Randomness of digits within pi
jonas.t...@hotmail.com
occurences of my personalnumber within PI i noticed that 333333 and
especially 666666 do not seem to occur as frequent as
111111,222222,444444,555555,777777,888888,999999 or XXXXXX (without
testing all ;)
Is this just a fluke result of to small sample size at the page, could
anyone verify searching in the big file with a program?
If that really the case that 333333 andd 666666 is a lot less frequent
what is the mathematical reason?
J
jank...@hotmail.com
If there are 4 million digits, that's a sample size that is far too
small to say anything about the frequency of 111111 and the others.
Each of them should only turn up once in one million digits on
average.
---
J K Haugland
http://home.no.net/zamunda
jonas.t...@hotmail.com
Yes i thought the downloadable sample file was bigger but i can see it
is same size now.
But what is known about the distribution of larger digits
(numberstrings?) within pi, is it really randomed distributed?
So i try again is six digit numbers randomly distributed within pi, if
not why?
J
David C. Ullrich
Nobody knows.
Of course the digits of pi cannot possibly be actually _random_.
What you're asking about is whether pi is a "normal" number -
does each finite string of digits occur with the "right"
frequency? People suspect that the answer is yes, but this
is not proven.
>So i try again is six digit numbers randomly distributed within pi, if
>not why?
>
>J
************************
David C. Ullrich
jonas.t...@hotmail.com
>
> - Visa citerad text -
A very interesting fact?
Lucky number 7 of "7777777" turns up two times in a sample of 4
million digits of pi
While 6 of 666666 only turns up two times in a sample of 4 million
digits of pi
Maybe the page do not calculate the real pi? Otherwise i can see
historical reason for 7 to be considered as a lucky number and 6 as
disaster.
J
George Marsaglia
<jonas.t...@hotmail.com> wrote in message
news:1194606172.5...@z9g2000hsf.googlegroups.com...
The pdf article
interstat.statjournals.net/YEAR/2005/articles/0510005.pdf
describes results from a number of tests on the randomness
of the digits of pi, as well as e, sqrt(2) and the decimal
expansions of various rationals.
A related article,
interstat.statjournals.net/YEAR/2006/articles/0601001.pdf
refutes claims from Physicists at Purdue that the digits
of pi are not as random as those from other sources.
George Marsaglia
jonas.t...@hotmail.com
Ooops that would be *ONE* time
>
> Maybe the page do not calculate the real pi? Otherwise i can see
> historical reason for 7 to be considered as a lucky number and 6 as
> disaster.
>
hagman
Little is known, since decimal digits are not really a
very natural property of a number.
You may want to read
http://en.wikipedia.org/wiki/Normal_number
hagman
jonas.t...@hotmail.com
> <jonas.thornv...@hotmail.com> wrote in message
>
> - Visa citerad text -
Maybe but for sure it is an interesting fact that two strings of
"7777777" turns up in just a sample of 4 million and that "666666"
only occur one time in 4 million digits.
Of course it does not say anything about the big picture, but i can
see while people studying pi historical did find 7 to be a lucky
number and 6 not that lucky.
J
Richard Tobin
<jonas.t...@hotmail.com> wrote:
>Lucky number 7 of "7777777" turns up two times in a sample of 4
>million digits of pi
>While 6 of 666666 only turns up two times in a sample of 4 million
>digits of pi
>Maybe the page do not calculate the real pi? Otherwise i can see
>historical reason for 7 to be considered as a lucky number and 6 as
>disaster.
Since pi was first calculated to 2000 places in 1949, a reason involving
4 million digits of it can't be *very* historical.
-- Richard
--
"Consideration shall be given to the need for as many as 32 characters
in some alphabets" - X3.4, 1963.
jonas.t...@hotmail.com
>
> - Visa citerad text -
Well in any number base the digits should anyway be normally
distributed for a random picked number of "VALUES" of the expanding
string of decimals if the number should be claimed to have a random
distribution.
So why do you say decimal digit strings is not a natural property of a
number. If i use a base converter and convert a random expanding
function i would assume that the represented digits will have a normal
distribution for any composition of digits within the string with
respect to size, but maybe i am wrong?
