Somewhat OT - Can a digital recording be described as a single number?

[Artie Turner]

As someone with an interest in intellectual property issues, I found
this article by "anarchist" Eben Moglen, where he makes some of the same
arguments we've heard from the Napster advocates. The author claims that
digital recordings can be described as a single number which can then be
copyrighted. I exchanged a few emails with the author to try to
understand this, but his answers left me more confused than when I
started. My question: can a digital recording be reduced to a single
integer like 767459083268?


from http://old.law.columbia.edu/my_pubs/anarchism.html

"We need to begin by considering the technical essence of the familiar
devices that surround us in the era of "cultural software." A CD player
is a good example. Its primary input is a bitstream read from an optical
storage disk. The bitstream describes music in terms of measurements,
taken 44,000 times per second, of frequency and amplitude in each of two
audio channels. The player's primary output is analog audio signals [7].
Like everything else in the digital world, music as seen by a CD player
is mere numeric information;"

So far, I agree, but then

"a particular recording of Beethoven's Ninth Symphony recorded by
Arturo Toscanini and the NBC Symphony Orchestra and Chorale is (to drop
a few insignificant digits) 1276749873424, while Glenn Gould's
peculiarly perverse last recording of the Goldberg Variations is
(similarly rather truncated) 767459083268."

and more on single numbers:

"Lastly, there's 588832161316. It doesn't do anything, it's just the
square of 767354. As far as I know, it isn't owned by anybody under any
of these rubrics. Yet."

Truncuated to not, this just seems fundamentally wrong to me. Can a
recording be accurately described as a single number?

Artie

[James Boyk]

Artie Turner wrote: > Can a recording be accurately described as a
single number?


Here are the first few samples from a 4-bit recording of something:

1111 1110 1100 1000 0111 0101 0011 ...


Remove the spaces and create a single number:
1111111011001000011101010011...


This number needs to be accompanied by an interpretation saying that it's 4-bit
linear PCM at such-and-such a sample rate. Voila!


Maybe there's some more fundamental way to do this, too, that's just not
occurring to me at the moment.



James Boyk

[Les Cargill]

Artie Turner wrote:
>
> As someone with an interest in intellectual property issues, I found
> this article by "anarchist" Eben Moglen, where he makes some of the same
> arguments we've heard from the Napster advocates. The author claims that
> digital recordings can be described as a single number which can then be
> copyrighted. I exchanged a few emails with the author to try to
> understand this, but his answers left me more confused than when I
> started. My question: can a digital recording be reduced to a single
> integer like 767459083268?
>
> from http://old.law.columbia.edu/my_pubs/anarchism.html
>
> "We need to begin by considering the technical essence of the familiar
> devices that surround us in the era of "cultural software." A CD player
> is a good example. Its primary input is a bitstream read from an optical
> storage disk. The bitstream describes music in terms of measurements,
> taken 44,000 times per second, of frequency and amplitude in each of two
> audio channels. The player's primary output is analog audio signals [7].
> Like everything else in the digital world, music as seen by a CD player
> is mere numeric information;"
>
> So far, I agree, but then
>
> "a particular recording of Beethoven's Ninth Symphony recorded by
> Arturo Toscanini and the NBC Symphony Orchestra and Chorale is (to drop
> a few insignificant digits) 1276749873424, while Glenn Gould's
> peculiarly perverse last recording of the Goldberg Variations is
> (similarly rather truncated) 767459083268."
>
> and more on single numbers:
>
> "Lastly, there's 588832161316. It doesn't do anything, it's just the
> square of 767354. As far as I know, it isn't owned by anybody under any
> of these rubrics. Yet."
>
> Truncuated to not, this just seems fundamentally wrong to me. Can a
> recording be accurately described as a single number?
>
> Artie

Yes. There is a one-to-one and onto map between the natural numbers
and any arbitrary digital audio stream.

--
Les Cargill

[Brian Takei]

Kurt Albershardt ) wrote:
> Artie Turner wrote:
> >
> > Truncuated to not, this just seems fundamentally wrong to me. Can a
> > recording be accurately described as a single number?
>
> Sure, if we agree on the transform (and ensure it produces unique
> results) used to derive the number.


And this of course would also apply to any book/document -- any class
that is a sequence of members of a set.

- Brian

[Artie Turner]

Kurt Albershardt wrote:
> Artie Turner wrote:
>
>>
>> Truncuated to not, this just seems fundamentally wrong to me. Can a
>> recording be accurately described as a single number?
>
>
> Sure, if we agree on the transform (and ensure it produces unique
> results) used to derive the number. Some business associates of mine
> patented such a system as part of an online backup project a few years
> back (to uniquely identify particular versions of common files like
> win.com and excel.exe) and leter sold the technology.

