Re: Bases, was Re: Stirling engine queries
- Original Message - From: David Hobby [EMAIL PROTECTED] To: Killer Bs Discussion [EMAIL PROTECTED] Sent: Friday, March 05, 2004 11:49 PM Subject: Re: Bases, was Re: Stirling engine queries Robert Seeberger wrote: ... I'd say that this stuff gets pretty fuzzy. One could argue that 5 is more important than 11 and 13. On the other hand, one could say that ending tests are better than sum of digits tests, and conclude that 12 is superior since it replaces sum of digits tests for 3,9,... with ending tests. Is this the kind of thing you were thinking about? ---David Who needs whole number divisibility when you have fractions and can work decimals? You would have to do these things no matter what the base you use, in the real world. Getting people to change bases would be whole magnitudes of difficulty greater than getting them to go metric. G xponent Numbers game Maru rob Of course we could use base 7 or whatever, and get by almost as well. And I agree that getting anyone to change would be hopeless. I sometimes teach a math course for future elementary school teachers, and wind up spending a week teaching them the metric system, for college credit (!!). At the end of it, half of them say things like a cubic meter is a liter, which weighs a gram. (So be prepared to teach your own children math...) Rob, the point of this discussion was to explain why we picked the base we did. I understand, but what I was saying is that it doesn't really make all that much a difference. There are just too many cases where you would still be using fractions and decimals, so a different base doesn't simplify things in the long run. Base 12 might be helpful when doing math in your head and it might be more intuitive in the most simple situations, but surely there would have to be some other overiding reason to use another base (other than the arbitrary numbers of digits, knuckles, and limbs), such as in the CS uses of Binary, Octal, And Hexadecimal. Having ten fingers is obviously a key factor, but there are examples of cultures that used base 20 or 60, so it's not exactly the only one. I imagine that we would use base 12 if we had 6 fingers. But suppose we had 3 hands with 7 fingers each. Would we really use base 21? WellI agree.but the point I was making implies that it doesn't really matter which base one uses in the long run. A value is a value no matter how it is expressed. And that's really what is being discussed isn't it? How values are expressed and if there are better ways to do this? (I'm thinking that calculation is a straightforward mechanical process in any base.) Am I wrong in thinking this? xponent 123456789ABCDEF Maru rob ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
I understand, but what I was saying is that it doesn't really make all that much a difference. There are just too many cases where you would still be using fractions and decimals, so a different base doesn't simplify things in the long run. Base 12 might be helpful when doing math in your head and it might be more intuitive in the most simple situations, but surely there would have to be some other overiding reason to use another base (other than the arbitrary numbers of digits, knuckles, and limbs), such as in the CS uses of Binary, Octal, And Hexadecimal. Having ten fingers is obviously a key factor, but there are examples of cultures that used base 20 or 60, so it's not exactly the only one. I imagine that we would use base 12 if we had 6 fingers. But suppose we had 3 hands with 7 fingers each. Would we really use base 21? WellI agree.but the point I was making implies that it doesn't really matter which base one uses in the long run. A value is a value no matter how it is expressed. And that's really what is being discussed isn't it? How values are expressed and if there are better ways to do this? (I'm thinking that calculation is a straightforward mechanical process in any base.) Am I wrong in thinking this? xponent No, you're right. To first order, any base would work. But there are some subtle reasons for prefering some bases over others. Take -pi as a base, for instance. Then pi^2 - 3*pi + 2*1 - 2*pi^(-1) + 2*pi^(-2) = 2.0108..., so we have that two is 132.22... in base -pi. If you pick the wrong base, all the numbers you care about will be infinite decimals. : ) ---David ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
- Original Message - From: David Hobby [EMAIL PROTECTED] To: Killer Bs Discussion [EMAIL PROTECTED] Sent: Saturday, March 06, 2004 2:22 PM Subject: Re: Bases, was Re: Stirling engine queries Am I wrong in thinking this? No, you're right. To first order, any base would work. But there are some subtle reasons for prefering some bases over others. Take -pi as a base, for instance. Then pi^2 - 3*pi + 2*1 - 2*pi^(-1) + 2*pi^(-2) = 2.0108..., so we have that two is 132.22... in base -pi. If you pick the wrong base, all the numbers you care about will be infinite decimals. : ) Which is the reason we strive for whole number intuitiveness. xponent Base Planks Constant Maru rob ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