J
jonas.t...@hotmail.com
> In article <1194608964.453391.42...@50g2000hsm.googlegroups.com>,
>
> <jonas.thornv...@hotmail.com> wrote:
> >Lucky number 7 of "7777777" turns up two times in a sample of 4
> >million digits of pi
> >While 6 of 666666 only turns up two times in a sample of 4 million
> >digits of pi
> >Maybe the page do not calculate the real pi? Otherwise i can see
> >historical reason for 7 to be considered as a lucky number and 6 as
> >disaster.
>
> Since pi was first calculated to 2000 places in 1949, a reason involving
> 4 million digits of it can't be *very* historical.
And then again maybe we underestimate the math and calculation power
of earlier civilizations.
I guess the would find both pi and the circle rather intruiging, and
spend alot of time decipher any knowledge that could be learnt from
it.
J
hagman
The influence of the base makes the decimal (or other) expansion
somewhat arbitrary; I'm not deniying that there *are* properties
of numbers that are reflected in the digit expansions (e.g.
rational <-> eventually periodic, but even the langth of that
period depends on the base).
This also explains why proving that a specific *useful*
(and far from random) number like pi is normal turns out
to be difficult, whereas any number easily proved to be normal
(like 0.12345678910111213...) is far from useful in usual contexts.
As you will have read by now, with the current state of knowlede
it may still betrue that the digit 7 occurs only finitely
often in the expansion of pi.
> If i use a base converter
You mean a piece of software?
> and convert a random expanding
> function
and therefore here a (pseudo) random number generator in a computer
system?
> i would assume that the represented digits will have a normal
> distribution for any composition of digits within the string with
> respect to size, but maybe i am wrong?
If I guessed correct above, then the short answwer is yes.
Even the Mersenne Twister is periodic, hence sufficiently long
bit sequence patterns will never occur (although small patterns
all appear with the same frequency -- which is of course
again far from random in the long run).
>
> J
jonas.t...@hotmail.com
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>
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Thanks for your reply, i think you interpretated me right. But i still
find it odd that 2 occurences of the string "7777777" occurs so early
and so few occurences of "666666".
Do any of you have a database with digits of pi and can calculate the
number of occurences of "666666" and "7777777" up to 100 million
digits note that there are 7 of 7 and 6 of 6.
Best regards J
jonas.t...@hotmail.com
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>
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How many strings of "7777777" in 100 million digits of pi would be
considered freaky lucky or pointing to the possibility that strings of
7 digits are not uniformly distributed within pi.
J
G.E. Ivey
> >
> > - Visa citerad text -
>
> Maybe but for sure it is an interesting fact that two
> strings of
> "7777777" turns up in just a sample of 4 million and
> that "666666"
> only occur one time in 4 million digits.
No, it's not at all interesting! As Jan Kristian Haugland told you in the very first response to you post "Each of them should only turn up once in one million digits on average." So might expect only 4 occurrances of ANY 6 digit number in 4 million digits. Occuring one or two times when the expected value is only 4 is not interesting at all.
> J
>
jonas.t...@hotmail.com
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Ok when i come to think of it maybe the digit patterns have a wave
like structure like big waves and and small waves. And somewhere in
this pi digit expansion pattern a gigant a real monster wave of 6 is
building i guess the probability of any number of connecting 6's in an
infinit expansion serie must be one, so what is the longest streak of
sixes and sevens in the known expansion of pi?
Yes this is just rambling i know, but i want to know anyhow about the
distribution of large 6 and 7 digit numbers in pi.
J
jonas.t...@hotmail.com
>
> > > - Visa citerad text -
>
> > Maybe but for sure it is an interesting fact that two
> > strings of
> > "7777777" turns up in just a sample of 4 million and
> > that "666666"
> > only occur one time in 4 million digits.
>
> No, it's not at all interesting! As Jan Kristian Haugland told you in the very first response to you post "Each of them should only turn up once in one million digits on average." So might expect only 4 occurrances of ANY 6 digit number in 4 million digits. Occuring one or two times when the expected value is only 4 is not interesting at all.
>
>
>
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But 7777777 occured two time in 4 million digits that is a little
better 1/2000 or am i wrong?
J
jonas.t...@hotmail.com
>
> > > - Visa citerad text -
>
> > Maybe but for sure it is an interesting fact that two
> > strings of
> > "7777777" turns up in just a sample of 4 million and
> > that "666666"
> > only occur one time in 4 million digits.
