What's a good numerical base?

[BeBMan]

Re: What's a good numerical base? (Quasi sincere maths question)

Originally posted by Alinestra Covelia
My friend Bing is working on a piece of fiction about a non-human intelligent civilization. He has decided that these creatures will have pseudopods, not fingers. Therefore they can have as many fingers as they want at any given time.

Because of this, their numerical system may start off arbitrarily, rather than going to decimal like we did.

We're trying to figure out what base would be better to use than 10, which is only divisible by 2 and 5.

Bing reckons the minimum number of fingers you really need for fine manipulation is three. But a base-3 system isn't very convenient. I'm suggesting a base-6 system, as that's divisible by 2 and 3. Bing has even toyed with a base-8 or a base-12 system.

What do you think?

He could give them 4 arms with 2 fingers each. And real pot instead of this pseudo pot.....

[Darius871]

Originally posted by BeBro
They only have one finger??? That sucks.

Sometimes one's all you need. [/ali]

[Alinestra Covelia]

Okay, it's looking like base-6 is winning out.

The creatures (fungi) can sprout limbs as needed. Because they spend most of their time standing still, Bing decided to make them favor a tripedal system. (Note how three legs is the minimum number of legs a chair needs in order to be stable, even on uneven ground.)

So with three legs, the creatures would favor three arms. With three arms of two fingers each, that leads to base-6.

They can sprout three fingers if they need to do things like write and craft, etc.

[snoopy369]

16 is probably best, but that's an awful lot of fingers. More is better at least up to a point, though - particularly in terms of the development of civilization, where the big issue is the zero as a placeholder (this took a long time to learn, and probably will in most maths); prior to this you need more 'letters' (think roman numerals) to represent larger numbers, and that's annoying.

However, I'd suggest Bing use something more clever than simply a non-decimal base. If you have a flexible number of fingers, you don't actually need to have a base at all... I'm not sure of where this could go, but I'm sure one of the math junkies could think of something, perhaps involving exponents or logs or multiplicative math, or ...

If you're going with 3 limbs, then why not 3 fingers (and thus 3x3=9 base math)? Nature favors symmetry.

[OneFootInTheGrave]

16 is a natural choice

[Alinestra Covelia]

9 would make sense (three hands, with three fingers each) but it's got problems it that it's only divisible by 3.

To OneFoot and others: Why 16 and not 12? 16 is a power of 2 so it all boils down to that prime. 12 has 2 and 3 as prime factors.

[Unimatrix11]

Re: Re: What's a good numerical base? (Quasi sincere maths question)

Originally posted by BeBro


He could give them 4 arms with 2 fingers each. And real pot instead of this pseudo pot.....

LOL ! Yeah - share !

[OneFootInTheGrave]

http://en.wikipedia.org/wiki/16_(number)

Sixteen is a composite number, and a square number, being 16 = 4 × 4. It is the smallest number with exactly five divisors, its proper divisors being 1, 2, 4 and 8.

It is the fourth power of two. For this reason, 16 was used in weighing light objects in several cultures. The British used to have 16 ounces in one pound, the Chinese used to have 16 liangs in one jin. In old days, weighing was done with a beam balance to make equal splits. It would be easier to split a heap of grains into sixteen equal parts through successive divisions than to split into ten parts.

also in modern use it is most flexible while not being too complicated, average human could compute in base 16 easily too... while it major advantage as a base is the natural interpretation of binary base.

[Q Classic]

Originally posted by Alinestra Covelia
Okay, it's looking like base-6 is winning out.

The creatures (fungi) can sprout limbs as needed. Because they spend most of their time standing still, Bing decided to make them favor a tripedal system. (Note how three legs is the minimum number of legs a chair needs in order to be stable, even on uneven ground.)

So with three legs, the creatures would favor three arms. With three arms of two fingers each, that leads to base-6.

They can sprout three fingers if they need to do things like write and craft, etc.

Why not base 7? If you go by that, with the three lower limbs, three upper limbs, yes, we might think 6.

But that doesn't mean they would, necessarily. Limbs + Head = 7, for instance.

Or, if they looked skyward, how many moons does the world have? 4? 12? 16? 7?

But then, would they really need a number system? There are languages that only have the words for "one", "two", and then "more"; admittedly, they're not really developed, but...

[Thue]

Base 12 is best - it has the handy divisors like 2,3,4, and 6. You need to divide by 3 relatively often, and then base 8 or base 16 doesn't cut it.

Base 6 could also be divided by 3, but it would take more space to write numbers in base 6. Algorithms like multiplication would take more steps with base 6 than base 12, but you would need to remember a smaller multiplication table.

With base 6 a two-digit number would hold 36 possible values, which a 2-digit base 12 number would hold 144 possible values. So I go with base 12 . (I actually calculated a but in different bases at one point for fun.)

[Unimatrix11]

forty-two, maybe ? (yeah, bad idea, i agree)

[Asher]

Originally posted by Thue
Base 12 is best - it has the handy divisors like 2,3,4, and 6. You need to divide by 3 relatively often, and then base 8 or base 16 doesn't cut it.

Why do you need to divide by 3 relatively often?

Have you ever seen binary data represented in base 12?

Hex is clearly the best. Base 16 FTW.

[Unimatrix11]

If those fungi can choose how many limbs they have, maybe Bing should focus not so much on what they have in common, but on their differencies. The numerical base could be one of which - some use 3 and some 6. They fight wars about it (or so they believe).

[Thue]

Originally posted by Asher

Why do you need to divide by 3 relatively often?

Have you ever seen binary data represented in base 12?

Hex is clearly the best. Base 16 FTW.

Base 2^n is great if you are a low lever programmer - I would never write a point value in anything but base 16. However, with proper abstraction interfaces there is no reason why anybody but a programmer user should ever care that a computer is based on binary numbers.

And low-level programming is simply not important enough that it has greater weight than the ability to easily divide by 3.

[Asher]

It's not just low-level programming.

Just what exactly do you do with computers, Thue?

I know you don't draw pretty pictures because I've seen FreeCiv and it is offensively ugly.