tag:blogger.com,1999:blog-3722233.post1366274814408588880..comments2022-12-01T12:05:03.445-06:00Comments on Computational Complexity: What would the best base be?Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger42125tag:blogger.com,1999:blog-3722233.post-54299539386292430032018-09-26T18:45:56.543-05:002018-09-26T18:45:56.543-05:00Usually they're represented as ↊ and ↋.
I vo...Usually they're represented as ↊ and ↋. <br /><br />I vote for base six. Reason one being, base-12 is not divisible by five. (Senary isn't either, but it represents 1/5 a lot nicer than duodecimal does). Reason two, it has a low radix economy. Reason three, it is the best finger-counting base. All numbers from 0-35 can be represented on just two hands.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-24979544045701706492018-05-05T12:28:21.965-05:002018-05-05T12:28:21.965-05:00Base 9Base 9Anonymoushttps://www.blogger.com/profile/05494055326933615807noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-57011825670420239082018-05-05T12:23:22.803-05:002018-05-05T12:23:22.803-05:00Base 9 the trig divisible functions representative...Base 9 the trig divisible functions representative as multiplesAnonymoushttps://www.blogger.com/profile/05494055326933615807noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-17123864937432215252018-05-05T12:23:20.513-05:002018-05-05T12:23:20.513-05:00Base 9 the trig divisible functions representative...Base 9 the trig divisible functions representative as multiplesAnonymoushttps://www.blogger.com/profile/05494055326933615807noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-58909673130095092902017-11-20T19:40:26.658-06:002017-11-20T19:40:26.658-06:001 hour to be comprised of 100 minutes is already a...1 hour to be comprised of 100 minutes is already a tried and given up amendment during the French Revolution.Anonymoushttps://www.blogger.com/profile/11876864940789829988noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-44017562223336941342017-08-29T04:29:26.679-05:002017-08-29T04:29:26.679-05:00Only good in some theoretical situations, but is l...Only good in some theoretical situations, but is largely impractical both for mathematics and computers. Normal maths is obvious (write 1 million, anyone?) and computers would simply not work (on, off). Anonymoushttps://www.blogger.com/profile/07509924198470404035noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-12125780602092571122016-12-26T03:22:46.982-06:002016-12-26T03:22:46.982-06:00A pound was actually twenty shillings. A shilling ...A pound was actually twenty shillings. A shilling was twelve pence.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-38634504720404037232016-12-14T12:33:12.558-06:002016-12-14T12:33:12.558-06:00But then pi will be 3.infinity. Which infinity? In...But then pi will be 3.infinity. Which infinity? Infinity/infinity makes no sense. 924789179/infinity is 0. While in decimal, 3.14159265359, it's a clear fraction (or sum of them): 3 1/10 4/100 1/1000 ... or 3141.../1000... and not confusing 3.$#*! in base infinity.Piotr Grochowskihttps://www.blogger.com/profile/16782132102347637343noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-81276289834666804262016-12-14T12:29:36.513-06:002016-12-14T12:29:36.513-06:00But it's a tradeoff, 5 is divisible by 60 but ...But it's a tradeoff, 5 is divisible by 60 but not in 72, but what is divisible in 72 is 8 and 9. Having 1/5 is as important as 1/8 and 1/9 as single digit. 120 has more (and divisible by 8) but is over limit.Piotr Grochowskihttps://www.blogger.com/profile/16782132102347637343noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-65885178752715069312016-12-06T11:17:20.350-06:002016-12-06T11:17:20.350-06:00You have the number of digits be the number.You have the number of digits be the number.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-76897561612387286892016-08-31T18:15:07.068-05:002016-08-31T18:15:07.068-05:00how would you represent numbers if the only digit ...how would you represent numbers if the only digit you had was 0?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-91870439521244606242015-12-07T05:17:05.616-06:002015-12-07T05:17:05.616-06:00Why not base infinity, binary has 2 symbols and in...Why not base infinity, binary has 2 symbols and infinite combonations (the smallest base as base 1 is i n effect the same as base infinity but with one symbol creating disgusting strings) whereas base infinity has infinite symbols but only ever uses each one twice, eg 1.32 would be 1. Symbol for 32 meaning that symbol can be used twice. This would allow Pi to be finite and therefore all irrational numbers be finite meaning determinism could be enacted. However ever it is unusable by any observer as nothing could percieve that many symbols.<br />Anonymoushttps://www.blogger.com/profile/12731916689766866235noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-51408085283646908612015-01-24T18:49:40.150-06:002015-01-24T18:49:40.150-06:00https://www.youtube.com/watch?v=U6xJfP7-HCc
