For all of the fools who can't face reality. If you ahve a problem
with these stats, take them up with the various governements
(US/UK/AUS/NZ) that compiled them.
Tony
By 1994, most European Union member states had an average 10 - 15 per cent
non-White population, with this figure effectively doubling every fifteen
years. This will mean that, unless current immigration trends are halted, all
of Western Europe will have a non-White majority population by the year 2090 at
the latest, and possibly earlier. These statistics are from the EU's own
official records, Eurostat, in Belgium.
Racial mixing has been extremely prevalent in Britain. According to the 1991
census, taken by the Office for National Statistics in London (ONS), 40 per
cent of young Black men in Britain are married to, or live with, a White
partner. The trend is less common on the other side of the sexual divide, where
one in five young Black women has a partner who is White. (Ethnicity in the
1991 Census, ONS, 1991).
(If white women are having black children, then the white race ceases to
exist.)
HISPANIC Immigration SET TO SWAMP MANY SOUTHERN STATES
A 1996 report on population trends in America, issued by that country's
official census office, revealed the full extent of Mexican and other Hispanic
immigration from Central and South America. The report predicted that natural
Hispanic reproduction rates will mean that by the 2005, Hispanics will surpass
Blacks as the largest minority. In that respect, the report failed to take into
account the effect of mass illegal immigration, ad Hispanics surpassed Blacks
as the largest minority group in mid 2003, when they officially topped 38.8
million in number.
From 2020, the US Census office says, more Mexicans will be added to the
population each year than Blacks, Asians and Amerinds combined. From 2019, the
relatively youthful Mexican population will have America's lowest death rate.
According to the census bureau, in 1998 there were over ten million Mexican
children under the age of eighteen. This has led to entire slices of many of
the southern states of America: New Mexico, Texas and southern California,
becoming virtual tiny replicas of Mexico, with the lingua franca becoming
Mexican Spanish rather than English.
White American Decline
The long-term rise in the number of Hispanics, who have the highest birth and
immigration rates in America, will coincide with a decline in the number of
Whites, the report states, predicting that by 2028, the number of White
Americans dying will exceed those being born.
The population as a whole is projected to increase by 50 per cent by 2050, to
394 million, from 263 million in 1995. Although the White population is set to
increase steadily in real numbers, expressed as a percentage of the entire
American population, their numbers are in radical decline: in 1996, Whites made
up 73.1 per cent of the population. That is projected to fall to 52.8 per cent
by 2050.
USA Population Projections, millions (rounded off)
total white %white
2010 298 202 68
2020 323 207 64
2050 394 208 53
2100 571 219 45
(Source: U.S. Bureau of the Census, Current Population Reports, Series
P25-1130, "Population Projections of the United States by Age, Sex, Race, and
Hispanic Origin: 1995 to 2050". )
CANADA - MASSIVE ASIAN IMMIGRATION
According to Canadian government figures, from 1981 to 1991, 74 per cent of all
legal immigrants to Canada came from non-White countries. During this time
there were 1.3 million legal immigrants: 26 per cent came from Europe; 47 per
cent came from Asia (Chinese is the fastest-growing mother tongue in Canada);
12 per cent from South America or the Caribbean; 9 per cent from North and
Central America, and 6 per cent from Africa.
Due to declining White birth rates - in 1997 the birth rate was 1.67 children
born per woman, (less than the replacement rate of 2.1) the Canadian government
formally decided in the 1980s to actively seek out further immigrants. The top
ten source countries (in order) in 1995, were Hong Kong, India, the
Philippines, China, Sri Lanka, Taiwan, Bosnia and Herzegovina, England, the
United States, and Pakistan.
In 1997, Amerinds officially made up three per cent of the population
(865,400), while officially Blacks made up two per cent (576,920). The
established Asian population was swelled by 962,000 immigrants in the 1980s -
pushing the total of Asians well over the 2,8 million mark.
These are all official figures of legal immigrants: illegal immigration always
shadows legal immigration, and it is possible that the actual figures may be
nearly double the legal ones.
Given that the total population of Canada in 1996 was 28,846,761, some three
million or more legal non-White immigrants have settled in that country prior
to the year 2000. In terms of illegal immigrants, the number is of course far
higher. All this translates to a non-White population of just under 5 million -
or 17 percent of the total population - in 1996. This figure is set to increase
exponentially.
AUSTRALIA AND NEW ZEALAND - ASIAN AND MIDDLE EASTERN INFLUX
Prior to the 1970s, virtually all immigration to Australia was White: however,
like the rest of Europe and North America, the last 25 years of the 20th
century has seen a massive increase in non-White immigration into Australia,
mostly from Asian countries.
According to the 1991 census, Australia had a population of 16,849,496. The
1995 estimated population, including Christmas Island, Cocos Islands, and
Norfolk Island, was 18,338,000.
Australia's total population grew at an annual rate of about 1.4 percent in the
early 1990s. The principal reasons for this growth were the continued high
level of immigration and the associated increase in the numbers of younger
people in the childbearing and childrearing age groups.
AUSTRALIA 27% ASIAN BY 2025
White Decline - from 30% of World's Population to 15% in 2000
The massive increases in the world's total non-White population also makes
serious food for thought: in 1900, the earth's population stood at 1,625
million, with some 485 million being White. This meant that some 30 per cent of
the earth's population was White at the beginning of the 20th century.
In the year 2000, the earth's population will stand at around 6,095 million,
with around 953 million being White. Although this is an increase, in terms of
the total planet's population, it marks a drop of over 50 per cent - in 2000,
Whites will make up only 15 per cent of the earth's population.
The exponential and explosive growth of the non-White population of the earth -
which effectively doubles itself every 34 years -(compared with White
population which now only doubles itself every 200 years), means that by the
year 2100, only three per cent of the earth's population will be White.
.
|
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| User: "MonsieurStat" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
08 Dec 2004 08:50:22 PM |
|
|
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cp8993$rvf$20@news8.svr.pol.co.uk...
You'll probably recall that I've always favoured a Universe, infinite in
space AND time.
A few weeks ago, by pure accident, a computer program was suddenly halted
when it reached the end of its calculations for Pi. They are checking the
program as we speak to make sure there weren't any computer related errors.
But if that holds, it means the end mathematical bases for the possibility of
infinity. Seems that everything must either come to an end, or keep repeating
itself forever. Personally, I prefer the former to the latter.
Stat.
.
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| User: "R. Foreman" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
08 Dec 2004 09:18:11 PM |
|
|
"MonsieurStat" <Monsieurstat@yahoo.com> Spat the Words
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cp8993$rvf$20@news8.svr.pol.co.uk...
You'll probably recall that I've always favoured a Universe, infinite
in space AND time.
A few weeks ago, by pure accident, a computer program was suddenly
halted when it reached the end of its calculations for Pi. They are
checking the program as we speak to make sure there weren't any computer
related errors. But if that holds, it means the end mathematical bases
for the possibility of infinity. Seems that everything must either come
to an end, or keep repeating itself forever. Personally, I prefer the
former to the latter. Stat.
What if it keeps repeating, but we can't tell that it's
repeating, so we think it's infinite (non-repeating, non-
terminating) ?
.
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|
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| User: "Absolute Zero" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
08 Dec 2004 09:48:19 PM |
|
|
MonsieurStat wrote:
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cp8993$rvf$20@news8.svr.pol.co.uk...
You'll probably recall that I've always favoured a Universe, infinite in
space AND time.
A few weeks ago, by pure accident, a computer program was suddenly halted
when it reached the end of its calculations for Pi. They are checking the
program as we speak to make sure there weren't any computer related errors.
But if that holds, it means the end mathematical bases for the possibility of
infinity. Seems that everything must either come to an end, or keep repeating
itself forever. Personally, I prefer the former to the latter.
Stat.
link?
I very much doubt that... and I'll give you an unconventional reason why.
About 10 years ago a discovery was made that was entirely unanticipated,
miraculous even. The Pi series is iterated each succeeding digit in turn.
Then, "The Miraculous Bailey-Borwein-Plouffe Pi Algorithm" was
discovered/invented.
http://www.andrews.edu/~calkins/physics/Miracle.pdf
This bizarre algorithm can go directly to the specified location in the
Pi series WITHOUT having to calculate the preceding digits.
Consequently, we know parts of the Pi series way beyond the complete
list (as currently known) generated by conventional means.
By 1997, two years after it's discovery, the trillionth binary digit of
Pi had been calculated. Waaaaaay beyond the determined series.
It is a "miracle" and it means something very important. It's ALL math.
-A
.
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| User: "MonsieurStat" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
09 Dec 2004 08:49:04 AM |
|
|
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cp8hqt$rvf$24@news8.svr.pol.co.uk...
MonsieurStat wrote:
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cp8993$rvf$20@news8.svr.pol.co.uk...
You'll probably recall that I've always favoured a Universe, infinite in
space AND time.
