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#11
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Alien number systems
Fred J. McCall wrote:
Sylvia Else wrote: :Fred J. McCall wrote: : Sylvia Else wrote: : : :Fred J. McCall wrote: : : Sylvia Else wrote: : : : : :Fred J. McCall wrote: : : : Sylvia Else wrote: : : : : : : :Orval Fairbairn wrote: : : : : In article : : : : , : : : : Frogwatch wrote: : : : : : : : : Most of us use the base 10 number system although civilizations such : : : : as the Romans used their number system. Many people think that base 2 : : : : is a universal number system but maybe it isnt. Perhaps a logical : : : : system would be based on only representing prime numbers. Any other : : : : numbers could be made up of symbols for primes indicating multiplying : : : : them to get composite numbers. : : : : : : : : Binary, octal and hexadecimal are the basis of computers, whereas e is : : : : the basis of natural logarithms; of course the number of fingers is yet : : : : another. : : : : : : : :There isn't really anything about those number systems that makes them : : : :intrinsically computer related. It's really more a matter of : : : racticality - it's easier, so far, to build computers that way. : : : : : : : :You could build computers around a tristate logic, for example. But it's : : : :more complicated, and these seems little point, particularly as it would : : : :be invisible to users, and indeed programmers for the most part. : : : : : : : : : : We could still build analog computers, too, but we don't. There's a : : : reason for that. : : : : : : Binary is the basis of digital computers for a lot of very good : : : reasons. : : : : : :Well they're all the same reason, really. The engineering is easier, : : :which makes the computers cheaper. : : : : : : : That's not it. : : : : : : : :But that still doesn't make binary : : :intrinsic to computers, any more than petrol is intrinsic to cars. : : : : : : : Do I really need to repost what I wrote so you can read it again, or : : will you go back and read it with brain engaged this time around? : : : : : :Please don't post it again - it'll just have exactly the same meaning as : :it did last time, which was not very much. You may know what you have in : :mind, but what you wrote doesn't convey it. : : : : Which indicates that you don't know enough about computer engineering : to be in this discussion. : :No, it just means that I'm not fixated on the current ways of doing things. : You have your own private laws of physics, do you? : : : Let me make it simple for you. It takes about twice as many circuit : elements to implement a tri-state element as it does to implement a : bi-state one. So, using the same amount of silicon I can either : implement two bi-state elements (count from 0-3) or a single tri-state : one (count from 0-2). Thus we see that trinary computers would have : to be larger and consume more power for the same amount of : computational ability when compared to binary computers. : : It's not that the engineering is easier for a binary computer than for : a trinary one. It just doesn't make good sense from a size/power : perspective. : :You're assuming a particular implementation. Who's to say how it would an-out using a different technology? You can't use the particular :implementation, which is based on binary, to justify a claim that binary :is best for implementing computers. It's merely the best for the current :technology - which means it's an engineering decision if ever there was one. : Semiconductor physics - learn something about them. So, computers have to be made out of semiconductors? Is that some kind of universal law? : : : Is it starting to sink in now? : : Oh, by the way, your comparison to cars and petrol makes no sense : whatsoever in this context. : : :With the currently available technology, the total cost of ownership of :a car is lowest when it runs on petrol. : Wrong. Really? Then why do people have petrol driven cars? : :With the currently available :technology, the total cost of ownership of a computer is lowest when :it's based on binary arithmetic. : :Total cost of ownership relates to capital cost, operating cost, and :reliability. : :Good engineering minimises total cost of ownership. : Again, learn something about semiconductor physics. |
#12
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Alien number systems
David Spain wrote:
Yeah, don't get me started on quantum computers when they are in the coherent superposition state! :-) Actually, I wouldn't mind getting you started. Despite reports of QCs doing some basic arithmetic, I'm still rather dubious about whether these things can really work. Show me factorisation of otherwise intractable composite numbers, and I'll start to believe I'll also be highly amused by the abrupt disappearance of important computer security infrastructure. Well, I did warn them.... Sylvia. |
