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: Stirling engine queries
Trent Shipley [EMAIL PROTECTED] wrote, I think that internal combustion gasoline and diesel engines would have been much more attractive in the 1930's and 1940's. They were more efficient and had better power to weight ratios. Gasoline internal combustion engines just offered *much* better power to weight ratios. That is a very good point! Given the technology of the times, what do you think would have been the power to weight ratio of a Stirling engine whose fluid was, say compressed hydrogen at 3000 lbs/sq-in (3000 psi, ~200 bar, or 20 megaPascals). How would that power to weight ratio compare to a gasoline internal combustion engine? Is hydrogen at that pressure a good heat fluid? I know helium at that pressure is good, but don't know about hydrogen. I picked hydrogen because it was much much cheaper than helium. If argon is better, then argon would be a good choice. It became available at an affordable price after 1900, as a side effect of liquifying air, before helium. What were good power to weight ratios? In the 1930s, did a good engine produce 1 hp of output for each 2 lbs of weight (i.e., approx 800 watts per kilogram or even 1 kw/kg) or was the ratio better than that? I don't know. -- 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: Stirling engine queries
On Saturday 2004-03-06 18:16, Robert J. Chassell wrote: Trent Shipley [EMAIL PROTECTED] wrote, Given the technology of the times, what do you think would have been the power to weight ratio of a Stirling engine whose fluid was, say compressed hydrogen at 3000 lbs/sq-in (3000 psi, ~200 bar, or 20 megaPascals). How would that power to weight ratio compare to a gasoline internal combustion engine? Is hydrogen at that pressure a good heat fluid? I know helium at that pressure is good, but don't know about hydrogen. I picked hydrogen because it was much much cheaper than helium. I have no clue. I guess if it works for He it should work for H2, probably better since there seems to be a preference for low mass gasses when designing Stirling engines. If argon is better, then argon would be a good choice. It became available at an affordable price after 1900, as a side effect of liquifying air, before helium. If you want a low-mass fluid, then we expect H2 to be better than Ar. What were good power to weight ratios? In the 1930s, did a good engine produce 1 hp of output for each 2 lbs of weight (i.e., approx 800 watts per kilogram or even 1 kw/kg) or was the ratio better than that? I don't know. I know that for a long time that 1hp/lb was the holy grail of aviation piston engine design. I cannot recall when the engineers got it, except I'm pretty sure they had it by the end of WWII. You will want to go hunting through aviation history. ___ 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: Stirling engine queries
--- In [EMAIL PROTECTED], Julia Thompson [EMAIL PROTECTED] wrote: Erik Reuter wrote: On Thu, Mar 04, 2004 at 01:40:47PM -0600, Julia Thompson wrote: Describe how to count up to 1023 on 10 fingers. :) 132 to you! Hay Erick, 198, 2, 198, 2, 198, 2 ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
--- In [EMAIL PROTECTED], Erik Reuter [EMAIL PROTECTED] wrote: On Thu, Mar 04, 2004 at 09:26:00PM -0600, Julia Thompson wrote: Erik Reuter wrote: On Thu, Mar 04, 2004 at 01:40:47PM -0600, Julia Thompson wrote: Describe how to count up to 1023 on 10 fingers. :) 132 to you! Erik! I didn't know you cared! Wouldn't that be 9 (thumbs in) or 18 (thumbs out)? No that would be Austin Prowd. Try 17. ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
--- In [EMAIL PROTECTED], Julia Thompson [EMAIL PROTECTED] wrote: Jan Coffey wrote: --- In [EMAIL PROTECTED], Julia Thompson [EMAIL PROTECTED] wrote: Describe how to count up to 1023 on 10 fingers. :) My wife and I (both CS) use this method exclusivly. I think I have even posted this here before. Anyway, one day we went to the grocer on our way for a long road trip. From across the store, she wanted to know how many Necterines to get total. Using hand signals I asked how many se whould like. She held up her index finger signeling that she would want 2. I then replied that I would also want 2 and responded that this made 4 total. A guy that had been standing close to me but between my wife and I came over and began to yell at me. I had no idea why, and I called for security. When security arived, several soccer moms close by got involved and told them that I had been rude to the man and that was why he was attacking me. I then realized what had happned and tried to explainIt did little good though, they just could not understand how I could have been counting in that manner. I like to use this now as a kind of insult, you hold up 4 fingers on one hand and ask the insult reciever to convert to binary. Oh, man, that story is even better than the one I