A few weeks ago, by pure accident, a computer program was suddenly halted
when it reached the end of its calculations for Pi. They are checking the
program as we speak to make sure there weren't any computer related
errors. But if that holds, it means the end mathematical bases for the
possibility of infinity. Seems that everything must either come to an end,
or keep repeating itself forever. Personally, I prefer the former to the
latter.
Stat.
link?
I don't know if you will like my link ;-)
It's a very short news flash in an online tech magazine, and it's in French
:-)
(if you don't read French I can attempt a translation)
I didn't do any other research on it - but apparently the computer in
question is called ASCII White (synchronicity!!), and is located at the
Center for Applied Scientific Computing.
The programm stopped at 8 758 314 260 548 377 digits after the decimal -
which I believe would be 8 quadrillions something.
Anyway, here's where I saw it.
http://www.pcinpact.com/actu/news/Fin_de_Pi_314_enfin_trouvee_par_hasard.htm
I very much doubt that... and I'll give you an unconventional reason why.
About 10 years ago a discovery was made that was entirely unanticipated,
miraculous even. The Pi series is iterated each succeeding digit in turn.
Then, "The Miraculous Bailey-Borwein-Plouffe Pi Algorithm" was
discovered/invented.
http://www.andrews.edu/~calkins/physics/Miracle.pdf
I am no mathematician but find this formula amazing as well. (but why would
anybody want to calculate a specific location in the PI sequence, or what are
some of its potential applications, is beyond me!?!!)
However, if the above info is not a hoax (refering to my link), then there
must either be a flaw in this formula (because after 8 quardillion something
there is nothing to calculate), or the formula is going where No Formula has
Gone Before! (The black hole maybe?)
This bizarre algorithm can go directly to the specified location in the Pi
series WITHOUT having to calculate the preceding digits.
Consequently, we know parts of the Pi series way beyond the complete list
(as currently known) generated by conventional means.
By 1997, two years after it's discovery, the trillionth binary digit of Pi
had been calculated. Waaaaaay beyond the determined series.
It is a "miracle" and it means something very important. It's ALL math.
There maybe an explanation for all this in this truly amazing article posted
by U.W.
http://www.angelfire.com/oh2/peterr/hologram/objectivereality.html
Stat.
-A
.
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| User: "Absolute Zero" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
09 Dec 2004 06:42:58 PM |
|
|
MonsieurStat wrote:
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cp8hqt$rvf$24@news8.svr.pol.co.uk...
MonsieurStat wrote:
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cp8993$rvf$20@news8.svr.pol.co.uk...
You'll probably recall that I've always favoured a Universe, infinite in
space AND time.
A few weeks ago, by pure accident, a computer program was suddenly halted
when it reached the end of its calculations for Pi. They are checking the
program as we speak to make sure there weren't any computer related
errors. But if that holds, it means the end mathematical bases for the
possibility of infinity. Seems that everything must either come to an end,
or keep repeating itself forever. Personally, I prefer the former to the
latter.
Stat.
link?
I don't know if you will like my link ;-)
It's a very short news flash in an online tech magazine, and it's in French
:-)
(if you don't read French I can attempt a translation)
I didn't do any other research on it - but apparently the computer in
question is called ASCII White (synchronicity!!), and is located at the
Center for Applied Scientific Computing.
The programm stopped at 8 758 314 260 548 377 digits after the decimal -
which I believe would be 8 quadrillions something.
Anyway, here's where I saw it.
http://www.pcinpact.com/actu/news/Fin_de_Pi_314_enfin_trouvee_par_hasard.htm
I couldn't find anything on the CASC site.
http://www.llnl.gov/CASC/
I very much doubt that... and I'll give you an unconventional reason why.
About 10 years ago a discovery was made that was entirely unanticipated,
miraculous even. The Pi series is iterated each succeeding digit in turn.
Then, "The Miraculous Bailey-Borwein-Plouffe Pi Algorithm" was
discovered/invented.
http://www.andrews.edu/~calkins/physics/Miracle.pdf
I am no mathematician but find this formula amazing as well. (but why would
anybody want to calculate a specific location in the PI sequence, or what are
some of its potential applications, is beyond me!?!!)
Academic interest mainly, though *I* think it's indicative of something
significant.
Forget your link, there's NO chance that the Pi series conks, NONE, I'll
eat my leg off. They've possibly uncovered a flaw in their
hardware--like the floating point bug that lay undiscovered in the early
Pentium CPU--or perhaps a flaw in the algorithm. If Pi really expires
then it'll make some MAJOR headlines.
Just for the fun of it...
In the binary representation of Pi we have an infinite and random (100%
unpredictable) series. That it's infinite brings some interesting
properties. Any sequence that you might think of, must appear within the
series somewhere... and what's more, an infinite number of times.
Let's take the complete works of Shakespeare in a text file and run it
through a decent file compressor. Now scan the binary representation of
Pi for a sequential match with the compressed text data.
When we find it. We can then express the entire works of Shakespeare as
an offset into the Pi series and it's length.
So I send you an email "Shakespeare found at offset x length y"
You don't need the complete series (up to and including the specified
offset + length) of Pi, you enter the numbers into the BBP algorithm,
tap, tap, tap, and out pops the complete works in compressed
form... decompress, read.
The flaw? Statistically, if the initial compressor eliminates all
redundancy, then on average, the offset (in binary) will be the same
size as the data it represented <== ON AVERAGE (I think, my gut feeling).
Oh well, if ever we needed crypto by obscurity, this would be a great
way to go.
As I say, just a thought experiment, a bit of fun.
I can email an exe if you wish.
Hey, TW... Cow-pile this (hehe, what a mess).
///////////////////////////////////////////////////
#include <iostream.h>
#include <math.h>
#include <stdio.h>
#include <time.h>
double time2;int dcount;const int dcountmax=9999;
long modexp(long b,long n,long c,long t){__int64
r=1;while(true){if(n>=t){r=b*r%c;n=n-t;}t>>=1;if(t==0)break;r=r*r%c;}return(long)r;}
double suma(long n,int t){dcount=0;long t1=1;while(t1<=n)t1<<=1;long
f8=t;double s=0;for(int nk=n;nk>=0;nk--){if(++dcount==dcountmax){float
fk=(float)100*(n-nk)/(float)(n+1);printf("\b\b\b\b\b\b\b\b\b\b\b\b\b\b%8.4f%%
done",fk);dcount=0;}if(nk>t1)t1>>=1;s+=(double)modexp(16,nk,f8,t1)/(double)f8;s=fmod(s,1);f8+=8;}double
f16=1,s1=0;for(nk=-1;nk>-19;nk--){f16/=16;s1=s+f16/f8;s=fmod(s,1);if(s1==s)break;s=s1;f8+=8;}printf("\b\b\b\b\b\b\b\b\b\b\b\b\b\b%8.4f%%
done",100.);cout<<endl;return s;}
double pisum(int d){long n=d-1;double s;s=4 * suma(n,1)-2 *
suma(n,4)-suma(n,5)-suma(n,6);s=fmod(s,1);if (s<0)s+=1;return
s;}unsigned long pihex(int d){double s=pisum(d);for(int
i=0;i<8;i++){s*=16;}return(unsigned long)s;}
void main(){long n;long ph;cout<<"Calculates hexadecimal digits (hexits)
of pi from position n using\nthe algorithm of Bailey, Borwein and
Plouffe\n"<<endl;cout<<"3.243F6A888... <-- pi in hex "<<endl;cout<<"0
123456789... <-- position (0, 379625063)\n"<< endl;cout<<"Enter a
negative number to exit"<<endl;cout<<"Hex numbers can be entered by
preceding with '0x'"<<endl<<endl;while(true){cout<<"Calculate hexits of
pi from position: "; cin >> n;if (n<0)
break;time2=clock();ph=pihex(n);time2=(double)(clock()-time2)/(double)CLOCKS_PER_SEC;printf("\n%.8X:
%X (%.2f seconds)\n\n",n,ph,time2);if(time2>10)cout<<"\a";}}
///////////////////////////////////////////////////
-A
.
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|
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| User: "tw" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
13 Dec 2004 06:38:39 AM |
|
|
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cparb9$3of$16@newsg2.svr.pol.co.uk...
Just for the fun of it...
In the binary representation of Pi we have an infinite and random (100%
unpredictable) series. That it's infinite brings some interesting
properties. Any sequence that you might think of, must appear within the
series somewhere... and what's more, an infinite number of times.
Let's take the complete works of Shakespeare in a text file and run it
through a decent file compressor. Now scan the binary representation of
Pi for a sequential match with the compressed text data.
When we find it. We can then express the entire works of Shakespeare as
an offset into the Pi series and it's length.
Eh? Am I missing something here.. doesn't that require that you have already
calculated pi to an infinite length? OR am I being thick (as usual). Or do
yo umean we can retrieve the offset from the sequence, and that's the whole
point?
