounteted binary more than just a few times. And even still, it never occurred to me that 10 in binary is just ".." And then 100 in binary is 1 order of magnitude of "..," 4. And 1,000 is just two orders of magntiude, 8. But still, intuitively this does not seem as natural as 10, and I guess that is completely cognitive bias.

Am I retarded to not have realized this? Maybe, but I actually was so curious about this that I tried to quiz some colleagues by asking what 1000 and 1001 is in binary and only one person got it right immediately, probably by understanding orders of magnitude and not by rote memorization. All the others got it by counting in binary, and one final person was annoyed and questioned why I was asking about binary (oops, sometimes being inquisitive is not socially acceptable). By the way, I work with app developers, most of whom do not have backgrounds in computer science, same as myself.

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

#192

Post by frosas »

skykooler wrote: post #164
xkgt wrote: post #101

Earlier quoted context omitted.

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.

For inches to cm in my head, I multiply by 10 and then divide by 2 twice. E.g. 7 inches -> 70 -> 35 -> ~17.5 cm.

I do something similar but, because I'm faster at multiplying, I do "its double plus its half". E.g. 7 inches = 14 + 3.5 = 17.5 cm

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

#193

Post by _ptgt »

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 = 8/5

So n miles = 8n / 5 km

And m km = 5m / 8 miles

Fraction multiplication is actually much easier than decimal multiplication imo. I'm surprised so many people seem to avoid it. Keeping track of where the decimal point should be is a significant cognitive load.

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

#194

Post by aquadrop »

eps wrote: post #4

In related news - pounds to kilos is "divide by 2, less 10%". Very precise too. 160lbs = 80 - 8 = 72kg

I have similar way of calculating square meters from square feet. "Subtract 10% divide by 10". So for example 900 square feet: 900 - 90 = 810/10 = 81. Real answer is 83.6, close enough for me.

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

#196

Post by madez »

wallace_f wrote: post #191
Stratoscope wrote: post #173

Earlier quoted context omitted.

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…

That is nice of you to provide such a well-written answer, and a human response at the end. Your reasoning seems quite obvious now with hindsight after having given it some thought; and yet, even still I have such a strong inclination that ".........." is a special number? Why? I guess it really is entirely my cognitive bias, because I can't find a reason for it. But I should have known better as I've--probably obvio…

It seems you are inutitively always converting everything to the decimal system and taking that as "the way" to think about numbers. That wouldn't be surprising, because we are brought up this way and even our language focusses on the decimal system. Not having good words to speak about the binary number 1101001 makes it difficult to think about it without converting it first. Two (I'm decimal again!) isn't a good base for human communication because there is a lot of repitition of simple symbols. Maybe a new way to pronounce hex numbers like a17c03 would be able to replace the decimal system.

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

#197

Post by whatever1 »

I had arrived to the same approach by accident, basically by looking at the car analog speedometer and noticing which denoted mile increments match almost exactly the km increment. You can see for example that the 80kph "tick" is located exactly where the 50mph is. Then if you observe all the ones that match, you can see a sequence emerging.

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

#198

Post by greggyb »

greggyb wrote: post #189
anamexis wrote: post #163

Earlier quoted context omitted.

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

Whoops! I did say I was imprecise, though (;

Double-checked earlier this morning, though. At least I got my Dante right! (:

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

#199

Post by anongraddebt »

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 +…

I often do mental math like this. However, sometimes it is faster to not split up calculations like this. For instance, in the case of converting 55 mi, it's faster (at least, for me) to just divide 54 by 6, move the decimal, and call it a day.

I've found that calculations are faster when you know when and when not to split calculations like the way you describe (even though at least 80% of the time it's faster to split them up).

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

#200

Post by martin_a »

runarberg wrote: post #50
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.

I've heard that and I don't disagree with it. But things fail really badly. E.g. 2 inches and 5 sixteenth

I find this hilarious when watching DIY videos on YouTube.

All the makers are talking about "5/16 of an inch" and I'm trying to convert this to a metric value and it doesn't make any sense at all, because "complex" fractions like this are not used in every day life.

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