have about that gesture! Ages ago, Dan was working on software to help make AutoCAD run faster. The software included a display list, which made things go faster, and they could add extra features that AutoCAD didn't have at the time. One such feature was True Erase(tm). (At least, I think it was trademarked, I could be wrong, though.) If you wanted to change a vector in AutoCAD, what it did initially was to put a black vector over the one that was there, and then create the new vector. True Erase would get rid of the old vector and the black vector a lot sooner than AutoCAD would, which helped boost performance. The company president was trying to explain this to a customer at a trade show, and held up three fingers -- one for the old vector, one for the new vector, one for the covering vector. He then went on to say how True Erase got rid of the old and covering vectors. He didn't pick the correct finger for the new vector. So one of our little inside jokes is to say True Erase! instead of the actual insult. The UT marching band went to south america and were thrown out of a band competition for using the hook-em-horns sign, which means something very vulgar. After a lot of explaining and a promise not to repeat the offense they were allowed back 3 years latter. At this point they decided that if they could not use the hoom-em then they would hold up an OK sign. Unfortunatly the hand signals are synonimous. Query: When was this? I don't know, it was told to me by someone in the band as an explination for why AM was going to some event and we were not. By the way, when Kim and I make a 4 we do so with our palms out and our index and thubm forming a C. This has made us consider that you could actualy represent a much larger set of numbers than 0 - 1023. For one thing you get twice as many bits if you turn your hand around. you also get twice again for 1/2 raised fingers. If you then use one hand to point to another whew...I never need to leave one hand. ___ 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: Stirling engine queries
I wrote However, a base 12 counting system would have been much better ... and Bryon Daly [EMAIL PROTECTED] asked Why base 12? Why not base 16, and then we'd at least benefit from easy conversion to/from binary? Because base 12 can be divided by both 2 and 3 (and by 4 and 6) but base 16 can be divided only by 2 (and by 4 and 8). For non-programming purposes, 12 is a much better base than 16. People frequently divide things in half, thirds, and quarters. Hence the value of base 12. Base 10 is worse. You have to move to 100s to get a `quarter', such as 25 cents -- indeed, base 10 is even more limited than base 16. It would be much nicer for a `quarter' to be 0.3, which it is in base 12, and a `third' to be 0.4; they are nice round numbers (albeit round number fractions). (It goes without saying that some children would be confused that a third is 0.4 and a quarter is 0.3; understanding and remembering the difference would be one of rites of schooldom.) For programmers, base 16 is excellent; but programmers are both recent in history and a small minority of people. 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 easy to count on your fingers. While programmers never count on their fingers, over the past millennia, many other people have. (Indeed, I have heard it claimed that societies in which children are first taught to count on their fingers end up having more technically competent adults who do not count on their fingers. I don't whether this is true.) -- 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
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: Stirling engine queries
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 ___ http://www.mccmedia.com/mailman/listinfo/brin-l
RE: Stirling engine queries
I think it was the babylonians who first used base 60, which is how we got hours, minutes and seconds, as well as the 360 points on a compass. Its worked pretty well so far. I found this on a web site as a possible reason for base 60. Here is one way that it could have happened. One can count up to 60 using your two hands. On your left hand there are three parts on each of four fingers (excluding the thumb). The parts are divided from each other by the joints in the fingers. Now one can count up to 60 by pointing at one of the twelve parts of the fingers of the left hand with one of the five fingers of the right hand. This gives a way of finger counting up to 60 rather than to 10. Anyone convinced? Nerd From Hell -Original Message- From: Nick Lidster [mailto:[EMAIL PROTECTED] Sent: Thursday, March 04, 2004 7:15 AM To: Killer Bs Discussion Subject: Re: Stirling engine queries 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 ___ http://www.mccmedia.com/mailman/listinfo/brin-l ___ 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: Stirling engine queries