So I send you an email "Shakespeare found at offset x length y"
You don't need the complete series (up to and including the specified
offset + length) of Pi, you enter the numbers into the BBP algorithm,
tap, tap, tap, and out pops the complete works in compressed
form... decompress, read.
ah.. I was being thick wasn't I?
The flaw? Statistically, if the initial compressor eliminates all
redundancy, then on average, the offset (in binary) will be the same
size as the data it represented <== ON AVERAGE (I think, my gut feeling).
Oh well, if ever we needed crypto by obscurity, this would be a great
way to go.
...except you'd have to encrypt your offsets.. it's sort of like using a book
code, where everybody knows what book you're referring to!
As I say, just a thought experiment, a bit of fun.
I can email an exe if you wish.
Hey, TW... Cow-pile this (hehe, what a mess).
I will, got to cow-pie a few other things frist though!
.
|
|
|
| User: "Absolute Zero" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
13 Dec 2004 09:25:56 AM |
|
|
tw wrote:
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cparb9$3of$16@newsg2.svr.pol.co.uk...
Just for the fun of it...
In the binary representation of Pi we have an infinite and random (100%
unpredictable) series. That it's infinite brings some interesting
properties. Any sequence that you might think of, must appear within the
series somewhere... and what's more, an infinite number of times.
Let's take the complete works of Shakespeare in a text file and run it
through a decent file compressor. Now scan the binary representation of
Pi for a sequential match with the compressed text data.
When we find it. We can then express the entire works of Shakespeare as
an offset into the Pi series and it's length.
Eh? Am I missing something here.. doesn't that require that you have already
calculated pi to an infinite length?
The required length, yes.
OR am I being thick (as usual). Or do
yo umean we can retrieve the offset from the sequence, and that's the whole
point?
If only.
So I send you an email "Shakespeare found at offset x length y"
You don't need the complete series (up to and including the specified
offset + length) of Pi, you enter the numbers into the BBP algorithm,
tap, tap, tap, and out pops the complete works in compressed
form... decompress, read.
ah.. I was being thick wasn't I?
You got it.
The flaw? Statistically, if the initial compressor eliminates all
redundancy, then on average, the offset (in binary) will be the same
size as the data it represented <== ON AVERAGE (I think, my gut feeling).
Oh well, if ever we needed crypto by obscurity, this would be a great
way to go.
...except you'd have to encrypt your offsets.. it's sort of like using a book
code, where everybody knows what book you're referring to!
Eggs actly, the perfect analogy...
As I say, just a thought experiment, a bit of fun.
I can email an exe if you wish.
Hey, TW... Cow-pile this (hehe, what a mess).
I will, got to cow-pie a few other things frist though!
Originally compliled on VC6
-A
.
|
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| User: "MonsieurStat" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
09 Dec 2004 08:13:40 PM |
|
|
This is absolutely mind boggling! Thank you very much. You're a very
intelligent lady ;-)
I need to think about this for a few days to fully digest it. What it implies
to me right now is that it is a confirmation of Quantum theory that there are
an infinite number of realities. Just imagine: Any sequence of numbers are
present in Pi, all there at the same time, an infinite number of times. So
the possibility of infinite realities exists and Pi is the proof of that.
BTW, I researched the initial link. It was a hoax. I should have looked at
the date it was posted: April 1 2004. Sorry about that, but I am happy it
brought forth this discussion which is blowing my mind off right now. I think
this discussion, combined with Uncle Walley's article on holograms are going
to do me in for a while.
Thanks very much and would love to play around with your script (please mail
it to monsieurstat@gmail.com)
Stat
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cparb9$3of$16@newsg2.svr.pol.co.uk...
MonsieurStat wrote:
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cp8hqt$rvf$24@news8.svr.pol.co.uk...
MonsieurStat wrote:
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cp8993$rvf$20@news8.svr.pol.co.uk...
You'll probably recall that I've always favoured a Universe, infinite in
space AND time.
A few weeks ago, by pure accident, a computer program was suddenly halted
when it reached the end of its calculations for Pi. They are checking the
program as we speak to make sure there weren't any computer related
errors. But if that holds, it means the end mathematical bases for the
possibility of infinity. Seems that everything must either come to an
end, or keep repeating itself forever. Personally, I prefer the former to
the latter.
Stat.
link?
I don't know if you will like my link ;-)
It's a very short news flash in an online tech magazine, and it's in
French :-)
(if you don't read French I can attempt a translation)
I didn't do any other research on it - but apparently the computer in
question is called ASCII White (synchronicity!!), and is located at the
Center for Applied Scientific Computing.
The programm stopped at 8 758 314 260 548 377 digits after the decimal -
which I believe would be 8 quadrillions something.
Anyway, here's where I saw it.
http://www.pcinpact.com/actu/news/Fin_de_Pi_314_enfin_trouvee_par_hasard.htm
I couldn't find anything on the CASC site.
http://www.llnl.gov/CASC/
I very much doubt that... and I'll give you an unconventional reason why.
About 10 years ago a discovery was made that was entirely unanticipated,
miraculous even. The Pi series is iterated each succeeding digit in turn.
Then, "The Miraculous Bailey-Borwein-Plouffe Pi Algorithm" was
discovered/invented.
http://www.andrews.edu/~calkins/physics/Miracle.pdf
I am no mathematician but find this formula amazing as well. (but why
would anybody want to calculate a specific location in the PI sequence, or
what are some of its potential applications, is beyond me!?!!)
Academic interest mainly, though *I* think it's indicative of something
significant.
Forget your link, there's NO chance that the Pi series conks, NONE, I'll
eat my leg off. They've possibly uncovered a flaw in their hardware--like
the floating point bug that lay undiscovered in the early Pentium CPU--or
perhaps a flaw in the algorithm. If Pi really expires then it'll make some
MAJOR headlines.
Just for the fun of it...
In the binary representation of Pi we have an infinite and random (100%
unpredictable) series. That it's infinite brings some interesting
properties. Any sequence that you might think of, must appear within the
series somewhere... and what's more, an infinite number of times.
Let's take the complete works of Shakespeare in a text file and run it
through a decent file compressor. Now scan the binary representation of Pi
for a sequential match with the compressed text data.
When we find it. We can then express the entire works of Shakespeare as an
offset into the Pi series and it's length.
So I send you an email "Shakespeare found at offset x length y"
You don't need the complete series (up to and including the specified
offset + length) of Pi, you enter the numbers into the BBP algorithm, tap,
tap, tap, and out pops the complete works in compressed
form... decompress, read.
The flaw? Statistically, if the initial compressor eliminates all
redundancy, then on average, the offset (in binary) will be the same
size as the data it represented <== ON AVERAGE (I think, my gut feeling).
Oh well, if ever we needed crypto by obscurity, this would be a great
way to go.
As I say, just a thought experiment, a bit of fun.
I can email an exe if you wish.
Hey, TW... Cow-pile this (hehe, what a mess).
///////////////////////////////////////////////////
#include <iostream.h>
#include <math.h>
#include <stdio.h>
#include <time.h>
double time2;int dcount;const int dcountmax=9999;
long modexp(long b,long n,long c,long t){__int64
r=1;while(true){if(n>=t){r=b*r%c;n=n-t;}t>>=1;if(t==0)break;r=r*r%c;}return(long)r;}
double suma(long n,int t){dcount=0;long t1=1;while(t1<=n)t1<<=1;long
f8=t;double s=0;for(int nk=n;nk>=0;nk--){if(++dcount==dcountmax){float
fk=(float)100*(n-nk)/(float)(n+1);printf("\b\b\b\b\b\b\b\b\b\b\b\b\b\b%8.4f%%
done",fk);dcount=0;}if(nk>t1)t1>>=1;s+=(double)modexp(16,nk,f8,t1)/(double)f8;s=fmod(s,1);f8+=8;}double
f16=1,s1=0;for(nk=-1;nk>-19;nk--){f16/=16;s1=s+f16/f8;s=fmod(s,1);if(s1==s)break;s=s1;f8+=8;}printf("\b\b\b\b\b\b\b\b\b\b\b\b\b\b%8.4f%%
done",100.);cout<<endl;return s;}
double pisum(int d){long n=d-1;double s;s=4 * suma(n,1)-2 *
suma(n,4)-suma(n,5)-suma(n,6);s=fmod(s,1);if (s<0)s+=1;return
s;}unsigned long pihex(int d){double s=pisum(d);for(int
i=0;i<8;i++){s*=16;}return(unsigned long)s;}
void main(){long n;long ph;cout<<"Calculates hexadecimal digits (hexits)
of pi from position n using\nthe algorithm of Bailey, Borwein and
Plouffe\n"<<endl;cout<<"3.243F6A888... <-- pi in hex "<<endl;cout<<"0
123456789... <-- position (0, 379625063)\n"<< endl;cout<<"Enter a
negative number to exit"<<endl;cout<<"Hex numbers can be entered by
preceding with '0x'"<<endl<<endl;while(true){cout<<"Calculate hexits of
pi from position: "; cin >> n;if (n<0)
break;time2=clock();ph=pihex(n);time2=(double)(clock()-time2)/(double)CLOCKS_PER_SEC;printf("\n%.8X:
%X (%.2f seconds)\n\n",n,ph,time2);if(time2>10)cout<<"\a";}}
///////////////////////////////////////////////////
-A
.
|
|
|
| User: "Absolute Zero" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
10 Dec 2004 07:25:31 AM |
|
|
MonsieurStat wrote:
This is absolutely mind boggling! Thank you very much. You're a very
intelligent lady ;-)
I need to think about this for a few days to fully digest it. What it implies
to me right now is that it is a confirmation of Quantum theory that there are
an infinite number of realities. Just imagine: Any sequence of numbers are
present in Pi, all there at the same time, an infinite number of times. So
the possibility of infinite realities exists and Pi is the proof of that.
