[Cliff says, I'm correct in saying that the entire
encylopedia is in pi. So it the Windows XP operating system and
Shakespeare's Julius Cesar. Are you saying I am wrong?]
Each of those things can be encoded as a series of bytes in sequence,
and the three things themselves can be sequenced. As I said, if you
can do that, it's a countable number (finite in this case) - it has
lesser cardinality than the digits of pi.
However, the (base 16 I assume) digits of pi are calculable in
sequence via one of several algorithms. For your conclusion to be
true, the sequence of bytes in those articles would also have to be
calculable by that algorithm, which I doubt.
The set of all possible infinite sequences is of cardinality greater
than |N| (it equals |N|^|N|) so there are possible infinite sequences
that are not contained in the digits of pi. That set might contain
all the information you're talking about, but it's much (infinitely :-
)) bigger than the number of digits in the expansion of pi. (Or any
other transcendent number.)
In any case, you were claiming rather more than those three things.
I'm not sure all the information you're talking about can be
sequenced (any more than the real numbers can be sequenced).
[Cliff says, if you don't think I'm coded in pi, do you think that there is a number that codes me?
Also, are you saying that I MIGHT not be coded in pi or that I AM NOT coded in pi? But if I don't have to be EXACTLY
coded in pi, I am probably encoded in pi.]
Anton says:
Pi does not contain the digits of the
square root of 2, which one member suggested would code a reality where beer is cheaper!
If does not contain square root of 2, then it is not infinite
in regard to containing everything possible, and then all
possible realities are not placed somewhere inside pi,
and therefore we will drink expensive beer just because we made
a mistake in which universe we would like to live.
That will mean that there are possible universes divided by
belonging to the particular transcendental number as a form of
coding.
[Cliff says, Pi may not contain SQRT 2 because SQRT 2 is infinite, but
doesn't PI code for all small finite sequences (like my DNA for example).
If it does not code ALL realities, it codes
for realities that are CLOSE ENOUGH.]
From: ollyhardy
I think Cliff's Pi idea is extremely interesting. If we put aside the goal of immortality for a second, we might consider other, more mundane
uses for pi. A pi based algorithm might alllow for some unbelievably efficent data compression. Think about it. You want to copy the
Encyclopedia Britannica, or a photo of your aunt, or the latest Scorcese flick? Just jump to the appropriate strings in pi.
Of course, exactly how we would be able to recognize and any given string in pi as the blue print for something we know in th ereal world is
easier said than done. Imagining sheerly speculative, sci fi type technology, I can envision a machine which scans objects, digitizes them and
then searches for those strings in pi. It then stores the "addresses" or locations in pi where the information for any given object can be found.
Once the machine knows "the address" or adresses in pi of any real world object, it can retrieve the information or build a copy as needed.
Even more intersting, imagine getting creative with pi machine. Imagine a brain interfaced with a "Pi Machine" such that it could translate
your thoughts into pi digits and then make your fantasies a reality? That'd be worth at least 50 bucks.
Cliff wrote:
[Cliff says, Pi may not contain SQRT 2 because SQRT 2 is infinite, but
doesn't PI code for all small finite sequences (like my DNA for example) If it does not code ALL realities, it codes
for realities that are CLOSE ENOUGH.]
Yes,but it is interesting that even pi is infinitive it does not contain every combination of numbers which will
imply that trancendental numbers are infinitives which are finitely diverse or that all trancendental numbers are one
number but seen started on different "point" of beginning.
Anton
From: "Chuck Gaydos"
A number can fail to ever repeat and still not contain every finite
sequence. How about .1001110000111110000001111111...? It never
repeats yet doesn't encode the number 1½. Pi could fail to repeat but
still not contain every possible finite sequence.
-Chuck
[Cliff says, it doesn't matter. For all intents and purposes, Pi codes for you. It doesn't matter if it actually
codes for a "you" that has several atoms misplaced.]
> Todd wrote:
Pi may be a never ending and never repeating decimal, but if we
could say that pi contained
every image, then it would necessarily have to contain copies of itself,
which would make it repeating.
Interesting remark.Pi is containing self not as copy but it is
containing self as being pi BUT it does not contain square root of 2
,as one member suggested to be place where beer is cheaper.
If does not contain square root of 2 then it is not infinitive in
regard of containing everything possible and then all possible
realities are not placed somewhere inside pi and therefore we will
drink expensive beer just because we made a mistake in which universe
we would like to live.
