# Converting Pi to binary

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### BlackShift

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May 4, 2001, 2:28:48 PM5/4/01
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Hi,
I've got a large amount of decimals of pi (4.2 bilion), but I think it
is much cooler (and more usefull?) to have pi in binary.
Does anyone has an idea on how to do that in a not so slow way?
I can only think of calculating 2^(-n), checking wether it can be
substracted, then substract and go to the next bit. But this will take
almost an eternity with files over 2GB I think...
Another way might be to convert all decimal digits to binary and add
them up then (.1 to binary then .04 .001 .0005 etc and add them then)
so the load can be distributed over multiple computers.
I don't nescecery want to convert all the digits of course but the
more the better :-)

groetjes,
BlackShift
pi=11.0010010000111111b (i thought)

### Paul Lutus

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May 4, 2001, 5:42:48 PM5/4/01
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"BlackShift" <hu...@doemaarwat.nl> wrote in message
news:3af2f33e...@news.rug.nl...

Why do you think this is difficult (in principle)? For one thing, if the
number is stored in your computer as a number, it is already in binary form.
All you have to do is shift out the bits and store them in that form.

Here is some digits of Pi in binary:

11.0010010000111111011010101000100010000101101000110000100011010011000100110
0011001100010100010111000000011

Here it is in hexadecimal:

3.243f6a8885a308d313198a2e03707344a4093822299f31d0082efa98ec4e6c89452821e638
d01377be5466cf34e90c6cc0ac29b7d

But you have to convert an entire approximation at once from one base to
another. You can't just convert a few digits, then add to them later (at
least, not easily). So if you decide to do this, you need to choose the size
of the set to be converted in advance.

--
Paul Lutus
www.arachnoid.com

### Steve Leibel

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May 4, 2001, 6:22:16 PM5/4/01
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In article <unFI6.210974\$lj4.6...@news6.giganews.com>, "Paul Lutus"
<nos...@nosite.com> wrote:

> Why do you think this is difficult (in principle)? For one thing, if the
> number is stored in your computer as a number, it is already in binary
> form.

I don't think that's necessarily true, or even likely.

If the original poster has billions of digits of pi, it's very unlikely
that he's using his computer's native representation of numbers. More
likely he's using a custom high-precision package that stores numbers in
a custom internal format. So converting to binary is a nontrivial
exercise in this case.

### GerardS

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May 4, 2001, 6:37:40 PM5/4/01
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| Paul Lutus wrote:
|> BlackShift asked:

No, if you have 10,000,000 digits of pi, the digits are stored as
characters, not
in "binary". I.E.: 3.14159 would be stored (in ascii)
as:

33 2e 31 34 41 35 39 (spaces added for readability).

To convert a (decimal) fraction to binary is pretty easy.

For 3.14159.... ---- first, convert the integer part (3) to binary ---
that's the
easy part.

Now, take the fraction (.14159...) and multiply times two, the binary
radix.
You get 0.28318 ... with the integer part being zero in this case.

so that's the first binary digit after the decimal point, zero.

So far, we have 11. (the integer part), plus that "zero", and
now we have
11.0 for pin in binary (so far).

Now take that .28318... and multiply by two again, and we get 0.56636
with
the integer part being zero (again). So we have 11.00 so far for
pi in
binary.

Now, take that .56636... and multiply by two again, and we get
1.13272 ... with
one being the interger part, so we now have 11.001 for pi in binary...

Now, take that .13272... and mulitply by two again, and we get
0.26544... with
zero as the integer part, so we have 11.0010 for pi in binary so far.

Now, take that .26544... and multiply by two again, and we get
0.53088... with
zero as the integer part, so we have 11.00100 for pi in binary so
far...

Now, take that .53088... and multiply by two again, and we get
1.16176... with
one as the integer part, so pi in binary will now be 11.001001 so
far.

Now, take that .16176... times two ... and so on.

I hope it's clearer than mud.

Gerard S.

### Paul Lutus

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May 4, 2001, 6:38:01 PM5/4/01
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"Steve Leibel" <ste...@bluetuna.com> wrote in message
news:stevel-CAF45C....@news-server.nyc.rr.com...

> In article <unFI6.210974\$lj4.6...@news6.giganews.com>, "Paul Lutus"
> <nos...@nosite.com> wrote:
>
> > Why do you think this is difficult (in principle)? For one thing, if the
> > number is stored in your computer as a number, it is already in binary
> > form.
>
> I don't think that's necessarily true, or even likely.
>
> If the original poster has billions of digits of pi, it's very unlikely
> that he's using his computer's native representation of numbers.

That is why I qualified my statement as I did.

> So converting to binary is a nontrivial
> exercise in this case.

True, because of the size, and it is nontrivial only in the sense that it
requires a lot of computer time, not because of the complexity of the
problem.

--
Paul Lutus
www.arachnoid.com

### GerardS

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May 4, 2001, 6:43:47 PM5/4/01
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| Paul Lutus wrote:
|> Steve Leibel wrote:

|>> Paul Lutus write:
|>> Why do you think this is difficult (in principle)? For one thing, if
the
|>> number is stored in your computer as a number, it is already in
binary
|>> form.
|>
|> I don't think that's necessarily true, or even likely.
|>
|> If the original poster has billions of digits of pi, it's very
unlikely
|> that he's using his computer's native representation of numbers.
|
| That is why I qualified my statement as I did.
|
|> So converting to binary is a nontrivial
|> exercise in this case.
|
| True, because of the size, and it is nontrivial only in the sense that
it
| requires a lot of computer time, not because of the complexity of the
| problem.

It shouldn't take that much time to convert. I would use REXX as it can
store
that ten-million digit number essentially, as is --- assumming the
3.14159 ...
string is stored as characters (as you see here). It would be a
trivial thing
to read in the digits from a (flat) file, assign them to a REXX variable
[80
bytes at a time?), then use the algorithm that I outlined in another
post.

No sweat.

Gerard S.

### Paul Lutus

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May 4, 2001, 6:44:45 PM5/4/01
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"GerardS" <Ger...@PrairieTech.Net> wrote in message
news:D8GI6.69\$Sf3...@newsfeed.slurp.net...

