Imperial vs. Metric, Base 2, Base 10, Base 12

erik · Post by **erik** » Thu Jan 03, 2013 2:02 pm

If you are counting past 100 on your hands they're already gonna think you're crazy.

Cynic · Post by **Cynic** » Thu Jan 03, 2013 4:31 pm

I used to use base 12 when I was a pious hindu and had to count my daily 108 chants in the morning (fucking monotonous) and then 32 in the afternoon and then 64 in the evening. As part of the ritual it was easier but this is literally what it's okay for. But technically this would also be more convenient if I used base 12 in the morning and then base 16 for the afternoon and evening count.

If I want to do some personal monotonous large number counting then fine, it's okay. But that's about it. There's no real reason to do the count to and use your figures to notate it to people. PL is (strangely) right. if you want to do some crazy counting, use a secondary device. An abacus is convenient but I'm sure stuff like a pencil & paper, a computer would also be more convenient.

Lago PARANOIA · Post by **Lago PARANOIA** » Thu Jan 03, 2013 4:51 pm

I know we have at least two expert math people in here; I wonder what they think about this whole debacle.

virgil · Post by **virgil** » Thu Jan 03, 2013 5:10 pm

Personally, I'm kind of confused at PL's furniture-chewing on metric vs imperial; as imperial isn't really base 12, so the rant is orthogonal to the OP.

As for comparing 12 and 10, it depends on the purpose and context. Were to I ask "oranges or peanuts?", personal preference will give a different answer as opposed to nutritional value or cost or storage...

nockermensch · Post by **nockermensch** » Thu Jan 03, 2013 6:40 pm

Lago PARANOIA wrote:I know we have at least two expert math people in here; I wonder what they think about this whole debacle.

It's arbitrary, Iago. As long as you're not using a huge mess like the imperial system, any baseN system will work.

Of course, our culture is already tightly coupled with the base 10 system, so anything but it requires extra thinking to understand. But you could have a modern technological civilization using base 12, 20, 16, 2 or whatever.

PS: Making your baseP for P = prime > 2, is generally a dick move. Don't do that.

RobbyPants · Post by **RobbyPants** » Thu Jan 03, 2013 7:01 pm

nockermensch wrote: PS: Making your baseP for P = prime > 2, is generally a dick move. Don't do that.

Why is that?

Emerald · Post by **Emerald** » Thu Jan 03, 2013 7:28 pm

RobbyPants wrote:
nockermensch wrote: PS: Making your baseP for P = prime > 2, is generally a dick move. Don't do that.
Why is that?

Fractions of prime bases like, say, 7 or 13 are ugly and often non-repeating, and when was the last time counting things in groups of 7 or 13 was useful to you?

RobbyPants · Post by **RobbyPants** » Thu Jan 03, 2013 8:05 pm

Emerald wrote:
RobbyPants wrote:
nockermensch wrote: PS: Making your baseP for P = prime > 2, is generally a dick move. Don't do that.
Why is that?
Fractions of prime bases like, say, 7 or 13 are ugly and often non-repeating, and when was the last time counting things in groups of 7 or 13 was useful to you?

Well, if you were working in base seven, wouldn't your "digits" all be 0 - 6? So, wouldn't 3/7 be something like 0.3 and 10/7 be 1.3? I could be entirely wrong on this. I don't know how decimals work in non-base 10 systems. Also, wouldn't counting things in groups of seven be entirely natural?

Or is this all from the context of using a different system while we're already used to base 10?

John Magnum · Post by **John Magnum** » Thu Jan 03, 2013 8:25 pm

I'm a math expert but not in arithmetic or number theory specifically, but as I said before it might be very slightly nicer to do base 12 but it's really not remotely a big deal.

To me, the big worrying innumeracies of human thought are hideously bad probability estimations and scope insensitivity, and neither of those is really affected by fiddling around with the number base.

Juton · Post by **Juton** » Thu Jan 03, 2013 8:29 pm

RobbyPants wrote:Well, if you were working in base seven, wouldn't your "digits" all be 0 - 6? So, wouldn't 3/7 be something like 0.3 and 10/7 be 1.3? I could be entirely wrong on this. I don't know how decimals work in non-base 10 systems. Also, wouldn't counting things in groups of seven be entirely natural?

Or is this all from the context of using a different system while we're already used to base 10?