That will mean that they are possible universes divided by belonging
to the particular transcendental number as form of coding.
Anton
From: "Tufrmone" to Chuck: The Pi sequence Chuck
has cited will eventually encode for 1.5. Actually it will encode for 1.5 a whole lot sooner than it will encode for the events surrounding Jesus,
which will also be encoded in one form or another. The sequence isn't simply Pi itself but any encoded sequence in the sequence itself as in
every third digit followed by the 42nd and divided by the first 5. Eventually you will find a sequence to accurately represent every possible event
and thing imaginable including fractions. Tufr
[Cliff says, my mathematician friend from IBM says:
"If the binary representation of pi is interpreted as a program in some computer language, perhaps it encodes a simulation of the universe that
includes itself, you and me... or maybe it is a movie of your live encoded in some yet-to-be-discovered version of MPEG..."
Chuck Gaydos wrote:A number can fail to ever repeat and still not contain every finite
sequence. How about the sequence...... It never
repeats yet doesn't encode the number 1½. Pi could fail to repeat but
still not contain every possible finite sequence.
Chuck
[Cliff says, it doesn't matter. For all intents and purposes, Pi codes for you. It doesn't matter if it actually codes for a "you" that has several
atoms misplaced.]
From: "Tufrmone" :
Dear Cliff:
I have not seen this aspect of Pi discussed before and it raises a number of immediate questions in my mind. The first one is that
assuming Pi does encode for every event and thing which ever occurred, may have occurred, may occur in the future and will occur
in the future --- does this provide a solution to the apparent fact that the delivery of material into a black hole violates the laws of
thermodynamics because would theoretically be destroying information in a manner which cannot be recovered. If Pi is a record,
such information could theoretically be recovered couldn't it?
Tufr
From: ollyhardy:
Cliff:
A couple of questions about Pi....
Just because all of the information describing us is in Pi, why does
that mean that we are necessarily immortal per se? Doesn't it really just mean
that all of the critical information necessary to "compute us" is available,
requiring still someone or some "thing" else to take the trouble to compute us?
After all, all of the information to create the movie "Goodfellas", or
you yourself and me for that matter was in Pi when the dinosaurs ruled the
earth, but the data only became such things as we call Goodfellas and Cliff
respectively when they were naturally selected for computation. We can take our
left hand and our right hand and do "karate chops" anywhere along the infinite
string of digits that is Pi and "compute" what lies between our hands, but what
does it really mean?
Also, what number is "pi" itself in?
I have your book "Keys To Infinity" and my friend tells me that this
idea that "we all live forever in PI" is in there, but I can't find it. Is he
right? If so, do you know off hand what section of the book I might find it in?
I have 6000 questions about this fascinating subject you brought up,
but unfortunately,or fortunately as the case may be, I have many more questions
than time, so I have to leave it here for now.
[Cliff says, you MUST read the SF novel Permutation City by Greg Egan. It gets close to this sort of thinking.
As you know, Chapter 7 in Keys to Infinity has a lot of fascinating pi information.
I don't recall if I made this exact comment here or in another book.
]
From: "mwganson" :
Regarding a
brain interfaced with a "Pi Machine":
This is an interesting idea. You just keep the address of the start
of the encoded string. The problem is that the address is a number
so long that it takes more space to store that value than the space
needed to store the data that is encoded.
As an example, in order to find the first occurrence of a particular
string of 4 digits, say, 1234, we don't find it until we get to the
13,386th digit in pi. If the address is longer than the data, not
only do we need more space to store the address, we also have the
overhead of producing the sequence each time.
--Mark
From: "Graham Cleverley"
[Cliff says, if you don't think I'm coded in pi, do you think that
there is a number that codes me?]
In theory, your physical body structure at a particular time could be
encoded as a long but finite string of bytes, and therefore as a
number. I suppose also that in theory that number could be used to
reconstitute you, given the technology to do it. Which is what
makes 'matter transmitters' theoretically possible, though they would
be better called 'matter duplicators'.
Whether you have a part that is non-physical (one or more 'souls') I
really have no idea. If you do, then I also have no idea whether that
could be similarly encoded.
Also, are you saying that I MIGHT not be coded in pi or that I AM
NOT coded in pi?