#13
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Alien number systems
Sylvia Else writes:
David Spain wrote: Yeah, don't get me started on quantum computers when they are in the coherent superposition state! :-) Actually, I wouldn't mind getting you started. Despite reports of QCs doing some basic arithmetic, I'm still rather dubious about whether these things can really work. Show me factorisation of otherwise intractable composite numbers, and I'll start to believe Don't base your public key encryption on 5 x 3: http://www.sciencemag.org/cgi/conten.../325/5945/1221 Granted far from intractable, but one must assume more is being spent on development of this than we read about in the papers. I'll also be highly amused by the abrupt disappearance of important computer security infrastructure. Well, I did warn them.... Sylvia. More like the abrupt disappearance of large sums of money, or perhaps the misplacement of an Army or Navy at a most in-opportune time. Warnings are good, but is anyone listening? Dave |
#14
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Alien number systems
Fred J. McCall wrote:
Sylvia Else wrote: :Fred J. McCall wrote: : Sylvia Else wrote: : : :Fred J. McCall wrote: : : Sylvia Else wrote: : : : : :Fred J. McCall wrote: : : : Sylvia Else wrote: : : : : : : :Fred J. McCall wrote: : : : : Sylvia Else wrote: : : : : : : : : :Orval Fairbairn wrote: : : : : : In article : : : : : , : : : : : Frogwatch wrote: : : : : : : : : : : Most of us use the base 10 number system although civilizations such : : : : : as the Romans used their number system. Many people think that base 2 : : : : : is a universal number system but maybe it isnt. Perhaps a logical : : : : : system would be based on only representing prime numbers. Any other : : : : : numbers could be made up of symbols for primes indicating multiplying : : : : : them to get composite numbers. : : : : : : : : : : Binary, octal and hexadecimal are the basis of computers, whereas e is : : : : : the basis of natural logarithms; of course the number of fingers is yet : : : : : another. : : : : : : : : : :There isn't really anything about those number systems that makes them : : : : :intrinsically computer related. It's really more a matter of : : : : racticality - it's easier, so far, to build computers that way. : : : : : : : : : :You could build computers around a tristate logic, for example. But it's : : : : :more complicated, and these seems little point, particularly as it would : : : : :be invisible to users, and indeed programmers for the most part. : : : : : : : : : : : : : We could still build analog computers, too, but we don't. There's a : : : : reason for that. : : : : : : : : Binary is the basis of digital computers for a lot of very good : : : : reasons. : : : : : : : :Well they're all the same reason, really. The engineering is easier, : : : :which makes the computers cheaper. : : : : : : : : : : That's not it. : : : : : : : : : : :But that still doesn't make binary : : : :intrinsic to computers, any more than petrol is intrinsic to cars. : : : : : : : : : : Do I really need to repost what I wrote so you can read it again, or : : : will you go back and read it with brain engaged this time around? : : : : : : : : :Please don't post it again - it'll just have exactly the same meaning as : : :it did last time, which was not very much. You may know what you have in : : :mind, but what you wrote doesn't convey it. : : : : : : : Which indicates that you don't know enough about computer engineering : : to be in this discussion. : : : :No, it just means that I'm not fixated on the current ways of doing things. : : : : You have your own private laws of physics, do you? : : : : : : : Let me make it simple for you. It takes about twice as many circuit : : elements to implement a tri-state element as it does to implement a : : bi-state one. So, using the same amount of silicon I can either : : implement two bi-state elements (count from 0-3) or a single tri-state : : one (count from 0-2). Thus we see that trinary computers would have : : to be larger and consume more power for the same amount of : : computational ability when compared to binary computers. : : : : It's not that the engineering is easier for a binary computer than for : : a trinary one. It just doesn't make good sense from a size/power : : perspective. : : : :You're assuming a particular implementation. Who's to say how it would : an-out using a different technology? You can't use the particular : :implementation, which is based