The Gaming Den

So. What are the big advantages of base 10 over base 12?

We have ten fingers and ten toes, so our number system is base 10. This makes counting by ten very easy, because the system is set up for counting by ten, and so decimal fractions - which is what all money these days uses - are also very easy. Metric makes conversions between units absurdly easy as well.

I was actually very surprised to learn how practical ye olde base-12 system was - it involved counting on the joints of your fingers with your thumb. 1s digit on one hand, and 12s digit on the other hand, you can easily get to 156 on just your fingers.

angelfromanotherpin wrote:I was actually very surprised to learn how practical ye olde base-12 system was - it involved counting on the joints of your fingers with your thumb. 1s digit on one hand, and 12s digit on the other hand, you can easily get to 156 on just your fingers.

I want to second this, this is easy to learn and I use it sometimes if I'm really tired and I have to count something large.

About base 2 vs 10 vs 12, it doesn't make much of a difference for the majority of metric calculations. The only ones it should affect are the ones involving logarithms, base 10 logarithms are different then base 12 logarithms. Decibels and pH are both base 10 logarithms so we'd have to reword all those values if we changed to a different numeric base, or just label them as log10.

Yeah, it's basically arbitrary. Since we all grew up using base 10, then a system that works in base 10 is easy to work with and "intuitive". If we all grew up using base 12, then the metric system would all be in powers of 12, and that would be the easy system.

The Imperial system is so weird, not only because it's not base 10, but because the conversion rates from one unit to the next are completely arbitrary.

So, when I want to go from milliliters to centiliters to deciliters to liters to decaliters to hecaliters to kiloliters, I know the rate is 10 -> 10 -> 10 -> 10 -> 10 -> 10.

If I want to go from teaspoons to tablespoons to ounces to cups to pints to quarts to gallons, I have to remember that shit is 3 -> 2 -> 8 -> 2 -> 2 -> 4, in addition to doing the weird math.

Remembering distances conversions of 12 -> 5280 or 12 -> 3 -> 1760 are just weird.

As someone who works with water a lot let me point out that the advantages of the metric system are numerous.

So its not JUST the whole planned system with sensible conversions and consistent units and the convenience of the number ten (no I don't care about your elaborate knuckle dragging imperial counting methodology. Get a fucking abacus like the ancient Chinese if you are into archaic large number counting action and laugh at the backward western methods).

It's things like the way the system interacts with/is based on weights and volumes of water. The 1 liter, 1 kilo, cubic 10cm, 1000 liter, cubic meter, metric ton, etc...

It of course isn't precisely perfect due to slight differences in density, temperature, water impurities etc... but the convenient short hand and conversion for all sorts of water related engineering endeavors is just pure gold.

There are MANY reasons imperial as a measurement system is dead in basically all sensible professions that rely on using measurement systems.

So get yourself a god damn abacus and a metric ton of water and stop trying to make excuses for the USA's odd obsession with the Mile and the Foot and the Inch.

(oh and thats the other advantage of metric, its the fucking world standard).

Being the world standard doesn't make actual metric a better measuring system than a theoretical Base 12 Metric, it just means it was more widely adopted. There's also no reason a metric-like system in some other base couldn't define its base units in a water-friendly fashion.

If I need to count something and don't want to count in my head, I often use base 6. One hand is units, the other is multiples of six. It only reaches 35, but that's better than 10. Base 6 results in significantly less compact written numbers than Base 10 though.
Base 12 is likely a good breakpoint because it is more compact than Base 10, can be evenly divided by three and four (at the expense of division by 5), and only requires memorizing the appearance of two more digits.

Base 12 gives no inherent advantage because our numeral notation system is ten digits. That's the reason we have to count 0 1 2 3 4 5 6 7 8 9 A B when we do base 12, we've literally run out of fucking numbers.

rampaging-poet wrote:Being the world standard doesn't make actual metric a better measuring system than a theoretical Base 12 Metric, it just means it was more widely adopted. There's also no reason a metric-like system in some other base couldn't define its base units in a water-friendly fashion.

If I need to count something and don't want to count in my head, I often use base 6. One hand is units, the other is multiples of six. It only reaches 35, but that's better than 10. Base 6 results in significantly less compact written numbers than Base 10 though.
Base 12 is likely a good breakpoint because it is more compact than Base 10, can be evenly divided by three and four (at the expense of division by 5), and only requires memorizing the appearance of two more digits.