That you might be, but that you might not, because there are
sequences of numbers that are not included in pi. Whether you are or
not is theoretically a testable hypothesis: how the test would turn
out is unknown.
And if you are encoded in pi, it doesn't mean I would be. I might be
included in 2*pi though - or e.
As I hinted earlier, I could more happily live with the assertion
that all the information you mentioned is included somewhere in the
set of all transcendent numbers.
[But if I don't have to be EXACTLY coded in pi, I am probably
encoded in pi.]
I guess the lower the exactness the higher the probability.
From: "Graham Cleverley"
[Cliff says, my mathematician friend from IBM says:
"If the binary representation of pi is interpreted as a program in
some computer language, perhaps it encodes a simulation of the
universe that includes itself, you and me... or maybe it is a movie
of your live encoded in some yet-to-be-discovered version of
MPEG..."]
The important things there are the words 'perhaps' and 'maybe'. I go
along with that.
From: "Chuck Gaydos":
Whether or not I'm encoded in Pi depends on the coding method. If we
choose a coding method such that you're encoded in Pi there's no
guarantee that I am as well. Since you don't insist that every atom
be exactly accounted for there would be a vast number of strings of
digits that could be said to encode me, but do any of them exist in
Pi? A number can fail to repeat and still not contain all possible
finite patterns. Are there a trillion consecutive zeros in Pi? It
seems likely to the best of our knowledge, but maybe not. It might
be that none of the strings that encode me exist. Of course, you
could choose a coding method that includes both of us, but that's
kind of arbitrary. I'd say I was encoded in the encoding method and
not in Pi itself. If you choose a sufficiently complex coding method
then the entire universe can be encoded by a single digit. It's
unremarkable that we're all encoded in Pi if the coding method forces
it.
-Chuck
From: "mwganson" :
Are there a trillion consecutive zeros in Pi?
Of course there are. The possibility that there are not is so small
that it is impractical to even consider it.
We can determine the probable number of times p that a consecutive
string of z zeros exists within a given subset of the first d digits
of pi as:
p == 1/10^z * d
For example, suppose we are wondering whether there are any strings
of 5 consecutive zeros within the first 100,000 digits of pi.
p == 1/10^5 * 100000
p == 1
This means we can expect to find 1 such string, which is exactly how
many there are. The string of 5 zeros has the same mathematical
probability of occurring as any other 5 values, such as 12345 or
99999. Each of these strings will probably occur once each. I will
test this by searching for, and counting, the occurrences of these 10
strings: 00000, 11111, 22222, ..., 99999. Stay tuned... Okay, I'm
back.
String: occurrences
00000: 1
11111: 1
22222: 1
33333: 1
44444: 0
55555: 2
66666: 1
77777: 0
88888: 0
99999: 4
Total: 4+0+0+1+2+1+1+1+1 == 11
We would have expected to have a total of 10 occurrences of all of
the searched for strings. Instead, I found 11, which is close enough
for me. (Arguably, however, the string 99999 only occurs 3 times
since there is a single occurrence of 6 consecutive 9's -- 999999,
which I counted as 2 separate occurrences of 5 consecutive 9's.)
Half of the strings (5 of them) had exactly 1 occurrence each. There
were 3 absent strings, but this was made up for by multiple
occurrences of 2 of the strings (2 times for 55555 and 4 times for
99999).
I can post a text file of about 100K in size, which contains all of
these 100,000 digits to the Files area if anyone is interested in
seeing it. You can probably find something similar through Google,
though... Be right back... Okay, I'm back. Here is a link to just
such a file:
http://www.geocities.com/thestarman3/math/pi/df/PI100KDP.ZIP
and, for other sizes:
http://www.geocities.com/thestarman3/math/pi/picalcs.htm
Now, back to the question of 1 trillion consecutive zeros. How many
digits of pi must we extract before we can reasonably expect to find
a single occurrence of 1 trillion (10^12) consecutive zeros?.p == 1/10^z * d
1 == 1/10^(10^12) * d
1/d == 1/10^(10^12)
d == 10^(10^12) (after cross multiplication)
So, after (just?) an expansion of 10^(10^12) digits, we can
reasonably expect to find an occurrence of a string of 1 trillion
consecutive digits. I say (just?) because, even though 10^(10^12) is
unimaginably huge, it is not even a drop in the ocean compared to
infinity. After an expansion of 10 * 10^(10^12), we can reasonably
expect to find 10 such strings of a trillion zeros. After an
expansion of, say, a billion times the amount needed to find a
trillion consecutive zeros (10^9 * 10^(10^12)), which is still not
even a drop in the bucket as compared to infinity, we could expect to
find a billion such strings of a trillion consecutive zeros. Does
this mean there is *definitely* at least one string of a trillion
consecutive zeros within the first 10^9 * 10^(10^12) digits of pi?