I believe you are correct about the decimals. Having a numerical base that is easily divisible is handy for a lot of things, but having a system with a base of 7 doesn't make things impossible. Off the top of my head doubling a number won't always mean that the product is even, which is a change from base 10. Dividing a number in half is also a little more awkward too.

John Magnum · Post by **John Magnum** » Thu Jan 03, 2013 8:45 pm

Well, by definition doubling a number makes the product even since it's divisible by two, but 2 x 6 = 15 in base 7 so the final digit of an even number is not always an even digit.

And yeah, the point isn't that X/7 will be ugly, it's that every fraction BUT X/7 will be ugly. 1/2 in base 7 is a big repeating decimal of ugliness, the way 1/7 in base 10 is 0.142857142857...

In base 10, X/2 and X/5 are both nice. In base 12, X/2, X/3, X/4, and X/6 are nice, but X/5 isn't. This would give us some nice new divisibility rules. It's a lot easier to tell a number is divisible by 3 by checking if the last digit is divisible by 3 than by adding up all the digits and seeing if the sum is divisible by 3.

RobbyPants · Post by **RobbyPants** » Thu Jan 03, 2013 8:57 pm

John Magnum wrote: And yeah, the point isn't that X/7 will be ugly, it's that every fraction BUT X/7 will be ugly. 1/2 in base 7 is a big repeating decimal of ugliness, the way 1/7 in base 10 is 0.142857142857...

In base 10, X/2 and X/5 are both nice. In base 12, X/2, X/3, X/4, and X/6 are nice, but X/5 isn't. This would give us some nice new divisibility rules. It's a lot easier to tell a number is divisible by 3 by checking if the last digit is divisible by 3 than by adding up all the digits and seeing if the sum is divisible by 3.

Oh, I see what you mean. That makes sense.

Juton, I think you broke the boards. Also, the way your tags are broken, you're making it look like I said what Emerald did, and you said what I did.

John Magnum · Post by **John Magnum** » Thu Jan 03, 2013 9:57 pm

Actually, 1/2 isn't that bad in base 7, it's just 0.3333..., but that's still not very nice. And EVERY OTHER fraction except 1/7 (or 1/49, etc.) will be some form of repeating decimal, because everything except multiples of 7 are relatively prime to 7.

erik · Post by **erik** » Thu Jan 03, 2013 10:28 pm

John Magnum wrote:In base 10, X/2 and X/5 are both nice. In base 12, X/2, X/3, X/4, and X/6 are nice, but X/5 isn't.

I'm almost sold on base 12 just on this. But I'd like to have x5 too, so how bout base 60? =-D

John Magnum · Post by **John Magnum** » Thu Jan 03, 2013 10:39 pm

The two obvious tradeoffs are new numerals and the expanded multiplication tables.

It's not very hard to come up with two new glyphs to use for 10 and 11, but you'd need a lot more to do base 60. If you don't want to come up with fifty new numerals, one possibility is to use a hybrid numeral system, where each base 60 "digit" is actually expressed as a base 10 multidigit number, so 100 in base 10 would be represented as (01) (40) = 1 * 60 + 40 * 1 = 100. But either way, changing the numeral system from 10 to 60 is much, much harder than going from 10 to 12.

The other issue, even smaller, is that the multiplication tables get bigger. In base 10, there's a hundred entries in the times table that you memorize before you can do arithmetic. In base 12, it's 144, which is bigger. But in base 60, it's 3,600, which is gargantuan. You would once again have to rewrite how you do pencil-and-paper arithmetic.

Obviously not a serious suggestion, but it's fun to point out the actual issues with systems that go above and beyond centuries of inertia.

Josh_Kablack · Post by **Josh_Kablack** » Fri Jan 04, 2013 5:50 am

So, any of you metric fans want to specify a useful body-part to metric-length-unit correspondence?

Username17 · Post by **Username17** » Fri Jan 04, 2013 10:31 am

Josh_Kablack wrote:So, any of you metric fans want to specify a useful body-part to metric-length-unit correspondence?

A centimeter is the height of my pinky. Not the length of the last segment (which is an inch), nor the width (which is a centimeter and a half), but the height. As in: if I put my hand palm-down on the table, anything I put on top of my pinky will be one centimeter off the table.

