Just for fun

[mansfiem]

On Fri, Mar 23, 2007 at 05:20:36PM +0900, Trans wrote:

On Mar 22, 11:45 pm, Clifford H. [email protected] wrote:

This is a very concise statement about what’s flawed in your analysis.
It’s not just about repetition, it’s about removing whatever is
predictable. All’s fair when it comes to improving predictability.

Of course. When I used the term “repetition” I didn’t mean to be so
narrow as to to suggest nothing more than “a a a a a”. A better term
would have been “patterns”.

(redundancy)

and along with it the file I sent you to uncompress had only one bit
of data in it, “1”, then how can it work? Of course, the algorithm
itself had the entire content of King James within it. Pretty
predictable again. But not general compression. When looking at
general compression its important to take the size of all the elements
involved as well, including the compression algorithm itself.

Given that Kolmogorov-Chaitin complexity is not computable, what’s wrong
with
finding practical algorithms that approximate it?

I don’t see the intention behind your remarks: surely, any practical
compression method we come up with is going to perform worse than the
optimum
one (whose performance we can only estimate… using inferior
compression
methods!), so what? The existence of an uncomputable lower bound on the
length
of the description of a message is no more of a deterrent to research on
better (practical) compression methods than e.g. Shannon’s theorem is to
channel coding.

Regarding your remark on the choice of the universal machine and some
choices
not being “general compression”, you could add that even if descriptive
complexity relative to two different universal machines differs at most
by a
constant term, the latter does matter when we’re approximating the
algorithmic
complexity in practical scenarios…

[mansfiem]

On Fri, Mar 23, 2007 at 07:38:28PM +0900, Trans wrote:

of surprise that BWT improved deflate, which I believe says more about
deflate’s deficiencies than BWT’s use as a means of compression. I’ve
only been trying to explain my reasoning for that thought ever since.

Ah I see, you were surprised at deflate being so bad… I was surprised
at
your surprise

intentionally obscure).
Sorry, I assumed you were familiar with Kolmogorov complexity and tried
to
remove some redundancy [1] from my message based on that premise
(you said
you had been thinking deeply about this so it wasn’t too unreasonable
[although this is all redundant ultimately and could be replaced by a
pointer
into e.g. Cover&Thomas’ Elements of information theory; BTW IIRC there’s
a new
edition in the works?]

What you hinted at in your prev. message is known as the
Kolmogorov(-Chaitin)/descriptive complexity, corresponding to the length
of
the minimal description of a string using a program in a given Turing
machine/programming language. It is therefore relative to the universal
machine/language you choose, but if you pick two different ones the
corresponding complexities for a given string can differ at most by a
constant
amount, the length of the string that emulates one machine on the other.

In theory, you often ignore such constant factors (just choose a string
long
enough :), but in the example you gave, the machine included a full copy
of
the KJV bible, allowing it to replicate it with a single instruction…
and as
you said the description of the machine itself made all the difference
and it
only worked for that particular string, making it of little interest.
There’s
a sort of trade-off between the complexity of the machine and that of
the
programs you feed into it and both parts matter in practice: a machine
able to
compress any English text to 1/1000th of its original size wouldn’t help
residential users if it included/required a (mildly compressed?) copy of
Google’s archive.

I probably wasn’t 100% intellectually honest in my prev. message, I
apologize
for that. I wasn’t as much giving new information as trying to drag this
thread into a more information-theoretic OT, hoping some terminology
would
trigger interesting replies.

[1] I’m sensitive to redundancy (as an EE, I’ve also learned a bit about
it…;). This why I rarely post to ruby-talk anymore; there’s very
little
surprise in the questions/issues being discussed, and the responses to
new-but-actually-old questions I could give would hardly convey new
information. If everybody killed his messages when they don’t pass the
“entropy criterion” the way I do, this ML would have a small fraction of
its
current traffic; I cannot ask people to only post things of interest to
me
(why would anybody consent to, and how would they know anyway), but I
can try
to only post messages that would have interested me. For instance, I was
going
to reply “inverse BWT!” to the OP when nobody had responded yet, but I
anticipated somebody would do eventually, so I killed my msg. I don’t
respond
to questions which are likely to be answered by somebody else (you can
call it
proactive global redundancy control by local self-censoring ;).