Alberto Monteiro wrote: Alberto Monteiro who spends his time in the traffic looking at the numbers of the cars and dividing them by 11. I spend my time making words from the three letters on the plates we have here. Keeps me amused for a while. Bonus points for naughty words. Did I say I hate traffic?? No! Well, I do. Regards, Ray. ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
Robert Seeberger wrote: ... I'd say that this stuff gets pretty fuzzy. One could argue that 5 is more important than 11 and 13. On the other hand, one could say that ending tests are better than sum of digits tests, and conclude that 12 is superior since it replaces sum of digits tests for 3,9,... with ending tests. Is this the kind of thing you were thinking about? ---David Who needs whole number divisibility when you have fractions and can work decimals? You would have to do these things no matter what the base you use, in the real world. Getting people to change bases would be whole magnitudes of difficulty greater than getting them to go metric. G xponent Numbers game Maru rob Of course we could use base 7 or whatever, and get by almost as well. And I agree that getting anyone to change would be hopeless. I sometimes teach a math course for future elementary school teachers, and wind up spending a week teaching them the metric system, for college credit (!!). At the end of it, half of them say things like a cubic meter is a liter, which weighs a gram. (So be prepared to teach your own children math...) Rob, the point of this discussion was to explain why we picked the base we did. Having ten fingers is obviously a key factor, but there are examples of cultures that used base 20 or 60, so it's not exactly the only one. I imagine that we would use base 12 if we had 6 fingers. But suppose we had 3 hands with 7 fingers each. Would we really use base 21? ---David Four score and seven ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
Julia Thompson wrote: David Hobby wrote: ... So base 12 is not bad, it gives nice tests for 2,4,8,... for 3,9,..., for 11 since 12 = 11 + 1 and it gives a poor test for 13 since 12^2 = 11*13 + 1. The situation for 5 and for 7 seems to be even worse. Contrast this with base 10, which gives a good test for 5 but has a worse test for 11 and none for 13. I'd say that this stuff gets pretty fuzzy. One could argue that 5 is more important than 11 and 13. On the other hand, one could say that ending tests are better than sum of digits tests, and conclude that 12 is superior since it replaces sum of digits tests for 3,9,... with ending tests. Is this the kind of thing you were thinking about? The sum of digits test for 3 only works because it's the square root of 9. As Alberto(?) pointed out, it works for all factors of 9. Well, that's a poor example, but you get the idea. Base 12 would give better tests for more numbers. And a sum of digits test would work for 11 there. Julia As would an alternating sum of digits test for 13, similar to the base 10 test for divisibility by 11. (Here's a good background link: http://www.jimloy.com/number/divis.htm ) We could also look at the problem in terms of which common fractions are represented by terminating decimals or by those with simple patterns of repetition. This is essentially the same thing as considering divisibility tests, and may seem more sensible. For example, in base 10 we have ending tests for divisibility by 2,4,5,8 and so on, and these are the denominators of the fractions that have terminating decimals. (1/2 = .5, 1/4 = .25, etc) We have sum of digits tests for 3 and 9, these correspond to the simple patterns: 1/3 = .3... and 1/9 = .11... Finally, 11 and 7 have divisibility tests which are poor and awful respectively. Now look at the decimal expansions of their reciprocals: 1/11 = .0909090909... and 1/7 = .142857142857... ---David ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