No. But, the probility is extremely high (I'd say: (10^9-1)/10^9? --
Someone please correct me if I'm wrong.) that there is at least one
such string within that finite expansion.
--Mark
From: "Chuck Gaydos":
All of this assumes that the digits of Pi are normally distributed.
They appear to be so far but we haven't looked at truly large
quantities of them. They're not randomly generated after all.
-Chuck
From: "bobomutin":
Chuck's observation seems sound regarding coding. I am still not sure
why Cliff made the statement below. What observation, research,
paper, mathematician(s) are his compelling statements based on?
Pythagoras? Kant, Reimann, someone more contemporary? Puzzled and
waiting, on Yahoo.
From: "Graham Cleverley":
The fact that they're not random is one of the things that makes me
doubt I'm encoded in it.
[Cliff says, can you explain why? If you assume pi is "normal", why wouldn't you think your are coded in it? When I
use the word "you" I allows for slight discrepencies. For example, I still call it "you" even if a few atoms are out
of place. After all...
As we age, the molecules in our bodies are constantly being
exchanged with our environment. With every breath, we inhale the world
lines of hundreds of millions of atoms of air exhaled yesterday by
someone on the other side of the planet. In some sense, our brains and
organs are vanishing into thin air, the cells being replaced as quickly
as they are destroyed. The entire skin replaces itself every month.
Our stomach linings replace themselves every five days. We are always
in flux. A year from now, 98 percent of the atoms in our bodies will
have been replaced with new ones. We are nothing more than a seething
mass of never-ending world lines, continuous threads in the
fabric of spacetime.
What does it mean that your body has nothing in common with the body
you had a few years ago? If you are something other than the collection
of atoms making up your body, what are you? You are not so much your
atoms as you are the pattern in which your atoms are
arranged. For example, some of the atomic patterns in your brain code
memories. We are persistent
spacetime tangles. In my book Time: A Traveler's Guide, in a diaram, a person is represented by
a set of four atom threads that have come close together. (An "atom
thread" is the spacetime trail of an individual atom.) Note that an
atom can leave one person's array and become part of another person.
Very likely you have an atom of Jesus of Nazareth coursing through your
body.
The nth digit doesn't just depend on the previous one, it depends on
all the previous ones, because it must take the whole number closer
to the value of pi. The numbers in my encoding would not have to
follow that rule (but one of their own, I assume, which might well
conflict).
From: "Graham Cleverley":
Something else I should have added.
The set of the digits of pi is sequenced and therefore has
cardinality |N|, just like the set of integers. However the set
[2,4,6,8,10,....] also has cardinality |N| but it does not include
the odd numbers.
Incidentally, the set of all infinite sequences in pi also has
cardinality |N|, whereas the set of all infinite sequences has
cardinality |N|^|N| which is greater.
From: "Cliff Pickover":
Hi, I'm not sure why I am getting push back on this. If we assume
that the digits of "pi" are normal (and indications are that they
probably are), then it seems clear to me that we are in pi. And,
never mind the fact that pi may code us a few atoms out of place.
As we age, the molecules in our bodies are constantly being
exchanged with our environment. With every breath, we inhale the
world
lines of hundreds of millions of atoms of air exhaled yesterday by
someone on the other side of the planet. In some sense, our brains
and
organs are vanishing into thin air, the cells being replaced as
quickly
as they are destroyed. The entire skin replaces itself every month.
Our stomach linings replace themselves every five days. We are always
in flux. A year from now, 98 percent of the atoms in our bodies will
have been replaced with new ones. We are nothing more than a seething
mass of never-ending world lines, continuous threads in the
fabric of spacetime.
What does it mean that your body has nothing in common with the
body
you had a few years ago? If you are something other than the
collection
of atoms making up your body, what are you? You are not so much your
atoms as you are the pattern in which your atoms are
arranged. For example, some of the atomic patterns in your brain code
memories. We are persistent
spacetime tangles. In my book Time: A Traveler's Guide, in a
diagram, a person is represented by
a set of four atom threads that have come close together. (An "atom
thread" is the spacetime trail of an individual atom.) Note that an
atom can leave one person's array and become part of another person.
