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May 16th, 2014, 10:09 PM  #11 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
...perhaps you can pray that Momma wakes up with 12 fingers...

May 16th, 2014, 11:33 PM  #12 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,270 Thanks: 934 Math Focus: Wibbly wobbly timeywimey stuff. 
I like base 20. I've leaned a way to count that on my fingers and it's great for providing some distraction at a graduation ceremony. Frankly, after base 10 I'd go to base 6 = 2 x 3. Then maybe progress to base 30 = 2 x 3 x 5. The prime factors just seem easier for me to deal with. Dan 
May 17th, 2014, 06:55 AM  #13 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,683 Thanks: 2664 Math Focus: Mainly analysis and algebra 
How many fewer digits are you going to use? Is it really going to save much? I can't see any need to shave a digit or two off figures in the world. Certainly not when there's re'education costs. And if you are trying to work out what power of twelve you need for 37 million, you are working in base 10 and converting to base 12 which is terriblly inefficient. 
May 17th, 2014, 09:08 AM  #14 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
I think you need to think carefully about what you mean by "more efficient". If you only meant that it takes fewer symbols to encode (large) numbers, why not use base one million? For a reasonable definition of "most efficient" the most efficient integer base is 3. But there are many, many ways to define this, and you can come up with lots of different answers. 
May 17th, 2014, 12:00 PM  #15  
Senior Member Joined: Nov 2013 Posts: 247 Thanks: 2  Quote:
I would say though that converting 37 trillion from base 10 to base 12 takes many less mod 12^x equations than converting that same number to binary using mod 2^x. as for saving digits if you take 1 trillion, that is 10^12. That same 13 digit number expressed in base 12 I bet will have many less digits because powers of 12 go up much faster than powers of 10. It might not have an effect much in tens and hundreds but as you go to thousands and millions and above it really takes effect. In the same way binary numbers are the longest because 2^x is the slowest of the integer exponential functions(by that I mean some integer taken to some power that doesn't have to be an integer) Last edited by caters; May 17th, 2014 at 12:06 PM.  
May 17th, 2014, 01:02 PM  #16 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,683 Thanks: 2664 Math Focus: Mainly analysis and algebra 
And how often do you see (far less use) a 13 digit number writtten out? We almost alway write 1 trillion, or 2.5 trillion or something similar. The main use for binary is in computers where it is used because it is easiest to tell whether a bit is on or off without error. We might be able to do ternary arithmetic in computing now (and maybe a little more at a push), but binary dovetails nicely with the logical side of computing too. 
May 17th, 2014, 05:53 PM  #17 
Senior Member Joined: Nov 2013 Posts: 247 Thanks: 2 
I actually see 13 digit numbers written out quite often, mostly in repeating decimals.

June 24th, 2014, 09:26 PM  #18  
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  Quote:
In essence we use use ALL bases already. binary for computers 12 for inches and a dozen eggs in a carton. 60 minutes, 60 seconds. Perfect. Digits MEANS fingers.  
June 25th, 2014, 04:10 PM  #19 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry 
Smart people use metric system. Perhaps, we should use dozenal version of metric system.


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