>
> No, it's not at all interesting! As Jan Kristian Haugland told you in the very first response to you post "Each of them should only >turn up once in one million digits on average." So might expect only 4 occurrances of ANY 6 digit number in 4 million >digits. Occuring one or two times when the expected value is only 4 is not interesting at all.
So it is just a fluke for 7 billion number "7777777" to turn up 2 two
times in the first 4 million of digits?
Could you be so kind to direct me to a file with the decimal expansion
of pi it would be nice with at least 100 million digits, that would be
a file of 800 MB and i am sure many of us have the space.
So we can research the properties of pi on our own, i do not know if
the there still is a 4GB file size limit for files in Windows, but 400
million digits would be nice if anyone have.
Of course if there is a fast algorithm to generate the first 400
million numbers even better, i do not have any compiler installed so a
executional file would be nice.
J
>
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>
> - Visa citerad text -- Dölj citerad text -
Daniel Grubb
>Could you be so kind to direct me to a file with the decimal expansion
>of pi it would be nice with at least 100 million digits, that would be
>a file of 800 MB and i am sure many of us have the space.
>So we can research the properties of pi on our own, i do not know if
>the there still is a 4GB file size limit for files in Windows, but 400
>million digits would be nice if anyone have.
>
>Of course if there is a fast algorithm to generate the first 400
>million numbers even better, i do not have any compiler installed so a
>executional file would be nice.
Here's a program that can calculate pi to 33 million places fairly quickly
on most modern machines.
jonas.t...@hotmail.com
Ok i admit i am being lazy anyone who can distribute it as file on
bittorent?
Someone must have run the program and burned it down?
Best regards Jonas
David Bernier
>> Here's a program that can calculate pi to 33 million places fairly quickly
>> on most modern machines.
>>
>> http://www.geocities.com/hjsmithh/Pi/Super_Pi.html
>
> Ok i admit i am being lazy anyone who can distribute it as file on
> bittorent?
> Someone must have run the program and burned it down?
You might want to send an e-mail to Xavier Gourdon, the author
of the program Pifast ...
I used Xavier Gourdon's PiFast43.exe program to compute
pi to 1 billion decimals. It took about 12 to 25 hours on a PC
with an Athlon XP 2200 32-bit processor and 1 GB of RAM.
The resulting file, at 1.28 GB, can be opened with Notepad
to see the first 50 or 100 lines or so, but it is so large that
it takes minutes to go down 2 pages.
I believe it would it would be easy to access the file
using C or C++ with fopen(), fscanf(), fclose().
I seem to remember that the file has line numbers,
line feeds/CR (the Windows CR+LF line breaks) and
some information about the start and finish of the
computation at the beginning of the file.
Cf.:
< http://numbers.computation.free.fr/Constants/PiProgram/pifast.html >
David Bernier
jonas.t...@hotmail.com
Forget it all i had a mental breakdown thinking that 7 millions was 7
billions.
lol
I am sure now they are uniformly distributed
J
Dave L. Renfro
> You may want to read
> http://en.wikipedia.org/wiki/Normal_number
"While a general proof can be given that "almost all"
numbers are normal, this proof is not constructive ..."
If anyone here edits these pages, you might want
to revisit this statement. First of all, "this proof"
seems inappropriate to me, since no specific
proof had been singled out prior to this. Second,
I strongly doubt the standard proof that one can find
in Niven's "Irrational Numbers" is not constructive,
or at least can't easily be reworded so that it is.
In fact, the result itself is due to Borel, who
had very strong constructivists leanings.
Dave L. Renfro
porky_...@my-deja.com
even if the frequence of occurence is the same for each number, there
always will be unpredictable but 'interesting' patterns, no matter
which sample size you take. To speculate that there is a special
meaning in '7777777' or '3333333' or '666666' because it appears more
or less frequently than other pattern is akin to numerology.
jonas.t...@hotmail.com
wrote:
No actually it is not akin to numerology if it was a random number or
a fluke occurence it would be, but if actually there was a anomaly of
uniform distributiion in pi with the actual numbers of "666666" and
"7777777" it would tell us that our ancestors new more about pi then
we had an idea about.
J
Marshall
To make your argument slightly less ridiculous it would need to be
the case that our ancestors thought 7777777 was a lucky number.
Marshall
jonas.t...@hotmail.com
>
> - Visa citerad text -
Yes they probably did think that such a number 7 of 7 would be a good
omen, and i am sure they beleived 6 of 6 to be a bad omen.