But in fact the answer is "yes," which you then go on to prove. In each
step, the entire digit set must be multiplied by 2, not part of it. As I
said, the OP must choose the size of the approximation to be converted in
advance, and convert the entire block of digits.

> I hope it's clearer than mud.

After your incorrect "no," not likely.

--
Paul Lutus
www.arachnoid.com

### BlackShift

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May 4, 2001, 6:47:20 PM5/4/01
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On Fri, 04 May 2001 22:22:16 GMT, Steve Leibel <ste...@bluetuna.com>
wrotf:

>In article <unFI6.210974\$lj4.6...@news6.giganews.com>, "Paul Lutus"
><nos...@nosite.com> wrote:
>
>> Why do you think this is difficult (in principle)? For one thing, if the
>> number is stored in your computer as a number, it is already in binary
>> form.

(my news server does not seem to have this reply so i haven't read any
other text then this quoted text)

>I don't think that's necessarily true, or even likely.
>
>If the original poster has billions of digits of pi, it's very unlikely
>that he's using his computer's native representation of numbers. More
>likely he's using a custom high-precision package that stores numbers in
>a custom internal format. So converting to binary is a nontrivial
>exercise in this case.

It is represented in 2 decimals/byte, 4bits/decimal, so not in binair
:-( Maybe if there is a program that can read that number in 'memory',
but i'm not sure wether such a program exists...
Maybe the creators of the number have it in binary, they calculated up
to 53trilion digits (I believe that's still the record, the first
4.2bilion are to download for free) but I don't think they did because
that will have cost even more processing power.
Maybe it will be easy when computers have a couple of gigs memory, but
then it is of course intresting to regard even more decimals :-)
groetjes,
hugo

### GerardS

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May 4, 2001, 7:08:08 PM5/4/01
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| Paul Lutus wrote:

Sheeesh ... why do you think I used ellispis after EACH number?

Of course you take two times the .14159... (fraction) --- all of it, or
the
part you want to convert to binary. And no, the OP doesn't have to
choose the
size of the approximation to be converted in advance. I thought
everybody
understood that .14159... meant more than 5 digits. I though I'd
save a
little bandwidth and not enter, say an approximation of pi with a
ga-jillion
digits, I thought five digits would do for the algorithm just fine.

Gerard S.

### Paul Lutus

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May 4, 2001, 7:16:03 PM5/4/01
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"GerardS" <Ger...@PrairieTech.Net> wrote in message
news:aBGI6.76\$Sf3....@newsfeed.slurp.net...

> | After your incorrect "no," not likely.
>
> Sheeesh ... why do you think I used ellispis after EACH number?
>
> Of course you take two times the .14159... (fraction) --- all of it, or
> the
> part you want to convert to binary. And no, the OP doesn't have to
> choose the
> size of the approximation to be converted in advance.

But he does! If he wants to convert the entire however-many-billions, that
must be a conscious, a priori decision. If he wants to convert only, say,
10,000 digits, that must be the choice. My point was and is that the OP must
decide once about the size to be converted. He cannot change his mind about
the size being converted once the algorithm is running, or add more digits
to an already-converted result.

I think there must be some simple kind of lexical misunderstanding here. The
point is too obvious.

--
Paul Lutus
www.arachnoid.com

### John Bailey

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May 5, 2001, 6:46:58 AM5/5/01
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On Fri, 4 May 2001 14:42:48 -0700, "Paul Lutus" <nos...@nosite.com>
wrote:

>"BlackShift" <hu...@doemaarwat.nl> wrote in message
>news:3af2f33e...@news.rug.nl...
>> Hi,
>> I've got a large amount of decimals of pi (4.2 bilion), but I think it
>> is much cooler (and more usefull?) to have pi in binary.
>> Does anyone has an idea on how to do that in a not so slow way?

>But you have to convert an entire approximation at once from one base to

>another. You can't just convert a few digits, then add to them later (at
>least, not easily). So if you decide to do this, you need to choose the size
>of the set to be converted in advance.

Was the orginal question a troll? I missed it in any case.
Calculating the binary representation of pi by converting from decimal
is doing it the hard way. It requires less memory and compute power
to recompute the hexidecimal digits and thence convert to binary.

From:
http://www.mathsoft.com/asolve/plouffe/plouffe.html
David Bailey, Peter Borwein and Simon Plouffe have recently (written
in 1996) computed the ten billionth digit in the hexadecimal expansion
of pi. They utilized an astonishing formula:which enables one to
calculate the dth digit of pi without being forced to calculate all
the preceding d-1 digits. No one had previously even conjectured that
such a digit-extraction algorithm for pi was possible.

John

### BlackShift

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May 5, 2001, 4:23:17 PM5/5/01
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On Sat, 05 May 2001 10:46:58 GMT, jmb...@frontiernet.net (John Bailey)
wrotf:

>On Fri, 4 May 2001 14:42:48 -0700, "Paul Lutus" <nos...@nosite.com>
>wrote:
>
>>"BlackShift" <hu...@doemaarwat.nl> wrote in message
>>news:3af2f33e...@news.rug.nl...
>>> Hi,
>>> I've got a large amount of decimals of pi (4.2 bilion), but I think it
>>> is much cooler (and more usefull?) to have pi in binary.
>>> Does anyone has an idea on how to do that in a not so slow way?
>
>>But you have to convert an entire approximation at once from one base to
>>another. You can't just convert a few digits, then add to them later (at
>>least, not easily). So if you decide to do this, you need to choose the size
>>of the set to be converted in advance.
>
>Was the orginal question a troll? I missed it in any case.

No :-) i just want to have pi in as much binairs as i can get (for fun
mostly), I got a lot of decimals, so I thought that it would be the
easiest to convert them, but i think you might be right that it is
faster to calculate them..

>Calculating the binary representation of pi by converting from decimal
>is doing it the hard way. It requires less memory and compute power
>to recompute the hexidecimal digits and thence convert to binary.

tnx, intresting site. I knew about the formula, but i forgot... There
also are some intresting links on that site, like:
http://www.lacim.uqam.ca/plouffe/Simon/articlepi.html
calculating pi in any base
I think indeed that recalculating it is faster, and at least more fun
:-)
groetjes,
BlackShift

### Paul Lutus

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May 5, 2001, 4:36:03 PM5/5/01
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"John Bailey" <jmb...@frontiernet.net> wrote in message
news:3af3d882...@news.frontiernet.net...