David Hobby wrote: At the end of it, half of them say things like a cubic meter is a liter, which weighs a gram. While we're already talking about changing our number systems, maybe we should change metric to make that true, because those definitions make a *lot* more sense than the real ones. :-) Honestly, why the heck is a liter defined as a cubic *decimeter*? Granted, a cubic meter would make an awfully big base unit of volume, but it wouldn't really be any more awkward than a gram, which is too *small* to be really useful in everyday life. If the metric units weren't so awkwardly sized, there would be no need for two different sets of metric base units, cgs (cm, grams, seconds) and SI (meters, kilograms, seconds). Each set has to fudge one of the units by a factor of 1000 to get it to play well together with the other unit. __ Steve Sloan . Huntsville, Alabama = [EMAIL PROTECTED] Brin-L list pages .. http://www.brin-l.org Science Fiction-themed online store . http://www.sloan3d.com/store Chmeee's 3D Objects http://www.sloan3d.com/chmeee 3D and Drawing Galleries .. http://www.sloansteady.com Software Science Fiction, Science, and Computer Links Science fiction scans . http://www.sloan3d.com ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
Alberto Monteiro wrote: David Hobby wrote: However, a base 12 counting system would have been much better; No, it wouldn't Well, a little better. A little worse. Depending how you count, you can argue that 12 has more factors than 10. This must be worth something, since I don't hear anyone pushing for prime bases such as 11. Agreed, it's not a big deal. It might be more to make a number base feel comfortable than a great aid in calculations. The problem with base 12 is that it has _2_ twice and _3_ once when you factor it, so that the practical man rules to check if a number is divisible by another would get a higher degree of confusion. Base 6 would be a much better choice than base 12. I'm not sure what you mean. I don't find the divisibility tests confusing. Some are simpler than others, yes. And we may well disagree on how to compare degrees of simplicity. I don't see many advantages in base 6 over base 10: the only one that comes to my mind is that base 10 has simple rules to check if a number is divisible by 2, 5, 3, 9 and 11; I think the rules for 4,6 and 8 are also simple. (Again, here's a link for background: http://www.jimloy.com/number/divis.htm ) with base 6, there would be simple rules for 2, 3, 5 and 7; maybe losing 11 and gaining 7 could count as a minor improvement. I would say that there are also simple rules for 4, 8, 9 and 10 when working base 6. (This is making base 6 look good. But there should be a way to lift divisibility rules from base 6 to base 12 (=2*6), at the price of adding some complexity.) OTOH, base 12 would have simple rules for 2, 3, 4, 6, 11 and 13, and since the base-10 rules for 4 and 6 are one bit less simple than the rules for 4 and 6 in base-12, we would _lose_ the rules for 5 and gain the rules for 13 - which is a bad trade. Again, I would count more rules as simple. I see that you are counting the base 10 rule for 4 as one bit less simple than the base 10 rule for 2. Would the base 10 rule for divisibility by 8 be two bits less simple? This is fuzzy, as I said. I would count the base 10 rule for 3 as much less simple than the base 10 rule for 8, even. I guess it depends on what size numbers one is expecting to use the divisibility tests on-- I'm imagining large numbers as input. ---David The divisibility by 3 test runs in linear time, Maru. ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
Well, a little better. Depending how you count, you can argue that 12 has more factors than 10. This must be worth something, since I don't hear anyone pushing for prime bases such as 11. Agreed, it's not a big deal. It might be more to make a number base feel comfortable than a great aid in calculations. Base 10 has a minor advantage in divisibility tests that I don't think you get with any other possible base between 5 and 17. And unlike 5 and 17, it's not prime. Julia There are two kinds of divisibility tests. They aren't usually given names, but let's call them ending tests and sum of digits tests. Working base 10, there are ending tests for 2,4,8,... and 5,25,... as well as for their products. (Let's ignore combined tests for products such as 6, since those can always be created.) In base 10, there are nice sum of digits tests for 3 and 9, and a poor one for 11. (There's a really messy one for divisibility by 7 as well, illustrating that it is always possible to produce a poor test.) The tests for 3 and 9 are based on the fact that 10 = 9 + 1, and the test for 11 uses that 100 = 9*11 + 1. So base 12 is not bad, it gives nice tests for 2,4,8,... for 3,9,..., for 11 since 12 = 11 + 1 and it gives a poor test for 13 since 12^2 = 11*13 + 1. The situation for 5 and for 7 seems to be even worse. Contrast this with base 10, which gives a good test for 5 but has a worse test for 11 and none for 13. I'd say that this stuff gets pretty fuzzy. One could argue that 5 is more important than 11 and 13. On the other hand, one could say that ending tests are better than sum of digits tests, and conclude that 12 is superior since it replaces sum of digits tests for 3,9,... with ending tests. Is this the kind of thing you were thinking about? ---David ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