A nice consequence of this is that it also filters out most unreasonable
content (would I be interested in some ad hominem argumentation? No, so
I
should not post any either. The temptation to do so is strong, as some
people,
including well-known/knowledgeable posters, use emotionally loaded
language
and sometimes defend their positions vehemently.)

sorry again

[mansfiem]

On Fri, Mar 23, 2007 at 07:15:05PM +0900, Clifford H. wrote:

Anyhow, interesting stuff, but not about Ruby… continue offline
if you wish…

Bummer. I was having fun spectating.

[mansfiem]

On Mar 23, 6:15 am, Clifford H. [email protected] wrote:

I don’t think either existed in 1983 :-). But I expect that
the answer is “no”. In any case, neither would suit, as the
compression existed to serve the purpose of full-text search
that had a separate compressed index for every word, and to
use the index, it was necessary to be able efficiently to
open the file at any word. Nowadays I’d open the file at any
disk block boundary, or bigger, since the CPU cost is
negligible next to the I/O cost. You’d probably use some
form of arithmetic coding these days anyhow.

Wow. You did that back in 83? I was just learning to code in C64
BASIC

“How it does it” is the interesting part. How does BWT improve
deflate? Ie. What’s that tell us about deflate?
It tells us that there’s more to the compressing typical data sets
That’s a little belittling, don’t you think? I mean, you’ve taken one
connotation of one word I used and seemingly made it the centerpiece

Ok, I’m sorry, I thought you meant literal repetition, I didn’t
mean to unfairly latch on to that, I just needed to clarify that
Shannon’s theorem doesn’t imply such repetition.

Thanks. I understand your take too. I should have been a little more
thoughtful in my wording.

words don’t evoke symbols in your thoughts that map to a similar
stream only has theoretical existence. All meaningful data streams
have structure. There are standard forms of mathematical pattern
search like finding repetition, using Fourier analysis, even
fractal analysis, but these cannot hope to find all possible
patterns - they can only find the kinds of structure they look
for. At some point, those structure types that are coded into the
de/compressors are encodings of human interpretations, not intrinsic
realities. The encoding of the human interpretation is “fair”, even
the extreme one in your URL example.

Fair enough. I guess I’m limiting my definition of predictability too
much. My point was really just that we have to take into account the
means of prediction along with the compressed data to measure
effectiveness.

I find this a very fascinating subject. I think ultimately it will
turn out to be very important, not just for compressing data, but for
understanding physics too.

I agree, though I hadn’t thought of the physics linkup. I think
that the very structure and nature of knowledge itself is hidden
here somewhere. So’s most of our non-conscious learning too, like
learning to walk… though the compression of patterns of movement
in our cerebellum requires an approach to using the time domain
in a way I haven’t seen a machine implement.

Hmm… interesting point. Perhaps OT, but I recall reading some time
ago about the discovery that out thoughts are not encoded by brain
signals in themselves, but in the timing of those signals. That really
threw me for a loop.

It is interesting to consider that all conceivable data can be
found somewhere in any transcendental number.

Since a transcendental number is just an infinite stream of digits,
there exist an infinite number of them that can encode any given
infinite stream of information. I don’t know how deep that insight
really is though.

I can see that they can encode any “finite” stream. I don’t know if
they can encode nay infinite stream though. In any case, I agree,
whether that’s right or not, its probably a minor point.

You might think, that
being the case, an excellent compression algorithm would be to find
the starting digit, say in Pi, for the data one is seeking. But
curiously it would do you know good. On average the number for the
starting digit would be just as long as the data itself.

Good one! I’m sure there’s some deep theoretical studies behind
that.

Actually it just occurs to me that is probably pretty simple to prove,
if you assume that the sequence of numbers of a transcendental are
effectively random (which I think is a safe bet). Don’t know why that
never occurred to me before.

knowledge could be encoded into that, if we knew how. The sum of
all human knowledge would doubtless be bigger than that, but I
found it an interesting thought. Some recent neurological research
I read indicated that, contrary to previous thought, our brains
actually do have a limited capacity. The previous assumption of
almost unlimited was based on thoughts about the likely failure
modes when “full” - and those were based on incorrect theories
about how memory works. I could perhaps dig up those papers
somewhere.

That’s all? Wow. I would have expected at least 100 times that. Of
course, that doesn’t means it’s readily accessible to our conscious
mind. Then again, it’s hard to judge such large sizes, so maybe 2CDs
is about right.

They should realize either the human brain is just that vast or
that human knowledge uses lossy compression.