on binary, to justify a claim that binary : :is best for implementing computers. It's merely the best for the current : :technology - which means it's an engineering decision if ever there was one. : : : : Semiconductor physics - learn something about them. : :So, computers have to be made out of semiconductors? Is that some kind f universal law? : If you have a better way, you should patent it now. I don't, but that's beside the point. Unless you can show that computers can only be made out of semiconductors (highly unlikely), you cannot use semiconductors in an argument about the general applicability of binary to computers. : : : : : : : : Is it starting to sink in now? : : : : Oh, by the way, your comparison to cars and petrol makes no sense : : whatsoever in this context. : : : : : :With the currently available technology, the total cost of ownership of : :a car is lowest when it runs on petrol. : : : : Wrong. : :Really? Then why do people have petrol driven cars? : Yes, really. Diesels have cheaper lifecycle costs. It depends very much how they're used. Diesel engines have a higher capital cost. They're only have lower total costs if they're used a lot. Otherwise the cost of capital is more than the lower cost of the fuel. Sylvia. |
#15
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Alien number systems
In article ,
Sylvia Else wrote: Fred J. McCall wrote: Sylvia Else wrote: :Fred J. McCall wrote: : Sylvia Else wrote: : : :Fred J. McCall wrote: : : Sylvia Else wrote: : : : : :Fred J. McCall wrote: : : : Sylvia Else wrote: : : : : : : :Fred J. McCall wrote: : : : : Sylvia Else wrote: : : : : : : : : :Orval Fairbairn wrote: : : : : : In article : : : : : : : : : : s.com, : : : : : Frogwatch wrote: : : : : : : : : : : Most of us use the base 10 number system although : : : : : civilizations such : : : : : as the Romans used their number system. Many people think : : : : : that base 2 : : : : : is a universal number system but maybe it isnt. Perhaps a : : : : : logical : : : : : system would be based on only representing prime numbers. : : : : : Any other : : : : : numbers could be made up of symbols for primes indicating : : : : : multiplying : : : : : them to get composite numbers. : : : : : : : : : : Binary, octal and hexadecimal are the basis of computers, : : : : : whereas e is : : : : : the basis of natural logarithms; of course the number of : : : : : fingers is yet : : : : : another. : : : : : : : : : :There isn't really anything about those number systems that : : : : :makes them : : : : :intrinsically computer related. It's really more a matter of : : : : racticality - it's easier, so far, to build computers that : : : : :way. : : : : : : : : : :You could build computers around a tristate logic, for : : : : :example. But it's : : : : :more complicated, and these seems little point, particularly : : : : :as it would : : : : :be invisible to users, and indeed programmers for the most : : : : art. : : : : : : : : : : : : : We could still build analog computers, too, but we don't. : : : : There's a : : : : reason for that. : : : : : : : : Binary is the basis of digital computers for a lot of very good : : : : reasons. : : : : : : : :Well they're all the same reason, really. The engineering is : : : :easier, : : : :which makes the computers cheaper. : : : : : : : : : : That's not it. : : : : : : : : : : :But that still doesn't make binary : : : :intrinsic to computers, any more than petrol is intrinsic to : : : :cars. : : : : : : : : : : Do I really need to repost what I wrote so you can read it again, : : : or : : : will you go back and read it with brain engaged this time around? : : : : : : : : :Please don't post it again - it'll just have exactly the same : : :meaning as : : :it did last time, which was not very much. You may know what you : : :have in : : :mind, but what you wrote doesn't convey it. : : : : : : : Which indicates that you don't know enough about computer engineering : : to be in this discussion. : : : :No, it just means that I'm not fixated on the current ways of doing : :things. : : : : You have your own private laws of physics, do you? : : : : : : : Let me make it simple for you. It takes about twice as many circuit : : elements to implement a tri-state element as it does to implement a : : bi-state one. So, using the same amount of silicon I can either : : implement two bi-state elements (count from 0-3) or a single : : tri-state : : one (count from 0-2). Thus we see that trinary computers would have : : to be larger and consume more power for the same amount of : : computational ability when compared to binary computers. : : : : It's not that the engineering is easier for a binary computer than : : for : : a trinary one. It