David Hobby wrote: However, a base 12 counting system would have been much better; No, it wouldn't Well, a little better. A little worse. Depending how you count, you can argue that 12 has more factors than 10. This must be worth something, since I don't hear anyone pushing for prime bases such as 11. Agreed, it's not a big deal. It might be more to make a number base feel comfortable than a great aid in calculations. The problem with base 12 is that it has _2_ twice and _3_ once when you factor it, so that the practical man rules to check if a number is divisible by another would get a higher degree of confusion. Base 6 would be a much better choice than base 12. I don't see many advantages in base 6 over base 10: the only one that comes to my mind is that base 10 has simple rules to check if a number is divisible by 2, 5, 3, 9 and 11; with base 6, there would be simple rules for 2, 3, 5 and 7; maybe losing 11 and gaining 7 could count as a minor improvement. OTOH, base 12 would have simple rules for 2, 3, 4, 6, 11 and 13, and since the base-10 rules for 4 and 6 are one bit less simple than the rules for 4 and 6 in base-12, we would _lose_ the rules for 5 and gain the rules for 13 - which is a bad trade. Alberto Monteiro who spends his time in the traffic looking at the numbers of the cars and dividing them by 11. ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
From: David Hobby [EMAIL PROTECTED] There are two kinds of divisibility tests. They aren't usually given names, but let's call them ending tests and sum of digits tests. Working base 10, there are ending tests for 2,4,8,... and 5,25,... as well as for their products. (Let's ignore combined tests for products such as 6, since those can always be created.) In base 10, there are nice sum of digits tests for 3 and 9, and a poor one for 11. (There's a really messy one for divisibility by 7 as well, illustrating that it is always possible to produce a poor test.) The tests for 3 and 9 are based on the fact that 10 = 9 + 1, and the test for 11 uses that 100 = 9*11 + 1. What are the divisibility tests for 7 and 11? -bryon _ Store more e-mails with MSN Hotmail Extra Storage 4 plans to choose from! http://click.atdmt.com/AVE/go/onm00200362ave/direct/01/ ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
David Hobby wrote: Well, a little better. Depending how you count, you can argue that 12 has more factors than 10. This must be worth something, since I don't hear anyone pushing for prime bases such as 11. Agreed, it's not a big deal. It might be more to make a number base feel comfortable than a great aid in calculations. Base 10 has a minor advantage in divisibility tests that I don't think you get with any other possible base between 5 and 17. And unlike 5 and 17, it's not prime. Julia There are two kinds of divisibility tests. They aren't usually given names, but let's call them ending tests and sum of digits tests. Working base 10, there are ending tests for 2,4,8,... and 5,25,... as well as for their products. (Let's ignore combined tests for products such as 6, since those can always be created.) In base 10, there are nice sum of digits tests for 3 and 9, and a poor one for 11. (There's a really messy one for divisibility by 7 as well, illustrating that it is always possible to produce a poor test.) The tests for 3 and 9 are based on the fact that 10 = 9 + 1, and the test for 11 uses that 100 = 9*11 + 1. So base 12 is not bad, it gives nice tests for 2,4,8,... for 3,9,..., for 11 since 12 = 11 + 1 and it gives a poor test for 13 since 12^2 = 11*13 + 1. The situation for 5 and for 7 seems to be even worse. Contrast this with base 10, which gives a good test for 5 but has a worse test for 11 and none for 13. I'd say that this stuff gets pretty fuzzy. One could argue that 5 is more important than 11 and 13. On the other hand, one could say that ending tests are better than sum of digits tests, and conclude that 12 is superior since it replaces sum of digits tests for 3,9,... with ending tests. Is this the kind of thing you were thinking about? The sum of digits test for 3 only works because it's the square root of 9. A sum of digits test would work for 2 and 4 in base 5. A sum of digits test would work for 4 and 16 in base 17. A sum of digits test would work for 5 and 25 in base 26. Etc. Base 12 would give better tests for more numbers. And a sum of digits test would work for 11 there. Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
Julia Thompson [EMAIL PROTECTED] wrote Base 10 has a minor advantage in divisibility tests that I don't think you get with any other possible base between 5 and 17. And unlike 5 and 17, it's not prime. What are the tests and the advantage? I don't know anything about this. Perhaps it will reconcile me to base 10! -- Robert J. Chassell Rattlesnake Enterprises http://www.rattlesnake.com GnuPG Key ID: 004B4AC8 http://www.teak.cc [EMAIL PROTECTED] ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
