Base-12 Math

[warpus]

OK. Then that's just like Roman Numerals without the refinements of V and X etc. But where's the identity element in base-1?

The identity element depends on the operator, right? Well, in this case, it's got to be 1, since that's the only symbol used. But don't quote me on that.

I think this sort of unary numeric system is only really used on birthday cakes.

 

[Perfection]

Tally marks are unary (albeit with grouping) and used quite frequently

The convenient thing about unary is you can add to a number without erasing what was there before.

 

[Rashiminos]

Er. Base-1 is what, Mr Soup?

This is what I thought he meant:

Base 10 : Base 1
0       : 0
1       : 00
2       : 000
3       : 0000
4       : 00000

and so on...

The identity element depends on the operator, right? Well, in this case, it's got to be 1, since that's the only symbol used. But don't quote me on that.

I think this sort of unary numeric system is only really used on birthday cakes.

Depends on the group in question, but it does have the form a*e = e*a = a where the operands are elements of the group and * is the operator for the group.

Additive identity of reals: 0
Multiplicative identity of reals: 1 (00 in base-1)

Edit: I should specify that the identity element is an unique element of the group for satisfying the above property.

Spoiler :

Base-1 doesn't describe a set of numbers. It describes a system of notation, not the mathematicians find notation to be unimportant, or uninteresting .

 

[Timsup2nothin]

I think in base 1 the base ten number 0 is represented by blank space. Base one is routinely used in score keeping.

 

[Rashiminos]

I think in base 1 the base ten number 0 is represented by blank space. Base one is routinely used in score keeping.

Unary has disadvantages.

 

[Borachio]

 

[tuckerkao]

Of positive integer bases binary of course would provide the biggest bump from 10 to 11 a full 50% boost.

However I would consider ternary as well because you still get a substantial 33% boost and 11 is 4 which is death. And what's more black than turning your amps up to death? None more black!

To Kozmos from post #28: Why not go for base 69 or base 420?

Even base 60 is too large, you need 60 unique symbols for that which will cause the additions and subtractions extremely hard.

Any odd base will make the number-rounding really complicated.


To Perfection from post #32: The real benefit of base 12 is that division by 3 or a power of 3 never results in continued fractions.

Division by 2 or a power of 2

Division by 3 or a power of 3

Division by (2 * 3) or a power of (2 * 3)

Thanks a lot, that gives me a new sub-project to work on. Check out the 1st attached image below, that's for you.


To Borachio from post #40:

3 * 5 = [dec] 15 = [duo] 13.

The duodecimal 13 is a composite number instead of a prime. So we have a luckier 13 there.

Isn't [dec] 13 being unlucky just a tradition?

Chinese people believe 4 and 44 being unlucky.

 

[Perfection]

Okay so do any prisoners actually count days on the wall like this?

Someone figure this out for me, I'm too tired to keep searching.

 

[Borachio]

I imagine they do. Or at least they have done in the past.

Given a period of solitary confinement, and no communication with the outside world, how else could one keep track of the days?

It wouldn't work for me, though. I was always useless at tallying things. "Did I count that one or didn't I?" Sometimes I'd count the same thing twice and sometimes I wouldn't count a thing at all. Hopeless.

 

[Perfection]

I mean it seems reasonable but I can't actually find an instance of it. Where does this ubiquitous stereotype come from?

 

[Timsup2nothin]

In my prison we just used calendars.

From a practical standpoint anyone in a prison of the 'deep dark dungeon' sort where they wouldn't have access to a calendar is probably never getting out, so they actually won't care enough about the passage of time to keep track of it.

Like most stereotypes about prisons and prisoners, this one likely has no basis at all...but it's useful in punch lines so it sticks.

I will say that in the navy almost everyone I knew had a 'short timer chain' which they ceremoniously snipped one link off of every day to keep the number of links equal to their remaining time in service.

 

[Perfection]

In my prison we just used calendars.

From a practical standpoint anyone in a prison of the 'deep dark dungeon' sort where they wouldn't have access to a calendar is probably never getting out, so they actually won't care enough about the passage of time to keep track of it.

Maybe it goes to the idea that under such circumstances with little else to do and solitary confinement what becomes more erratic and perhaps marking time has some important meaning?

Like most stereotypes about prisons and prisoners, this one likely has no basis at all...but it's useful in punch lines so it sticks.

Maybe it's just a stereotype that rose up out of nothing? I dunno, it's just weird how such a thing seems to propagate. Why is it so ubiquitous? I feel like there should be more of an explanation.

I will say that in the navy almost everyone I knew had a 'short timer chain' which they ceremoniously snipped one link off of every day to keep the number of links equal to their remaining time in service.

Interesting. Perhaps that practice is somehow related to the stereotype.

I AM NOT GETTING SATISFACTORY ANSWERS HERE, I IRRATIONALLY FEEL THE NEED TO KNOW HOW THIS THING CAME INTO BEING. THANKS FOR THE INPUT BUT I NEED MORE. WHY DOES THIS CARICATURE EXIST?

 

[Hygro]

I wonder if it started as a POW thing, to keep track of time without calendars.