If you have the desire to read the article at the URL I posted, (Napster
fans will find an ally there) you'll see that the author is basically
saying that Beethoven's Fifth is a unique number, just as the square of
57044 is a unique number. I can see how you could arrive at a single
number by using a sum or tranform function of some kind on digital
audio, but that same unique number could be derived by many other
processes.

Is this where intellectual property and copyright law will take us?
Distilling a digital recording to a single number and copyrighting that
number?

AT
>
>
>
>

[James Boyk]

Artie Turner wrote:
> Is this where intellectual property and copyright law will take us?
> Distilling a digital recording to a single number and copyrighting that
> number?


"4" is another way of saying "2+2." They're equivalent. The "single-number"
view of a digital recording is equivalent to any other view of it. Nothing's new
about it.


James Boyk

[ryanm]

"James Boyk" > wrote in message
...
>
> Here are the first few samples from a 4-bit recording of something:
> 1111 1110 1100 1000 0111 0101 0011 ...
>
Simply convert it to integers:

1111 = 15
1110 = 14
1100 = 12
1000 = 8
0111 = 7
0101 = 5
0011= 3

> Remove the spaces and create a single number:
> 1111111011001000011101010011...
>

1111111011001000011101010011 = 267159379

Every bitstream, if taken as a single binary number, can be converted to
an integer. There would also be header info, though. I wonder if that would
be included as part of the integer, making the same song in a different
format a unique work as well?

ryanm

[Artie Turner]

James Boyk wrote:
> Artie Turner wrote:
>
>> Is this where intellectual property and copyright law will take us?
>> Distilling a digital recording to a single number and copyrighting
>> that number?
>
>
>
> "4" is another way of saying "2+2." They're equivalent. The
> "single-number" view of a digital recording is equivalent to any other
> view of it. Nothing's new about it.

"1+1+1+1" is another way of saying "4" as is "3+1" - it's not the same
song as "2+2" if you catch my drift. And "4" describes a lot of other
things as well. Should someone be able to copyright "4?"

Seems to me it's all about context.

AT
>
>
> James Boyk
>

[Brian Takei]

ryanm ) wrote:
> 1111111011001000011101010011 = 267159379
>
> Every bitstream, if taken as a single binary number, can be converted to
> an integer.


It already is an integer.

- Brian

[James Boyk]

Artie Turner wrote: > ...Should someone be able to copyright "4?"


I wasn't addressing that issue but just the technical question.


Since you raise the question, my LAYMAN's understanding is that copyright is
protection for the written form of something. From a copyright point of view, 4
is thus different from 2+2 and sqrt(16). But I believe that, to be copyrighted,
material must be original; and there's nothing original about "4" or "2+2" or
"sqrt(16)." (On the other hand, 7309505824/1827376456 --another form of 4-- is
very likely original with me, as it's unlikely that anyone has previously
created this particular written form. I'd guess it's not copyrightable, but
maybe it is. This is a question for an expert.


James Boyk

[Artie Turner]

James Boyk wrote:
> Artie Turner wrote: > ...Should someone be able to copyright "4?"
>
>
> I wasn't addressing that issue but just the technical question.
>
>
> Since you raise the question, my LAYMAN's understanding is that
> copyright is protection for the written form of something. From a
> copyright point of view, 4 is thus different from 2+2 and sqrt(16).

That was the gist of my original question, prompted by this article by
an "expert" who claims to be a professor of law and an opponent of
intellectual property -

http://old.law.columbia.edu/my_pubs/anarchism.html

Read it if you have the time - strange to hear anarchy from a professor
of law.

AT


But
> I believe that, to be copyrighted, material must be original; and
> there's nothing original about "4" or "2+2" or "sqrt(16)." (On the
> other hand, 7309505824/1827376456 --another form of 4-- is very likely
> original with me, as it's unlikely that anyone has previously created
> this particular written form. I'd guess it's not copyrightable, but
> maybe it is. This is a question for an expert.
>
>
> James Boyk
>
>

[Kurt Albershardt]

Artie Turner wrote:

> Kurt Albershardt wrote:
>
>> Artie Turner wrote:
>>
>>>
>>> Truncuated to not, this just seems fundamentally wrong to me. Can a
>>> recording be accurately described as a single number?
>>
>>
>> Sure, if we agree on the transform (and ensure it produces unique
>> results) used to derive the number. Some business associates of mine
>> patented such a system as part of an online backup project a few years
>> back (to uniquely identify particular versions of common files like
>> win.com and excel.exe) and leter sold the technology.
>
>
> I can see how you could arrive at a single
> number by using a sum or tranform function of some kind on digital
> audio, but that same unique number could be derived by many other
> processes.

