Decent speaker cables at last! (soft troll)
 

In article , Jim H
wrote:
Jim Lesurf in uk.rec.audio:


Btw, I mention this because I'm writing a kind of specy/bytecode
converter. The digital/analogue thing gets really interesting when I
copy the sound of speccy tapes to CD, so that they can be more easily
played on my old ZX. One way of thinking of this is as digital in
analogue in digital!

That is a superb example. :-) I'll probably now quote it in my
lectures!

I'm honored, but won't your class be too young to remember computer
programs on audio tape?

Probably. That is one of the reasons it is a nice example as I can explain
that as well to help break down their pre-assumptions. :-)


Yes. You can apply all the same formal Information Theory ideas to
'analogue', but 'digital' systems tend to make these things easier to
explain, quantify, etc. However need to take care here as we've tended
to develop our units, etc, with binary digital in mind. e.g. we now
use 'bit' for quantity of info, but this was not always the case in
early work IIRC.

Interesting, what was considered the lowest possible unit of
information?

My memory is unreliable on this as I only came across references to it many
years ago. Note they weren't regarded as the 'lowest unit' any more than a
metre is the 'lowest unit' in the sense of being indivisible. IIRC one unit
was based upon 'e'. I think these units appear in, for example, some of the
books on the work at Bletchly Park during WW2. Afraid I'd need to find the
books and search through them to see what I could find about this, although
I suppose it may also be "out there" on the web as most things are, these
days!

I sometimes think of 'half bits' as a theoretical thing but know that
half a bit cannot really be transmitted.

Depends upon what you mean. Symbols (and hence symbol patterns) can quite
easily communicate non-integer amounts of information as measured in
'bits'. Indeed, if you do an entropic analysis of English, most letters in
a meassage contribute a non-integer amount of info.

Its interesting that people do tend to think that the 'bit' is somehow a
different kind of unit to a 'metre' or a 'kilo' or a 'degree'. However it
is just a defined amount used as a reference for measurement purposes. Just
happens to have become so much the standard that no-one even thinks of
using an alternative.


I have wondered about building 'digital' CPUs which included a thermal
noise generator to randomise the lowest bit ot two for floating point
computations. This might have an interesting effect upon the
computation of results via very involved methods from large data sets.
"Run until you get the same answer three times in a row!" ;-)

I *think* you could do this without special hardware. I'm not a c++
programmer, but couldn't you override the multiplication operator for
floating point numbers to be off by a pseudo-random value?

Yes, you can do this in software. However you'd still need a source of
'truly random' number sequences [1], and I suspect it would be quicker to
build this into hardware. Just one of my madder thoughts, though... 8-]

I suspect I'll be retired before 'quantum computing' really makes an
impact. This will be useful as I may need the spare time to really
understand it.

Ambitious!


Well, I'm hoping to live long enough... although this may take a while.
;-)

Slainte,

Jim

[1] Can of worms. :-)

--
Electronics http://www.st-and.ac.uk/~www_pa/Scot...o/electron.htm
Audio Misc http://www.st-and.demon.co.uk/AudioMisc/index.html
Armstrong Audio http://www.st-and.demon.co.uk/Audio/armstrong.html
Barbirolli Soc. http://www.st-and.demon.co.uk/JBSoc/JBSoc.html

Decent speaker cables at last! (soft troll)
 

Jim Lesurf in uk.rec.audio:

Interesting, what was considered the lowest possible unit of
information?

My memory is unreliable on this as I only came across references to it
many years ago. Note they weren't regarded as the 'lowest unit' any
more than a metre is the 'lowest unit' in the sense of being
indivisible. IIRC one unit was based upon 'e'. I think these units
appear in, for example, some of the books on the work at Bletchly Park
during WW2. Afraid I'd need to find the books and search through them
to see what I could find about this, although I suppose it may also be
"out there" on the web as most things are, these days!

I sometimes think of 'half bits' as a theoretical thing but know that
half a bit cannot really be transmitted.

Depends upon what you mean. Symbols (and hence symbol patterns) can
quite easily communicate non-integer amounts of information as
measured in 'bits'. Indeed, if you do an entropic analysis of English,
most letters in a meassage contribute a non-integer amount of info.

This makes sense if I understand correctly. 'qu' contains less than two
letters' worth of information in English since q is almost always
followed by u.

Its interesting that people do tend to think that the 'bit' is somehow
a different kind of unit to a 'metre' or a 'kilo' or a 'degree'.
However it is just a defined amount used as a reference for
measurement purposes. Just happens to have become so much the standard
that no-one even thinks of using an alternative.

I'm venturing a guess here, but I can see how less than a bit's worth of
information can be transmitted, but not less than a bit of actual data. I
may have the definitions wrong, what I mean is that one bit may have less
informational significence than another, but no smaller unit may be
transfered in a digital system.

When I first mentioned half-bits I was thinking back to ZX days again, in
which I'd sometimes set up, for example, one 5.5 and one 2.5 bit value in
a byte. Memory really was tight in those days!

I suspect I'll be retired before 'quantum computing' really makes
an impact. This will be useful as I may need the spare time to
really understand it.

Ambitious!


Well, I'm hoping to live long enough... although this may take a
while. ;-)

I think I understand most the fundementals now, its difficult because we
don't normally have to think of things like a quantum guess as being
compatable with the 'real world'.