Just don't get me started on primes!
BTW, I researched the initial link. It was a hoax. I should have looked at
the date it was posted: April 1 2004.
LOL
Sorry about that, but I am happy it
brought forth this discussion which is blowing my mind off right now. I think
this discussion, combined with Uncle Walley's article on holograms are going
to do me in for a while.
Holographic multi-verse eh? I've read enough of that kind of stuff to
last me a lifetime. I'm slightly interested in String/M theory for its
mathematical beauty... but generally I try to avoid thinking too hard
about material that is (almost certainly) intrinsically unprovable,
ironic "science".
Thanks very much and would love to play around with your script (please mail
it to monsieurstat@gmail.com)
Pi.exe (4kb) sent.
[edit - delivery failure... are you set for .exe attachments?]
I don't know if I've made it clear but the BBP algorithm iterates as
well. Think of it as intersecting with the Pi series at the desired
location. IOW, don't go mad with the offset... unless you're very
patient. I'll compile a new version when they get around to releasing
quantum computers ;)
I've added a few clarifications below just in case you really plan to
try it (in a very limited form). I experimented just enough this morning
to prove (to myself at least) that it's a nil sum game in terms of
compression.
Just for the fun of it...
In the binary representation of Pi we have an infinite and random (100%
unpredictable) series. That it's infinite brings some interesting
properties. Any sequence that you might think of, must appear within the
series somewhere... and what's more, an infinite number of times.
Let's take the complete works of Shakespeare in a text file and run it
through a decent file compressor.
The full, uncompressed text will be in the series as well... it's just
that being redundancy free and <20% of the size, your chances of
actually finding the compressed text are increased dramatically - maybe
a by a factor of a googolplex or three (not really, but you get the idea).
Now scan the binary representation of Pi
for a sequential match with the compressed text data.
When we find it. We can then express the entire works of Shakespeare as an
offset into the Pi series and it's length.
So I send you an email "Shakespeare found at offset x length y"
You don't need the complete series (up to and including the specified
offset + length) of Pi, you enter the numbers into the BBP algorithm, tap,
tap, tap, and out pops the complete works in compressed
form... decompress, read.
The flaw? Statistically, if the initial compressor eliminates all
redundancy, then on average, the offset (in binary) will be the same
size as the data it represented <== ON AVERAGE (I think, my gut feeling).
When I say flaw, I mean there's no hope that this could be used for
compression... the consequences would be outrageous.
If the offset + length data (written as a massive binary number) were
smaller than the original data, hey guess what.. recurse, run again,
this time looking for the joined length & offset within the Pi series,
over and over... poof! Hell, you might destroy the Universe. ;)
Zen huh?
-A
Oh well, if ever we needed crypto by obscurity, this would be a great
way to go.
As I say, just a thought experiment, a bit of fun.
.
|
|
|
| User: "MonsieurStat" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
11 Dec 2004 01:11:35 AM |
|
|
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cpc80v$du2$1@news7.svr.pol.co.uk...
MonsieurStat wrote:
This is absolutely mind boggling! Thank you very much. You're a very
intelligent lady ;-)
I need to think about this for a few days to fully digest it. What it
implies to me right now is that it is a confirmation of Quantum theory
that there are an infinite number of realities. Just imagine: Any sequence
of numbers are present in Pi, all there at the same time, an infinite
number of times. So the possibility of infinite realities exists and Pi is
the proof of that.
Just don't get me started on primes!
No worries, I think I've had enough math in the past few days to last me for
a while:-)
Primes are 1, 3, 7, 11, 13... ? right?
BTW, I researched the initial link. It was a hoax. I should have looked at
the date it was posted: April 1 2004.
LOL
Sorry about that, but I am happy it brought forth this discussion which is
blowing my mind off right now. I think this discussion, combined with
Uncle Walley's article on holograms are going to do me in for a while.
Holographic multi-verse eh? I've read enough of that kind of stuff to last
me a lifetime. I'm slightly interested in String/M theory for its
mathematical beauty... but generally I try to avoid thinking too hard about
material that is (almost certainly) intrinsically unprovable, ironic
"science".
I don't know much about it, am just amazed at how many unexplainable
phenomena it can explain. I know it's just a theory but as scientifics say we
shouldn't discarfd a theory that explain a number of things unless we can
replace it with another theory that explains them better. So I think I'll
integrate it until further notice. But do tell us more if you feel like it.
You seem quite ressourceful!
Thanks very much and would love to play around with your script (please
mail it to monsieurstat@gmail.com)
Pi.exe (4kb) sent.
[edit - delivery failure... are you set for .exe attachments?]
It should, but don't worry I'll probably won't be able to run it unless it's
got a nice clickable GUI :-(
I don't know if I've made it clear but the BBP algorithm iterates as well.
Think of it as intersecting with the Pi series at the desired location.
IOW, don't go mad with the offset... unless you're very patient. I'll
compile a new version when they get around to releasing quantum computers
;)
I need to confirm this with you. If I understand correctly, as with your
example of a text file converted into a sequence of digits, I can find the
position of the number sequence in PI using the BBP algo. But on the other
end, I need to have the value of Pi calculated up at least the point that
would contain that sequence. Another words, I canb't use the Algo in reverse
mode asking it to tell me what are the number sequences between positions X
and Y in PI are. Is that correct?
I've added a few clarifications below just in case you really plan to try
it (in a very limited form). I experimented just enough this morning to
prove (to myself at least) that it's a nil sum game in terms of
compression.
Just for the fun of it...
In the binary representation of Pi we have an infinite and random (100%
unpredictable) series. That it's infinite brings some interesting
properties. Any sequence that you might think of, must appear within the
series somewhere... and what's more, an infinite number of times.
Let's take the complete works of Shakespeare in a text file and run it
through a decent file compressor.
The full, uncompressed text will be in the series as well... it's just that
being redundancy free and <20% of the size, your chances of actually
finding the compressed text are increased dramatically - maybe a by a
factor of a googolplex or three (not really, but you get the idea).
This actually almost confirms my sucpicions that the Algo can't be used
backwards. But if it could... what a powerful tool that would be!! Imagine
sending somebody a whole book that only weighs around 10 bits. Just enough
information to indicate the start and end positions. Could easily be applied
to any file in fact. A song, a movie... We'd be putting the DVD industry out
of business!
Now scan the binary representation of Pi for a sequential match with the
compressed text data.
When we find it. We can then express the entire works of Shakespeare as an
offset into the Pi series and it's length.
So I send you an email "Shakespeare found at offset x length y"
You don't need the complete series (up to and including the specified
offset + length) of Pi, you enter the numbers into the BBP algorithm, tap,
tap, tap, and out pops the complete works in compressed
form... decompress, read.
The flaw? Statistically, if the initial compressor eliminates all
redundancy, then on average, the offset (in binary) will be the same
size as the data it represented <== ON AVERAGE (I think, my gut feeling).
When I say flaw, I mean there's no hope that this could be used for
compression... the consequences would be outrageous.
Of course, again if I understand this correctly, there would be no point in
compression unless you want to increase the chances of have a digit sequence
that is within the calculated part of PI.
If the offset + length data (written as a massive binary number) were
smaller than the original data, hey guess what.. recurse, run again, this
time looking for the joined length & offset within the Pi series, over and
over... poof! Hell, you might destroy the Universe. ;)
Hummm... I feel dense. Maybe I'll understand this in the morning.
Stat.
Zen huh?
-A
Oh well, if ever we needed crypto by obscurity, this would be a great
way to go.
As I say, just a thought experiment, a bit of fun.
.
|
|
|
| User: "Absolute Zero" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
11 Dec 2004 12:16:45 PM |
|
|
MonsieurStat wrote:
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cpc80v$du2$1@news7.svr.pol.co.uk...
