Oli Filth wrote:

> glen herrmannsfeldt wrote:

(snip on energy and entropy)

>>It mostly comes out when trying to build a system with minimal
>>operating power.

> How do you mean?

Someone could ask about building a computer that used zero power.
A reversible system in thermodynamics terms.  Some operations
can be done reversibly, some can't.  Assuming you want to do
some that can't, such as store data in memory, what is the smallest
amount of power that can be used to run such a computer?

(There are people in IEEE who want to build a computer running
on less than one microwatt.)

>>There are stories based on those assumptions that show that base e is
>>optimal, and that three is the closest.  As far as I know, there is no
>>currently available electronics to implement such a system.

> Optimal in what sense?

I don't remember anymore, and I wasn't all that convinced.

Here is what I found in Google.

http://www.americanscientist.org/template/AssetDetail/assetid/14405?&print=yes

-- glen

glen herrmannsfeldt wrote:
> Oli Charlesworth wrote:
>
> (snip on energy and digital filters)
>
> > However, the amount of energy required is unrelated to the input signal.
> >  The number of bits that alter (and hence energy that is consumed) from
> > sample point to sample point is essentially uncorrelated with any
> > characteristic such as the frequency response, or even amplitude, of the
> > input signal.
>
> It mostly comes out when trying to build a system with minimal
> operating power.

How do you mean?


> > And if we could somehow implement the filter in a different numerical
> > base, such as ternary, the number of ternary digits (tits?) that would
> > change would be unrelated to the number that changed in the binary system.
>
> There are stories based on those assumptions that show that base e is
> optimal, and that three is the closest.  As far as I know, there is no
> currently available electronics to implement such a system.

Optimal in what sense?

-- 
Oli

glen herrmannsfeldt skrev:
> Rune Allnor wrote:
>
> (I wrote)
>
> >>dU=T dS  The connection between energy and entropy is temperature.
> >>At constant temperature they are proportional.
>
> > And the temperature relation between, say, an ASCII text and its
> > corresponding Huffman code is...?
>
> The question only becomes important when trying to design minimal power
> (or energy) systems.

And these are *physical* systems. The Huffman code "exists" in a
purely mathematical setting. My point was that thereis a difference
between physics and mathematgics. "Energy" and "temperature"
only make sense in the realm of physics. "Entropy" makes sense
as a purely mathematical concept as well.

Rune

Rune Allnor wrote:

(I wrote)

>>dU=T dS  The connection between energy and entropy is temperature.
>>At constant temperature they are proportional.

> And the temperature relation between, say, an ASCII text and its
> corresponding Huffman code is...?

The question only becomes important when trying to design minimal power
(or energy) systems.   A binary memory unit needs a bistable system
to store one bit.  There is some probability of thermal noise causing
a bit transition, which increases with temperature or with a lower
threshold for the bistable system.   Current systems operate so far
above the thermal noise limit that it is hard to see the connection.

It will take fewer bits to store the huffman code data, but it will
be more sensitive to bit changes.  Those bit changes increase
with temperature.

-- glen

Oli Charlesworth wrote:

(snip on energy and digital filters)

> However, the amount of energy required is unrelated to the input signal. 
>  The number of bits that alter (and hence energy that is consumed) from 
> sample point to sample point is essentially uncorrelated with any 
> characteristic such as the frequency response, or even amplitude, of the 
> input signal.

It mostly comes out when trying to build a system with minimal
operating power.

> And if we could somehow implement the filter in a different numerical 
> base, such as ternary, the number of ternary digits (tits?) that would 
> change would be unrelated to the number that changed in the binary system.

There are stories based on those assumptions that show that base e is
optimal, and that three is the closest.  As far as I know, there is no
currently available electronics to implement such a system.

-- glen

Oli Charlesworth wrote:

> Jerry Avins said the following on 15/10/2006 17:09:

>> Oli Charlesworth wrote:

>>>   ... the number of ternary digits (tits?) ...

>> Trits.

> How disappointing...

There is an old joke with the punchline

"Silly Wabbit, kicks are for trids."   Close enough for me.

-- glen

Oli Charlesworth <catch@olifilth.co.uk> writes:

> ternary digits (tits?) 

How many tits does your computer have? This is particularly
apropo for the .sig below (which is randomly generated)!
-- 
%  Randy Yates                  % "I met someone who looks alot like you,
%% Fuquay-Varina, NC            %             she does the things you do, 
%%% 919-577-9882                %                     but she is an IBM."
%%%% <yates@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO   
http://home.earthlink.net/~yatescr

Jerry Avins said the following on 15/10/2006 17:09:
> Oli Charlesworth wrote:
> 
>>   ... the number of ternary digits (tits?) ...
> 
> Trits.

How disappointing...


-- 
Oli

Oli Charlesworth wrote:

>   ... the number of ternary digits (tits?) ...

Trits.

Jerry
-- 
        "The rights of the best of men are secured only as the
        rights of the vilest and most abhorrent are protected."
            - Chief Justice Charles Evans Hughes, 1927
���������������������������������������������������������������������

glen herrmannsfeldt said the following on 12/10/2006 06:50:
> Rune Allnor wrote:
> 
> (snip)
> 
>> While the laws of physics have to comply the laws of maths,
>> the converse is not true. This is why digital filters can do stuff
>> that is not possible with analog filters.
> 
> I agree so far.
> 
>> More to the point what
>> this thread is concerned, the concepts of "energy" and "power"
>> make no sense in the mathematical world.
> 
> Entropy makes sense in the mathematical world, and entropy
> can be connected to energy.
> 
> The first time I saw this discussed had to do with the
> energy of computation.  Can you design a binary adder
> that, theoretically, uses no energy?  If you represent
> bits through moving balls on ramps, in theory it is
> possible to design an adder using frictionless balls.
> A binary non-saturating adder does not lose any information.
> 
> It is the process of forgetting that takes energy.  In
> thermodynamic terms, it requires a non-reversible system,
> and that goes along with an increase in entropy and
> decrease in free energy.

However, the amount of energy required is unrelated to the input signal. 
  The number of bits that alter (and hence energy that is consumed) from 
sample point to sample point is essentially uncorrelated with any 
characteristic such as the frequency response, or even amplitude, of the 
input signal.

And if we could somehow implement the filter in a different numerical 
base, such as ternary, the number of ternary digits (tits?) that would 
change would be unrelated to the number that changed in the binary system.



-- 
Oli