Yes, but if we agree on the process then it should uniquely represent
the original bitstream. Forgive my very rusty crypto theory but it
might well be a sort of trap-door function, not reversible without some
sort of index pointing at the original source. A unique signature as it
were--but change one bit in the original and yuo get a completely
different result. Useful for music? Maybe.

[Brian Takei]

Artie Turner ) wrote:
<snip>
> http://old.law.columbia.edu/my_pubs/anarchism.html
>
> Read it if you have the time -

I don't, but I did skim the first screen or so, then ran out of
time/interest when I saw this thread's initial quote in context, and it
didn't seem any less ridiculous. But on a whim, I did jump to the
bottom of the page...

> strange to hear anarchy from a professor of law.

Not as strange and ridiculous as the fact that his web page (which I/we
received as a unique bitstream of numbers that seems to have the same
essential attributes that he ascribes to a digital recording), is
apparently COPYRIGHTED. Uh huh...

Or maybe the rest of his article would resolve that for me, if I had the
time...

Regards,
- Brian

[Josh Snider]

Not really. It's just binary data. Since its an audio waveform converted
to a binary number, it's never existed as a decimal number, and so must be
converted from the binary string to a decimal number.

Symantics most likely.

However in terms of the copyright issue, it ONLY applies to digital music.
You'd have to have the music exist in a digital format and then you could
ONLY copyright the digital format of the waveform, since the analog
equivalent (or the music written on a page) wouldn't be covered...

Or at least, that¹s my understanding...

J



in article , Brian Takei at
wrote on 9/9/03 16.53:

> ryanm ) wrote:
>> 1111111011001000011101010011 = 267159379
>>
>> Every bitstream, if taken as a single binary number, can be converted to
>> an integer.
>
>
> It already is an integer.
>
> - Brian

--
josh.snider
cave.productions
416.524.6927

[Brian Takei]

Josh Snider ) wrote:
> Not really. It's just binary data. Since its an audio waveform converted
> to a binary number, it's never existed as a decimal number, and so must be
> converted from the binary string to a decimal number.

Perhaps I should have been more explicit. I was referring to the
"single binary number", not the "bitstream".

- Brian


> in article , Brian Takei at
> wrote on 9/9/03 16.53:
>
> > ryanm ) wrote:
> >> 1111111011001000011101010011 = 267159379
> >>
> >> Every bitstream, if taken as a single binary number, can be converted to
> >> an integer.
> >
> >
> > It already is an integer.
> >
> > - Brian

[Monte P McGuire]

In article >,
Kurt Albershardt > wrote:
>Yes, but if we agree on the process then it should uniquely represent
>the original bitstream.

And, to have a 1:1 relationship, the 'key' would be just as long as
the audio data itself. Otherwise, there'd have to be more than one
audio files that would map to the same key, and I think that'd be a
problem. It'd also mean that a lot of sound-alike files would
generate completely different keys, probably not something useful.

>Forgive my very rusty crypto theory but it
>might well be a sort of trap-door function, not reversible without some
>sort of index pointing at the original source. A unique signature as it
>were--but change one bit in the original and yuo get a completely
>different result. Useful for music? Maybe.

I still don't know what the point of all this is, but what do I
know...

One 'single number' thingie I use all the time for hard disk image
file backups is an MD5 signature. This single number can be generated
from the original file, and if you store that along with the original
file and then regenerate the MD5 from the file after you use it and
compare the two MD5s, you know if the file has been altered. Of
course, it's a given that there will be more than one file that maps
to the same MD5, but the sort of transformation required to damage a
file and end up with the same MD5 is extremely complex and therefore
unlikely.

I use it to make sure my backup images aren't corrupted before I use
them, and it seems to work well. On the Mac, a freeware utility
called 'Shorten' will create an MD5 from any sort of file.


Have fun,

Monte McGuire

[Bob Smith]

Monte P McGuire wrote:

> One 'single number' thingie I use all the time for hard disk image
> file backups is an MD5 signature. This single number can be generated

what is an MD5 signature? Is it like a CRC?

bobs

Bob Smith
BS Studios
we organize chaos
http://www.bsstudios.com

[David Satz]

Artie Turner wrote:

> [Truncated or] not, this just seems fundamentally wrong to me. Can a
> recording be accurately described as a single number?

The question you've asked is MUCH simpler than it appears to be, for at
least two reasons.