I don’t agree at all. There surely is a limit to the achievable
compression, but we’re nowhere near it, and the search will tell
us much about the nature of knowledge.

Maybe, but I think the idea that human knowledge is more (lossless)
compressible just b/c it is human knowledge is flawed. I’m surprised
to hear we are nowhere near the limit though. Not sure why, but I
thought we were fairly close, say within 10-20% or so.

Anyhow, interesting stuff, but not about Ruby… continue offline
if you wish…

Cool. Thanks for the discussion. Unfortunately I’m pretty busy and
need to focus on work, but maybe down the road…

T.

[mansfiem]

Sorry about the delayed response. I just have too much one my mind…

On Mar 23, 8:18 am, Mauricio F. [email protected] wrote:

Ah I see, you were surprised at deflate being so bad… I was surprised at
your surprise

Truly surprised. Makes me wonder why other formats like 7z aren’t more
widely used. Is decompression speed really that much more important
than size?

intentionally obscure).

Sorry, I assumed you were familiar with Kolmogorov complexity and tried to
remove some redundancy [1] from my message based on that premise (you said
you had been thinking deeply about this so it wasn’t too unreasonable
[although this is all redundant ultimately and could be replaced by a pointer
into e.g. Cover&Thomas’ Elements of information theory; BTW IIRC there’s a new
edition in the works?]

I will have to look for that book. Thanks.

the KJV bible, allowing it to replicate it with a single instruction… and as
you said the description of the machine itself made all the difference and it
only worked for that particular string, making it of little interest. There’s
a sort of trade-off between the complexity of the machine and that of the
programs you feed into it and both parts matter in practice: a machine able to
compress any English text to 1/1000th of its original size wouldn’t help
residential users if it included/required a (mildly compressed?) copy of
Google’s archive.

Thanks. Makes perfect sense and now I know what to call it. Which is
always good.

I probably wasn’t 100% intellectually honest in my prev. message, I apologize
for that. I wasn’t as much giving new information as trying to drag this
thread into a more information-theoretic OT, hoping some terminology would
trigger interesting replies.

Sounds like you know more about it than anyone else here. So I’m not
sure if I can hold your interest at all. But I might entertain you a
bit with a related story.

When I first learned about the concept of compression, I did some
experimentation. Now, at this point, I had no idea how it was done, or
anything about Huffman coding, or anything like that. But I generally
learn best by experimenting, and that usually means thought
experiments which, aside, also accounts a bit for my lack of “book
smarts”. But in any case, I thought about how one might compress data
by algebraic means. I imagined the data as one giant number, and then
considered formula to rapidly approach that number. Exponents of
course grew rapidly, But I figured I needed to grow even faster, so I
“invented” the operation subsequent to “power”. I called it, for no
apparent reason: “milk”. So

3 milk 3 = 3 ** (3 ** 3)

And I then postulated the next operation as well, which I called
“cheese”.

3 cheese 3 = 3 milk (3 milk 3)

Needles to say, 3 cheese 3 is a huge number. I took the final step and
abstracted the set of all such operation starting with addition (O0),
to multiplication (O1), to power (O2), milk (O3), etc. And so I
figured any large number could be represented as a vector Xi, such
that:

Number = Sum(i…0) Oi(Xi+1, Xi)

At that point the problem became trying to salve for this equation
with a given number. I must have filled up every chalk board at my
school working on that. My fellow students thought I had lost my mind!
And I did to as I found myself trying to perform Integration on this
beast! That in fact turned out to be impossible.

Pretty nuts, eh? Of course, I later realized, after solving the
equation manually a number of times, the solutions would be no more
compressed than the original figure. My original idea of “rapid
growth” was flawed. And so it was that I got my first hint of what I
now learn is called “Kolmogorov(-Chaitin)/descriptive complexity”.

anticipated somebody would do eventually, so I killed my msg. I don’t respond
to questions which are likely to be answered by somebody else (you can call it
proactive global redundancy control by local self-censoring ;).

A nice consequence of this is that it also filters out most unreasonable
content (would I be interested in some ad hominem argumentation? No, so I
should not post any either. The temptation to do so is strong, as some people,
including well-known/knowledgeable posters, use emotionally loaded language
and sometimes defend their positions vehemently.)

sorry again

No need for apologies. No doubt you know that I am far from exemplary
in these affairs, but I believe (or at least hope) that I have gotten
better with time. But with you, well, it almost sounds like you are
playing a game of Prisoner’s Dilemma with your posts. And in that
case, I wonder who’s winning?