Base not 10 may have some benefits to it. But people think in base 10, so whatever benefits they are, they will always be not as important for measurement systems. If you want to convert to base 12 metric you need to do one of the following shitty things:

1) Have your measurement system be a super secret high level math only system that only scientists use, while all the plebeians must continue buying in liters that are base 10.

2) Make a sudden violent shift in teaching so that you totally teach everyone in the entire fucking world to count in base 12 all the time for everything as the default and introduce them to base 10 in like 7th grade. Good luck with that, as they have to live in a base 10 world until their parents die.

3) Have a shitty unintuitive measurement system.

Literally the best thing you could possibly say about a base 12 measuring system is that it is like dvorak keyboards, only with an even larger inertia block, but frankly, you can't even say they that until you give some compelling reason why base 12 is better than base 10, and I don't think anyone in this thread has done that.

Well, forget about cultural inertia. Assume that you had a Very Specific Genie that would only granted wishes that retroactively rewrote the number system so that everyone and everything was cool all along with it.

What advantages insofar as human civilization is concerned does base 12 or base whatever have over base 10?

Easy divisibility by 3 and 4 is probably worth slightly more than easy divisibility by 5, but it's very small beans one way or another.

Ancient History wrote:Base 12 gives no inherent advantage because our numeral notation system is ten digits. That's the reason we have to count 0 1 2 3 4 5 6 7 8 9 A B when we do base 12, we've literally run out of fucking numbers.

This is daft. There is no reason we cannot come up with new glyphs to use as numerals.

At the moment, not many. The big reason base 12 had any adherents at all is because British coinage (remember when Britain ruled the world?) used an archaic system where 1 pound = 12 shillings = 240 pence, and everyone in the world still uses an archaic time system where days are 24 hours (and a bit) and years are 360 days (and a bit).

Which is to say, when you have a 1:12:20 and a 1:24:60:60 system, you get really good at certain fractions. You cannot cleanly divvy up 100 into thirds for example, but 3 is a factor of 12. It is very easy to say that a third of a pound is 80 p, or that a fifth of a shilling is 4 p, or that a twelfth of an hour is 5 minutes.

But that's not a perfect base 12 system, and it is still a very arbitrary system of measurement. I mean we talk about a gross (12^2), but it doesn't get used in much.

rampaging-poet wrote:Being the world standard doesn't make actual metric a better measuring system

Actually. It totally does and it was the ONE argument the pro imperial measurement system had going for it back when it was the world standard.

Being able to take your blue prints and measurements to another country and have everyone be able to read them is MASSIVELY important and massively better than being the one major western nation to still be stuck with an archaic system.

The thing is Imperial was so much more inferior than Metric that basically every nation, scientist and engineer in the world decided to ditch it despite the massive advantage of it being widely used and already known to everyone.

Imagine if Esperanto were in fact SO good that everyone really had switched to it from English/Spanish/French/Etc... That's what DID happen with Metric and Imperial.

Ancient History wrote:Base 12 gives no inherent advantage because our numeral notation system is ten digits. That's the reason we have to count 0 1 2 3 4 5 6 7 8 9 A B when we do base 12, we've literally run out of fucking numbers.

John Magnum beat me to it, but I'll post my response anyway. People who read various Asian languages memorize hundreds of symbols that each correspond to a concept rather than a pronounced word. There is no shortage of symbols that humans can write, and we can (with training and immersion) learn to recognize many more than the seventy-odd ones we most commonly use. Adding two more symbols won't break English or anything similar to it. We could even continue to use 7-dash lights on our calculators if the new digits are underlined and overlined circles or backward 7 and backward 9.

The only real advantage of Base 12 is the that there's more ways to divide it into smaller numbers without fractions than Base 10. There's a limit to how large your base can practically be (memorizing 12 digits is possible, but 60 probably isn't worth it), and 12 provides a slight boost in usability for an incremental increase in difficulty to learn. The utility isn't enough to justify reteaching the world, but it might have been better if we'd all learned it that way to begin with.

rampaging-poet wrote:If I need to count something and don't want to count in my head, I often use base 6. One hand is units, the other is multiples of six. It only reaches 35, but that's better than 10. Base 6 results in significantly less compact written numbers than Base 10 though.
Base 12 is likely a good breakpoint because it is more compact than Base 10, can be evenly divided by three and four (at the expense of division by 5), and only requires memorizing the appearance of two more digits.