... but can someone please count to 12 using the tips and top knuckels of one hand, 'cause i only get 10. I count 12: Looking at my left hand, palm towards my eyes, with my fingers curled over, I see the four tips of my fingers and four of the knuckles closest to my finger tips and four more which are the knuckles second closest to my finger tips. I can either divide that 12 into either * three sets of four: tips, first set of knuckles, second set of knuckles, each a set of four in three rows; or into * four sets of three: for each of four fingers, the tip, first, and second knuckle, each finger having three obvious and visible places on it. -- Robert J. Chassell Rattlesnake Enterprises http://www.rattlesnake.com GnuPG Key ID: 004B4AC8 http://www.teak.cc [EMAIL PROTECTED] ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
Alberto Monteiro [EMAIL PROTECTED] wrote The problem with base 12 is that it has _2_ twice and _3_ once when you factor it, so that the practical man rules to check if a number is divisible by another would get a higher degree of confusion. Ah, I see your point. However, I don't use those rules. I learned them many years ago, but don't remember them. You raise an interesting point. My question is whether the application of those rules provides enough of a issue to have made much of a difference these last 800 (base 10) years? Base 6 would be a much better choice than base 12. No, it would not, since 6 is not readily divisible by 4. If you want to make halves, thirds, and quarters easy, then 12 is the minimum. -- Robert J. Chassell Rattlesnake Enterprises http://www.rattlesnake.com GnuPG Key ID: 004B4AC8 http://www.teak.cc [EMAIL PROTECTED] ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
- Original Message - From: Robert J. Chassell [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Thursday, March 04, 2004 6:38 PM Subject: Re: Bases, was Re: Stirling engine queries ... but can someone please count to 12 using the tips and top knuckels of one hand, 'cause i only get 10. I count 12: Looking at my left hand, palm towards my eyes, with my fingers curled over, I see the four tips of my fingers and four of the knuckles closest to my finger tips and four more which are the knuckles second closest to my finger tips. I can either divide that 12 into either * three sets of four: tips, first set of knuckles, second set of knuckles, each a set of four in three rows; or into * four sets of three: for each of four fingers, the tip, first, and second knuckle, each finger having three obvious and visible places on it. -- Robert J. Chassell Rattlesnake Enterprises http://www.rattlesnake.com GnuPG Key ID: 004B4AC8 http://www.teak.cc [EMAIL PROTECTED] ___ http://www.mccmedia.com/mailman/listinfo/brin-l ill repost as you have missed my count, and how we were to make the count using your provided rules. ( Also, if you look at the tips of your fingers and those knuckles closest to the tips, you will see 12 of them on one hand -- so it is Robert J. Chassell Rattlesnake Enterprises http://www.rattlesnake.com GnuPG Key ID: 004B4AC8 http://www.teak.cc [EMAIL PROTECTED] ___ http://www.mccmedia.com/mailman/listinfo/brin-l yeh im probley stupid or forgot how to count.. but can someone please count to 12 using the tips and top knuckels of one hand, 'cause i only get 10. I can see how one can do it, exclude teh thumb and the base knuckles, use the tips and the top 2 knuckles of each finger, again rembering to exclude the thumb. So as far as my base 10 counting skills go, it is impossible to get 12 using 5 fingers, and 2 points of refrence. Nick I cant count Lidster) as you can see you stipulated that you were to use the tips of your fingers, and the closest knucle to the tip, not all of the knuckles minus the base knuckle as I stated in my rebuttle. I stand on the threshold of tommorow, atop the stairway of yesterday, holding the key to today, staring through the door into the future. -Nick Lidster 26 May 2003 http://capelites.no-ip.com ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