Even if the numbers were a bit to big to look for in their ordinary
lifes, but if you scale it down to 777 and 666 they still today have
significance to people of many religions and beleifs.
jonas.t...@hotmail.com
>
> - Visa citerad text -
Can you really be so sure that the importance that some religions
attach to 666, 777, 666666 and 7777777 did not steem from some
mathematical insight?
Do you know for sure how beleif systems or religions emerge or what
type of events that make them popup.
J
Marshall
I know that they can't arise from information that wasn't available.
Such as, say, the digits of pi beyond the first handful.
http://en.wikipedia.org/wiki/Chronology_of_computation_of_%CF%80
Marshall
jonas.t...@hotmail.com
Of course you are right noone could ever anywhere have had computation
power like ours and i see you even have the chronology of computation
to support your far reachin conclusion, i mean look at our computers
how fast they are in only 50 years of development that my friend must
be a signifikant timespan in both the universal and planetar frame.
No you are quite right they can not have been available because you
have the chronology of computation right?
J
matt271...@yahoo.co.uk
> When i was playing around at "http://zenwerx.com/pi.phplooking" for
> occurences of my personalnumber within PI i noticed that 333333 and
> especially 666666 do not seem to occur as frequent as
> 111111,222222,444444,555555,777777,888888,999999 or XXXXXX (without
> testing all ;)
>
> Is this just a fluke result of to small sample size at the page, could
> anyone verify searching in the big file with a program?
>
> If that really the case that 333333 andd 666666 is a lot less frequent
> what is the mathematical reason?
Someone may have already mentioned this, but another thing you need to
be cautious of is fishing around in random sequences for anything that
"looks unusual", rather than deciding beforehand what you're looking
for. The more patterns there are that strike you as "unusual" once you
find them, the more likely it is that you'll find one of them, even
though individually they may be unlikely.
mensa...@aol.com
I think it's safe to say that religious significance came
from the math, not the other way around.
How many people do you know who've summoned the Devil using
pentagrams and 666?
>
> Do you know for sure how beleif systems or religions emerge or what
> type of events that make them popup.
People are in awe of what they can't understand.
>
> J
jonas.t...@hotmail.com
>
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>
> - Visa citerad text -
Well i do think the 333333 666666 and 7777777 are uniformly
distributed now in the 4 million first decimal digits of pi, although
i initially did think that 1 of 666666 and 7 of 777777 did stick out
as odd and even more after noticing that 2 of them actually had a
reoccurence of seven of seven "7777777" however i do not have any
larger samplematerial of pi to investigate it further.
But probably it will even out.
J
jonas.t...@hotmail.com
Yes i also think that math can have been a great influence in the
start of many religions, because it numbers and math is intruiging and
surely have useful insights in any creation process. And of this i am
sure the early religious people were a where putting importance to
numbers were aware.
I guess noone really now where the properties of numbers come from
because it is not fully explored.
J
>
>
>
> > J- Dölj citerad text -
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> - Visa citerad text -- Dölj citerad text -
G. Frege
>
> distributed now in the 4 million first decimal digits of pi [...]
> however i do not have any larger samplematerial of pi to investigate
> it further.
>
Check:
http://www.angio.net/pi/piquery
or
50 Million Digits of Pi:
http://oldweb.cecm.sfu.ca/projects/ISC/data/pi.html
or
(at least) 200 Million Digits from here:
ftp://pi.super-computing.org/
check directory ".1"
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We have successfully obtained 4,294,960,000 decimal digits of
pi and 1/pi by 28st Aug. 15:09 JST 1995.
In our ftp server, 200,000,000 digits of both pi and 1/pi are
opened to all (anonymous users) and 4,200,000,000 digits of pi
and 1/pi are opened to guest (registered) users. If you want
to get 4,200,000,000 digits of pi or 1/pi,
1) Please email to the following address with the subject of
'PI registration'. Since the emails are processed automatically,
please do not inlcude your message in the mail body.
^^^
Email: req...@ww.cc.u-tokyo.ac.jp
2) We will send you the registration form via email. If you
agree with the contents, write in the following data in the
form, and send us the form via fax.
^^^
- your name and pronounciation
- affiliation
- address
- telphone number
- fax number
- email address
- purpse and comment
- signature
3) We will send you the temporary guest id and the password for it,
via email. The password for the guest ID will be changed in 1 month.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
F.