Thanks for the details, btw!
T.

[mansfiem]

Phillip G. wrote:

Taking at todays cheap processing time and even cheaper mass storage,
I’d say, all else being equal, size isn’t that important to the end user.

That sentence should read “Taking a look at…”

D’oh.

–
Phillip “CynicalRyan” Gawlowski
http://cynicalryan.110mb.com/

Rule of Open-Source Programming #5:

A project is never finished.

[mansfiem]

On Thu, Mar 29, 2007 at 09:56:17AM +0900, Phillip G. wrote:

than size?

Taking at todays cheap processing time and even cheaper mass storage,
I’d say, all else being equal, size isn’t that important to the end user.

in other environments (transferring large files across a thin pipe),
size is more important than speed.

Actually, I suspect that there are a couple reasons for the greater
popularity of some compression schemes, despite their poorer compression
performance:

1. When you wish to use compression “on the fly”, as it were, speed is
   very important. You want opening, closing, and otherwise using files
   that are kept in a compressed format, to be about as quick and
   responsive as using uncompressed files. This is probably not anywhere
   near as big a reason as the other one, though. . . .

2. Certain compression programs are very well known, and “everyone” has
   them (for some definition of “everyone”, depending on OS platform, et
   cetera). Thus, “everyone” uses them. Short of producing a hugely
   popular program that handles both old and new compression algorithms (or
   both old and new file formats, in other examples of this phenomenon in
   action), adoption of something new is going to be very slow and prone to
   failure despite any technical advantages to the new algorithm/format.
   This is illustrated by the demonstration of the commercial end-user
   market failure of the Betamax – VHS won that little skirmish simply
   because it was more widely available, quickly became a household word,
   and prevented migration to Betamax simply by way of market inertia.

[mansfiem]

Trans wrote:

Sorry about the delayed response. I just have too much one my mind…

On Mar 23, 8:18 am, Mauricio F. [email protected] wrote:

Ah I see, you were surprised at deflate being so bad… I was surprised at
your surprise

Truly surprised. Makes me wonder why other formats like 7z aren’t more
widely used. Is decompression speed really that much more important
than size?

Taking at todays cheap processing time and even cheaper mass storage,
I’d say, all else being equal, size isn’t that important to the end
user.

in other environments (transferring large files across a thin pipe),
size is more important than speed.

It’s good to have choice in different scenarios.

–
Phillip “CynicalRyan” Gawlowski
http://cynicalryan.110mb.com/

Rule of Open-Source Programming #11:

When a developer says he will work on something, he or she means
“maybe”.

[mansfiem]

Chad P. wrote:

and prevented migration to Betamax simply by way of market inertia.
This needn’t be the end of the story. For example, WinZip 5 (if I
remember correctly) didn’t handle tar.gz files. Modern WinZip does. I
think it also handles tar.bz2 files. I wouldn’t be at all surprised if
the next version handled .7zs.

[mansfiem]

On Fri, Mar 30, 2007 at 11:47:33AM +0900, Kristoffer Lund??n wrote:

some other formats is also negligible as in no user would actually
Not that it’s really the best solution for many reasons, but if you
want to be really practical, people should use zip for all their
compression needs - because that’s the only format all modern OS:es
can open with no extra software, at least that I know of.

In general, I agree with your assessment of the situation, but I’m not
entirely sure about one thing you said.

Is zip format really available with all OSes without extra software?
I’m pretty sure MS Windows requires one to install additional software
still, and I don’t seem to recall zip being standard on all major Linux
distributions. I haven’t bothered to check whether it’s available on
FreeBSD, mostly just because I haven’t needed an unzipper in quite a
while.

[mansfiem]

On 3/29/07, Chad P. [email protected] wrote:

and prevented migration to Betamax simply by way of market inertia.

Or just witness the huge popularity out there for the RAR format - a
format that is popular only because it once got popular - and the only
reason for that was that it made it easy to split archives into many
small parts. This was important (especially for the pirate market, of
course) in the days that a huge download could be corrupted. RAR
allowed people to only redownload one small part when that happened.

Today, with torrents and hashes in all major protocols, this is
essentially a moot issue, and the slightly better compression than
some other formats is also negligible as in no user would actually
notice any difference except for byte count in the file manager…
Today it’s just one big bad hassle, because people use it a LOT and
this means installing an extra program on every computer you use if
you want to participate - a non-free program at that, for those of us
who care.