> Was the orginal question a troll? I missed it in any case.
> Calculating the binary representation of pi by converting from decimal
> is doing it the hard way. It requires less memory and compute power
> to recompute the hexidecimal digits and thence convert to binary.

Well, since hex is for all practical purposes binary, this is rather
tautological. The original question presumed a source set of decimal digits.
It is also easier in general to perform the original computation in binary
for a number of reasons.

--
Paul Lutus
www.arachnoid.com

### Bob Harris

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May 6, 2001, 9:14:19 AM5/6/01
to
Expanding on the original post...

If I know a number to great precision in decimal, is there an efficient way
to convert that to binary?

For example, suppose I have the first billion digits of a number x between 0
and 1. The simple-minded algorithm would be to multiply x by two and
extract the first binary bit (by testing for the result >= 1), then repeat
for each bit. The problem of course is that the multiply requires us to
operate on every one of those billion digits.

A different algorithm would work by comparing the number to increasing
powers of 1/2. If the number is no less than .5, the first bit is 1 and we
can subtract .5 from the number. Then compare to .25, .125, and so on.
These operations will be much quicker since we don't have to look at all of
the billion digits to generate the next bit. Every power of 1/2 will
increase the size of our test number though, so eventually we're going to
need an awful lot of memory to store our test number (less than half a
billion digits, but still quite a lot).

Combining those two algorithms, we could perform the second algorithm until
the test number had too many digits, then perform one multiply of x by a
power of two, to bring the test number back to 1/2.

Are there better algorithms?

### Paul Lutus

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May 6, 2001, 9:52:09 AM5/6/01
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"Bob Harris" <nit...@mindspring.com> wrote in message
news:B71AC66B.14EB3%nit...@mindspring.com...

> Expanding on the original post...
>
> If I know a number to great precision in decimal, is there an efficient
way
> to convert that to binary?
>

That depends on whether the number is expressed in fixed- or floating-point
notation, and more importantly whether there is an exponent, as in
scientific notation.

For integers, it is a simple matter of dividing the number repeatedly by the
desired base while assembling the new number out of the remainders of the
division until the original number is exhausted. A variation of this idea
can be used for floating-point numbers -- repeatedly dividing the
whole-number part as above, then processing the fractional part in a similar
way (but reversed left-to-right).

Here is sample C++ code for integer conversion:

#include <iostream>
#include <string>

string dispBase(long v,int base)
{
string digits = "0123456789abcdef";
string s;
do {
s = digits[v % base] + s;
v /= base;
}
while(v);
return s;
}

int main()
{
long v = 64206;
cout << dispBase(v,16) << endl;
cout << dispBase(v,10) << endl;
cout << dispBase(v,8) << endl;
cout << dispBase(v,2) << endl;
return 0;
}

Example run as shown:

face
64206
175316
1111101011001110

BTW your second method won't work for any arbitrary base. You always must
operate on the entire number.

--
Paul Lutus
www.arachnoid.com

### John Bailey

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May 6, 2001, 6:12:51 PM5/6/01
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On Sat, 5 May 2001 13:36:03 -0700, "Paul Lutus" <nos...@nosite.com>
wrote:

>"John Bailey" <jmb...@frontiernet.net> wrote in message

The issue is the number base, not the architecture of the computers
representation of values.. While Plouffe has made some program in
computing the decimal digits of pi (reference:
http://www.lacim.uqam.ca/plouffe/Simon/articlepi.html) decimal Nth
digit calculations are not consider quick and efficient.
On the other hand, computation using a NUMBER BASE of hex or binary,
its possible to calculate an arbitraily large Nth digit value with a
very small amount of memory and compute power.
(reference:
http://numbers.computation.free.fr/Constants/Algorithms/nthdigit.html)

It seems widely held that it requires a large amount of memory and at
least modest compute power to convert any very large number from a
NUMBER BASE of 2 to a NUMBER BASE of 10, I suggest therefore:
1) That the same costs apply to converting 10 Base to 2 BASE and
2) that there is less computation involved in going directly to the
binary result, rather than attempt to perform a conversion.

John

### John Bailey

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May 6, 2001, 7:56:58 PM5/6/01
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On Sat, 5 May 2001 13:36:03 -0700, "Paul Lutus" <nos...@nosite.com>
wrote:

>"John Bailey" <jmb...@frontiernet.net> wrote in message

The issue is the number base, not the architecture of the computers

### John Bailey

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May 6, 2001, 8:00:26 PM5/6/01
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On Sat, 5 May 2001 13:36:03 -0700, "Paul Lutus" <nos...@nosite.com>
wrote:

>"John Bailey" <jmb...@frontiernet.net> wrote in message

The issue is the number base, not the architecture of the computers

### Graham Jones

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May 7, 2001, 11:38:35 AM5/7/01
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In article <B71AC66B.14EB3%nit...@mindspring.com>, Bob Harris
<nit...@mindspring.com> writes

>Expanding on the original post...
>
>If I know a number to great precision in decimal, is there an efficient way
>to convert that to binary?
[...]

I think you can do it in O(N*(log N)*(log N)) time, which is a lot
better than the O(N*N) time of a simple method. I have not proved this
rigorously, and am not an expert in this area or anything, but...

The key fact is that you can multiply two polynomials of degree N
together in O(N*(log N)) time using the Fast Fourier Transform. This is
a standard method. A number written in some base can be regarded as a
polynomial with restrictions on the coefficients. After multiplying two
such polynomials, the restrictions will longer hold and there are a lot
of carry's to deal with, but the multiplication itself it is the slow
bit.

To convert a decimal fraction to binary, first convert a very large
power of 2 to decimal (by multiplying smaller powers of course), then
multiply the fraction by this (working in decimal). This reduces the
problem to converting a large integer in decimal to binary.