Nick Lidster wrote: 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. How's this: Use your thumb as a pointer. You have 3 segments each on 4 fingers. Count the segments in some particular order using your thumb as the pointer for each count. With 2 hands, you can get up to 144. Next exercise: Describe how to count up to 1023 on 10 fingers. :) Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
- Original Message - From: Julia Thompson [EMAIL PROTECTED] To: Killer Bs Discussion [EMAIL PROTECTED] Sent: Thursday, March 04, 2004 1:40 PM Subject: Re: Stirling engine queries Describe how to count up to 1023 on 10 fingers. :) I'm not sure that regestered with me. :-) Dan M. ___ 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: Stirling engine queries
Julia, et al, Describe how to count up to 1023 on 10 fingers. :) That's easy to describe, but a whole lot more difficult to use :-). I remember seeing Doug Engelbart (inventor of the computer mouse, etc) http://tinyurl.com/9km7 using a one-handed chorded keyboard http://tinyurl.com/3ajld that worked like your suggestion. Imagine having to learn the binary representation of ASCII characters and repeat it reliably! He claimed that it only took a couple of hours to learn. But then again, he was Doug Engelbart. Towards the more day-to-day end of the scale, I learned a very usable way to count to 100 on two hands. It's interesting in that it mixes bases 5 and 10 to work its magic. Poise your hands just above a surface, as over a piano keyboard. In this position, your hands represent that famous Arabic contribution to mathematics, the invaluable zero. Starting with your pinky and moving towards your index finger, count off 1-2-3-4 by lowering each successive finger to the surface (and keeping it there), as you might when drumming your fingers. Next, lift all four fingers and drop your thumb for 5. Repeat steps 1-2-3-4 (with your thumb down) to represent 6-7-8-9. Here's where base 10 comes in. Raise all five fingers and drop your other pinky to represent 10. Repeat as necessary. I think you can take it from there. It's really fast -- I've used it when I had to count noses of people coming into a room. Dave David M. Land [EMAIL PROTECTED] 408-551-0427 ___ 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
Finger math (was RE: Stirling engine queries)
--- Robert J. Chassell [EMAIL PROTECTED] wrote: snippage 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 easy to count on your fingers. While programmers never count on their fingers, over the past millennia, many other people have... http://personal.cfw.com/~clayford/finger.html Using fingers to perform math computations is known as Chisenbop. Here's a site that will tell you all you want to know. In the meantime, here's a couple of examples of Chisenbop to get you started...Multiplying by 9... Now _my_ recall of the name of this method was Chismbob - which was nearly the name of my 'tuxedo cat' (the woman who gave him to me wanted me to call him Bob after her husband, but I gave her the choice of Chismbob or 'Zimbobwe' -- thus Zimba joined the household). Lo and behold, there is indeed Chismbob on the web: http://www.eyrie.org/~drizzt/mylnh/tfw3-1.html [Third section down] Chismbob Boy strode proudly into the LNH lobby. I'm here to be a Legionnaire! he announced proudly. Lester the receptionist looked up blandly. Uh huh. Isn't this a school day? Evil knows no tardy bell. Alllright. what's your name, son? I am Chismbob Boy -- when Evil needs accounting! Lester sucked his teeth, staring at the dramatic pose the skinny adolescent had assumed. He pressed the intercom. Master Blaster, Frat Boy, Incredible-Man-With-No-Life to the lobby please. Are they going to guide me in? Kewl! The summoned Net.Heroes burst into the lobby. Lester gestured a thumb at the garish hero-wannabe. Ah! Look out, guys. It's Continuity Champ's Tailor Jr.! quipped Master Blaster. I'm, ah, Chismbob Boy. Sarcastic Lad sent me to join up. The three heroes looked to each other. Chismbob Boy? Ahhahahahah! They broke out into laughter so intense tears were flying. Oh man, Sarc has the best one yet! Frat Boy said between guffaws. That's better than Lawn-Flamingo Lass you sent in last week, MB. Incredible-Man-With-No-Life started waggling his fingers. The answer is...10 to life! Sorry Clueless Master, it adds up to jail for you! Beware, these fingers are weapons of math fu! Much, much, much more on-site... ;) Debbi who still thinks that most folks, if they count on their fingers, are gonna wind up with base 10 __ Do you Yahoo!? Yahoo! Search - Find what youre looking for faster http://search.yahoo.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: Stirling engine queries
On Thu, Mar 04, 2004 at 01:40:47PM -0600, Julia Thompson wrote: Describe how to count up to 1023 on 10 fingers. :) 132 to you! -- Erik Reuter http://www.erikreuter.net/ ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