- Original Message - From: David Hobby [EMAIL PROTECTED] To: Killer Bs Discussion [EMAIL PROTECTED] Sent: Thursday, March 04, 2004 7:38 AM Subject: Re: Bases, was Re: Stirling engine queries Well, a little better. Depending how you count, you can argue that 12 has more factors than 10. This must be worth something, since I don't hear anyone pushing for prime bases such as 11. Agreed, it's not a big deal. It might be more to make a number base feel comfortable than a great aid in calculations. Base 10 has a minor advantage in divisibility tests that I don't think you get with any other possible base between 5 and 17. And unlike 5 and 17, it's not prime. Julia There are two kinds of divisibility tests. They aren't usually given names, but let's call them ending tests and sum of digits tests. Working base 10, there are ending tests for 2,4,8,... and 5,25,... as well as for their products. (Let's ignore combined tests for products such as 6, since those can always be created.) In base 10, there are nice sum of digits tests for 3 and 9, and a poor one for 11. (There's a really messy one for divisibility by 7 as well, illustrating that it is always possible to produce a poor test.) The tests for 3 and 9 are based on the fact that 10 = 9 + 1, and the test for 11 uses that 100 = 9*11 + 1. So base 12 is not bad, it gives nice tests for 2,4,8,... for 3,9,..., for 11 since 12 = 11 + 1 and it gives a poor test for 13 since 12^2 = 11*13 + 1. The situation for 5 and for 7 seems to be even worse. Contrast this with base 10, which gives a good test for 5 but has a worse test for 11 and none for 13. I'd say that this stuff gets pretty fuzzy. One could argue that 5 is more important than 11 and 13. On the other hand, one could say that ending tests are better than sum of digits tests, and conclude that 12 is superior since it replaces sum of digits tests for 3,9,... with ending tests. Is this the kind of thing you were thinking about? ---David Who needs whole number divisibility when you have fractions and can work decimals? You would have to do these things no matter what the base you use, in the real world. Getting people to change bases would be whole magnitudes of difficulty greater than getting them to go metric. G xponent Numbers game Maru rob ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
Robert J. Chassell wrote: Julia Thompson [EMAIL PROTECTED] wrote Base 10 has a minor advantage in divisibility tests that I don't think you get with any other possible base between 5 and 17. And unlike 5 and 17, it's not prime. What are the tests and the advantage? I don't know anything about this. Perhaps it will reconcile me to base 10! In base N, to check to see if a number is divisible by N-1, just add the digits, and if their sum is divisible by N-1, the number itself is. So in base 10, if the sum of the digits of a number add up to 9 or 18 or 27, etc., the number is divisible by 9. If N-1 is a square, a similar divisibility test will work on sqrt(N-1). So if the sum of digits of a number in base 10 is divisible by 3, the number itself is divisible by 3. If you like having that nifty little extra divisibility test, your base must be N^2+1 for some N. So 5, 10 and 17 all work as bases with that feature. Base 12 has easier divisibility tests for more numbers, though. Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Bases, was Re: Stirling engine queries
Alberto Monteiro wrote: Robert J. Chassell wrote: However, a base 12 counting system would have been much better; No, it wouldn't Alberto Monteiro Well, a little better. Depending how you count, you can argue that 12 has more factors than 10. This must be worth something, since I don't hear anyone pushing for prime bases such as 11. Agreed, it's not a big deal. It might be more to make a number base feel comfortable than a great aid in calculations. ---David All your base--no, forget I said that! ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
David Hobby wrote: Alberto Monteiro wrote: Robert J. Chassell wrote: However, a base 12 counting system would have been much better; No, it wouldn't Alberto Monteiro Well, a little better. Depending how you count, you can argue that 12 has more factors than 10. This must be worth something, since I don't hear anyone pushing for prime bases such as 11. Agreed, it's not a big deal. It might be more to make a number base feel comfortable than a great aid in calculations. Base 10 has a minor advantage in divisibility tests that I don't think you get with any other possible base between 5 and 17. And unlike 5 and 17, it's not prime. Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Bases, was Re: Stirling engine queries
From: Julia Thompson [EMAIL PROTECTED] David Hobby wrote: Alberto Monteiro wrote: Robert J. Chassell wrote: However, a base 12 counting system would have been much better; No, it wouldn't Alberto Monteiro Well, a little better. Depending how you count, you can argue that 12 has more factors than 10. This must be worth something, since I don't hear anyone pushing for prime bases such as 11. Agreed, it's not a big deal. It might be more to make a number base feel comfortable than a great aid in calculations. Base 10 has a minor advantage in divisibility tests that I don't think you get with any other possible base between 5 and 17. And unlike 5 and 17, it's not prime. I endorse base 17. Heptodecaphilia. ___ http://www.mccmedia.com/mailman/listinfo/brin-l