[1] Can of worms. :-)
[in reference to a pure random source]
I take it you mean the 'random yet deterministic' thing; a program for
the digits of pi gives random numbers, but deterministic random numbers.
It goes beyond what we comonly think of as random for it to be
deterministic. Most computer PRNGs just stretch and fold with very large
period.
There is a 'hotbits' web server somewhere that provides completely random
numbers free to academics, using quantum uncertainty as the source. I
wrote a java implementation of the Random interface that connects to the
server if you ever need it.

--
Jim H

Decent speaker cables at last! (soft troll)
 

On 31 Jul, wrote:
In article , Jim H
wrote:
Jim Lesurf in uk.rec.audio:

Did some looking through books, etc, today on this...

we now use 'bit' for quantity of info, but this was not always the
case in early work IIRC.

Interesting, what was considered the lowest possible unit of
information?

My memory is unreliable on this as I only came across references to it
many years ago. Note they weren't regarded as the 'lowest unit' any more
than a metre is the 'lowest unit' in the sense of being indivisible.
IIRC one unit was based upon 'e'. I think these units appear in, for
example, some of the books on the work at Bletchly Park during WW2.
Afraid I'd need to find the books and search through them to see what I
could find about this, although I suppose it may also be "out there" on
the web as most things are, these days!

I'm fairly sure this crops up in one of the more technical articles in "The
Inside Story of Bletchly Park" edited by Hinsley and Stripp. However a
look-through today didn't find a reference. It is, however, mentioned in
"Information Theory for Information Technologists" by M. J. Usher.

There it specifies 'nats' as the unit when using base 'e' and 'trits' when
using base 3 as examples. My recollection was that base 'e' was used a fair
bit for early work, but vanished once most processing, computing, etc
became binary digital. Looking through Shannon's early papers he refers to
other unit systems in his initial works on information theory, but refers
back to Hartley in the 1920's and to others for this and I didn't have the
papers to hand.

For work on 'natural' sic languages like English using 'nats' makes as
much sense in theoretical terms as using 'bits'. Similary for 'analog'
signalling and symbol systems. However base 2 makes good sense when most
processing, etc, tends to be done with binary digital methods. It is also
easier to explain in lectures. :-)

Slainte,

Jim

--
Electronics http://www.st-and.ac.uk/~www_pa/Scot...o/electron.htm
Audio Misc http://www.st-and.demon.co.uk/AudioMisc/index.html
Armstrong Audio http://www.st-and.demon.co.uk/Audio/armstrong.html
Barbirolli Soc. http://www.st-and.demon.co.uk/JBSoc/JBSoc.html

Decent speaker cables at last! (soft troll)
 

Jim Lesurf in uk.rec.audio:

On 31 Jul, wrote:
In article , Jim H
wrote:
Jim Lesurf in uk.rec.audio:

Did some looking through books, etc, today on this...

we now use 'bit' for quantity of info, but this was not always
the case in early work IIRC.

Interesting, what was considered the lowest possible unit of
information?

My memory is unreliable on this as I only came across references to
it many years ago. Note they weren't regarded as the 'lowest unit'
any more than a metre is the 'lowest unit' in the sense of being
indivisible. IIRC one unit was based upon 'e'. I think these units
appear in, for example, some of the books on the work at Bletchly
Park during WW2. Afraid I'd need to find the books and search through
them to see what I could find about this, although I suppose it may
also be "out there" on the web as most things are, these days!

I'm fairly sure this crops up in one of the more technical articles in
"The Inside Story of Bletchly Park" edited by Hinsley and Stripp.
However a look-through today didn't find a reference. It is, however,
mentioned in "Information Theory for Information Technologists" by M.
J. Usher.

There it specifies 'nats' as the unit when using base 'e' and 'trits'
when using base 3 as examples. My recollection was that base 'e' was
used a fair bit for early work, but vanished once most processing,
computing, etc became binary digital. Looking through Shannon's early
papers he refers to other unit systems in his initial works on
information theory, but refers back to Hartley in the 1920's and to
others for this and I didn't have the papers to hand.

For work on 'natural' sic languages like English using 'nats' makes
as much sense in theoretical terms as using 'bits'. Similary for
'analog' signalling and symbol systems. However base 2 makes good
sense when most processing, etc, tends to be done with binary digital
methods. It is also easier to explain in lectures. :-)

I've never come across non integer radix (radies?) such as e before, but
I don't see any contradiction in their use. A system unable to express
integers exactly must have very limited aplication though. This makes me
reevaluate my concept of number, I'm going to try a few thought-
experiments about this tonight.

Have you ever come across balanced ternary systems? The elegence makes
binary two's complement seem like a nasty hack. Like 'normal' base three
but the digits used are 0,1 and -1 (with -1 usually written as an
underlined one) the beauty of this system is the unification of poitive
and negative, indicated in the digits themselves without a sign. I can't
find a reference to it in any of my computer science books. [1]

It is certainly true that a trit cannot be expressed as a whole nuber of
bits, and therefore that not all digital data contains information
equivalent to an integer number of bits.

[1] but see http://perun.hscs.wmin.ac.uk/~jra/ternary/ternary.html if
interested in the number theory side of this. I find this kind of stuff
very, very interesting!!

--
Jim H