I can do it to 1024.. but to 1023 i have no idea 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 - Original Message - From: Erik Reuter [EMAIL PROTECTED] To: Killer Bs Discussion [EMAIL PROTECTED] Sent: Thursday, March 04, 2004 9:23 PM Subject: Re: Stirling engine queries On Thu, Mar 04, 2004 at 01:40:47PM -0600, Julia Thompson wrote: Describe how to count up to 1023 on 10 fingers. :) 132 to you! -- Erik Reuter http://www.erikreuter.net/ ___ http://www.mccmedia.com/mailman/listinfo/brin-l ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
--- In [EMAIL PROTECTED], Julia Thompson [EMAIL PROTECTED] wrote: Describe how to count up to 1023 on 10 fingers. :) My wife and I (both CS) use this method exclusivly. I think I have even posted this here before. Anyway, one day we went to the grocer on our way for a long road trip. From across the store, she wanted to know how many Necterines to get total. Using hand signals I asked how many se whould like. She held up her index finger signeling that she would want 2. I then replied that I would also want 2 and responded that this made 4 total. A guy that had been standing close to me but between my wife and I came over and began to yell at me. I had no idea why, and I called for security. When security arived, several soccer moms close by got involved and told them that I had been rude to the man and that was why he was attacking me. I then realized what had happned and tried to explainIt did little good though, they just could not understand how I could have been counting in that manner. I like to use this now as a kind of insult, you hold up 4 fingers on one hand and ask the insult reciever to convert to binary. The UT marching band went to south america and were thrown out of a band competition for using the hook-em-horns sign, which means something very vulgar. After a lot of explaining and a promise not to repeat the offense they were allowed back 3 years latter. At this point they decided that if they could not use the hoom-em then they would hold up an OK sign. Unfortunatly the hand signals are synonimous. ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
On 5 Mar 2004, at 1:03 am, Nick Lidster wrote: I can do it to 1024.. but to 1023 i have no idea Your fingers must have had a fencepost accident :) -- William T Goodall Mail : [EMAIL PROTECTED] Web : http://www.wtgab.demon.co.uk Blog : http://radio.weblogs.com/0111221/ It is our belief, however, that serious professional users will run out of things they can do with UNIX. - Ken Olsen, President of DEC, 1984. ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
Nick, I can do it to 1024.. but to 1023 i have no idea Zero counts, but for nothing. I stand on the threshold of tommorow, atop the stairway of yesterday, holding the key to today, staring through the door into the future. Bully for you. As for me, I generally stumble up the stairway of my lost youth, only to stand on the threshhold of tomorrow with the cold rain of the future ruining the belated birthday card I clutch in my hand as I pat myself down frantically, searching for the key to today, only to realize that it's in the right-front pocket of trousers of yesterday, which I left on the floor of my ancestors at the foot of the bed of overstretched metaphors. Dave David M. Land [EMAIL PROTECTED] 408-551-0427 ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
Jan, Anyway, one day we went to the grocer on our way for a long road trip... Great story. It reminded me of the Gangs Kill Sign Language Users urban legend that http://tinyurl.com/2a8vf. So be careful: you and your wife could end up dead, or worse -- an urban legend! I like to use this now as a kind of insult, you hold up 4 fingers on one hand and ask the insult reciever to convert to binary. In what culture is 15 an insult? ;-) Dave Hand Signs are Evil and Should be Eradicated Land David M. Land [EMAIL PROTECTED] 408-551-0427 ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
- Original Message - From: William T Goodall [EMAIL PROTECTED] To: Killer Bs Discussion [EMAIL PROTECTED] Sent: Thursday, March 04, 2004 10:01 PM Subject: Re: Stirling engine queries On 5 Mar 2004, at 1:03 am, Nick Lidster wrote: I can do it to 1024.. but to 1023 i have no idea Your fingers must have had a fencepost accident :) -- William T Goodall Mail : [EMAIL PROTECTED] Web : http://www.wtgab.demon.co.uk Blog : http://radio.weblogs.com/0111221/ It is our belief, however, that serious professional users will run out of things they can do with UNIX. - Ken Olsen, President of DEC, 1984. ___ http://www.mccmedia.com/mailman/listinfo/brin-l no no... If i remeber my diagram, I excluded teh thumbs untill last, although this has no real bearing on teh final outcome. You then use the tips and all knuckles of your fingers, it breaks down something like: 16*4=64 64*4=256 now at this point you bring back the thumbs using the tips and first knucle, 256*4=1024 the way it is done is that you use your left hand as your counter, and your right as the pointer using all points of reference that are used on the left hand. doing that gives you 1024 nick going number boggled lidster ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