Well, hell, if you want to do that, use binary. Each finger is a bit. You can count to 31 on one hand and 1,023 on two (starting at zero).

Babylon used base 60, and it worked out okay for them.
Each digit was sort of like a set of roman numerals too, so it kind of works for tallies too.

If you've played Assassin's Creed 2, a couple of the puzzles use Babylonian numeration. That's because it's intuitive enough that you can decode it without any hints,

Counting in binary is pretty cool, the only downside other than being unwieldy to write out is that you gotta keep your hand low when you have to hold onto the number 4 for any length of time or you'll get shot; in the face.

Hicks wrote:Counting in binary is pretty cool, the only downside other than being unwieldy to write out is that you gotta keep your hand low when you have to hold onto the number 4 for any length of time or you'll get shot; in the face.

Couldn't you just point your palm outwards and that finger well within your outline when viewed from behind?

It's fairly uncomfortable for me to hold out 10. My 4-finger wants to extend, so I have to hold it out halfsies.

erik wrote:It's fairly uncomfortable for me to hold out 10. My 4-finger wants to extend, so I have to hold it out halfsies.

I use my 1-finger to hold my 4-finger and my 16-finger in place when storing 10. (Or is it my 16-finger holding the 4-finger and the 1-finger in place? This depends on which way you count from, unlike which fingers are actually up for 10)

Didn't the Mayans use base 20 or something? I remember having to decode that for some puzzle/adventure game.

Hicks wrote:Counting in binary is pretty cool, the only downside other than being unwieldy to write out is that you gotta keep your hand low when you have to hold onto the number 4 for any length of time or you'll get shot; in the face.

That's why you switch to hexadecimal (base-16). Four binary digits (bits) can be represented in a single hexadecimal digit so you can condense numbers like "0110 1101 0001" to "8C1". Now you've just represented 2,257 more concisely. I've used hex as a mnemonic for needing to keep track of things in a hurry: 3 lefts (000), 2 rights (11), a left (0), a right (1), a left (0) becomes 0001 1010, which becomes "1A". I can remember that more reliably over spans of time (http://en.wikipedia.org/wiki/Chunking_(psychology)). I've used binary and hex in a few DnD puzzles and fantasy cultures as well.

The problem any non-decimal number system has is a lack of familiarity, but binary, octal (base-8), and hexadecimal are a little better off because of how computers have become a fixture in mainstream culture, so "computery" number systems have become at least somewhat familiar to more people than you'd expect; if nothing else, people think "binary" when they see Matrix-esque strings of 1s and 0s, and hexadecimal when they see Blue Screen of Death memory error locations. Also, you can spell a few things with hexadecimal (since the number system is 0, 1, ..., 9, A, B, C, D, E, F), which allows for more puzzle-potential.


This reminds me of an old quip that I first came across in an Isaac Asimov short-story. "Christmas and Halloween are precisely the same." This is because Dec 25 = Oct 31, or 31 in Octal = 25 in Decimal.

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On a completely unrelated note, does anyone know how to get this forum's url tag to handle urls with parentheses in them?

Shatner wrote:On a completely unrelated note, does anyone know how to get this forum's url tag to handle urls with parentheses in them?

Like this:

http://en.wikipedia.org/wiki/Chunking_%28psychology%29

=-)

erik wrote:

Shatner wrote:On a completely unrelated note, does anyone know how to get this forum's url tag to handle urls with parentheses in them?

Like this:

http://en.wikipedia.org/wiki/Chunking_%28psychology%29

=-)

You could technically also use a url shortener but that has the potential to rick-rolling or other more heinous assholish-ness.

Rick rolled or not rick rolled?

It's the same fucking link if you didn't realize it until now.

Hicks wrote:Counting in binary is pretty cool, the only downside other than being unwieldy to write out is that you gotta keep your hand low when you have to hold onto the number 4 for any length of time or you'll get shot; in the face.

128 and 132 can also be problems. If you make it up to 132, they might think you're giving them both barrels.