[1] (a semi-smart-aleck answer, but valid logically nonetheless): As
long as there is a unique and reliable one-to-one mapping of numbers to
particular recordings, then you've successfully encoded the recording as
a single number. That could be done simply by putting a tape of each
recording onto a shelf, then numbering each tape in sequence.

[2] (technically more sophisticated): For digital recordings, there exists
one sample value per channel for every sampling interval represented in the
recording. Say that it's a CD (16-bit PCM at 44.1 kHz). There's about 10
10 MB of audio sample data per minute of stereo recording at that rate.

For each sampling interval, you can string the four bytes of sample data
together in any predetermined sequence--let's say, the low-order L channel
byte followed by the high-order L channel byte followed by the same for the
R channel.

Then you'll have a combined 32-bit representation for that one sampling
interval, which can be regarded as a single integer value. All you need
to do is concatenate all the integer representations for all the succeeding
sampling intervals that are represented in the recording.

OK, you'll probably use up a fair number of lead pencils in the process,
but it is thoroughly "do-able" if you have enough patience and a long
enough life span. There would be an absolute 1:1 mapping of recordings
to the resulting (VERY large) integer values; no two different recordings
could possibly yield the same integer result value or vice versa.

Whether you wish to express an integer value in decimal, binary or in any
other given number base is purely a matter of whim, since the value is the
same regardless of the base in which it is expressed.

--best regards

[Artie Turner]

David Satz wrote:

> Whether you wish to express an integer value in decimal, binary or in any
> other given number base is purely a matter of whim, since the value is the
> same regardless of the base in which it is expressed.

The question that concerns me most here (per the link in the original
post) is can this single integer, this large concatenated number, be
said to represent a work or art or intellectual property for copyright
purposes WITHOUT a lot other contextual identifiers like bit depth,
sample rate, number of channels, time duration, etc? Like I mention to
James Boyk, there are lots of ways to get "4" ie 2+2, 3+1, etc. Same for
your concatenated number, yes?

The "property is theft" anti-intellectual property crowd is making some
bizarre claims, and while I agree that some digital rights management
cures MIGHT be worse than the disease of theft, I at least want to
understand the basics of this "single number" argument.

Artie
>
> --best regards

[LeBaron & Alrich]

Monte P McGuire > wrote:

> I still don't know what the point of all this is, but what do I
> know...

So one can know whether Song A, B or C, is actualy 42...


....whatever that means.

What song is four twenty?

--
ha

[LeBaron & Alrich]

Bob Smith > wrote:

> what is an MD5 signature?

"Middle Digit out of Five"?

> Is it like a CRC?

You got me there.

--
ha

[Ben Bradley]

In rec.audio.pro, Brian Takei > wrote:

>Josh Snider ) wrote:
>> Not really. It's just binary data. Since its an audio waveform converted
>> to a binary number, it's never existed as a decimal number, and so must be
>> converted from the binary string to a decimal number.
>
>Perhaps I should have been more explicit. I was referring to the
>"single binary number", not the "bitstream".

I understood you. An integer can be represented as a binary number
or a decimal number. You don't have to convert it to decimal for it to
be an integer. If you put a string of ones and zeros together, you
have an integer.

11111111 binary, when converted to decimal, is the integer 255.
100000000 binary is also an integer.

To answer the original question, yes. The thing is that the number
corresponding to a CD is a really big number.
Suppose we have a 15 second CD recording that we want to convert to
a number. The actual number of binary digits (bits) in a 15 second
recording of 44,100 samples per second, 16 bits per sample, two
channels is: 15*44100*16*2=21168000. That's 21 million (and change)
characters of 0's and 1's if you wanted to print this number in
binary, or only 7 million digits if you convert it to decimal.
To get the number of digits that represent a one-hour-long CD,
multiply this by 240 (four 15-second segments per minute, 60 minutes
per hour). This would be 240*7 million, or a decimal number with 1.68
billion digits. Stock up on those expensive ink-jet ink cartriges.

But if you just want to uniquely identify a CD, you can probably
just use the first five or ten samples, which would result in a number
with (5*16*2) 160 to 320 bits, or in decimal, about 50 to 100 digits.
The chances of any two CD recordings having the same numbers in the
first few samples, or in ANY few consecutive samples, is small, and
becomes much smaller with more samples. So, unless someone
intentionally uses the first few samples from another's CD, this
number would be enough to represent the CD.
Scanning over the mentioned article, the 'few digits' they give for
a musical work may be enough to uniquely identify a CD (because those
digits in that sequence occur somewhere on the disc, but not anywhere
on any other disc, though I doubt they actually searched for it on
every other available CD), but when converted to sound, it is nowhere
near enough for a human ear to recognize the work. A few samples (in a
wave editor, make some off-center samples in the middle of a few
seconds of silence) is less than a millisecond of sound, and will just
result in a tick when played back. You can try it in CE2000 or
whatever Adobe is offering thesedays. But you can still make a
semi-legitimate argument that the number is "part of a copyrighted
work."


