Alien number systems
Frogwatch
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.
Van Chocstraw
Depends on how many fingers they had when they evolved from primitive
morons. If they had 8 fingers on each hand then base 16 might come up.
Orval Fairbairn
<77186630-ab3d-4253...@v30g2000yqm.googlegroups.com>,
Frogwatch <dbo...@mindspring.com> wrote:
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.
--
Remove _'s from email address to talk to me.
Sylvia Else
> 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.
>
> Depends on how many fingers they had when they evolved from primitive
> morons.
Indeed, and that's likely to be long before they had notions about prime
numbers and such like.
If they had 8 fingers on each hand then base 16 might come up.
Imagine having to learn your times-tables up to 16!
Sylvia.
Sylvia Else
There isn't really anything about those number systems that makes them
intrinsically computer related. It's really more a matter of
practicality - 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.
Sylvia.
Doug Freyburger
>
> Most of us use the base 10 number system although civilizations such
> as the Romans used their number system.
If you look at our language it's clear that base ten has not always been
in use. Eleven, twelve, dozen, hundred, long hundred, gross. The
English words suggest a mixture of bases ten and twelve. That pattern
also changes near a score - nineteen, twenty, twenty-one.
The invention of the zero was a change so profound it changed the way
folks think about numbers, but the language still shows a time before
that.
> 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.
Use you use zero, any experimentation with other bases automatically
leads to the use of binary. Computers do not have to be universal, but
any society that does calculation should figure out binary.
Van Chocstraw
> Sylvia Else <syl...@not.at.this.address> wrote:
>
> 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. Octal and Hex are mere conveniences for the humans because
> they translate so easily to and from binary.
>
How do you represent zero in Roman Numerals?
Sylvia Else
> Sylvia Else <syl...@not.at.this.address> wrote:
>
>
> 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. But that still doesn't make binary
intrinsic to computers, any more than petrol is intrinsic to cars.
Sylvia.
Sylvia Else
> Sylvia Else <syl...@not.at.this.address> wrote:
>
>
> That's not it.
>
> :
> :But that still doesn't make binary
>
> 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.
Sylvia.
Harold Groot
<dfre...@yahoo.com> wrote:
>> 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.
>Use you use zero, any experimentation with other bases automatically
>leads to the use of binary. Computers do not have to be universal, but
>any society that does calculation should figure out binary.
I no longer recall the theory behind it, but in one of my college
courses in Computer Science they compared the theoretical efficiency
of using various number bases for computers. It turned out the
theoretical optimum point was to have a base of e
(2.7182818284590....).
Obviously integer bases are more practical. Base 2 is pretty close to
that optimum point, but base 3 even closer. So a trinary computer
makes a certain amount of sense if the hardware is up to it and the
designers are up to it.
Sylvia Else
> Sylvia Else <syl...@not.at.this.address> wrote:
>
> :Fred J. McCall wrote:
> :> Sylvia Else <syl...@not.at.this.address> wrote:
> :>
>
> 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.
>
> 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
pan-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.
>
> 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. 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.
Sylvia.
David Spain
> Most of us use the base 10 number system although
> civilizations such as the Romans used their number system.
Zeros? We don't need no stinking zeros! Catch XXII.
> Many people think that base 2
> is a universal number system but maybe it isnt.
A mathematician would find the above amusing.
No more so than base 3, base 8, base 13, or base 11.
If your aliens have six fingers, I'll bet they use base 6.
> 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.
http://en.wikipedia.org/wiki/Chinese_remainder_theorem
> 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.
See above.
> There isn't really anything about those number systems that makes
> intrinsically computer related. It's really more a matter of
> practicality - it's easier, so far, to build computers that way.
> You could build computers around a tristate logic, for example. But
> more complicated, and these seems little point, particularly as
> it would be invisible to users, and indeed programmers for the most
> part.