You can now use a recursive 'divide-and-conquer' algorithm on this. If
there are N digits, write it as (N/2 digits)*(10^(N/2)) + (N/2 digits),
apply recursion to the two N/2 digit numbers and put the parts together.
The most time-consuming part is lots of polynomial multiplications, and
the total time is O(N*(log N)*(log N)) by my calculations.

Graham

### Keith F. Lynch

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May 12, 2001, 5:12:06 PM5/12/01
to
WARNING: Do NOT calculate Pi in binary. It is conjectured that this
number is normal, meaning that it contains ALL finite bit strings.

If you compute it, you will be guilty of:

* Copyright infringement (of all books, all short stories, all
newspapers, all magazines, all web sites, all music, all movies,
and all software, including the complete Windows source code)
* Trademark infringement
* Possession of child pornography
* Espionage (unauthorized possession of top secret information)
* Possession of DVD-cracking software
* Possession of threats to the President
* Possession of everyone's SSN, everyone's credit card numbers,
everyone's PIN numbers, everyone's unlisted phone numbers, and
everyone's passwords
* Defaming Islam. Not technically illegal, but you'll have to go
into hiding along with Salman Rushdie.
* Defaming Scientology. Which IS illegal -- just ask Keith Henson.

Also, your computer will contain all of the nastiest known computer
viruses. In fact, all of the nastiest POSSIBLE computer viruses.

Some of the files on my PC are intensely personal, and I for one
don't want you snooping through a copy of them.

You might get away with computing just a few digits, but why risk it?
There's no telling how far into Pi you can go without finding the
secret documents about the JFK assassination, a photograph of your
neighbor's six year old daughter doing the nasty with the family dog,
or a complete copy of the not-yet-released Pearl Harbor movie. So
just don't do it.

The same warning applies to e, the square root of 2, Euler's constant,
Phi, the cosine of any non-zero algebraic number, and the vast
majority of all other real numbers.

There's a reason why these numbers are always computed and shown in
decimal, after all.
--
Keith F. Lynch - k...@keithlynch.net - http://keithlynch.net/
I always welcome replies to my e-mail, postings, and web pages, but
unsolicited bulk e-mail sent to thousands of randomly collected
addresses is not acceptable, and I do complain to the spammer's ISP.

### Paul Lutus

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May 12, 2001, 8:40:07 PM5/12/01
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"Keith F. Lynch" <k...@KeithLynch.net> wrote in message
news:9dk8v6\$i6q\$1...@saltmine.radix.net...

> The same warning applies to e, the square root of 2, Euler's constant,
> Phi, the cosine of any non-zero algebraic number, and the vast
> majority of all other real numbers.

Actually, there are (1) a subset of square roots (all roots of perfect
squares) and (2) some trigonometric arguments, that avoid this serious
threat to civic order that you have so kindly brought to our attention. :)

> There's a reason why these numbers are always computed and shown in
> decimal, after all.

What? They don't become "safe" by being displayed in decimal -- or, for that
matter, by being computed that way. You can hide all the works of
Shakespeare in a string of decimal digits just as easily as in binary, or
any other number base.

Imagine how much more paranoid we should all feel when confronted by the
*real* threat -- any random number, any number base. Yipes!

Here is an integer in base 10, that if rendered in base 128 instead (as
characters), is a message familiar to people in communications. Care to read
it?

24900035293015749005578991446132
52533765089957549507274748319026
29774586963869379388101958907956
76673041298862

It's not encrypted, it is merely a string turned into a number.

--
Paul Lutus
www.arachnoid.com

### Keith F. Lynch

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May 13, 2001, 3:21:04 AM5/13/01
to
Paul Lutus <nos...@nosite.com> wrote:
> Actually, there are (1) a subset of square roots (all roots of
> perfect squares) and (2) some trigonometric arguments, that avoid
> this serious threat to civic order that you have so kindly brought
> to our attention. :)

I never said otherwise. However, I will maintain that the full binary
expansions of the cosines of ALL non-zero algebraic real numbers
contain child pornography. Prove me wrong.

> What? They don't become "safe" by being displayed in decimal -- or,
> for that matter, by being computed that way.

Certainly they do.

> You can hide all the works of Shakespeare in a string of decimal
> digits just as easily as in binary, or any other number base.

True, but nobody cares. You can even convert the collected works of
Harlan Ellison into decimal, and print them, and he won't sue. Try
it and see!

> Here is an integer in base 10, that if rendered in base 128
> instead (as characters), is a message familiar to people in
> communications. Care to read it?

> 24900035293015749005578991446132
> 52533765089957549507274748319026
> 29774586963869379388101958907956
> 76673041298862

Sigh. I can't believe I stayed up until 3 am to figure this out.
Looks like you really foxed me. At least nobody can call me lazy,
though I should have been more quick about it.

> It's not encrypted, it is merely a string turned into a number.

You could have made it more interesting by having it in EBCDIC.
Or Baudot.

I looked at your website. If you're so much in favor of free speech,
why do you hide your email address so thoroughly? (You could maybe
provide it decimal? If a spammer figures THAT out, print the spam on
paper and I'll eat it.) You're letting spammers interfere with our
ability to communicate with each other.

I've always refused to munge, to filter, or to run and hide. I prefer
to fight back. Take back the net!

### Paul Lutus

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May 13, 2001, 4:57:37 AM5/13/01
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"Keith F. Lynch" <k...@KeithLynch.net> wrote in message
news:9dlcl0\$rn6\$1...@saltmine.radix.net...

> Paul Lutus <nos...@nosite.com> wrote:
> > Actually, there are (1) a subset of square roots (all roots of
> > perfect squares) and (2) some trigonometric arguments, that avoid
> > this serious threat to civic order that you have so kindly brought
> > to our attention. :)
>
> I never said otherwise. However, I will maintain that the full binary
> expansions of the cosines of ALL non-zero algebraic real numbers
> contain child pornography. Prove me wrong.

What? Apart from the fact that you contradict yourself in a single
paragraph, there is this:

cos(Pi/3) = 1/2
cos(2 Pi/3) = -1/2
cos(Pi) = -1
cos(4 Pi/3) = -1/2
cos(5 Pi/3) = 1/2
cos(2 Pi) = 1

Etc., ad infinitum, with similar examples for all trig functions. No child
pornography here.