MonsieurStat wrote:
This is absolutely mind boggling! Thank you very much. You're a very
intelligent lady ;-)
I need to think about this for a few days to fully digest it. What it
implies to me right now is that it is a confirmation of Quantum theory
that there are an infinite number of realities. Just imagine: Any
sequence
of numbers are present in Pi, all there at the same time, an infinite
number of times. So the possibility of infinite realities exists and
Pi is
the proof of that.
Just don't get me started on primes!
No worries, I think I've had enough math in the past few days to last
me for
a while:-)
Primes are 1, 3, 7, 11, 13... ? right?
I warned you ;)
2, 3, 5, 7, 11, 13, 17 ...
1 isn't conventionally included.
2 is only divisible by itself and one.
5 you missed.
It's still unproven, though massively tested, that all even integers
greater than two, can be written as the product of two primes.
(Goldbach's conjecture, one of the greatest, unsolved problems in number
theory)
4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7 = 5 + 5
12 = 5 + 7
14 = 3 + 11 = 7 + 7
.. . .
In a sense they’re the real integers (all others being products), the
sub-atomic particles of mathematics... hence prime.
BTW, I researched the initial link. It was a hoax. I should have
looked at
the date it was posted: April 1 2004.
LOL
Sorry about that, but I am happy it brought forth this discussion
which is
blowing my mind off right now. I think this discussion, combined with
Uncle Walley's article on holograms are going to do me in for a while.
Holographic multi-verse eh? I've read enough of that kind of stuff to
last
me a lifetime. I'm slightly interested in String/M theory for its
mathematical beauty... but generally I try to avoid thinking too hard
about
material that is (almost certainly) intrinsically unprovable, ironic
"science".
I don't know much about it, am just amazed at how many unexplainable
phenomena it can explain. I know it's just a theory but as
scientifics say we
shouldn't discarfd a theory that explain a number of things unless we
can
replace it with another theory that explains them better. So I think
I'll
integrate it until further notice. But do tell us more if you feel
like it.
You seem quite ressourceful!
Noooooooo, here be dragons!
I'll just state that I *could* proffer a model of the Universe that
allowed for a flat earth. It would twist and convolve, invoke extra
dimensions and parallels... but it could be done. The important thing is
to apply Occam’s razor... methodological reductionism, the principle of
parsimony etc.
Because I profoundly believe that maths was discovered rather than
invented; that it is fundamental... I expect solutions to literally and
figuratively add up.
Pythagoras believed that the Universe *was* math. Not a tool to describe
reality but reality itself.
^What he said.
This would be kewl in that it responds to the BIG question... how can
you have something where logically there ought to be nothing? Given a
creationist God, then the same question devolves to her ;)
Answer: the Universe is built of nothing... or rather, something that
most assume to be purely conceptual and insubstantial ==> dancing numbers.
Put baldly, and in light of what I previously said about a certain type
of integer: da universe(s) be built from da prime numba's.
IMHO
Thanks very much and would love to play around with your script (please
mail it to monsieurstat@gmail.com)
Pi.exe (4kb) sent.
[edit - delivery failure... are you set for .exe attachments?]
It should, but don't worry I'll probably won't be able to run it
unless it's
got a nice clickable GUI :-(
I don't know if I've made it clear but the BBP algorithm iterates as
well.
Think of it as intersecting with the Pi series at the desired location.
IOW, don't go mad with the offset... unless you're very patient. I'll
compile a new version when they get around to releasing quantum
computers
;)
I need to confirm this with you. If I understand correctly, as with your
example of a text file converted into a sequence of digits, I can
find the
position of the number sequence in PI using the BBP algo. But on the
other
end, I need to have the value of Pi calculated up at least the point
that
would contain that sequence.
No, the encoder has the complete known series of Pi. He finds the offset
location which is sent to the decoder… who uses the algorithm alone
(sans enormous list) to extract the series from the specified offset
location.
Another words, I canb't use the Algo in reverse
mode asking it to tell me what are the number sequences between
positions X
and Y in PI are. Is that correct?
We must be misunderstanding each other because that is exactly what the
BBP algorithm does… extract digits from the series at a specified offset.
I've added a few clarifications below just in case you really plan to
try
it (in a very limited form). I experimented just enough this morning to
prove (to myself at least) that it's a nil sum game in terms of
compression.
Just for the fun of it...
In the binary representation of Pi we have an infinite and random (100%
unpredictable) series. That it's infinite brings some interesting
properties. Any sequence that you might think of, must appear within the
series somewhere... and what's more, an infinite number of times.
Let's take the complete works of Shakespeare in a text file and run it
through a decent file compressor.
The full, uncompressed text will be in the series as well... it's
just that
being redundancy free and <20% of the size, your chances of actually
finding the compressed text are increased dramatically - maybe a by a
factor of a googolplex or three (not really, but you get the idea).
This actually almost confirms my sucpicions that the Algo can't be used
backwards. But if it could... what a powerful tool that would be!!
Imagine
sending somebody a whole book that only weighs around 10 bits. Just
enough
information to indicate the start and end positions. Could easily be
applied
to any file in fact. A song, a movie... We'd be putting the DVD
industry out
of business!
Remember that the offset in binary will almost always exceed the size of
the data it’s describing… otherwise number theory is in serious trouble.
That’s why I described the notion as a bit of fun… better suited to
encryption by obscurity.
Now scan the binary representation of Pi for a sequential match with
the
compressed text data.
When we find it. We can then express the entire works of Shakespeare
as an
offset into the Pi series and it's length.
So I send you an email "Shakespeare found at offset x length y"
You don't need the complete series (up to and including the specified
offset + length) of Pi, you enter the numbers into the BBP
algorithm, tap,
tap, tap, and out pops the complete works in compressed
form... decompress, read.
The flaw? Statistically, if the initial compressor eliminates all
redundancy, then on average, the offset (in binary) will be the same
size as the data it represented <== ON AVERAGE (I think, my gut
feeling).
When I say flaw, I mean there's no hope that this could be used for
compression... the consequences would be outrageous.
Of course, again if I understand this correctly, there would be no
point in
compression unless you want to increase the chances of have a digit
sequence
that is within the calculated part of PI.
If the offset + length data (written as a massive binary number) were
smaller than the original data, hey guess what.. recurse, run again,
this
time looking for the joined length & offset within the Pi series,
over and
over... poof! Hell, you might destroy the Universe. ;)
Hummm... I feel dense. Maybe I'll understand this in the morning.
I could express it quite easily in pseudo code.
BTW, the current record for the series is 1.2411 trillion places, set
last Wednesday.
-A
.
|
|
|
| User: "MonsieurStat" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
12 Dec 2004 12:23:59 AM |
|
|
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cpfdes$c0d$10@news7.svr.pol.co.uk...
MonsieurStat wrote:
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cpc80v$du2$1@news7.svr.pol.co.uk...
MonsieurStat wrote:
This is absolutely mind boggling! Thank you very much. You're a very
intelligent lady ;-)
I need to think about this for a few days to fully digest it. What it
implies to me right now is that it is a confirmation of Quantum theory
that there are an infinite number of realities. Just imagine: Any
sequence
of numbers are present in Pi, all there at the same time, an infinite
number of times. So the possibility of infinite realities exists and
Pi is
the proof of that.
Just don't get me started on primes!
No worries, I think I've had enough math in the past few days to last
me for
a while:-)
Primes are 1, 3, 7, 11, 13... ? right?
I warned you ;)
2, 3, 5, 7, 11, 13, 17 ...
1 isn't conventionally included.
2 is only divisible by itself and one.
5 you missed.
It's still unproven, though massively tested, that all even integers
greater than two, can be written as the product of two primes.
(Goldbach's conjecture, one of the greatest, unsolved problems in number
theory)
4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7 = 5 + 5
12 = 5 + 7
14 = 3 + 11 = 7 + 7
. . .
In a sense they’re the real integers (all others being products), the
sub-atomic particles of mathematics... hence prime.
WOW! That's the first time I heard prime numbers described in this way. Gives
me a whole new perspective on primes :-)
I'll definitely remember this one too. Do you think there may be some
application for this?
BTW, I researched the initial link. It was a hoax. I should have
looked at
the date it was posted: April 1 2004.
LOL
Sorry about that, but I am happy it brought forth this discussion
which is
blowing my mind off right now. I think this discussion, combined with
Uncle Walley's article on holograms are going to do me in for a while.
Holographic multi-verse eh? I've read enough of that kind of stuff to
last
me a lifetime. I'm slightly interested in String/M theory for its
mathematical beauty... but generally I try to avoid thinking too hard
about
material that is (almost certainly) intrinsically unprovable, ironic
"science".
I don't know much about it, am just amazed at how many unexplainable
phenomena it can explain. I know it's just a theory but as
scientifics say we
shouldn't discarfd a theory that explain a number of things unless we
can
replace it with another theory that explains them better. So I think
I'll
integrate it until further notice. But do tell us more if you feel
like it.