just doesn't make good sense from a size/power : : perspective. : : : :You're assuming a particular implementation. Who's to say how it would : an-out using a different technology? You can't use the particular : :implementation, which is based on binary, to justify a claim that : :binary : :is best for implementing computers. It's merely the best for the : :current : :technology - which means it's an engineering decision if ever there was : ne. : : : : Semiconductor physics - learn something about them. : :So, computers have to be made out of semiconductors? Is that some kind f universal law? : If you have a better way, you should patent it now. I don't, but that's beside the point. Unless you can show that computers can only be made out of semiconductors (highly unlikely), you cannot use semiconductors in an argument about the general applicability of binary to computers. : : : : : : : : Is it starting to sink in now? : : : : Oh, by the way, your comparison to cars and petrol makes no sense : : whatsoever in this context. : : : : : :With the currently available technology, the total cost of ownership of : :a car is lowest when it runs on petrol. : : : : Wrong. : :Really? Then why do people have petrol driven cars? : Yes, really. Diesels have cheaper lifecycle costs. It depends very much how they're used. Diesel engines have a higher capital cost. They're only have lower total costs if they're used a lot. Otherwise the cost of capital is more than the lower cost of the fuel. Sylvia. Diesel engines also work best at partial throttle, whereas ignition engines work best at high power. Applications such as airplanes are better served with gasoline engines. -- Remove _'s from email address to talk to me. |
#16
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Alien number systems
Fred J. McCall wrote:
: :It depends very much how they're used. Diesel engines have a higher :capital cost. They're only have lower total costs if they're used a lot. : Otherwise the cost of capital is more than the lower cost of the fuel. : For a very small definition of 'a lot'. I said 'lifecycle costs'. Fuel costs are about the same. Short term maintenance costs are cheaper on a gasoline engine, generally. Longer term maintenance costs are MUCH lower on a diesel. Yes, if you're just going to buy a vehicle and park it, a diesel will be more expensive. But in that case, why buy a vehicle? Are you using proper discounted cash flow in reaching that conclusion? Sylvia. |
#17
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Alien number systems
Fred J. McCall wrote:
Sylvia Else wrote: :Fred J. McCall wrote: : : : : :It depends very much how they're used. Diesel engines have a higher : :capital cost. They're only have lower total costs if they're used a lot. : : Otherwise the cost of capital is more than the lower cost of the fuel. : : : : For a very small definition of 'a lot'. I said 'lifecycle costs'. : Fuel costs are about the same. Short term maintenance costs are : cheaper on a gasoline engine, generally. Longer term maintenance : costs are MUCH lower on a diesel. : : Yes, if you're just going to buy a vehicle and park it, a diesel will : be more expensive. But in that case, why buy a vehicle? : : :Are you using proper discounted cash flow in reaching that conclusion? : You say that like it means something. It doesn't in this case. If you have two possible patterns of expenditure for the same benefit, where the patterns differ in how payments are made over time, then the only meaningful way of comparing them is to use discounted cash flow. If you don't then you're ignoring the time value of money, which is an important component of the cost. Sylvia. |
#18
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Alien number systems
Fred J. McCall wrote:
Sylvia Else wrote: :Fred J. McCall wrote: : Sylvia Else wrote: : : :Fred J. McCall wrote: : : : : : : : :It depends very much how they're used. Diesel engines have a higher : : :capital cost. They're only have lower total costs if they're used a lot. : : : Otherwise the cost of capital is more than the lower cost of the fuel. : : : : : : : For a very small definition of 'a lot'. I said 'lifecycle costs'. : : Fuel costs are about the same. Short term maintenance costs are : : cheaper on a gasoline engine, generally. Longer term maintenance : : costs are MUCH lower on a diesel. : : : : Yes, if you're just going to buy a vehicle and park it, a diesel will : : be more expensive. But in that case, why buy a vehicle? : : : : : :Are you using proper discounted cash flow in reaching that conclusion? : : : : You say that like it means something. It doesn't in this case. : : :If you have two possible patterns of expenditure for the same benefit, :where the patterns differ in how payments are made over time, then the nly meaningful way of comparing them is to use discounted cash flow. If : you don't then you're ignoring the time value of money, which is an :important component of the cost. : I'll be sure and let the people that signed my sheepskin for Economics know all about that. Hint: Since we're comparing costs over the same amount of time, there is no need to use discounted cash flow. We're not talking about present value cost, but total lifecycle costs. Did you notice the bit about patterns differing over time? I suppose not. Sylvia. |