> > What? They don't become "safe" by being displayed in decimal -- or,
> > for that matter, by being computed that way.
>
> Certainly they do.

No, because they are the same number, expressed in a different base. Numbers
are numbers, bases are a convenience that doesn't change the number's
identity. Do you think there are different prime numbers in binary than in
decimal? Do you think an irrational number in decimal becomes rational in
binary?

> > You can hide all the works of Shakespeare in a string of decimal
> > digits just as easily as in binary, or any other number base.
>
> True, but nobody cares. You can even convert the collected works of
> Harlan Ellison into decimal, and print them, and he won't sue. Try
> it and see!

You just tried to change the subject. Feeling insecure about your position?
But it is not true. A ZIP file containing a copyrighted work is an
infringement. This has been accepted in the courts for obvious reasons.

> > 24900035293015749005578991446132
> > 52533765089957549507274748319026
> > 29774586963869379388101958907956
> > 76673041298862
>
> Sigh. I can't believe I stayed up until 3 am to figure this out.
> Looks like you really foxed me. At least nobody can call me lazy,
> though I should have been more quick about it.

In that case, I apologize. It is easy to create such a thing in a program
like Mathematica. Two lines of code, one for the encoder, one for the
decoder.

> > It's not encrypted, it is merely a string turned into a number.
>
> You could have made it more interesting by having it in EBCDIC.
> Or Baudot.

True, but I wasn't going for obscure, just interesting.

> I looked at your website. If you're so much in favor of free speech,
> why do you hide your email address so thoroughly?

Are you serious? Freedom of speech is not a requirement that anyone listen.
In any case, I have excellent reasons, all explained on my public message
board, where anyone can post anything.

> You're letting spammers interfere with our
> ability to communicate with each other.

1. You didn't find the message board?

2. No, spammers are doing that, not me.

> I've always refused to munge, to filter, or to run and hide. I prefer
> to fight back. Take back the net!

I have more experience at this than you do. I also have a Web site that gets
100,000 hits per day. This is a different class of problem than you are
talking about.

--
Paul Lutus
www.arachnoid.com

### Bob Harris

unread,
May 13, 2001, 10:24:37 AM5/13/01
to
Keith F. Lynch recently warned us not to compute pi in binary, because (if I
understand the issue) it contains several bitstrings which we are not
legally allowed to posess.

There is a practical issue here, though. I'll accept that pi contains any
given bit string (I'm not sure that has been proven, but it doesn't seem to
matter). But how many bits of pi would I have to calculate (and store on my
hard drive) before my hard drive would contain any of the forbidden
bitstrings?

Seems to me that it would be so large that I couldn't store it with today's
technology. Am I wrong?

-- Bob

### Keith F. Lynch

unread,
May 13, 2001, 11:55:19 AM5/13/01
to
Paul Lutus <nos...@nosite.com> wrote:

>"Keith F. Lynch" <k...@KeithLynch.net> wrote:
>> Paul Lutus <nos...@nosite.com> wrote:
>>> Actually, there are (1) a subset of square roots (all roots of
>>> perfect squares) and (2) some trigonometric arguments, that avoid
>>> this serious threat to civic order that you have so kindly brought
>>> to our attention. :)

>> I never said otherwise. However, I will maintain that the full binary
>> expansions of the cosines of ALL non-zero algebraic real numbers
>> contain child pornography. Prove me wrong.

> What? Apart from the fact that you contradict yourself in a single
> paragraph,

Sorry, "I never said otherwise" referred to the square roots, and to
SOME trigonometric arguments.

> there is this:

> cos(Pi/3) = 1/2
> cos(2 Pi/3) = -1/2
> cos(Pi) = -1
> cos(4 Pi/3) = -1/2
> cos(5 Pi/3) = 1/2
> cos(2 Pi) = 1

None of Pi/3, 2 Pi/3, Pi, 4 Pi/3, 5 Pi/3, and 2 Pi are algebraic
numbers. They are not roots to integer polynomials.

> But it is not true. A ZIP file containing a copyrighted work is
> an infringement. This has been accepted in the courts for obvious
> reasons.

Only because unzip software is common. Software for turning decimal
numbers into binary is not. If you were to post a copyrighted work
in decimal, chances are nobody would download and decode it, and thus
that the copyright owner wouldn't care that you'd posted it.

> Are you serious? Freedom of speech is not a requirement that anyone
> listen.

I never said otherwise. But if you would have made your email address
available if not for spammers, then you're letting spammers interfere
with freedom of speech. You're letting the spammers win.

>> I've always refused to munge, to filter, or to run and hide.
>> I prefer to fight back. Take back the net!

> I have more experience at this than you do.

I doubt this very much. I've been using email for 27 years, I've been
fighting spam for 16 years, and I host over 10,000 web pages. I've
often received over 100 spams per day.

I have a collection of angry replies from spammers. This is the best
proof that I'm having an effect.

The only reason email is still usable at all is because of those of us
who fight back. Not because of those who "just hit delete" or who run
and hide.

### Paul Lutus

unread,
May 13, 2001, 2:13:23 PM5/13/01
to
"Keith F. Lynch" <k...@KeithLynch.net> wrote in message
news:9dmap7\$sis\$1...@saltmine.radix.net...

> Sorry, "I never said otherwise" referred to the square roots, and to
> SOME trigonometric arguments.

That is false! Here is what you said:

> >> I will maintain that the full binary
> >> expansions of the cosines of ALL non-zero algebraic real numbers
> >> contain child pornography. Prove me wrong.

The word "ALL" and the word "SOME" have different meanings. Look this up if
you need to, in a book called a "dictionary."

> > there is this:
>
> > cos(Pi/3) = 1/2
> > cos(2 Pi/3) = -1/2
> > cos(Pi) = -1
> > cos(4 Pi/3) = -1/2
> > cos(5 Pi/3) = 1/2
> > cos(2 Pi) = 1
>
> None of Pi/3, 2 Pi/3, Pi, 4 Pi/3, 5 Pi/3, and 2 Pi are algebraic
> numbers. They are not roots to integer polynomials.