Very likely you have an atom of Jesus of Nazareth coursing through
your
body.
From: "nick_hobson":
Is it possible to make money betting on the digits of pi, without
actually calculating pi?
Nick
From Mark:
You are correct in that I assume the digits are randomly
distributed. I believe this is a good working assumption. The fact
that the digits of pi bring pi to a specific, non-random, value is
not relevant. As an analogy, consider the estimated number of atoms
in the observable universe: 10^78 (some estimates have it at 10^81).
Now, the *exact* number, if we could count them, is probably not be
exactly 10^78. The actual number would probably look a lot like a
random string of about 78 digits, with each of the 10 possible digits
(0 through 9) being represented rougly an equal number of times
each. In other words, we'd expect to see 7 or 8 zeros, 7 or 8 ones,
etc., despite the fact that we are looking at a number that is not
itself a randomly generated value.
We can reasonably expect that after n digits of expansion we will
have roughly equal representations of all 10 digits in pi. The
larger the value for n, the closer the count totals for each digit
will approach n/10. As I have shown, within the first 10^9 * 10^
(10^12) digits, we will have a billion different strings of a
trillion consecutive zeros. This also holds true for any particular
sequence of a trillion digits, including the first trillion digits of
pi, a trillion consecutive nines, etc.
The encoding scheme is quite irrelevant, whether it be mpeg, dna,
machine language, ascii text, or whatever, just so long as the
encoding sequence is capable of encoding the data, any finite string
of digits is sure to exist not just once, but an infinite number of
times. There are an infinite number of strings of a trillion
consecutive zeros within the infinite expansion of pi.
I have done some more calculating. Given any randomly generated
stream of an infinite number of (base 10) digits, the probability
that there exists a number n, such that the first n digits in the
stream is exactly duplicated by the second n digits in the stream is
1/9.
This is based on the sum of the infinite series defined as 1/10^n
where n ranges from 1 to infinity.
Mathematica code:
Sum[1/10^n,{n,1,Infinity}]
output: 1/9
I calculated this because I was curious to know if there was such a
number n for pi where the first n digits of pi were exactly
duplicated by the next n digits. I wondered what the probability for
this was, and whether it was closer to 0 or to 1. The fact that if
such a number n exists for pi, then such a number must be quite
large, means that the probability of this ever happening for pi is
quite low. The bulk of the value of 1/9 comes when n is very low.
With each successive value for n, the probability gets lower and
lower. Given this calculation, I conclude that the probability that
the first n digits of pi are duplicated by the next n digits anywhere
along the stream is extremely unlikely and very close to 0. But, pi
is not the only transcendental number out there. Given 9 different
transcendental numbers, the chances are good that at least one of
them will have a cycle of repeated digits, most probably occurring
within the first 10 digits.
--Mark
From: ollyhardy:
This is essentially a statement of the pattern theory of identity, an idea that is at least as old as the ancient Greeks who spoke of the ship of
Theseus. The Greeks imagined a ship- the ship of Theseus- which over the years, owing to wear and tear, has to have a piece here replaced
and a piece there replaced until finally, after a hundred years or so, not one component of the ship of Theseus was a part of the original
construction. Is it the same ship?
If the ancient Greeks were aware of the fact that all of the atoms making up the ship of Thesus were being replaced so frequently that there
was probably not a single original atom in it's structure by the time the first 4 x 4 had to be replaced, it would have rendered the answer to this
ancient riddle acadamic. Of course it's the same ship; it's the pattern that determines identity, not the physical continuity of the pattern's
components.
When people express doubts about the pattern theory of identity, it is usually in the context of discussions about simulated beings. Some
people find it hard to accept that a machine which faithfully dupilcated the patterns that make us up would really be us. The problem is not with
the pattern theory of identity, which is really the only viable identity theory, but with their understanding of it. The idea that there is some static
"stuff' that we are made up of from moment to moment is an illusion. We are all like ships of Theseus.
From Mark:
Cliff,
It doesn't matter that we are in a constant state of change. We can
pinpoint our atomic makeup to an instant in time and use that. In
fact, given the infinite nature of pi, we can expect that there are
continuous encodings strung sequentially representing our exact
atomic makeup for every second of our existence from birth to death.