--
E-mail: info<at>simple-line<dot>de
Marshall
Right. Now you've got it.
Marshall
David Bernier
I wrote a program in C to read the 1.28 GB file, so as to ignore all
characters that are spaces, line feeds,
carriage returns, whitespace, text, "3." and the line numbers (each line
had 50 digits).
Up to 800 million decimals after the point, I got a distribution of:
0s: 79991897
1s: 79997003
2s: 80003316
3s: 79989651
4s: 80016073
5s: 79996120
6s: 80004148
7s: 79995109
8s: 80002933
9s: 80003750
This agrees with Yasumasa Kanada's data here:
< ftp://pi.super-computing.org/pub/pi/pi.all.freq.3b >
At 1000 million decimals, my counts were off by about 0 to 10.
Comparing with "Billion Digit Pi" at:
< http://web.ukonline.co.uk/home52365/pi.htm > ,
out of the last 300 digits, roughly the first 220 to 225 agree (when
asking for last 1000 of the billion digits).
So it seems likely the first 999,999,900 decimals in my file are right.
I went looking for MD5 hash values and didn't have much success. By
writing the first
1 million decimals to a file (and no other characters), I get an MD5 hash of
e668904c195521a2a2dfef948ac54c8e .
"The Starman" gets an MD5 hash of e668904c195521a2a2dfef948ac54c8e for
the same file (or file description ... ) here:
< http://www.geocities.com/tsrmath/pi/picalcs.htm#PMD5 > .
Quite interesting is his "PI Error at UCLA" page:
< http://www.geocities.com/tsrmath/pi/UCLApiError.html >
David Bernier
jonas.t...@hotmail.com
> David Bernier wrote:
But i hope you people *of any should understand* that counting
standalone decimal digits will tell you nothing about any pattern in
the string?
It only tell you that each standalone decimal digit is uniform
distributed, and that really say nothing.
I know about diehard, and statistic tests, but if you really looking
for pinning down an anomaly to show that a expanding function do not
output uniform distribution of output you should look for anomalies of
longer digit lengths i understand that only around 350 billions or was
it 3,5 billions values of pi is known.
I would pick a value of say one 100 000 to 10 millions to look for in
the data and try to find anomalies, because if you find an anomaly of
that size it would certainly say something about the function itself.
So why can't you make a search for 111111,222222,... to 999999 and
1111111,2222222,7777777... to 9999999 if you already programmed a
short snippet.
I do not remember much about standard deviation and how large that
would be normal in using a number of size xxxxxx or xxxxxxx within 1,2
billion.
Maybe someone could inform me what would be considered normal standard
deviation and how many of size xxxxxx and xxxxxxx one would presume to
find within 1,2 billion, i do not have the formula.
But i would guess 1200 and 120 of xxxxxx sized number and xxxxxxx
sized?
> At 1000 million decimals, my counts were off by about 0 to 10.
>
> Comparing with "Billion Digit Pi" at:
> <http://web.ukonline.co.uk/home52365/pi.htm> ,
> out of the last 300 digits, roughly the first 220 to 225 agree (when
> asking for last 1000 of the billion digits).
>
> So it seems likely the first 999,999,900 decimals in my file are right.
>
> I went looking for MD5 hash values and didn't have much success. By
> writing the first
> 1 million decimals to a file (and no other characters), I get an MD5 hash of
> e668904c195521a2a2dfef948ac54c8e .
>
> "The Starman" gets an MD5 hash of e668904c195521a2a2dfef948ac54c8e for
> the same file (or file description ... ) here:
> <http://www.geocities.com/tsrmath/pi/picalcs.htm#PMD5> .
>
> Quite interesting is his "PI Error at UCLA" page:
> <http://www.geocities.com/tsrmath/pi/UCLApiError.html>
>
> David Bernier- Dölj citerad text -
jonas.t...@hotmail.com
>
> - Visa citerad text -- Dölj citerad text -
>
> - Visa citerad text -
And i think there is a good reason to look for repeating patterns of
same digit
mensa...@aol.com
> same digit
What reason?
Marshall
wrote:
"If it feels good do it."
Marshall
jonas.t...@hotmail.com
>
> - Visa citerad text -
I guess one could see a number like 33333333333333333333333333333333
as a repeating fractal of divisors where each slice share the same
proportion to the former slice. They are for sure all as probable of
any number of size xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx but if there is
anomalies in the distribution i suspect it would be more probable to
find a repeating number of for example 3333333333333333333333333333
than a more normaly distributed digit number "of that size".
