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Old 2012-08-17, 16:19   #1
blistervol
 
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Default A Bigfoot number system

I had a question like, why isn't there a number system developed already for large numbers, like a base-giga or base-tera or base-peta( at least a base-Mega) and use these number systems for FFT algorithm so that the computations would be mega times faster compared to zillions of blocks of tiny information to pass through every iteration. I know there is a number system with base-100 developed for many practical uses like for processing very large information.
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Old 2012-08-17, 17:40   #2
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Quote:
Originally Posted by blistervol View Post
I had a question like, why isn't there a number system developed already for large numbers, like a base-giga or base-tera or base-peta( at least a base-Mega) and use these number systems for FFT algorithm so that the computations would be mega times faster compared to zillions of blocks of tiny information to pass through every iteration. I know there is a number system with base-100 developed for many practical uses like for processing very large information.
I don't know but I do know that unless it's base 2^44 or higher it'll take close to 1 million characters in a string to represent the biggest known prime.
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Old 2012-08-17, 17:46   #3
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Quote:
Originally Posted by blistervol View Post
why isn't there
There is. All big-num algorithms work base 2^30 or so, including FFT multiplication. We can't see it, because we don't have so many fingers. As we are limited of our finger amount, the "big base" used in computers is limited by the internal register size. Having a bigger base you just move the problem from having many sets of fingers, to having many fingers in one set, but at the end, you will need as many fingers as the number you want to represent, to count them one by one. For me, base 10 is already too much, base 2 would be perfect. In base 2 you don't need to memorize addition and multiplication tables... Imagine how it would be when your grade 5 teacher asks you to memorize multiplication table base 2^44...

edit: or to have names and symbols for all "figures" up to 2^44...

Last fiddled with by LaurV on 2012-08-17 at 17:54
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Old 2012-08-17, 18:07   #4
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Originally Posted by LaurV View Post
...
edit: or to have names and symbols for all "figures" up to 2^44...
This alone is enough to make any base above, say, 100 impractical. Some people would like to see us use base 12. There would be so many advantages.

http://en.wikipedia.org/wiki/Duodecimal
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Old 2012-08-17, 18:21   #5
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Quote:
Originally Posted by Puzzle-Peter View Post
This alone is enough to make any base above, say, 100 impractical. Some people would like to see us use base 12. There would be so many advantages.

http://en.wikipedia.org/wiki/Duodecimal
outside of the need of reordering vectors in PARI I could probably get close to 255- number of control characters in Strchr(n) and still work:

Code:
a=vector(255,n,Strchr(n))
it just might need reordering as stated above.
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Old 2012-08-17, 18:41   #6
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Some people would like to see us use base 12. There would be so many advantages.
Shall we talk about "imperial" vs. "metric"?

Interestingly, the imperial units system is generally base-12 or base-16. And some got really good at converting between them. "What's 3/12?" "1/4! "What's 12/16?" "3/4!"

But can anyone explain to me why a mile is 5280 feet?

Now we have the metric system; we've had it for thirty plus years...

"How many treads per centimeter should I expect on this thread?" "I have no idea...."

NASA itself lost a spacecraft because of this...

Even today "Great" Britain claims to be metric, but all their road signs are posted in miles....
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Old 2012-08-17, 18:44   #7
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But can anyone explain to me why a mile is 5280 feet?
possible explanation
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Old 2012-08-17, 19:07   #8
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I always found the "regularity" arguments of the decimal fetishists rather amusing, because there is in fact a lot of regularity, in the powers of two for many of its scales (gradations of an inch, volume measures, etc). Yes, there are a lot of mixed bases, but humans have long embraced those for other things, such as time measurement.

And I appreciate the historicity embodied in every aspect of the imperial system - as reflected in most of the basic units having a very "human" quality. An inch is small enough to characterize common household items, but large enough to not introduce excessive granularity into everyday human-scale measurements. A foot is literally on the order of the length of a large man's foot, or better, similar to the historic "ell" which literally refers to the length of one's arm from wrist to elbow, both convenient measurement tools when rulers are lacking. A yard is roughly the length of a tall man's arm (or perhaps a typical sword) from shoulder to fingertip, a mile is roughly 1000 double-strides, etc. 100 degrees is frickin' hot (in a human sense), whereas 0 is frickin' cold. (Boiling water is too hot to put your hand in anyway, so who cares how many degrees it is? :)

An ounce is the weight of a solidly large coin or bite-sized chunk of food. A gram? WTF use have I for a gram? I'm not ordering food by the gram for my per gerbil here. (For this too-small-to-be-everyday-useful reason, a typical European food shop or deli will deal almost entirely in decagrams, which are just large enough in the single-digit-quantity-is-useful sense).

(OTOH a Chinese person might argue than a cm is roughly the length of a rice grain, which would make sense - if the mettic system had its origins there, which it doesn't.)

Last fiddled with by ewmayer on 2012-08-17 at 19:20
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Old 2012-08-17, 19:22   #9
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Originally Posted by ewmayer View Post
A gram? WTF use have I for a gram?
Depends.

The advantage of the metric system is it is based on measurements which anyone can compare against.

WTF is a gram? It's approximately the same mass of 1 CC of pure water.

WTF is a CC? It's one Cubic Centimeter.

WTF is 1 Kg? It's one thousand Grams.

On the other hand, we used to have something like this...

WTF is a yard? A fundamental unit of length in both the U.S. Customary System and the British Imperial System, equal to 3 feet, or 36 inches

WTF is an inch? A unit of linear measure equal to one twelfth of a foot.

WTF is a foot? A foot is a unit of length defined as being 0.3048 m exactly and used in the imperial system of units and United States customary units. It is subdivided into 12 inches.
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Old 2012-08-17, 20:23   #10
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Quote:
Originally Posted by ewmayer View Post
100 degrees is frickin' hot (in a human sense), whereas 0 is frickin' cold. (Boiling water is too hot to put your hand in anyway, so who cares how many degrees it is? :)
I spend somewhere between 1% and 2% of my life these days at a temperature ~100C. I know people, at least one of whom is also a MF member, who spend at least 2% at those sorts of temperatures.

The sauna I generally use has been set at 98 \pm 2 C for the last few months. I rarely spend less than 30 minutes in there and sometimes over an hour; typical is 45 - 50 minutes. Ok, so I'm a wimp and take in a half-litre water bottle otherwise I'd have to keep dashing in and out.

Can't manage more than 10 - 15 minutes at 110C, whether or not drinking water is to hand. 120C is rather unpleasant IMO.

Some time I should take an egg in with me. I'm certain it will be (over-)cooked by the time I get out again.

Paul
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Old 2012-08-17, 20:34   #11
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It's hard to imagine spending even a few minutes (or seconds!) at or above boiling. I am the most heat tolerant person I know of, but I draw the line above ~105 F in any situation except a sauna.

Last fiddled with by kladner on 2012-08-17 at 20:34
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