-Username17

PhoneLobster · Post by **PhoneLobster** » Fri Jan 04, 2013 10:23 pm

Josh_Kablack wrote:So, any of you metric fans want to specify a useful body-part to metric-length-unit correspondence?

Is your foot actually a foot long?

WTF body part is a Yard?

Etc...

The imperial length measurements based on body parts thing was scrapped for a reason. That being that it was inconsistent and led to confusion and arguments. Because, fuck you I am 6 foot 7... in my own feet lengths and only in my own feet lengths... (edit: And a reasonable 6 foot in Ypres Belgium, nearly 5 foot 5 in modern short lived international imperial, and no more than 4 foot 8 just down the road in Angoulême France)

The inconsistency in body parts as measurements can be observed in the many different lengths of feet used prior to both metric and the various (apparently rather short lived?) internationalized imperial measures in various countries. So go check out the vast table on this page for an idea.

Feet ain't feet. Simple as that.

(and before you say that someone somewhere surely has foot long feet and golly how convenient it must be for that one guy... my girlish tiny (hairy flat) feet turn out to be nearly exactly 25cm long. So suck on the convenience of the 4 foot meter! Lets standardize it? No? Damn, didn't think so...)

virgil · Post by **virgil** » Sat Jan 05, 2013 12:25 am

PhoneLobster wrote:WARGLBLARGLL!!!

Y'know, you could've taken it in a good natured manner like Frank did, rather than rant and rave like a bitter jerk at imagined praise for imperial.

Maj · Post by **Maj** » Sat Jan 05, 2013 2:32 am

I thought that inches were defined as the length of three barley grains. Unless you're a scarecrow, I don't imagine that's a body part.

PhoneLobster · Post by **PhoneLobster** » Sat Jan 05, 2013 5:02 am

virgil wrote:Y'know

Why gee. I wouldnt want to be posting bitter content free thread shitting nonsense would I so I gue...

...wait... thats what YOU are doing!

virgil · Post by **virgil** » Sat Jan 05, 2013 5:10 am

PhoneLobster wrote:
virgil wrote:Y'know
Why gee. I wouldnt want to be posting bitter content free thread shitting nonsense would I so I gue...

...wait... thats what YOU are doing!

I freely admit to my black pot.

Prak · Post by **Prak** » Sat Jan 05, 2013 5:13 am

Maj wrote:I thought that inches were defined as the length of three barley grains. Unless you're a scarecrow, I don't imagine that's a body part.

So far as I know, the foot was the length of some king's foot, the inch something to do with his thumb, etc.

Count Arioch the 28th · Sat Jan 05, 2013 6:28 am

I can measure 26 cm...

erik · Post by **erik** » Sat Jan 05, 2013 6:50 am

So, if the world goes sane and we finally dump imperial crap for metric, will there no longer be any inching along? I'll be sad to lose that verb.

[edit: and moar because I have base 12 n' 60 thoughts unrelated to this post and didn't feel like double-posting.]

The multiplication table concern seems a bit weird. We actually started by memorizing up to 12x12 anyway in my school.

Minor nitpick, there aren't really 100 calculations to memorize in the 10x10 multiplication tables (nor 3600 in the 60x60). There's 55 unique calculations in the 10x10 grid. 45 if you don't count the 1's. 36 if you don't count the 10's either. I don't count the 1's and 10's since they're more of a memorization of a simple replacement rule rather than a product of 2 terms, and the duplicates are just learning the commutative property of multiplication. So 39 things to memorize in the 10x10 table in all, 36 of which are raw calculations.

It's certainly possible to memorize the 1700ish calculations necessary for a 60x60 multiplication table, but oy. OY. But I wonder if you really need to even bother. I wonder how miserable or not my math classes would have been if I hadn't had multiplication tables beaten into my brain. Hrm. I am having a hard time framing 37*49 in base 60 in my mind without first converting it back into base 10, but maybe that's just because I can't even frame it in base 60 to begin with.

Having 60 numeral symbols seems outrageous to me, but then again I never did learn a logogram language, I dunno. Still, it seems like in math it would take up unnecessary contextual space causing arithmetic to go more slowly.

For funsies, I made up base numerals 12 using 1 or 2 strokes for each numeral in such a way that hopefully they are all easy to distinguish, easy to write, and don't overlap with math essentials like: x = - + / < >

No idea if this would be easier or harder for people with dyslexia.