Using RAR amounts to Cargo Cult Compression in my opinion, as it’s
only invoking the old ritual of times past because “we have always
done it this way” with no understanding on why and no actual benefits.

Not that it’s really the best solution for many reasons, but if you
want to be really practical, people should use zip for all their
compression needs - because that’s the only format all modern OS:es
can open with no extra software, at least that I know of.

Just goes to show…

– Kristoffer

[mansfiem]

On Mar 29, 9:44 pm, Chad P. [email protected] wrote:

essentially a moot issue, and the slightly better compression than

still, and I don’t seem to recall zip being standard on all major Linux
distributions. I haven’t bothered to check whether it’s available on
FreeBSD, mostly just because I haven’t needed an unzipper in quite a
while.

–
CCD CopyWrite Chad P. [http://ccd.apotheon.org]
Leon Festinger: “A man with a conviction is a hard man to change. Tell
him you disagree and he turns away. Show him facts and figures and he
questions your sources. Appeal to logic and he fails to see your point.”

Zip has been handled by the base Windows install since the first
release of XP. In fact, I think since about that same time, I’ve
never had the need to install anything for handling zip files across
Windows, Linux, and Mac.

Chris

[mansfiem]

On 3/30/07, Chad P. [email protected] wrote:

Is zip format really available with all OSes without extra software?
I’m pretty sure MS Windows requires one to install additional software
still, and I don’t seem to recall zip being standard on all major Linux
distributions. I haven’t bothered to check whether it’s available on
FreeBSD, mostly just because I haven’t needed an unzipper in quite a
while.

It works on XP, or at least it did a few years ago when I used it the
last time, and as far as I’ve seen it works OOTB on any Linux/BSD/*nix
distro that ships GNOME or KDE. To be honest, I don’t know about OS/X,
but I just assumed they handle this

From this point on, it’s all arguing what a “major” OS or distribution
is. I’d personally draw the line at Windows, Mac, and the 3-6
biggest Linuxes, but I know a lot of people would include a lot more,
just as a lot of people would only include Windows.

I do think that I’m mostly right, though.

– Kristoffer

[mansfiem]

On Fri, Mar 30, 2007 at 01:51:27PM +0900, Kristoffer Lund??n wrote:

last time, and as far as I’ve seen it works OOTB on any Linux/BSD/*nix
distro that ships GNOME or KDE. To be honest, I don’t know about OS/X,
but I just assumed they handle this

From this point on, it’s all arguing what a “major” OS or distribution
is. I’d personally draw the line at Windows, Mac, and the 3-6
biggest Linuxes, but I know a lot of people would include a lot more,
just as a lot of people would only include Windows.

I do think that I’m mostly right, though.

With the above in mind, yeah, you’re probably “mostly right” at least.
I just got so used to installing a zip/unzip utility on MS Windows that
I always installed it as one of the first things I did with my own
systems whenever I had need of XP (increasingly rare now), and since I
tend to do minimal installs with Debian or FreeBSD (for instance), no
KDE, GNOME, or zip utilities need apply in my “default” installs. I
guess the culprit in this case is the simple fact that I’m pretty
atypical, as computer users go.

[mansfiem]

On 3/30/07, Trans [email protected] wrote:

Yet, this is practical only in the short-run, and because too many
people follow this kind of tenant, the long-run never gets here. In
other words, by not collectively working together to adopt better
technologies we are ultimately being less practical.

Like I said, not ideal. And I have nothing against going forward, and
would applaud any open standard (free to implement by anyone)
becoming widespread across all platforms.

Meanwhile, however, compression becomes steadily less and less of any
real value for the average desktop user, for almost any scenario -
today, archiving is mainly done to group files, and any compression is
mostly a nice side effect. A certain group of people who believe in
doing things as efficiently and correct as possible (they call us
nerds ;-)) will not agree, but it’s true nonetheless and easy to
observe in almost any computer user - it’s when a directory, or even
more than 2-3 files is to be mailed that the archivers are used,
almost never because of size issues. Talking general computer use
here.

Of course, if I release some code only meant to be used on Linux, I
usually tar.gz or .bz2 it, and Mac users probably still sit things in
general?