J
David Bernier
Well, the frequency of each digit should not stray too far from 10%.
I wanted to know if my 800 million decimals were right. That's
the real reason I counted the number of 0s, 1s, .... 9s in my file
and compared that with Kanada's results.
> It only tell you that each standalone decimal digit is uniform
> distributed, and that really say nothing.
> I know about diehard, and statistic tests, but if you really looking
> for pinning down an anomaly to show that a expanding function do not
> output uniform distribution of output you should look for anomalies of
> longer digit lengths i understand that only around 350 billions or was
> it 3,5 billions values of pi is known.
I think Kanada and his collaborators have passed the 10^12 decimal
digit mark.
Actually, the Diehard battery (for base 10) has "runs tests" where
digits are grouped in threes to represent a number from 0.000 to
0.999 . The base 10 version of the runs tests (and other tests) was
done for
10^9 decimals of pi and the results reported in George Marsaglia's
article which he mentioned in this thread :
< http://interstat.statjournals.net/YEAR/2005/articles/0510005.pdf >
So you propose a repeated digits test. It could be done.
But the first 10^9 decimals of pi didn't produce really suspicious results,
from looking at Marsaglia's article.
> I would pick a value of say one 100 000 to 10 millions to look for in
> the data and try to find anomalies, because if you find an anomaly of
> that size it would certainly say something about the function itself.
>
> So why can't you make a search for 111111,222222,... to 999999 and
> 1111111,2222222,7777777... to 9999999 if you already programmed a
> short snippet.
I think Marsaglia's "Monkey tests" are at least as good. But the first
billion digits of pi passed the "Monkey tests".
I have no ideas for new tests. I compressed a one million-byte
file with the first million decimals, and it was 0.2% larger than
the critical value of 1000000* log(10)/log(256) = 415,241.01 bytes.
David Bernier
Major Quaternion Dirt Quantum
in tables of logarithms e.g.?
fractions & powers of pi, gamma of pi etc. must also have this
"nornmal" property;
really, why should they *not* have it, and be abnormal?
> >> Up to 800 million decimals after the point, I got a distribution of:
> >> 0s: 79991897
> >> 1s: 79997003
> >> 2s: 80003316
> >> 3s: 79989651
> >> 4s: 80016073
> >> 5s: 79996120
> >> 6s: 80004148
> >> 7s: 79995109
> >> 8s: 80002933
> >> 9s: 80003750
> I think Marsaglia's "Monkey tests" are at least as good. But the first
> billion digits of pi passed the "Monkey tests".
>
> I have no ideas for new tests. I compressed a one million-byte
> file with the first million decimals, and it was 0.2% larger than
> the critical value of 1000000* log(10)/log(256) = 415,241.01 bytes.
thus:
if you cannot get Shakespeare, you don't get English,
yet. all of my sentences parse grammatically, syntactically,
logically & even spellingly, in spite of your pro-hominem.
Dick Cheeny is in charge of the Darfur policy,
which would be the 3rd British invasion of "the" Sudan
(that is the calling-card of all ivyleague-ed Sudanese folks, but
maybe also a common Sudanese usage).
>Is this English? I recognize most of the words... but
>at the sentence level it all comes crashing down.
> A word about your hearsay about Her Upness, below,
> from another forum. Also, if you really want to know,
> what the Harry Potter PSs and the Tory and Labor media have
> misstated for decades, you can look 'er "up"
> in Burke's Peerage. That's an annual book. Very expensive!
>
> I mean, who do you think got us into Iraq, both times?...
> Hey, George; let's you and Saddam fight!
> thus:
> that's Princeton for you-all, and the Ivy League *ad vomitorium*.
>
> anyway, I generally include mathematical stuff
> of interest, such as my challenge to B*z*
> to actually prove the pythagorean theorem -- and
> I want every one of you to do it for *both* forms
> of the spatial PT; so, there.
>
> if you don't, woe ... and Whoah --
> no navigational duties for you, tonight!
thus:
I wonder if there's really any thing of significance in it,
that is not "horseshit is a *perfect* example
of omni-intertransformabilites," which is perfectly true.