You didn't say the *arguments* to cos(x) were or were not irrational or

nonalgebraic, you said all the *expansions* were. You said:

> >> I will maintain that the full binary
> >> expansions of the cosines of ALL non-zero algebraic real numbers
> >> contain child pornography. Prove me wrong.

Note your use of "full binary expansions of the cosines of ALL non-zero
algebraic real numbers." My posted results are (1) the full binary
expansions of the cosines of some non-zero algebraic real numbers, and they
are (2) themselves rational and algebraic. Therefore you are wrong.

> > But it is not true. A ZIP file containing a copyrighted work is
> > an infringement. This has been accepted in the courts for obvious
> > reasons.
>
> Only because unzip software is common.

No, that is not the reason. Any unauthorized dissemination of copyrighted
works is illegal, it doesn't matter what form it takes. It could be
encrypted, it could be in some exotic form, it doesn't matter. Shall I give
you an example? DVDs are encrypted, and it is illegal to copy them.

You are discussing the punishment phase of a trial, not the determination of
a violation, which always judges unauthorized copying to be illegal. The
degree of punishment depends on how much harm was done.

> Software for turning decimal
> numbers into binary is not.

A silly argument, since doing this is trivial, much simpler than unZIPing a
file from first principles. And, now that Java has a standard long integer
class, anyone can obtain the required tools for free, to decode an arbitrary
length string encoded this way. Not that it is anything but an intellectual
curiosity.

If you were to post a copyrighted work
> in decimal, chances are nobody would download and decode it, and thus
> that the copyright owner wouldn't care that you'd posted it.

You just tried to change the subject AGAIN. Whether the copyright owner
cares is not the issue. The issue before us is whether it is illegal to copy
copyrighted works. You clearly don't know how debates work.

> >> I've always refused to munge, to filter, or to run and hide.
> >> I prefer to fight back. Take back the net!
>
> > I have more experience at this than you do.
>
> I doubt this very much. I've been using email for 27 years, I've been
> fighting spam for 16 years, and I host over 10,000 web pages. I've
> often received over 100 spams per day.

You just tried to change the subject AGAIN. I have more experience at this
(fighting spam) than you do. You haven't even visited my anti-spam page.

And -- don't you realize how silly you sound? -- you are an expert at
stopping spam, and the proof is you "often received over 100 spams per day."
Honestly.

> The only reason email is still usable at all is because of those of us
> who fight back. Not because of those who "just hit delete" or who run
> and hide.

No, that is not the reason. The reason is people like me who teach
webmasters how to *code* their e-mail systems to resist the efforts of
spammers (to the degree that this is effective), not people who have a file
of angry replies from spammers. You haven't found out anything about my
anti-spam efforts, you only know that I don't have a public e-mail address,
a very common practice.

Your position on spam is incredibly naive. If you reply to spam with a valid
e-mail address, a logical inference from your stated position, than you are
part of the problem. This contradicts the accepted industry-wide practice,
and is the behavior of a rube.

And you have totally misrepresented yourself. You don't even have a Web site
with Web pages. Your remark "I host over 10,000 web pages" is false. The
document at http://KeithLynch.net isn't a valid Web page, it is a corrupted
file that is neither text nor HTML, as any modestly experienced high-school
page designer would tell you, if you were to ask. All of the remaining pages
on the site are similarly corrupted, amateurish hacks.

As to what is presented in those documents, they speak for themselves. I
recommend that anyone interested in clinical paranoia most definitely visit
this site. Some browsers will not successfully display the documents because
they are corrupted and incompetently created (some Netscape browser versions
will not display them at all) but it is definitely worth a visit if
possible.

--
Paul Lutus
www.arachnoid.com

### Paul Lutus

unread,
May 13, 2001, 2:25:43 PM5/13/01
to
"Bob Harris" <nit...@mindspring.com> wrote in message
news:B7241165.1532F%nit...@mindspring.com...

> Keith F. Lynch recently warned us not to compute pi in binary, because (if
I
> understand the issue) it contains several bitstrings which we are not
> legally allowed to posess.
>
> There is a practical issue here, though. I'll accept that pi contains any
> given bit string (I'm not sure that has been proven, but it doesn't seem
to
> matter).

It's true in principle -- an infinite expansion of Pi by definition must
contain everything ever written. But this is not Lynch's claim -- he
confuses an infinite expansion with a finite one.

But how many bits of pi would I have to calculate (and store on my
> hard drive) before my hard drive would contain any of the forbidden
> bitstrings?
>
> Seems to me that it would be so large that I couldn't store it with
today's
> technology. Am I wrong?

No, of course you are right. The probability that a copyrighted work will
appear in a finite, random series of digits is very slight, and it increases
very slowly as the string of digits increases in length. I seriously doubt
that the briefest copyrighted work is located in the largest current
expansion of Pi (billions of digits). I also seriously doubt that anyone
would be able to identify or extract it.

Even searching for such a match becomes increasingly difficult as the length
of the digit string, and the length of the sought work, increase. In fact,
the general problem of locating any protected work in, say, the digits of
Pi, is much more difficult than computing Pi in the first place.

I took Lynch's position to be a joke at first, but then I visited his Web
site -- KeithLynch.net. A few minute's reading reveals he is actually
serious -- seriously paranoid. Some browsers will not display his pages,
because they are not syntactically correct Web pages, but with any luck you
will have a relatively recent browser that will tolerate his syntax errors.

And I definitely recommend a visit. The guy is certifiable. :)

--
Paul Lutus
www.arachnoid.com

### Keith F. Lynch

unread,
May 13, 2001, 4:12:23 PM5/13/01
to
Paul Lutus <nos...@nosite.com> wrote:
> The word "ALL" and the word "SOME" have different meanings. Look
> this up if you need to, in a book called a "dictionary."

This is getting ridiculous. "SOME trigonometric arguments" does not
contradict "the cosines of ALL non-zero algebraic real numbers".

> You didn't say the *arguments* to cos(x) were or were not irrational
> or nonalgebraic, you said all the *expansions* were.

Wrong.

> I have more experience at this (fighting spam) than you do.

Very unlikely.

> You haven't even visited my anti-spam page.