By this, I mean that you could create an encoding scheme that would
allow you to map every atom in a human being. This encoding scheme
would create a series of base 10 digits, which could then be decoded
and used to reproduce a 3D map of the human being all the way down to
the atomic level. Now, use this encoding scheme to take a "snapshot"
of any person every second of that person's life. (Or, every
microsecond, if you prefer.) If this person lives to be n seconds of
age, then we have n sets of snapshots encoded sequentially in the
scheme. We can delimit the snapshots any way you like, such as by
separating them by a stream of a trillion consecutive zeros. For
every person that has ever lived there exists an infinite number of
these life strings within the infinite expansion of pi.
If we view the string of digits in pi as the stream of digits in an
mpeg movie, there exists an infinite number of strings of such digits.that exactly duplicate the new Matrix movie. There are also versions
with different endings, in different languages, even with different
actors and actresses. There are even versions where you and I get to
be the stars in it!
--Mark
From: "ENAM" :
I think the problem simplified down to whether the
representation of a system as complex as me in a
string of binary digits is same as me ,and I think the
answer is yes ,my reasoning is simple ,whatever atoms
or elimentary perticle creates me ,they are nothing
but a representation of some complex mathematical
formulation ,and within it it holds no extraordinary
principle ,except how it will change according to
global time or coordinate or what ever,
so if I am really nothing but a representation then in
whatever format I exist ,they don't differ by a long
way ,however some represtentation may act differently
then other ,such as I am now writing the letter ,but
my binary self may not be doing that .... :)
Enam.
From: "Graham Cleverley":
Cliff you are getting push baack for two reasons.
One is that you don't take into consideration that there are
(infinitely) many different orders of infinity. A smaller one cannot
contain elements that map to all the elements of a larger one.
The digits of pi are a set of cardinality aleph0, also written as
|N|, the same as the set of all integers. We know that because each
nth digit of pi can be mapped to the integer n.
A little harder to see is that the set of infinite sequences in pi is
of the same cardinality. This is because the only infinite sequences
in it are, spelling it out, the one that starts with the first digit,
the one that starts with the second digit, and so on. They can
therefore be mapped to the set of integers, which means they are
another set of order |N|. You can therefore take the union of the two
sets, but that does not increase the cardinality, since it is
provable that |N| + |N| = |N|.
The set of finite sequences in pi is harder. But take the first
digit: it starts one finite sequence for each following digit (3, 3-
1,3-1-4,3-1-4-1 etc. There are therefore |N| of them. There are also
|N| starting with the second digit, |N| with the third and so on.
There are therefore |N|*|N| finite sequences - but |N|*|N| also
equals |N|.
Add all the three together and you still have only |N| elements. That
is not enough for instance to map all the real numbers, which have
cardinality |R| > |N|.
So, before you can validly make your assertion you have to
demonstrate that the set of things you want to map is of cardinality
<= |N|. And that is only a necessary condition, not a sufficient one.
Then there is the second problem, the distribution of the digits of
pi. They do not seem to be random in any strictly definable sense. If
they were, then the n+1th digit could be any one of the ten. In fact
it is constrained to be one and one only of them.
But even if they were random, they might not be normally distributed.
They might instead be like the faces of a die - all equally likely,
whereas if they were normally distributed the numbers most common
would be 5 and 6.
You are therefore making two assumptions without adequate foundation.
Primarily that |N| has sufficient cardinality and secondarily that
the digits are random.
It's not as though all infinities were equal.
Tufr says:
Continuing this thread for a moment, there is something as equally intriguing in the Pi sequence as everyone's human genome. All things being equal, sequenced in Pi is a book or a very very large set of books entitled somethlng like - the The Nature and Secrets of Universal Reality or some such thing.
Once decoded and printed the reader will find that the book is indeed the legitimate answer to man's every question about the universe, his place in it, and each and every question the reader ever had or will ever have, including what stock will jump 6 points on Tuesday and what horse will win the 5 at Belmont and the numbers for every state lottery from now to Kingdom come.
Some versions will contain a genuine moment to moment biography of every person who ever lived or will ever live. Others will contain detailed accurate instructions to create just about anything and everything that can be created, made or manufactured.
In fact, based upon the theory of Pi as expressed in this group, there are nearly an infinite number of such books. Moreover, there is at least one subset containing a personalized dedication to the specific reader from the great unknown.