This is done all the time. It is employed when a hardware resource
is shared between functional units. Tri-state logic allows multiple
source drivers to share a common set of data wires. The elements not
driving the wires (bus) switch to the third state (called the Z state)
which allows the one active driver to override the signals on the bus
to the active receiver(s).
[snip disagreement over analog vs binary computers]
Well, binary computer design has been somewhat standardized.
This is why you see binary computers dominate over analog computers.
I argue its mainly about cost. You could certainly design analog computers
using existing technology, but it would be more expensive since it
is customized per application. The design cost (NRE) of
software typically beats it out.
>> 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.
>
:-)
>> 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 pan-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.
Yeah, don't get me started on quantum computers when they are in the
coherent superposition state!
:-)
Dave
Sylvia Else
>
> 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
> :pan-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.
>
>
Sylvia Else
> 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.
David Spain
> 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/content/abstract/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
Sylvia Else
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.
Orval Fairbairn
Sylvia Else <syl...@not.at.this.address> wrote:
> Fred J. McCall wrote:
> > Sylvia Else <syl...@not.at.this.address> wrote:
> >
> > :Fred J. McCall wrote:
> > :> Sylvia Else <syl...@not.at.this.address> wrote:
> > :>
> > :> :Fred J. McCall wrote:
> > :> :> Sylvia Else <syl...@not.at.this.address> wrote:
> > :> :>
> > :> :> :Fred J. McCall wrote:
> > :> :> :> Sylvia Else <syl...@not.at.this.address> wrote:
> > :> :> :>
> > :> :> :> :Fred J. McCall wrote:
> > :> :> :> :> Sylvia Else <syl...@not.at.this.address> wrote:
> > :> :> :> :>
> > :> :> :> :> :Orval Fairbairn wrote:
> > :> :> :> :> :> In article
> > :> :> :> :> :> <77186630-ab3d-4253...@v30g2000yqm.googlegroup
> > :> :> :> :> :> s.com>,
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.
Sylvia Else
:
> :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.
Sylvia Else
> Sylvia Else <syl...@not.at.this.address> wrote:
>
>
> 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.
Sylvia Else
> Sylvia Else <syl...@not.at.this.address> wrote:
>
> :Fred J. McCall wrote:
>
> 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.
Jeff Findley
"Fred J. McCall" <fjmc...@gmail.com> wrote in message
news:u7oag59h5ltoogm8g...@4ax.com...
> Sylvia Else <syl...@not.at.this.address> wrote:
>
> :Fred J. McCall wrote:
> :> Sylvia Else <syl...@not.at.this.address> wrote:
> :>
> :> :Fred J. McCall wrote:
>
> 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
Alain Fournier
>>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
Doug Freyburger
> Sylvia Else <syl...@not.at.this.address> wrote:
> :Fred J. McCall wrote:
> :> Sylvia Else <syl...@not.at.this.address> wrote:
>
>
> :> Wrong.
>
> :Really? Then why do people have petrol driven cars?
>
Compared to alternative techologies the difference between the types of
internal combustion petroleum fueled engines is tiny. For the purpose
of discussing alien number systems and trinary logic, diesels are petrol
driven cars. Alcohol/LOX and kerosene/LOX rockets are different but
they both count as liquid fueled rockets when compared to technologies
like ion drives or fusion.
Diving into the details, are diesel cars lower total cost of ownership
than diesel? The experience of trucks suggests that it depends on the
size of the vehicle so it's not a slam-dunk. There has to be more to it.
Sylvia Else
I think you're rather missed the point. The contention was that binary
(and the related octal and hexadecimal) are the basis of computers. This
contention was offered in the context of a previous statement that "Many
people think that base 2 is a universal number system but maybe it isnt."
The fact that current computer engineering is based on binary arithmetic
is a long way short of a justification of the universality of base 2.
Indeed, building a computer around base 3 would probably not even be
that difficult. Just uneconomic and pointless.
Sylvia.