Wrong again. You're just looking for hits from KeithLynch.net?
That's where I host my web pages, and my reply address. That's not
where I browse from.

> And -- don't you realize how silly you sound? -- you are an expert
> at stopping spam, and the proof is you "often received over 100
> spams per day."

Note the past tense. I don't get that many any more. And not because
I ran away and hid. Because I fought back.

> No, that is not the reason. The reason is people like me who teach
> webmasters how to *code* their e-mail systems to resist the efforts
> of spammers (to the degree that this is effective),

What do webmasters have to do with email? Email is not part of the web.

So, you teach sysadmins to close open relays? Good for you. That's
important. But that alone does little to stop spam even given a 99.9%
success rate. It takes little time for a spammer to scan 1000 relays
to find one open one. For that matter, half of all spammers do
without, and aren't slowed down at all by closed relays.

> Your position on spam is incredibly naive. If you reply to spam with
> a valid e-mail address, a logical inference from your stated position,

True.

> than you are part of the problem.

False. Even though spammers are scum, I believe everyone has the
right to confront their accusers. Some are falsely accused ("Joe
jobs") and need evidence to pursue legal action against whoever is
using their email address in spams. And a few honestly don't know
that anyone is bothered by spam, or why.

> This contradicts the accepted industry-wide practice, and is the
> behavior of a rube.

What practice is that? Name some RFCs.

> And you have totally misrepresented yourself. You don't even have a
> Web site with Web pages.

Wrong.

> Your remark "I host over 10,000 web pages" is false.

Wrong.

> The document at http://KeithLynch.net isn't a valid Web page, it is
> a corrupted file that is neither text nor HTML,

Wrong. Nor is that the only site I host or maintain.

> All of the remaining pages on the site are similarly corrupted,
> amateurish hacks.

You checked ALL of them? In what way are they corrupted? Nobody else
has noticed any problems.

> As to what is presented in those documents, they speak for themselves.

True.

> Some browsers will not successfully display the documents because
> they are corrupted and incompetently created (some Netscape browser

> versions will not display them at all) ...

Which pages and which versions of Netscape? After several million
hits, yours is the first such claim I've received.

> It's true in principle -- an infinite expansion of Pi by definition
> must contain everything ever written.

Actually, this has never been proven. I said "It is conjectured that

this number is normal, meaning that it contains ALL finite bit
strings."

> But this is not Lynch's claim -- he confuses an infinite expansion
> with a finite one.

Wrong.

> I took Lynch's position to be a joke at first,

As did everyone else. As it was intended.

> but then I visited his Web site -- KeithLynch.net. A few minute's
> reading reveals he is actually serious -- seriously paranoid.

Paranoid? I'm not the one with the secret email address. My email
address, phone number, and street address are all public information,
and always have been.

Nor do I think anyone's out to get me, which is the definition of
paranoia.

Nor is there anything on my website that would lead anyone to believe
that my message was not a joke.

> Some browsers will not display his pages,

Wrong.

> because they are not syntactically correct Web pages,

Wrong.

> but with any luck you will have a relatively recent browser that
> will tolerate his syntax errors.

Many of my pages are six or seven years old. I guess it's a good
thing everyone back then was using a "relatively recent browser".

And unlike your pages, none of mine require Javascript or anything
else not shared by all browsers.

> And I definitely recommend a visit. The guy is certifiable. :)

Wrong. I'm familiar with DSM-IV (I have to be for my line of work),
and I don't qualify under any of the categories.

Maybe they should add a category for people who waste time responding
to idiots and trolls on the net. I'd qualify for that, as I just
proved. But since I haven't received any spams since 9 am this
morning (despite my several email addresses having appeared in tens of
thousands of postings, and on thousands of web pages), I have plenty
of time on this lazy Sunday afternoon to taunt mere trolls.

### Paul Lutus

unread,
May 13, 2001, 5:08:44 PM5/13/01
to
"Keith F. Lynch" <k...@KeithLynch.net> wrote in message
news:9dmpr7\$gt5\$1...@saltmine.radix.net...

> Paul Lutus <nos...@nosite.com> wrote:
> > The word "ALL" and the word "SOME" have different meanings. Look
> > this up if you need to, in a book called a "dictionary."
>
> This is getting ridiculous. "SOME trigonometric arguments" does not
> contradict "the cosines of ALL non-zero algebraic real numbers".
>
> > You didn't say the *arguments* to cos(x) were or were not irrational
> > or nonalgebraic, you said all the *expansions* were.
>
> Wrong.

I quoted you directly, word for word, in the part of my message that you
snipped. You are now lying.

> > No, that is not the reason. The reason is people like me who teach
> > webmasters how to *code* their e-mail systems to resist the efforts
> > of spammers (to the degree that this is effective),
>
> What do webmasters have to do with email? Email is not part of the web.

This is yet another effort to change the subject, to cover up your abysmally
poor accuracy record. E-mail is a crucial, integral part of a modern Web
site, and real webmasters know this.

> > And you have totally misrepresented yourself. You don't even have a
> > Web site with Web pages.
>
> Wrong.

I proved the truth of my statement. You must now either post evidence, or
retract the lie you have just posted. Your documents are not syntactically
correct Web pages, and because of their errors, they crash some versions of
some browsers. You have posted zero Web pages, and some documents.

> > Your remark "I host over 10,000 web pages" is false.
>
> Wrong.

Post evidence, not lies. The above is a lie.

> > It's true in principle -- an infinite expansion of Pi by definition
> > must contain everything ever written.
>
> Actually, this has never been proven.

A separate claim, one I haven't made, and the fourth (or is it the fifth)
time you have tried to change the subject.

> > Some browsers will not display his pages,
>
> Wrong.

Prove it. I posted a proven statement.

>
> > because they are not syntactically correct Web pages,
>
> Wrong.

Prove it. I posted a proven statement. None of your pages contain
syntactically correct HTML. Any beginner in HTML coding can see that in a
flash.

> > And I definitely recommend a visit. The guy is certifiable. :)
>
> Wrong. I'm familiar with DSM-IV (I have to be for my line of work),
> and I don't qualify under any of the categories.