in ba...https://www.youtube.com/watch?v=U6xJfP7-HCc<br /><br />in base 12 the following changes occur<br /><br />10 >>> X<br />11 >>> E<br />12 >>> 10 <br />13 >>> 11<br />14 >>> 12<br /><br />watch the Sixty Symbols video for a fuller explanation raphaelhttps://www.blogger.com/profile/14026633549868642810noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-42144371118826016242014-02-21T20:34:22.143-06:002014-02-21T20:34:22.143-06:00If one wants the most "efficient" base w...If one wants the most "efficient" base where the cost of a digit in inventory and the cost of a digit place in the representation of numbers are costed equally, then the most efficient base is e - the base of the natural logarithm.<br /><br />This follows from the function for cost that can be represented:<br /><br />L(b) = logb(N) + b<br /><br />where logb(N) is the base b log of N.<br /><br />taking dL/db (the first derivative) = 0 yeilds a single solution of e<br /><br />taking d2L/db2 (the second derivative) at b = e yeilds a positive result making the result a minimum. Also the N quantity drops out entirely meaning that the base is the "most efficient" for all N.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-12359460221294687952013-02-09T10:37:49.151-06:002013-02-09T10:37:49.151-06:00Another vote for base 12 because of it's nice...Another vote for base 12 because of it's nice divisibility. This is why traditional weights and measures use base 12. The problem has always been with using base 10 to count.<br /><br />For those complaining about the need to invent to additional symbols, I would suggest base 6 as an alternative. Has many of the features as base 12 with no need for additional symbols.Anonymoushttps://www.blogger.com/profile/01377247964786280223noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-63705175990592241822012-12-20T17:53:16.302-06:002012-12-20T17:53:16.302-06:00in that case 60 would be superiorin that case 60 would be superiorAnonymoushttps://www.blogger.com/profile/07022589187434263214noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-91672702650919836932012-06-25T16:15:40.393-05:002012-06-25T16:15:40.393-05:00Nor base 1. But 121 doesn't exist in either ba...Nor base 1. But 121 doesn't exist in either base. So 11 x 11 = 121 in any base where 121 exists.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-55340585428552780832012-04-22T20:58:34.273-05:002012-04-22T20:58:34.273-05:00Not base 2Not base 2Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-25248042437124579052008-05-03T13:21:00.000-05:002008-05-03T13:21:00.000-05:00Actually, 72 and 60 are equally divisible by 12 nu...Actually, 72 and 60 are equally divisible by 12 numbers (including 12, coincidentally. But 60 is smaller and has more primes. 72 only has 2 and 3 as primes. 60 has 2, 3, and 5. 60 has the edge and gets my vote. Now we just have to come up with the digits to do it.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-50317581144819951572008-05-03T02:55:00.000-05:002008-05-03T02:55:00.000-05:00base zero or base infinitybase zero or base infinityAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-21978224300440688812008-05-01T07:49:00.000-05:002008-05-01T07:49:00.000-05:0060 is more densely divisible than 721,2,3,4,5,6,10...60 is more densely divisible than 72<BR/>1,2,3,4,5,6,10,12,15,20,30,60Brandon Reesehttps://www.blogger.com/profile/17005170507423425670noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-89118993140579569602008-04-30T20:09:00.000-05:002008-04-30T20:09:00.000-05:00A bit of trivia:11 X 11 = 121in any base.A bit of trivia:<BR/><BR/>11 X 11 = 121<BR/><BR/>in any base.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-4584821967536069792008-04-30T20:08:00.000-05:002008-04-30T20:08:00.000-05:00Base two has a huge problem for us humanoids. Wit...Base two has a huge problem for us humanoids. Without training we have about a 7 digit short-term memory. This severely limits the largest number that we can work with in mental math. This excludes binary for most uses, but a binary based numbering would be excellent: 4, 8, 16. Probably the easiest to change to would be hex, because it is big enough to overcome many memory problems, and it is in common use in some segments of society (nerds).<BR/><BR/>If we had enough digits, I would vote for base 72, it claims as factors, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. It is probably the most densely divisible number under 100. Its biggest drawback is that it is not binary based.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-90932976211660148952008-04-30T20:00:00.000-05:002008-04-30T20:00:00.000-05:00Bigendian is a must. The Chinese have it right. ...Bigendian is a must. The Chinese have it right. Dates, addresses, names, etc. are already in the proper sort order, and in the easiest order to understand. I hate it when I hear dates and addresses in English and I don't know the complete context until the very end. The small stuff is not important until you know the context.<BR/><BR/>638 ..... MacArthur Str. ..... Clayton ....... Ohio <BR/><BR/>You can't imagine a place until the very end. But as you start from the general and move to the specific, it is so much easier to comprehend and to remember. Each segment of the address has some value to us.<BR/><BR/>Ohio, clayton, MacArthur Str 638.<BR/><BR/>Ahhh. So much better.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-15396309058495366092008-04-29T10:39:00.000-05:002008-04-29T10:39:00.000-05:00While you're at it, why is our numeric system big ...While you're at it, why is our numeric system big endian? Wouldn't addition and multiplication be more natural for Western readers if the values carried from left to right? I suppose though it would confuse long division.Anonymousnoreply@blogger.com