You seem quite ressourceful!
Noooooooo, here be dragons!
I'll just state that I *could* proffer a model of the Universe that allowed
for a flat earth. It would twist and convolve, invoke extra dimensions and
parallels... but it could be done. The important thing is to apply Occam’s
razor... methodological reductionism, the principle of parsimony etc.
Thank you for bringing up Occam’s razor. I of course had to look it up, but
am pretty glad I did :-)
[Extract] One should not increase, beyond what is necessary, the number of
entities required to explain anything
http://pespmc1.vub.ac.be/OCCAMRAZ.html
Because I profoundly believe that maths was discovered rather than
invented; that it is fundamental... I expect solutions to literally and
figuratively add up.
Pythagoras believed that the Universe *was* math. Not a tool to describe
reality but reality itself.
^What he said.
This would be kewl in that it responds to the BIG question... how can you
have something where logically there ought to be nothing? Given a
creationist God, then the same question devolves to her ;)
Answer: the Universe is built of nothing... or rather, something that most
assume to be purely conceptual and insubstantial ==> dancing numbers.
Put baldly, and in light of what I previously said about a certain type of
integer: da universe(s) be built from da prime numba's.
IMHO
Very interesting thought!
Could maths exist without language though?
I believe language is the foundation of all systems accessible to human mind.
All systems are a sub-system to language.
Language => system of systems.
At least as far as the human mind is concerned.
Is there anything beyond human mind?
Maybe Dats the Da question.
Thanks very much and would love to play around with your script (please
mail it to monsieurstat@gmail.com)
Pi.exe (4kb) sent.
[edit - delivery failure... are you set for .exe attachments?]
It should, but don't worry I'll probably won't be able to run it
unless it's
got a nice clickable GUI :-(
I don't know if I've made it clear but the BBP algorithm iterates as
well.
Think of it as intersecting with the Pi series at the desired location.
IOW, don't go mad with the offset... unless you're very patient. I'll
compile a new version when they get around to releasing quantum
computers
;)
I need to confirm this with you. If I understand correctly, as with your
example of a text file converted into a sequence of digits, I can
find the
position of the number sequence in PI using the BBP algo. But on the
other
end, I need to have the value of Pi calculated up at least the point
that
would contain that sequence.
No, the encoder has the complete known series of Pi. He finds the offset
location which is sent to the decoder… who uses the algorithm alone (sans
enormous list) to extract the series from the specified offset location.
Another words, I canb't use the Algo in reverse
mode asking it to tell me what are the number sequences between
positions X
and Y in PI are. Is that correct?
We must be misunderstanding each other because that is exactly what the BBP
algorithm does… extract digits from the series at a specified offset.
Ok please bear with me a little more. I really like to get this straight.
Let me go through an example to show you what I like to do. You tell me if it
is possible:
I want to take my name, "Stat" and convert it to hexa decimal in this way:
S = 83
t = 116
a = 97
t = 116
So Stat becomes 8311697116
Can I use the BBA algo to find the location of the first occurrence of
8311697116 in PI?
(the only value for PI that I have accessible to me is 3.14, which of course
doesn't contain the sequence)
If yes, and supposing the algo returns: 8311697116 found at 2.2411 trillion
places
Can I then use BBA to extract the digit that occupys the position 2.2411
trillion? (if yes, it should return 8). I would then continue with (2.2411
trillion + 1), (1.2411 trillion + 2) ... (2.2411 trillion + 10) to get the
whole 8311697116, which I just then need to reconvert back to ascii to get
Stat.
There is of course a little flaw in here for the re-conversion – not as bad
as the zip file example :-) but if the method works both ways (locating
position and retrieval), I think we are in business.
Is this possible with BBA Algo without using any known values for PI?
BTW, how fast does something like this take to run? The formula in that paper
you referenced looked very simple. But you did mention needing Quantum based
computers at some point :-)
Thanks again,
Stat.
I've added a few clarifications below just in case you really plan to
try
it (in a very limited form). I experimented just enough this morning to
prove (to myself at least) that it's a nil sum game in terms of
compression.
Just for the fun of it...
In the binary representation of Pi we have an infinite and random (100%
unpredictable) series. That it's infinite brings some interesting
properties. Any sequence that you might think of, must appear within the
series somewhere... and what's more, an infinite number of times.
Let's take the complete works of Shakespeare in a text file and run it
through a decent file compressor.
The full, uncompressed text will be in the series as well... it's
just that
being redundancy free and <20% of the size, your chances of actually
finding the compressed text are increased dramatically - maybe a by a
factor of a googolplex or three (not really, but you get the idea).
This actually almost confirms my sucpicions that the Algo can't be used
backwards. But if it could... what a powerful tool that would be!!
Imagine
sending somebody a whole book that only weighs around 10 bits. Just
enough
information to indicate the start and end positions. Could easily be
applied
to any file in fact. A song, a movie... We'd be putting the DVD
industry out
of business!
Remember that the offset in binary will almost always exceed the size of
the data it’s describing… otherwise number theory is in serious trouble.
That’s why I described the notion as a bit of fun… better suited to
encryption by obscurity.
Now scan the binary representation of Pi for a sequential match with
the
compressed text data.
When we find it. We can then express the entire works of Shakespeare
as an
offset into the Pi series and it's length.
So I send you an email "Shakespeare found at offset x length y"
You don't need the complete series (up to and including the specified
offset + length) of Pi, you enter the numbers into the BBP
algorithm, tap,
tap, tap, and out pops the complete works in compressed
form... decompress, read.
The flaw? Statistically, if the initial compressor eliminates all
redundancy, then on average, the offset (in binary) will be the same
size as the data it represented <== ON AVERAGE (I think, my gut
feeling).
When I say flaw, I mean there's no hope that this could be used for
compression... the consequences would be outrageous.
Of course, again if I understand this correctly, there would be no
point in
compression unless you want to increase the chances of have a digit
sequence
that is within the calculated part of PI.
If the offset + length data (written as a massive binary number) were
smaller than the original data, hey guess what.. recurse, run again,
this
time looking for the joined length & offset within the Pi series,
over and
over... poof! Hell, you might destroy the Universe. ;)
Hummm... I feel dense. Maybe I'll understand this in the morning.
I could express it quite easily in pseudo code.
BTW, the current record for the series is 1.2411 trillion places, set last
Wednesday.
-A
.
|
|
|
| User: "Absolute Zero" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
12 Dec 2004 02:13:25 PM |
|
|
MonsieurStat wrote:
"Absolute Zero" <amycaton@hotmail.com> wrote in message
8<
I warned you ;)
2, 3, 5, 7, 11, 13, 17 ...
1 isn't conventionally included.
2 is only divisible by itself and one.
5 you missed.
It's still unproven, though massively tested, that all even integers
greater than two, can be written as the product of two primes.
(Goldbach's conjecture, one of the greatest, unsolved problems in number
theory)
4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7 = 5 + 5
12 = 5 + 7
14 = 3 + 11 = 7 + 7
. . .
In a sense they’re the real integers (all others being products), the
sub-atomic particles of mathematics... hence prime.
WOW! That's the first time I heard prime numbers described in this
way. Gives
me a whole new perspective on primes :-)
I'll definitely remember this one too. Do you think there may be some
application for this?
For Goldbach's conjecture?
Prime numbers are the basis of modern encryption. Stated very simply,
multiplying two large primes produces a product that is only
evenly-divisible by the two original primes. Determining the original
factors from the product can only be tackled by brute force … you can
only test each and every prime up to the square root of the product.
With sufficiently large primes it becomes impractical… thousands of
years of compute time.
You must have noticed this stuff in DJM’s posts
-----BEGIN PGP SIGNATURE-----
iQA/AwUBQbv9RJljD7YrHM/nEQLjiwCfWM6IDX6TUSB8oEPSXrPBn17+HxUAn3gG
ueQfSnpji0DYyHHulK15cZk6
=5qbp
-----END PGP SIGNATURE-----
PGP stands for Pretty Good Privacy... it’s being used to generate a
signature that makes it impossible for others to successfully fake a
message as being from him.
8<
I'll just state that I *could* proffer a model of the Universe that
allowed
for a flat earth. It would twist and convolve, invoke extra
dimensions and
parallels... but it could be done. The important thing is to apply
Occam’s
razor... methodological reductionism, the principle of parsimony etc.
Thank you for bringing up Occam’s razor. I of course had to look it
up, but
am pretty glad I did :-)
[Extract] One should not increase, beyond what is necessary, the
number of
entities required to explain anything
http://pespmc1.vub.ac.be/OCCAMRAZ.html
Because I profoundly believe that maths was discovered rather than
invented; that it is fundamental... I expect solutions to literally and
figuratively add up.
Pythagoras believed that the Universe *was* math. Not a tool to describe
reality but reality itself.
^What he said.