Well, off our topic, but now that the current DSM attempts to define the
inability to spell common words as evidence of mental illness (to nearly
universal ridicule), any effort to use the current DSM as an authority on,
or rational guide to, diagnosis is extremely ill-advised.

To say it another way, because of the irrational, monomaniacal efforts of
the writers of the DSM to cast their diagnostic net over a wider and wider
area, they have succeeded in making anyone certifiable (by their own
standards), which was clearly the original goal. So my remark is correct --
you are certifiable. I originally meant something else, but this is also
true.

> Maybe they should add a category for people who waste time responding
> to idiots and trolls on the net.

Interesting self-description.

Every statement you offered an opinion on in this thread has been false. No
exceptions. And you seem unable to recognize the role of evidence. You think
saying "wrong" is sufficient to dismiss a claim accompanied by concrete
evidence.

--
Paul Lutus
www.arachnoid.com

### Keith F. Lynch

unread,
May 13, 2001, 5:25:37 PM5/13/01
to
Paul Lutus <nos...@nosite.com> wrote:
> To say it another way, because of the irrational, monomaniacal
> efforts of the writers of the DSM to cast their diagnostic net
> over a wider and wider area, they have succeeded in making anyone
> certifiable (by their own standards),

Wrong.

> which was clearly the original goal.

Wrong.

> Every statement you offered an opinion on in this thread has been
> false. No exceptions. And you seem unable to recognize the role of
> evidence. You think saying "wrong" is sufficient to dismiss a claim
> accompanied by concrete evidence.

Wrong.

Among much else, you asserted that some unspecified subset of my
thousands of web pages have crashed some unspecified version of
Netscape. How am I supposed to disprove that?

You also asserted that "all" of my web pages are syntatically
incorrect, but you haven't named a single syntax error in a single
page. Nor have you viewed all my pages, so you're obviously lying.

You also asserted that my CCing my spam reports to the spammer,
using a real email address "contradicts the accepted industry-wide
practice," but failed to provide pointers to RFCs or other standards.
How am I supposed to disprove the claim that I violated some
unspecified standard? How else can respond except to say "prove
it" or "wrong"?

You falsely asserted that I had not visited your anti-spam pages.
How am I supposed to disprove that? Will there be a quiz?

You made assertions about what I did and didn't post earlier in this
thread. I don't need to say anything except "wrong," as those
messages speak for themselves.

I'm sure everyone's bored by this thread, and is perfectly capable of
reading the previous articles to see which one of us is lying. In the
unlikely case that anyone cares.

What set you off, anyway? Or are you always like this?

### Paul Lutus

unread,
May 13, 2001, 6:16:07 PM5/13/01
to
"Keith F. Lynch" <k...@KeithLynch.net> wrote in message
news:9dmu4h\$n86\$1...@saltmine.radix.net...

> Paul Lutus <nos...@nosite.com> wrote:
> > To say it another way, because of the irrational, monomaniacal
> > efforts of the writers of the DSM to cast their diagnostic net
> > over a wider and wider area, they have succeeded in making anyone
> > certifiable (by their own standards),
>
> Wrong.

Start posting evidence or shut the fuck up, you troll. Every one of your
assertions is false.

> You also asserted that "all" of my web pages are syntatically
> incorrect, but you haven't named a single syntax error in a single
> page.

They're your pages. None of them meet the minimum standards of a
syntactically correct HTML page. I am not going to educate you. Compare your
Web pages to any other Web pages anywhere. Notice what's missing?

> You also asserted that my CCing my spam reports to the spammer,
> using a real email address "contradicts the accepted industry-wide
> practice,"

This is a lie. You made up this lie and posted it in full appreciation of
the fact that it is a lie. I NEVER SAID ANY SUCH THING, JACKASS.

> but failed to provide pointers to RFCs or other standards.

Either point out a contradiction or don't bother posting. I said it was the
industry standard, which is true. You said there is no RFC, which is true
and irrelevant.

> You falsely asserted that I had not visited your anti-spam pages.
> How am I supposed to disprove that?

But you already proved it, making the disproof doubly difficult.

> You made assertions about what I did and didn't post earlier in this
> thread. I don't need to say anything except "wrong," as those
> messages speak for themselves.

As a matter of fact, you lied about what you said. The I posted what you did
in fact say and directly compared it to your lie, proving that you lied.
Then you lied about that.

> I'm sure everyone's bored by this thread, and is perfectly capable of
> reading the previous articles to see which one of us is lying.

Yep. What is surprising is that your credibility and reality testing are so
poor than you cannot tell that you are lying, and that that fact is
accessible to anyone.

> What set you off, anyway? Or are you always like this?

Oh, I always "get this way" when confronted by ignorant, psychotic liars.

--
Paul Lutus
www.arachnoid.com

### BlackShift

unread,
May 17, 2001, 9:40:51 PM5/17/01
to
On Sun, 13 May 2001 11:25:43 -0700, "Paul Lutus" <nos...@nosite.com>
wrotf:

>"Bob Harris" <nit...@mindspring.com> wrote in message
>news:B7241165.1532F%nit...@mindspring.com...
>>

>> There is a practical issue here, though. I'll accept that pi contains any
>> given bit string (I'm not sure that has been proven, but it doesn't seem
>to
>> matter).
>
>It's true in principle -- an infinite expansion of Pi by definition must
>contain everything ever written.

why is that?
for al I know it is very well possible that in the decimal expansion
of Pi there isn't any 8 in it after about 100trilion digits. It is
very very unlikely, but why would it be impossible?
groetjes,
BlackShift

### Paul Lutus

unread,
May 17, 2001, 11:24:02 PM5/17/01
to
"BlackShift" <hu...@doemaarwat.nl> wrote in message
news:3b047cd4...@news.rug.nl...

The poster to whom you responded said:

> >It's true in principle -- an infinite expansion of Pi by definition must
> >contain everything ever written.

Note the words "true in principle." That principle includes validation of
something that cannot be validated - proof that Pi is infinitely random.

So you are objecting to something that was not asserted. He never said his
assertion was true, proven, beyond refutation. He said "in principle."

And it's true -- in principle. *If* Pi really was infinite and infinitely
random, everything imaginable would be found in it.

--
Paul Lutus
www.arachnoid.com

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