monkeys with typewriters and stationarity

Hello,

Maybe everybody knows the idea that
an infinite number of monkeys with typewriters would
type the complete works of shakespeare.

In reality there is little chance for that to happen:
http://www.guardian.co.uk/uk/2003/may/09/science.arts

Anyway..

If one replaces the monkeys with a random process
how would that relate to the property of "stationarity" of
the process if a continous part of the output would
be pcm samples that resemble Orson Well's voice reading the
complete works of Shakespear.

The output wouldn't look stationary at all, but there still
should be a possibility (with extremely small probability)
that this happens within a stationary random process, or
am I wrong with this?

gr.
Bjoern

On May 16, 7:30&#4294967295;pm, "banton" <bant...@web.de> wrote:
> Hello,
>
> Maybe everybody knows the idea that
> an infinite number of monkeys with typewriters would
> type the complete works of shakespeare.
>
> In reality there is little chance for that to happen:http://www.guardian.co.uk/uk/2003/may/09/science.arts
>
> Anyway..
>
I always preferred the idea that creating a library containing every
book with every possible combination of words would (it would also
contain a book describing the cure for cancer, your life story,
correct theory of the universe etc)

On May 17, 7:30 am, "banton" <bant...@web.de> wrote:
> Hello,
>
> Maybe everybody knows the idea that
> an infinite number of monkeys with typewriters would
> type the complete works of shakespeare.
>
> In reality there is little chance for that to happen:http://www.guardian.co.uk/uk/2003/may/09/science.arts
>
> Anyway..
>
> If one replaces the monkeys with a random process
> how would that relate to the property of "stationarity" of
> the process if a continous part of the output would
> be pcm samples that resemble Orson Well's voice reading the
> complete works of Shakespear.
>
> The output wouldn't look stationary at all, but there still
> should be a possibility (with extremely small probability)
> that this happens within a stationary random process, or
> am I wrong with this?
>
> gr.
> Bjoern

This principle is infact used in CELP based speech coders.

banton wrote:

> The output wouldn't look stationary at all, but there still
> should be a possibility (with extremely small probability)
> that this happens within a stationary random process, or
> am I wrong with this?

I'm not sure I got your question, but if I give you
two (finite) sequences generated by a random process,
can you tell me which one is stationary and which one
is not?

Actually, can you tell me which one is random and which
one is not random?

I think if a random process generate something that does
not "look" random, someone might argue is not random.

Anyhow, as wrote at the beginning, maybe I did not get
the question right.

bye,

-- 

piergiorgio

>banton wrote:
>
>> The output wouldn't look stationary at all, but there still
>> should be a possibility (with extremely small probability)
>> that this happens within a stationary random process, or
>> am I wrong with this?
>
>I'm not sure I got your question, but if I give you
>two (finite) sequences generated by a random process,
>can you tell me which one is stationary and which one
>is not?
>
>Actually, can you tell me which one is random and which
>one is not random?
>

For a stationary process the autocorrelation should not change,
if evaluated at different times.
But as I see it, it always would if the process is random.
Just if you average over time it would be the same.
So there must be some idea of time-scale in connection
with stationarity.

Or similary.
White noise should have an FFT of 1.
Now if you evaluate an DFT over a finite time interval,
the SFT itself would not look contant at all, but
if you average enough DFT results it would be constant.
So I wonder if there is any idea (or measure) that
deals with the time-scale in connection to this?

"banton" <bantone@web.de> wrote in message 
news:xp-dnSmAoNit3rPVnZ2dnUVZ_obinZ2d@giganews.com...
>
> Hello,
>
> Maybe everybody knows the idea that
> an infinite number of monkeys with typewriters would
> type the complete works of shakespeare.
>
> In reality there is little chance for that to happen:
> http://www.guardian.co.uk/uk/2003/may/09/science.arts
>

After a billion years someone will plot a graph and call it 'The Great 
Guassian Monkey Curve,' then go home for tea.

: )
VC

"banton" <bantone@web.de> writes:
> [...]
> The output wouldn't look stationary at all, 

This is where your presumption is revealed. Random processes and the
stationary property utilize ensemble averages - you're referring to a
specific realization. The statistics of the two are not at all
necessarily equivalent unless the process is ergodic.
-- 
%  Randy Yates                  % "The dreamer, the unwoken fool - 
%% Fuquay-Varina, NC            %  in dreams, no pain will kiss the brow..."
%%% 919-577-9882                %  
%%%% <yates@ieee.org>           % 'Eldorado Overture', *Eldorado*, ELO
http://www.digitalsignallabs.com

"Randy Yates" <yates@ieee.org> wrote in message 
news:m3abioju6i.fsf@ieee.org...
> "banton" <bantone@web.de> writes:
>> [...]
>> The output wouldn't look stationary at all,
>


Well, if the monkeys were using old-fashioned typewriters
instead of modern keyboards and computers, their output
could be categorized as (used) stationery, no?

Hi Bjoern,
This is a difference between probability and statistics.  For instance,
the probability of a flipped coin being "heads" is exactly 50%.  However,
if you flip the coin 100 times, it is certainly possible that it might be
heads all 100 times.  Thst is, the statistics of the actual outcome is one
thing, and the probability of the underlying process is another.  The
statement that a process is "stationary" refers to probability.  The actual
outcomes (statistics) will contain a random component. 
Regards,
Steve

banton wrote:

> For a stationary process the autocorrelation should not change,
> if evaluated at different times.

 From -inf to +inf, difficult to compute...

> White noise should have an FFT of 1.

Maybe I did not get it correctly, but the FFT
of white noise is still white noise...

The FFT of the auto-correlation is constant one,
since the auto-correlation is a "pulse", by
_definition_.

> So I wonder if there is any idea (or measure) that
> deals with the time-scale in connection to this?

Usually not, if I get your problem right.

I mean, how can be decided if a sequence is random?

bye,

-- 

piergiorgio