For example there is at least one version specifically dedicated to Clifford Pickover, thinker extraordinare. Of course, the whole trick is simply to find it.
I suppose a very very large computer programmed with the right sequences could make a stab at it. The chances of obtaining meaningful and accurate results would probably be no greater than winning the state lottery on a date certain.
Jim says: even if one accepts Cliff's proposal that Pi contains all possible information sets,
there is a key difference between the existence of *information*
(whether it is PC source code, genetic code, or a coded representation
of the current state of every atom in my body) and the retrieval/execution of that information.
Every one of my cells contains my genetic code -- yet I don't feel bad when I get my hair cut and watch a few billion cells get swept into the trash, and I don't take any comfort in the (unlikely) possibility that one of these cells might one day be cloned.
"A little rhetorically overwrought, I think. But in any case, it
depends on an open conjecture."
(professional mathematician, noted skeptic and author)
"People will believe in anything if it promises immortality."
(retired physicist)
"Even if there is ultimately a discreteness to everything, it still
doesn't follow - the above is only true if the above are finite, and
that pi is normal, which I seem to remember is still to be proved.."
"I suspect the puckish Pickover of engaging in parody here. I'm not
sure of the target: John Barrow, Frank Tipler, or perhaps Max
Tegmark. In any event, I thinking he's kidding, because it must be
obvious that to represent is not to replicate. It must also be
obvious that if a segment of pi perfectly represents our lives, it
must also represent our deaths. The 'immortal' part is a
nonsequitor...
Grog knows, I'm no mathematician, but I have yet to encounter a
single one of these infinite replication speculations that doesn't
strike me as problematic. Here's one general stumbling block:
We don't know whether organic experience can be entirely digitized. A
CD recording of Pavarotti may be a damn good representation of the
singer, but it is a sampling, not a replication. Unless you can make
a one-for-one digital representation of organic experience, you
cannot claim to replicate it. This, in a quantum world, strikes me as
unlikely. It would likely require infinite probability ranges within
a finite set of numbers representing you."
Ned says: Oh God, Pi contains a scene in which I am making love to Britney Spears. Fabulous!
I am now a happy man.
 The discussion of our lives being encoded in pi continues on the
next page. Here, we'll also delve deeper into the mathematics
of finding ourselves in pi.
|
In May of 2003, I asked my
Pickover Discussion Group to consider a concept that
had been on my mind for many years.
Ollyhardy responds:
This is a fascinating speculation, on many levels.If the digits of pi include every possible finite sequence, than in principle a hypothetical
super-and I mean really super- computer could "crank out" all of the permutations and thus produce a copyof everything that has ever lived. In
theory, all of the information is there to produce a trilobyte, or Cliff at 15, or, interesting, Ciff at 80, or an infinite number of parallel reality Cliff's.
Rogue physicist Frank Tipler wrote a book some years back called "The Physics of Immortality" in which he argued that under special
circumstances, in a collapsing universe, right before the final collapse there would be enough power (watts) for a universal computer to produce
simulations of everything that has ever lived in it. Tipler's thesis involves some rather elaborate and unlikely physics in order for his "Omega
Point" computer to be able to somehow access and manipulate all of the infoirmation that has ever existed in our universe. However, if Tipler
had been aware of what Cliff is saying about Pi, then in theory the information is already available, if only we knew what to look for in Pi. In
principle, the information is already here, the main obstacle might be how to obtain the massive amount of power-sheer wattage- required to
generate such simulations. Perhaps the power required to fuel such machines may one day be available to us, whet Now all we need is for
Cliff to crank out a beta version of the hardware/software. Could you have somethiing on my desk by say, early next week?
From: "Tufrmone" :
The logical conclusion of what you are speculating is that there is not simply one of every person, there is an infinite number of
variations of ourselves, each one one number different. There is also an infinite number of realities encompassing the genetic codes,
the molecular structures and the past and future events of every living and non-living thing.
A computer powerful and fast enough would theoretically be capable of using pi to decode, record and rerun every event from the
birth of the universe to the present and into the future. One could for example watch Jesus give the sermon on the mount or see him
raise the dead.
The problem of course is that one could never know with certainty if it was our reality we were seeing or another reality similar but
different from the events of our own past with respect to the one critical event we are at that moment concerned with.
Tufr