#19
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Alien number systems
"Fred J. McCall" wrote in message ... Sylvia Else wrote: :Fred J. McCall wrote: : Sylvia Else wrote: : : :Fred J. McCall wrote: : : Sylvia Else wrote: : : : : :Fred J. McCall wrote: : : : : : : : : : : :It depends very much how they're used. Diesel engines have a higher : : : :capital cost. They're only have lower total costs if they're used a lot. : : : : Otherwise the cost of capital is more than the lower cost of the fuel. : : : : : : : : : : For a very small definition of 'a lot'. I said 'lifecycle costs'. : : : Fuel costs are about the same. Short term maintenance costs are : : : cheaper on a gasoline engine, generally. Longer term maintenance : : : costs are MUCH lower on a diesel. : : : : : : Yes, if you're just going to buy a vehicle and park it, a diesel will : : : be more expensive. But in that case, why buy a vehicle? : : : : : : : : :Are you using proper discounted cash flow in reaching that conclusion? : : : : : : : You say that like it means something. It doesn't in this case. : : : : : :If you have two possible patterns of expenditure for the same benefit, : :where the patterns differ in how payments are made over time, then the : nly meaningful way of comparing them is to use discounted cash flow. If : : you don't then you're ignoring the time value of money, which is an : :important component of the cost. : : : : I'll be sure and let the people that signed my sheepskin for Economics : know all about that. : : Hint: Since we're comparing costs over the same amount of time, there : is no need to use discounted cash flow. We're not talking about : present value cost, but total lifecycle costs. : id you notice the bit about patterns differing over time? : :I suppose not. : You may now take the last word, what with you having dragged things off into the irrelevancies of you trying to 'defend' your inappropriate analogy between computer technology and automobiles. Bored now.... I've read this whole thread and it's more than a bit silly. Sylvia's idea of "preconceived notions" that the current way to build a computer (binary storage and logic using silicon chips) is the only way is everyone else's reality. Until something ground breaking discovery alters that reality, Sylvia's assertions are pure science fiction. Jeff -- "Take heart amid the deepening gloom that your dog is finally getting enough cheese" - Deteriorata - National Lampoon |
#20
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Alien number systems
David Spain wrote:
Perhaps a logical system would be based on only representing prime numbers. Any other numbers could be made up of symbols for primes indicating multiplying them to get composite numbers. In fact there is the well-known Chinese Remainder Theorem that is based on powers of primes. It has the unique ability to add and multiply numbers without the use of digit carries. The drawback is that there is more than one representation for the same number. And no one has really figured out a good way to do division this way. I'm not sure why you say that. You can define numbers in a unique way using a system based on powers of their prime factors. If you define 0 and 1 separately, then you can have a unique representation for all integers. You put the prime factors in say increasing order, their powers will be well defined. Once integers are uniquely defined, rational numbers can be uniquely defined in the usual way, then real and complex numbers can also be constructed in the usual way (and quaternions if so you wish). Of course if the number 1 is not posited to exist independently of prime power system, then you have to say something like 1 = 2^0. But if you accept to put primes to the power zero in your number definition system then you get into non unique representation problems (or you can avoid the non unique representation problem by representing numbers by the entire infinite series of primes with powers, powers which will all be zero safe for a finite set, this brings in serious problems). Alain Fournier |
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