>- Brian
>
>
>> in article , Brian Takei at
>> wrote on 9/9/03 16.53:
>>
>> > ryanm ) wrote:
>> >> 1111111011001000011101010011 = 267159379
>> >>
>> >> Every bitstream, if taken as a single binary number, can be converted to
>> >> an integer.
>> >
>> >
>> > It already is an integer.
>> >
>> > - Brian

[Ben Bradley]

In rec.audio.pro, Artie Turner > wrote:

>David Satz wrote:
>
>> Whether you wish to express an integer value in decimal, binary or in any
>> other given number base is purely a matter of whim, since the value is the
>> same regardless of the base in which it is expressed.
>
>The question that concerns me most here (per the link in the original
>post) is can this single integer, this large concatenated number, be
>said to represent a work or art or intellectual property for copyright
>purposes WITHOUT a lot other contextual identifiers like bit depth,
>sample rate, number of channels, time duration, etc? Like I mention to
>James Boyk, there are lots of ways to get "4" ie 2+2, 3+1, etc. Same for
>your concatenated number, yes?

If you have a sequence of numbers and you know it represents music,
it's really not hard to figure out bit depth (even if it's not 8, 16,
or 24, but especially easy if it is), sample rate (even 44.1 vs 48 is
clealy audible), number of channels and such, if it's any kind of
standard PCM file. If it's encoded with a lossless (.shn?) or lossy
(.mp3, .ra) format, it will be a little harder, but it's still doable.
Of course, all this is for a substantial number of samples (several
seconds of audible music), not these short ten-digit snippets they
give in the article. They might say they don't need to give the format
to be covered by copyright, but that sort of detail might be for
lawyers to argue over.

>The "property is theft" anti-intellectual property crowd is making some
>bizarre claims, and while I agree that some digital rights management
>cures MIGHT be worse than the disease of theft, I at least want to
>understand the basics of this "single number" argument.

Here's a related link that might help explain it. This describes
the 'illegal prime' number that encodes the C source of the infamous
"DeCSS" program:

http://primes.utm.edu/glossary/page.php?sort=Illegal

>Artie
>>
>> --best regards
>

[Kurt Albershardt]

LeBaron & Alrich wrote:

> Bob Smith > wrote:
>
>> what is an MD5 signature?
>
> "Middle Digit out of Five"?


Message Digest, from Ron Rivest (the R in RSA)
http://userpages.umbc.edu/~mabzug1/cs/md5/md5.html

[ryanm]

"Bob Smith" > wrote in message
...
>
> what is an MD5 signature? Is it like a CRC?
>
MD5 is an algorithm often used to encrypt data. It can be used for CRC,
in that changing a single bit in the data will drastically change the MD5
signature, telling you that your data has been corrupted if the sigs don't
match.

ryanm

[ryanm]

"Artie Turner" > wrote in message
. ..
>
> The question that concerns me most here (per the link in the original
> post) is can this single integer, this large concatenated number, be
> said to represent a work or art or intellectual property for copyright
> purposes WITHOUT a lot other contextual identifiers like bit depth,
> sample rate, number of channels, time duration, etc? Like I mention to
> James Boyk, there are lots of ways to get "4" ie 2+2, 3+1, etc. Same for
> your concatenated number, yes?
>
> The "property is theft" anti-intellectual property crowd is making some
> bizarre claims, and while I agree that some digital rights management
> cures MIGHT be worse than the disease of theft, I at least want to
> understand the basics of this "single number" argument.
>
It is useless because without context the integer would be so large as
to be extraordinarily inefficient. Even if efficiency wasn't an issue, a
shortened, radio-version of a song would be a unique work, as would a live
recording even if it were note for note accurate to the original.

Add to that, all you would have to do to get around the copyright would
be to remove a single sample of silence at the end and it would be a whole
new unique integer. Or reduce the overall volume by 1/100th of a db. Or add
a fade out at the end. Changing the file in any way at all changes the
unique integer, so then it could be claimed that it's no longer a copy of
the copyrighted integer. It's useless. Far more useful would be a way of
actually describing the *music* with a unique integer, but that would also
be extraordinarily complex and time consuming.

ryanm

[Gary]

Just remember that one is the loneliest number.