This would be kewl in that it responds to the BIG question... how can
you
have something where logically there ought to be nothing? Given a
creationist God, then the same question devolves to her ;)
Answer: the Universe is built of nothing... or rather, something that
most
assume to be purely conceptual and insubstantial ==> dancing numbers.
Put baldly, and in light of what I previously said about a certain
type of
integer: da universe(s) be built from da prime numba's.
IMHO
Very interesting thought!
Could maths exist without language though?
If invented, no.
If discovered, then obviously so.
I believe language is the foundation of all systems accessible to
human mind.
All systems are a sub-system to language.
Language => system of systems.
At least as far as the human mind is concerned.
Is there anything beyond human mind?
Maybe Dats the Da question.
Don’t forget the mice <== hyper intelligent pan dimensional beings. (HHGTTG)
You’re in the same ballpark as the ‘Copenhagen Interpretation’ of
quantum mechanics... perhaps the most successful explanation of the
particle/wave duality of light. Einstein hated it with a passion… hence
"God does not play dice…" and "Do you really think the moon isn't there
if you aren't looking at it?" – Bohr’s retort: “Einstein, don't tell God
what to do”.
I don’t like it either.
Thanks very much and would love to play around with your script
(please
mail it to monsieurstat@gmail.com)
Pi.exe (4kb) sent.
[edit - delivery failure... are you set for .exe attachments?]
It should, but don't worry I'll probably won't be able to run it
unless it's
got a nice clickable GUI :-(
I don't know if I've made it clear but the BBP algorithm iterates as
well.
Think of it as intersecting with the Pi series at the desired location.
IOW, don't go mad with the offset... unless you're very patient. I'll
compile a new version when they get around to releasing quantum
computers
;)
I need to confirm this with you. If I understand correctly, as with your
example of a text file converted into a sequence of digits, I can
find the
position of the number sequence in PI using the BBP algo. But on the
other
end, I need to have the value of Pi calculated up at least the point
that
would contain that sequence.
No, the encoder has the complete known series of Pi. He finds the offset
location which is sent to the decoder… who uses the algorithm alone
(sans
enormous list) to extract the series from the specified offset location.
Another words, I canb't use the Algo in reverse
mode asking it to tell me what are the number sequences between
positions X
and Y in PI are. Is that correct?
We must be misunderstanding each other because that is exactly what
the BBP
algorithm does… extract digits from the series at a specified offset.
Ok please bear with me a little more. I really like to get this straight.
Let me go through an example to show you what I like to do. You tell
me if it
is possible:
I want to take my name, "Stat" and convert it to hexa decimal in this
way:
S = 83
t = 116
a = 97
t = 116
So Stat becomes 8311697116
Can I use the BBA algo to find the location of the first occurrence of
8311697116 in PI?
No, you need the list… having gotten the location you can pull it out of
the series directly using the BBP routine without having the list.
Incidentally, if you want to search the regular decimal series, go here...
http://www.pisearch.de.vu/
Sample:
'12345678' found at position 186557266 in pi's digits after the decimal
point!
(the only value for PI that I have accessible to me is 3.14, which of
course
doesn't contain the sequence)
The world record for memory is 40,000+ decimal places, IIRC.
How sad is that?
If yes, and supposing the algo returns: 8311697116 found at 2.2411
trillion
places
Can I then use BBA to extract the digit that occupys the position 2.2411
trillion? (if yes, it should return 8). I would then continue with
(2.2411
trillion + 1), (1.2411 trillion + 2) ... (2.2411 trillion + 10) to
get the
whole 8311697116, which I just then need to reconvert back to ascii
to get
Stat.
There is of course a little flaw in here for the re-conversion – not
as bad
as the zip file example :-) but if the method works both ways (locating
position and retrieval), I think we are in business.
It doesn’t, we’re not. ;)
Is this possible with BBA Algo without using any known values for PI?
You’ve lost me.
BTW, how fast does something like this take to run? The formula in
that paper
you referenced looked very simple. But you did mention needing
Quantum based
computers at some point :-)
The PiHex project took 3 Pentium-90 years to calculate the
5,000,000,000,000 bit of Pi.
http://www.cecm.sfu.ca/projects/pihex/status.html
-A
.
|
|
|
| User: "MonsieurStat" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
13 Dec 2004 07:03:35 AM |
|
|
Thank you for this discussion.
It's been almost like a religious experience for me.
I think I understand now why the BBA algorithm is considered a miracle.
Pi being infinite, the capacity to go and fetch information from any location
in the infinite, is like going to some future or past time, take note of what
is there, and come back. Of course the beauty of it is that we can't go and
look for any specific information. We can only go to a specific location to
see what is there. I guess the BBA algorithm also proves that Pi is
determinist. So if numbers are the universe - or at least a model of it -
universe itself must be determinist.
I also see a lot of close correlations with other cases that have been
explained by the hologram model - that I found out about only when we started
this discussion. For example the girl on LSD who hallucinated into another
point in time and was looking out from a prehistoric lizard's eyes during her
session... LSD in this case might be considered acting like the BBA
algorithm?
Anyway it's all truly fascinating for me. But beyond philosophical
considerations, I am still wondering if it would be possible to come up with
a way to use the BBA algo to find the position of a number sequence in Pi -
in order to use it as a data transfer system. The one that will make us very
rich and a little famous :-)
Here's an idea:
You said we have already calculated some 1.2411 trillion decimal places in
Pi. This will certainly take care of many number sequences, but not the vast
majority that we might need (i.e. works of Shakespeare converted into
hexadecimal which is a number sequence not found in the already calculated
Pi).
So supposing that we create an algorithm that will try to guess the position
of any number sequence in Pi - the hexadecimalised works of Shakespeare for
example.
It already knows that it is not in the first 1.2411 trillions. So it will try
to find it in the next range, let's say the next 1.2 trillions. The trick of
course is to not do all the calculations. Just make a few spot checks here
and there - using the BBA algo to see if parts of Shakespear are there or
not. If yes, then try to find the other parts, if not move on to the next 1.2
trillions, until all of Shakespeare is found in Pi.
Is this completely crazy, or do you think we could develop a smart algo which
is able to move from one range to another in a matter of a few seconds? I
think from a commercial stand point it would be quite reasonable to use
something like a year's worth of CPU time to find a number sequence as
extensive as that of Shakespear's complete works. We just have to do it once
after all.
Stat (scratching his head a lot these days)
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cpi8lg$hj2$6@news7.svr.pol.co.uk...
MonsieurStat wrote:
"Absolute Zero" <amycaton@hotmail.com> wrote in message
8<
I warned you ;)
2, 3, 5, 7, 11, 13, 17 ...
1 isn't conventionally included.
2 is only divisible by itself and one.
5 you missed.
It's still unproven, though massively tested, that all even integers
greater than two, can be written as the product of two primes.
(Goldbach's conjecture, one of the greatest, unsolved problems in number
theory)
4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7 = 5 + 5
12 = 5 + 7
14 = 3 + 11 = 7 + 7
. . .
In a sense they’re the real integers (all others being products), the
sub-atomic particles of mathematics... hence prime.
WOW! That's the first time I heard prime numbers described in this
way. Gives
me a whole new perspective on primes :-)
I'll definitely remember this one too. Do you think there may be some
application for this?
For Goldbach's conjecture?
Prime numbers are the basis of modern encryption. Stated very simply,
multiplying two large primes produces a product that is only
evenly-divisible by the two original primes. Determining the original
factors from the product can only be tackled by brute force … you can only
test each and every prime up to the square root of the product. With
sufficiently large primes it becomes impractical… thousands of years of
compute time.
You must have noticed this stuff in DJM’s posts
-----BEGIN PGP SIGNATURE-----
iQA/AwUBQbv9RJljD7YrHM/nEQLjiwCfWM6IDX6TUSB8oEPSXrPBn17+HxUAn3gG
ueQfSnpji0DYyHHulK15cZk6
=5qbp
-----END PGP SIGNATURE-----
PGP stands for Pretty Good Privacy... it’s being used to generate a
signature that makes it impossible for others to successfully fake a
message as being from him.
8<
I'll just state that I *could* proffer a model of the Universe that
allowed
for a flat earth. It would twist and convolve, invoke extra
dimensions and
parallels... but it could be done. The important thing is to apply
Occam’s
razor... methodological reductionism, the principle of parsimony etc.
Thank you for bringing up Occam’s razor. I of course had to look it
up, but
am pretty glad I did :-)
[Extract] One should not increase, beyond what is necessary, the
number of
entities required to explain anything
http://pespmc1.vub.ac.be/OCCAMRAZ.html
Because I profoundly believe that maths was discovered rather than
invented; that it is fundamental... I expect solutions to literally and
figuratively add up.
Pythagoras believed that the Universe *was* math. Not a tool to describe
reality but reality itself.
^What he said.