so it should be 123?...man what a long day, first teh federation declears war on me and now this... lol... if only i could beat the Kobayashi Maru - Original Message - From: Dave Land [EMAIL PROTECTED] To: Killer Bs Discussion [EMAIL PROTECTED] Sent: Thursday, March 04, 2004 10:01 PM Subject: Re: Stirling engine queries Nick, I can do it to 1024.. but to 1023 i have no idea Zero counts, but for nothing. I stand on the threshold of tommorow, atop the stairway of yesterday, holding the key to today, staring through the door into the future. Bully for you. As for me, I generally stumble up the stairway of my lost youth, only to stand on the threshhold of tomorrow with the cold rain of the future ruining the belated birthday card I clutch in my hand as I pat myself down frantically, searching for the key to today, only to realize that it's in the right-front pocket of trousers of yesterday, which I left on the floor of my ancestors at the foot of the bed of overstretched metaphors. Dave David M. Land [EMAIL PROTECTED] 408-551-0427 ___ http://www.mccmedia.com/mailman/listinfo/brin-l ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
Jan Coffey wrote: --- In [EMAIL PROTECTED], Julia Thompson [EMAIL PROTECTED] wrote: Describe how to count up to 1023 on 10 fingers. :) My wife and I (both CS) use this method exclusivly. I think I have even posted this here before. Anyway, one day we went to the grocer on our way for a long road trip. From across the store, she wanted to know how many Necterines to get total. Using hand signals I asked how many se whould like. She held up her index finger signeling that she would want 2. I then replied that I would also want 2 and responded that this made 4 total. A guy that had been standing close to me but between my wife and I came over and began to yell at me. I had no idea why, and I called for security. When security arived, several soccer moms close by got involved and told them that I had been rude to the man and that was why he was attacking me. I then realized what had happned and tried to explainIt did little good though, they just could not understand how I could have been counting in that manner. I like to use this now as a kind of insult, you hold up 4 fingers on one hand and ask the insult reciever to convert to binary. Oh, man, that story is even better than the one I have about that gesture! Ages ago, Dan was working on software to help make AutoCAD run faster. The software included a display list, which made things go faster, and they could add extra features that AutoCAD didn't have at the time. One such feature was True Erase(tm). (At least, I think it was trademarked, I could be wrong, though.) If you wanted to change a vector in AutoCAD, what it did initially was to put a black vector over the one that was there, and then create the new vector. True Erase would get rid of the old vector and the black vector a lot sooner than AutoCAD would, which helped boost performance. The company president was trying to explain this to a customer at a trade show, and held up three fingers -- one for the old vector, one for the new vector, one for the covering vector. He then went on to say how True Erase got rid of the old and covering vectors. He didn't pick the correct finger for the new vector. So one of our little inside jokes is to say True Erase! instead of the actual insult. The UT marching band went to south america and were thrown out of a band competition for using the hook-em-horns sign, which means something very vulgar. After a lot of explaining and a promise not to repeat the offense they were allowed back 3 years latter. At this point they decided that if they could not use the hoom-em then they would hold up an OK sign. Unfortunatly the hand signals are synonimous. Query: When was this? Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
Erik Reuter wrote: On Thu, Mar 04, 2004 at 01:40:47PM -0600, Julia Thompson wrote: Describe how to count up to 1023 on 10 fingers. :) 132 to you! Erik! I didn't know you cared! Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
On Thu, Mar 04, 2004 at 09:26:00PM -0600, Julia Thompson wrote: Erik Reuter wrote: On Thu, Mar 04, 2004 at 01:40:47PM -0600, Julia Thompson wrote: Describe how to count up to 1023 on 10 fingers. :) 132 to you! Erik! I didn't know you cared! Wouldn't that be 9 (thumbs in) or 18 (thumbs out)? -- Erik Reuter http://www.erikreuter.net/ ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