The point is, by defaulting to zip, you may hold back the revolution a
bit, but it also ensures that your mom, your boss, your customers, and
just about everyone except Perrin can open it. This is convenient
and pragmatic, but it’s also important: there’s a lot of busy people
out there who will not even bother to reply wit a complaint if they
can’t open the files directly, they will just junk the message and
move on. A lot of people out the aren’t interested in installing
anything, no matter how good it is. A lot of these people may pay your
salary or sponsor your next project.

I have about 40 students I work with, computer literate and in the
ages 18-30, and I am writing this because this has shown to be a real
problem, before I got them all to only send stuff in formats as
standard as possible - this includes not sending MS files unless
requested. Students have, in a very real sense, lost internship
opportunities, and maybe even job offers (who knows?) because of this,
and it has only a long time after shown that it was only because it
was a RAR archive or funnily, an Open Document, or something like
that.

Some will say it’s a matter of education, to which I wish you the best
of luck. It hasn’t worked so far, because most people are not
interested. However, I sincerely support any movements to getting say
7zip built in in the next Windows service pack… that’s what it is
gonna take at this moment.

– Kristoffer

[mansfiem]

On Mar 29, 10:47 pm, “Kristoffer Lundén” [email protected]
wrote:

Not that it’s really the best solution for many reasons, but if you
want to be really practical, people should use zip for all their
compression needs - because that’s the only format all modern OS:es
can open with no extra software, at least that I know of.

Yet, this is practical only in the short-run, and because too many
people follow this kind of tenant, the long-run never gets here. In
other words, by not collectively working together to adopt better
technologies we are ultimately being less practical.

T.

[mansfiem]

On Fri, Mar 30, 2007 at 10:35:38PM +0900, Kristoffer Lund??n wrote:

The point is, by defaulting to zip, you may hold back the revolution a
bit, but it also ensures that your mom, your boss, your customers, and
just about everyone except Perrin can open it. This is convenient
and pragmatic, but it’s also important: there’s a lot of busy people
out there who will not even bother to reply wit a complaint if they
can’t open the files directly, they will just junk the message and
move on. A lot of people out the aren’t interested in installing
anything, no matter how good it is. A lot of these people may pay your
salary or sponsor your next project.

Well . . . to be fair, I can open it, but I usually need to type
something like one of the following first:

apt-get install unzip

cd /usr/ports/archivers/unzip; make install clean

Thanks for thinking of me, though.

I have about 40 students I work with, computer literate and in the
ages 18-30, and I am writing this because this has shown to be a real
problem, before I got them all to only send stuff in formats as
standard as possible - this includes not sending MS files unless
requested. Students have, in a very real sense, lost internship
opportunities, and maybe even job offers (who knows?) because of this,
and it has only a long time after shown that it was only because it
was a RAR archive or funnily, an Open Document, or something like
that.

It always pays to find out what the person on the other end wants, when
that person has something you need.

[mansfiem]

On 3/23/07, Trans [email protected] wrote:

When did I say otherwise? I believe my original point was simply one
of surprise that BWT improved deflate, which I believe says more about
deflate’s deficiencies than BWT’s use as a means of compression. I’ve
only been trying to explain my reasoning for that thought ever since.

I’d like to ask a question Tom, as this is becoming a little bit
obscure, as you put it.

BWT is used for bzip2 too, frankly I am surprised that you are
surprised Tom.
As BWT will create repetitions, which is quite clear, and allows for
an easy undoing of its transformation would it not help a whole class
of compression algorithms.

When you talked about a deficiency would that not mean -in your setup

• that a compression algorithm should implicitly find “clever”
  transformations…
  If this was your thought it is an incredible advanced and frankly
  optimistic idea.

And that is my question BTW (not BWT;) do you indeed look at this
issue from this angle?

I can accept it as a 100% true statement though

But I guess putting them together (transformation and compression), by
hand is quite clever already and pretty much state of the art.

Cheers
Robert
<snip

T.

[mansfiem]

On 3/30/07, Christian N. [email protected] wrote:

Reminds me a lot of my idea of just “indexing” all data by their
offset in Pi.

I think most geeks have come up with that one at least once in their
lives

martin

[mansfiem]

“Trans” [email protected] writes:

Pretty nuts, eh? Of course, I later realized, after solving the
equation manually a number of times, the solutions would be no more
compressed than the original figure. My original idea of “rapid
growth” was flawed. And so it was that I got my first hint of what I
now learn is called “Kolmogorov(-Chaitin)/descriptive complexity”.

Reminds me a lot of my idea of just “indexing” all data by their
offset in Pi.