Base-12 Math

[tuckerkao]

The multiplications and divisions are much easier in duodecimal. Clocks and Piano Keyboards are on the 12 scales.

http://www.mathsisfun.com/numbers/convert-base.php

In decimal, 5 is important because it's half of 10. The duodecimal 6 replaces the major importance of decimal 5.


It's the best when the 6th fingers are configured with the adductor pollicis (thumb joint&tendon) connections and with the 3 segmented finger bodies (widest possible stretching on the piano keyboards) -

http://www.livescience.com/20241-hands-fingers.html

If human beings can have the nailless 6th toes, they should grow with the smaller elbow/wrist joint configurations forward from the inner-frontal corners of the heels so the additional toe supports will be directly under the inner foot arches where the adductor pollicis connect the arches and the toes.

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[Timsup2nothin]

I am afraid my mind is too old. I cannot think directly in any alternative base other than binary. So a large amount of mental energy is being squandered on translations to decimal and I do not find anything easy to do in duodecimal.

Good on you though!

 

[onejayhawk]

12 divides by 2,3,4 and 6. 144 divides by 8 and 9. That makes it convenient to use. My biggest problem is the symbols for dec and el (10 and 11).

J

 

[warpus]

Yeah, those symbols are stupid.

I always ever used A and B. What's wrong with those?

 

[Timsup2nothin]

Yeah, those symbols are stupid.

I always ever used A and B. What's wrong with those?

Already in common usage. While they are certainly usable they do tend to push the mind away from thinking in the alternative base as fluidly as it thinks in decimal. Ideally, to train yourself to operate in an alternative base system you should replace all of the symbols.

 

[warpus]

Aren't A, B, C, D, E, and F the standard in hexadecimal notation? From my experience that works far better than symbols people aren't familiar with.

 

[Hygro]

The symbols could at least look like they're from the same family as the other numbers.

But I do agree that base 12 has a lot of conveniences. 60 is quite a deliciously divisible number.

 

[Timsup2nothin]

Aren't A, B, C, D, E, and F the standard in hexadecimal notation? From my experience that works far better than symbols people aren't familiar with.

Yeah they are, and they do work. But from a practical standpoint the only virtue of hex is that it's useful shorthand for binary. To be useful as an alternative base system for 'everyday' use it not only has to make the operations convenient (which as shown base 12 really does) it also needs to draw the mind away from the 'base ten is natural' response...otherwise the calculations have to be done under a burden of constant distraction as conversions fire off automatically. It's similar to taking someone raised, educated, and experienced with English measure and having them do problems in metric measure...the metric measure is easier to work with and makes more sense, and they know it, but they will still be constantly and automatically converting.

It would be interesting to produce a base 12 numeric system with all new symbols and just start from scratch learning basic arithmetic and see if it would be possible to pull the mind completely into a new track.

 

[warpus]

I'm looking at this thing from a completely different perspective - when I was going through university I had to do math in several numeral systems, and the standard always seemed to be that you use a capital letter A for 10, B for 11, and so on..

The reason this was done is because it works well.. and everybody is used to that being the standard. So there is 0 confusion in whatever number system you are working in - whether it's base 14 or base 23. When you're a math/cs person and you see 233F on a test you think to yourself.. "hex? maybe some other base?".. but when you see 233{something that looks like a Greek letter} you think "Oh crap, a variable I didn't get to in the readings.. I .. am.. screwed..."

But like, that is not really neither here nor there nor wherever else. 12 makes for a pretty good and well balanced numeral system - we do use it for time after all. If only we all had 6 fingers on each hand, then maybe things could have gone even better for base-12.

 

[FriendlyFire]

I though that the US did everything in imperial ???

 

[Perfection]

Base-12 is Gross

 

[sophie]

I though that the US did everything in imperial ???

We do, except for the number system. Given that all US measurements are in multiples of 3 or 4, we should probably do a base-12 or similar numbering system. Just to be different :3

 

[onejayhawk]

Base-12 is Gross

Nah. Base-12^2 would be.

J

 

[Kozmos]

Go Hex or go home.

 

[Perfection]

16, babe!

Deface 12, a dead fad!

 

[tuckerkao]

Yeah, those symbols are stupid.

I always ever used A and B. What's wrong with those?

8 and A: Verbally very hard to distinguish.

18-> eighteen, 1A-> A-teen, (88, 8A, A8, AA)

8 and B: Visually very hard to distinguish on the digital clock.


[dec] 151 = [duo] 107 = [hex] 97

[duo] 107 / 3 = 42.4
[hex] 97 / 3 = 32.555555555555

[duo] 107 / 6 = 21.2
[hex] 97 / 6 = 19.2AAAAAAAAAAA

[duo] 107 / 9 = 14.94
[hex] 97 / 9 = 10.C71C71C71C71

 

[warpus]

While those sound like for the most part reasonable objections, in practice I don't remember running into any such problems, during all of my computer science/math university career. And of course that's anecdotal, but I also don't remember any prof or any other student ever complaining.

Are these symbols you've posted accepted as standard ones by any group?

 

[tuckerkao]

The main reason I use the 2 different symbols is to avoid the confusions between duodecimal and hex. Most people think hex when they see A and B.

The 2 symbols (I created them) are actually one line visually apart from '10' and '11' with the sort rotated angle.

It has to take a special poll to the students whether verbal 8 and A, visual 8 and B on digital clock will affect them if the new numerical system applies on their daily life basis.

For Base 20+, I know many people jumping from H to J because of I and 1.

 

[Rashiminos]

Maybe instead of trying to use one base representation XOR the other, we could instead employ each representation based on the convenience it lends to the subject at hand?

 

[Borachio]

Base-12 is Gross

A gross being 12^2, of course.

12 could be a useful stacking number in logistics. A layer of boxes on a pallet, for instance, can be 3 x 4, so that the next layer 4 x 3 binds in naturally.

In practice, though it isn't used like that. Not as I remember, anyway.