Alien number systems

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.

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.

--
Remove _'s from email address to talk to me.

Van Chocstraw wrote:
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.

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
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.

Frogwatch wrote:

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.

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. But that still doesn't make binary
intrinsic to computers, any more than petrol is intrinsic to cars.

Sylvia.






Octal and Hex are mere conveniences for the humans because
they translate so easily to and from binary.

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.

Sylvia.

On Mon, 16 Nov 2009 18:00:26 +0000 (UTC), Doug Freyburger
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.

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.


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.

I missed this thread originally. Something in my field!! A few observations.

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