>http://buckminster.info/Biblio/About/About-BkTOC-SynergeticsDictionary,vol4.htm
>(BTW, vol 4 has an excellent article about Synergetics by William Morrell.)
--The Lyyn Cheeny Factor: 25 Hours til the campus jihad!
http://larouchepub.com/pr/2007/071107impeach_momentum.html
http://www.9-11commission.gov/hearings/hearing12/leidig_statement.pdf
(more circumstantial BS; sorry, but they didn't have a link
to the "rest of the story")
>thus:
>"pancake collapse" and all other putative muzlim fiziks is immaterial;
>everyone saw the massive impact & explosion,
>unlike any prior trashfire in a tall building, or
>the say-so of one contractor that it could withstand several such attacks.
>
>look; the plane was almost as wide as the building.
>
>unfirtunately, there was virtually no asbestos cladding
>on the main beams, because of teh asbestos hoax being launched,
>just after the start of construction. such refractant
>might have kept the steel from getting weak enough to collapse
>(it did not have to "melt," as stated
>vy the MIT welder's analysis).
>
>thus:
>perhaps, the ordinary aircraft black box,
>is just a 4-gimbalthingy plus a harddisk.
--I don't Yahoo(tm)s!... welcome to the googolplex;
youcanlogoutanytimeyoulikebut, Sir Rupert has your face in his space.
matt271...@yahoo.co.uk
<Qnc...@netscape.net> wrote:
> what's that "law" about the occurence of more 1s than 9s (and so on)
> in tables of logarithms e.g.?
>
> fractions & powers of pi, gamma of pi etc. must also have this
> "nornmal" property;
Yeah -- if I'm thinking of the same thing -- what *is* that theory
about tables of "random" numbers generated from apparently adequate
pseudo-random sources actually being systematically biased towards
certain numbers? I remember reading about it once and, as I recall,
failing to understand it. Is it something to do with the first digits
of numbers? That rings a faint bell.
No joy with Google ... could anyone explain or give a reference?
mensa...@aol.com
>
> > - Visa citerad text -
>
> I guess one could see a number like 33333333333333333333333333333333
> as a repeating fractal of divisors where each slice share the same
> proportion to the former slice. They are for sure all as probable of
> any number of size xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx but if there is
> anomalies in the distribution i suspect it would be more probable to
> find a repeating number of for example 3333333333333333333333333333
> than a more normaly distributed digit number "of that size".
But there is no reason for any such theoretical abnormality
to involve such patterns of digits. You still haven't given
a reason for that particular abnormality to be present.
Many of the abnormalities tested for by Diehard won't be
easily recognized by observation.
>
> J- Hide quoted text -
>
> - Show quoted text -
Major Quaternion Dirt Quantum
> pseudo-random sources actually being systematically biased towards
> certain numbers? I remember reading about it once and, as I recall,
thus:
let's see; how about,
"every second-power (or 'skware' number) is of the form,
2m + n, where n must be between one and 2m-1 (so as
to satisfy the trilateral inequality)" ??
fascinating, doctor Benjamin Spock!
so, you can do it in the form of a list,
with n running through the naturals -- and
in how many ways can you do it for each skware?
maybe, you could produce a tighter factoid out of this 1^2 = 1*2 = 1+2
= 3 "relation;"
seems to be transcendentally transitive.
thus:
I reapeat: computerized simulacra of all parties are immaterial;
there is no "uncontrolled demilotion" of similar magnitude
with which to compare, and the comparison with actual demos is,
"orders of magnitude" with precision placement of **** (globs
thereof). thermate/thermite/thermote/thermute, your ***!
I'd have liked a link to the rest of the Congressional testimony
in the bottom URL, but nothing is more common in the military,
than delegation of one's authority -- it's a requirement,
called "training."
monsieur Griffin should go back & rate these anomalies,
in order of importance, if not of foolishness.
matt271...@yahoo.co.uk
<Qnc...@netscape.net> wrote:
> Benton's law?
I think you may be right, but surprisingly Google gives only one
relevant hit for "Benton's law" -- a review from the Church Times that
says:
"Simon Singh's series on numbers - this time called A Further Five
Numbers (Radio 4, Tuesday) - is back, packed full of handy tips. In
the first programme, we heard about Benton's Law, which enables
accountants to spot fraudulent expense claims. The law states that in
any set of naturally occurring numbers - be they the populations of
countries, the lengths of rivers, or the cost of 100 business lunches
- there will be a higher proportion of figures beginning with the
number one than any other number. Counter-intuitive, but true. Fellow
journalists, take heed."