Dave Land wrote: Julia, et al, Describe how to count up to 1023 on 10 fingers. :) That's easy to describe, but a whole lot more difficult to use :-). I remember seeing Doug Engelbart (inventor of the computer mouse, etc) http://tinyurl.com/9km7 using a one-handed chorded keyboard http://tinyurl.com/3ajld that worked like your suggestion. Imagine having to learn the binary representation of ASCII characters and repeat it reliably! He claimed that it only took a couple of hours to learn. But then again, he was Doug Engelbart. Sounds like something I might like to play with one day. Towards the more day-to-day end of the scale, I learned a very usable way to count to 100 on two hands. It's interesting in that it mixes bases 5 and 10 to work its magic. Poise your hands just above a surface, as over a piano keyboard. In this position, your hands represent that famous Arabic contribution to mathematics, the invaluable zero. Starting with your pinky and moving towards your index finger, count off 1-2-3-4 by lowering each successive finger to the surface (and keeping it there), as you might when drumming your fingers. Next, lift all four fingers and drop your thumb for 5. Repeat steps 1-2-3-4 (with your thumb down) to represent 6-7-8-9. Here's where base 10 comes in. Raise all five fingers and drop your other pinky to represent 10. Repeat as necessary. I think you can take it from there. It's really fast -- I've used it when I had to count noses of people coming into a room. I go index to pinky, not pinky to index. Otherwise, this is the system I've used for counting on my fingers for awhile. I read an article about it when I was in 6th grade or so. (Maybe 7th.) It's useful for keeping track of a total when you're adding a lot of smallish numbers. (The last time I used it was to count the number of great-grandchildren my mother-in-law's parents have. Not that either of them are still alive, but it tells me how many people from that branch are in my children's generation.) Julia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
- Original Message - From: Julia Thompson [EMAIL PROTECTED] To: Killer Bs Discussion [EMAIL PROTECTED] Sent: Thursday, March 04, 2004 9:26 PM Subject: Re: Stirling engine queries Erik Reuter wrote: On Thu, Mar 04, 2004 at 01:40:47PM -0600, Julia Thompson wrote: Describe how to count up to 1023 on 10 fingers. :) 132 to you! Erik! I didn't know you cared! He's a real stand up guy. xponent Multiplier 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
RE: Stirling engine queries
From: Robert J. Chassell [EMAIL PROTECTED] However, a base 12 counting system would have been much better; but base 10 became the standard and the cost of shifting is too high. Why base 12? Why not base 16, and then we'd at least benefit from easy conversion to/from binary? (Sorry, nothing to add about Stirling engines...) -Bryon _ Create a Job Alert on MSN Careers and enter for a chance to win $1000! http://msn.careerbuilder.com/promo/kaday.htm?siteid=CBMSN_1Ksc_extcmp=JS_JASweep_MSNHotm2 ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
On Wednesday 2004-03-03 09:58, Robert J. Chassell wrote: Could Stirling engines have been developed for airship or hybrid car use in the 1910 - 1920 period, or was the technology of the time too primitive? Could such engines have been developed 20 years later? I think that internal combustion gasoline and diesel engines would have been much more attractive in the 1930's and 1940's. They were more efficient and had better power to weight ratios. Pollution and depletion of fossil fuels were not major concerns. Even the quiet of a stirling wasn't much of an appeal to submariners who were just developing sonic warfare. *** Another thought: the use of a Stirling engine for a car or airship is not so much an `invention' as a `development'. Is it more fair to ask whether the lack of Stirling engined cars and airships is the result of other technologies gaining a sufficient functionality first, and then the cost of switching becoming too high? I think that is exactly it. Gasoline internal combustion engines just offered *much* better power to weight ratios. *** Another query: Would a Stirling engine work well in a hybrid vehicle? Would its efficiency be much better than the efficiency of a vehicle using an internal combustion engine? I expect the efficiency would approach the efficiency of a disiel-hybrid engine, but it would pollute less and be easy to multi-fuel. What would be the cost to the various auto manufacturers of replacing the skills and equipment they use now to manufacture internal combustion engines with the the skills and equipment necessary to manufacture Stirling engines for a hybrid? Expensive, but not prohibitive. http://www.sesusa.org/ http://www.stirlingsouth.com/ http://www.bekkoame.ne.jp/~khirata/ ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Stirling engine queries
Robert J. Chassell wrote: However, a base 12 counting system would have been much better; No, it wouldn't Alberto Monteiro ___ 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