This would be kewl in that it responds to the BIG question... how can
you
have something where logically there ought to be nothing? Given a
creationist God, then the same question devolves to her ;)
Answer: the Universe is built of nothing... or rather, something that
most
assume to be purely conceptual and insubstantial ==> dancing numbers.
Put baldly, and in light of what I previously said about a certain
type of
integer: da universe(s) be built from da prime numba's.
IMHO
Very interesting thought!
Could maths exist without language though?
If invented, no.
If discovered, then obviously so.
I believe language is the foundation of all systems accessible to
human mind.
All systems are a sub-system to language.
Language => system of systems.
At least as far as the human mind is concerned.
Is there anything beyond human mind?
Maybe Dats the Da question.
Don’t forget the mice <== hyper intelligent pan dimensional beings.
(HHGTTG)
You’re in the same ballpark as the ‘Copenhagen Interpretation’ of quantum
mechanics... perhaps the most successful explanation of the particle/wave
duality of light. Einstein hated it with a passion… hence "God does not
play dice…" and "Do you really think the moon isn't there if you aren't
looking at it?" – Bohr’s retort: “Einstein, don't tell God what to do”.
I don’t like it either.
Thanks very much and would love to play around with your script
(please
mail it to monsieurstat@gmail.com)
Pi.exe (4kb) sent.
[edit - delivery failure... are you set for .exe attachments?]
It should, but don't worry I'll probably won't be able to run it
unless it's
got a nice clickable GUI :-(
I don't know if I've made it clear but the BBP algorithm iterates as
well.
Think of it as intersecting with the Pi series at the desired location.
IOW, don't go mad with the offset... unless you're very patient. I'll
compile a new version when they get around to releasing quantum
computers
;)
I need to confirm this with you. If I understand correctly, as with your
example of a text file converted into a sequence of digits, I can
find the
position of the number sequence in PI using the BBP algo. But on the
other
end, I need to have the value of Pi calculated up at least the point
that
would contain that sequence.
No, the encoder has the complete known series of Pi. He finds the offset
location which is sent to the decoder… who uses the algorithm alone
(sans
enormous list) to extract the series from the specified offset location.
Another words, I canb't use the Algo in reverse
mode asking it to tell me what are the number sequences between
positions X
and Y in PI are. Is that correct?
We must be misunderstanding each other because that is exactly what
the BBP
algorithm does… extract digits from the series at a specified offset.
Ok please bear with me a little more. I really like to get this straight.
Let me go through an example to show you what I like to do. You tell
me if it
is possible:
I want to take my name, "Stat" and convert it to hexa decimal in this
way:
S = 83
t = 116
a = 97
t = 116
So Stat becomes 8311697116
Can I use the BBA algo to find the location of the first occurrence of
8311697116 in PI?
No, you need the list… having gotten the location you can pull it out of
the series directly using the BBP routine without having the list.
Incidentally, if you want to search the regular decimal series, go here...
http://www.pisearch.de.vu/
Sample:
'12345678' found at position 186557266 in pi's digits after the decimal
point!
(the only value for PI that I have accessible to me is 3.14, which of
course
doesn't contain the sequence)
The world record for memory is 40,000+ decimal places, IIRC.
How sad is that?
If yes, and supposing the algo returns: 8311697116 found at 2.2411
trillion
places
Can I then use BBA to extract the digit that occupys the position 2.2411
trillion? (if yes, it should return 8). I would then continue with
(2.2411
trillion + 1), (1.2411 trillion + 2) ... (2.2411 trillion + 10) to
get the
whole 8311697116, which I just then need to reconvert back to ascii
to get
Stat.
There is of course a little flaw in here for the re-conversion – not
as bad
as the zip file example :-) but if the method works both ways (locating
position and retrieval), I think we are in business.
It doesn’t, we’re not. ;)
Is this possible with BBA Algo without using any known values for PI?
You’ve lost me.
BTW, how fast does something like this take to run? The formula in
that paper
you referenced looked very simple. But you did mention needing
Quantum based
computers at some point :-)
The PiHex project took 3 Pentium-90 years to calculate the
5,000,000,000,000 bit of Pi.
http://www.cecm.sfu.ca/projects/pihex/status.html
-A
.
|
|
|
| User: "tw" |
|
| Title: Re: Whites will be 3% of the World's population in 2100 |
13 Dec 2004 08:18:00 AM |
|
|
"MonsieurStat" <Monsieurstat@yahoo.com> wrote in message
news:Nqgvd.3603$%p1.410276@news20.bellglobal.com...
Thank you for this discussion.
It's been almost like a religious experience for me.
I think I understand now why the BBA algorithm is considered a miracle.
Pi being infinite, the capacity to go and fetch information from any
location
in the infinite, is like going to some future or past time, take note of
what
is there, and come back. Of course the beauty of it is that we can't go
and
look for any specific information. We can only go to a specific location
to
see what is there.
Hunh? I thought it worked both ways.. i-e- you can go and find the location
from your data, or the data from your location... but Amy hasn't answered
whether I was being thick or not yet, so I'm not sure I got this properly...
;-)
I guess the BBA algorithm also proves that Pi is
determinist. So if numbers are the universe - or at least a model of it -
universe itself must be determinist.
I also see a lot of close correlations with other cases that have been
explained by the hologram model - that I found out about only when we
started
this discussion. For example the girl on LSD who hallucinated into another
point in time and was looking out from a prehistoric lizard's eyes during
her
session... LSD in this case might be considered acting like the BBA
algorithm?
Anyway it's all truly fascinating for me. But beyond philosophical
considerations, I am still wondering if it would be possible to come up
with
a way to use the BBA algo to find the position of a number sequence in
Pi -
in order to use it as a data transfer system. The one that will make us
very
rich and a little famous :-)
Here's an idea:
You said we have already calculated some 1.2411 trillion decimal places in
Pi. This will certainly take care of many number sequences, but not the
vast
majority that we might need (i.e. works of Shakespeare converted into
hexadecimal which is a number sequence not found in the already calculated
Pi).
So supposing that we create an algorithm that will try to guess the
position
of any number sequence in Pi - the hexadecimalised works of Shakespeare
for
example.
It already knows that it is not in the first 1.2411 trillions. So it will
try
to find it in the next range, let's say the next 1.2 trillions. The trick
of
course is to not do all the calculations. Just make a few spot checks here
and there - using the BBA algo to see if parts of Shakespear are there or
not. If yes, then try to find the other parts, if not move on to the next
1.2
trillions, until all of Shakespeare is found in Pi.
Is this completely crazy, or do you think we could develop a smart algo
which
is able to move from one range to another in a matter of a few seconds? I
think from a commercial stand point it would be quite reasonable to use
something like a year's worth of CPU time to find a number sequence as
extensive as that of Shakespear's complete works. We just have to do it
once
after all.
Stat (scratching his head a lot these days)
"Absolute Zero" <amycaton@hotmail.com> wrote in message
news:cpi8lg$hj2$6@news7.svr.pol.co.uk...
MonsieurStat wrote:
"Absolute Zero" <amycaton@hotmail.com> wrote in message
8<
I warned you ;)
2, 3, 5, 7, 11, 13, 17 ...
1 isn't conventionally included.
2 is only divisible by itself and one.
5 you missed.
It's still unproven, though massively tested, that all even integers
greater than two, can be written as the product of two primes.
(Goldbach's conjecture, one of the greatest, unsolved problems in
number
theory)
4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7 = 5 + 5
12 = 5 + 7
14 = 3 + 11 = 7 + 7
. . .
In a sense they’re the real integers (all others being products), the
sub-atomic particles of mathematics... hence prime.
WOW! That's the first time I heard prime numbers described in this
way. Gives
me a whole new perspective on primes :-)
I'll definitely remember this one too. Do you think there may be some
application for this?
For Goldbach's conjecture?
Prime numbers are the basis of modern encryption. Stated very simply,
multiplying two large primes produces a product that is only
evenly-divisible by the two original primes. Determining the original
factors from the product can only be tackled by brute force … you can
only
test each and every prime up to the square root of the product. With
sufficiently large primes it becomes impractical… thousands of years of
compute time.
You must have noticed this stuff in DJM’s posts
-----BEGIN PGP SIGNATURE-----
iQA/AwUBQbv9RJljD7YrHM/nEQLjiwCfWM6IDX6TUSB8oEPSXrPBn17+HxUAn3gG
ueQfSnpji0DYyHHulK15cZk6
=5qbp
-----END PGP SIGNATURE-----
PGP stands for Pretty Good Privacy... it’s being used to generate a
signature that makes it impossible for others to successfully fake a
message as being from him.
8<
I'll just state that I *could* proffer a model of the Universe that
allowed
for a flat earth. It would twist and convolve, invoke extra
dimensions and
parallels... but it could be done. The important thing is to apply
Occam’s
razor... methodological reductionism, the principle of parsimony etc.
< | | | | | | | | | | | | |