This is definitely what I was thinking of. Perhaps it has another more
common name. Any more details anyone? Why should this bias happen?
Phil Carmody
> On Nov 12, 3:37 am, Major Quaternion Dirt Quantum
> <Qnc...@netscape.net> wrote:
> > Benton's law?
Benford's law.
Phil
--
Dear aunt, let's set so double the killer delete select all.
-- Microsoft voice recognition live demonstration
Venkat Reddy
> On 9 Nov., 12:02, jonas.thornv...@hotmail.com wrote:
>
>
>
>
>
> > On 9 Nov, 11:53, jankri...@hotmail.com wrote:
>
> > > On 9 Nov, 11:41, jonas.thornv...@hotmail.com wrote:
>
> > > > When i was playing around at "http://zenwerx.com/pi.phplooking" for
> > > > occurences of my personalnumber within PI i noticed that 333333 and
> > > > especially 666666 do not seem to occur as frequent as
> > > > 111111,222222,444444,555555,777777,888888,999999 or XXXXXX (without
> > > > testing all ;)
>
> > > > Is this just a fluke result of to small sample size at the page, could
> > > > anyone verify searching in the big file with a program?
>
> > > > If that really the case that 333333 andd 666666 is a lot less frequent
> > > > what is the mathematical reason?
>
> > > > J
>
> > > small to say anything about the frequency of 111111 and the others.
> > > Each of them should only turn up once in one million digits on
> > > average.
>
> > > ---
> > > J K Hauglandhttp://home.no.net/zamunda
>
> > Yes i thought the downloadable sample file was bigger but i can see it
> > is same size now.
> > But what is known about the distribution of larger digits
> > (numberstrings?) within pi, is it really randomed distributed?
>
> > So i try again is six digit numbers randomly distributed within pi, if
> > not why?
>
> > J
>
> Little is known, since decimal digits are not really a
> very natural property of a number.
ya, decimal digits are bad. Try continued fractions.
- venkat
hagman
The straightforward heuristic explanation is that the distribution of
leading digits should be independant of units.
Thus if we pay 100 business lunches in $ or convert the amount
into Euros or Yens according to the exchange rate of the hour -
the probability that the amount starts with digit d should be
unaffected.
And *if* there is a such unit independant probability distribution
then the probability of beginning with digit d must be proportional
to log(d+1)-log(d)
matt271...@yahoo.co.uk
wrote:
> matt271829-n...@yahoo.co.uk writes:
> > On Nov 12, 3:37 am, Major Quaternion Dirt Quantum
> > <Qnc...@netscape.net> wrote:
> > > Benton's law?
>
> Benford's law.
Aha! That would explain it... thanks.
Major Quaternion Dirt Quantum
maybe, it was just that he didn't think that
Fermat could have proved his First Theorem.
> Benford's law.
thus:
the mandelbugs are artifacts;
this can be told at a glance.
> understand Wiles' proof, the tools needed to understand the Mandelbrot
> set are quite easy (I would say 5/6 years of university...) On the other
thus:
of the three, elRon, elRob & elDick,
even Heinlein could get awfully woefull. I don't even want
to read Dick, since the governeurateur was only the second guy
from Hollywood to do his paranoid schtick.
I only read one of Hubbard's books, one of his first "sci fi,"
called _Final Blackout_, which was really a good evocation
of ww2, although it didn't turn-out as badly as he imagined.
that was well-after having been to two Scientology classes --
e-gadz!... probably, it was the enormity of the "data"
of Sc. that ultimately caused me to get out:
how'd you have any time to read any thing, else?
> Since we're going off-topic here: I'm in the middle of _Strange
> Angel_, a biography of Jack Parsons. L Ron Hoover^H^H^H^H^Hubbard
thus:
if anyone could comprehend, what in Hell you are trying
to type, you'd actually have a competent critic. unfortunately, it
seems that
the following is incapable of an English transliteration. (that is,
from your pidgin into Shakesepeare's biblical form;
see Psalm 46.)
I mean, I guesss that it has to do
avec le Premiere Theoreme d'AP on 2+2 = 2*2 = 2^2 = etc. but,
How?
> Reals are infinity only between 2 and 3 and between 3 and 4.