Note that I have written a book on this subject. In this same book, I explain how our thoughts reside in the vibrational patterns of a cube of Jello.





[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?]

[Cliff says, Pi may not contain SQRT 2, because SQRT 2 is infinite, but doesn't PI almost surely 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.]

[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.]

[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. ]

[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..."]

[Cliff says, can you explain why? If you assume pi is "normal", why wouldn't you think you are coded in it? When I use the word "you" I allow 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.

"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."





Perhaps I can shed some light on this matter. The property of the decimal expansion of a number containing every possible FINITE (my emphasis) sequence of digits is called (appropriately enough) being a lexicon. Many numbers are lexicons.

All Borel normal are lexicons. This includes all numbers which are truly random in a certain precise mathematical sense. It is not known if PI is a lexicon. However there are simply constructed lexicons for example 0.123456789 10 11 12 13 14 15 16 17 18 19 ... (I put the spaces for pedagogical reasons). constructed by just counting! This number will contain the library of congress infinitely often as ASCII code. 0, 1, 01, 11, 100, etc will all occur infinitely often.

Now this number is not random but contains every possible pattern of digits (finite patterns) infinitely often. It doesn't contain the square root of 2, since this is infinite. But it certainly contains Greg Bear's Blood Music infinitely often as well as every episode of Monty Python's flying circus. Basically a random real number (many equivalent definitions of random, see for example Greg Chaitin) between 0 and 1 will have this remarkable property. But I am not sure if PI is a lexicon. I believe that it is but I don't believe that it has been proven. -- Jim Cox

Martin responds: Another question about pi: Is pi normal ? It looks like e is not normal. See:

http://www.mathpages.com/home/kmath519/kmath519.htm





The square root of two is encoded in pi. Somewhere in those digits there's a computer program that can generate the digits of the square root of two. That's an encoding method. An encoding method doesn't mean that the actual digits are there. -Chuck





No computer program anywhere could ever generate the digits of the square root of two or of Pi or of any other irrational or transcendental number, Chuck. So no, the square root of two is not "encoded" in Pi.

Even the vast assortment of known mathematical functions we have to "generate" Pi are not really Pi generators, in reality they can never generate more than finite approximations of the actual infinite value of Pi. Any and all of those are so trivial in content compared to the true infinite entity as to be totally negligible as true absolute and complete representations of Pi itself. They all can only physically be used to generate exactly zero percent of the true infinite string of digits comprising the exact value of Pi, and all of the known calculated results therefore actually differ from the true infinite string of digits of Pi by an infinite amount of digits.

Nothing is "encoded" in Pi except Pi itself. Finally, the term "encoding" as you use it is the same as saying that the symbol "2" is an "encoding" of the abstract mathematical value 2, which is true bit is totally trivial.

Pete B

My real point is that it is only the human mind that actually encodes anything, not the contents of patterns in abstract entities. Without humans to recognize such patterns, Pi does not encode anything, not even its own value; the **mathematical-described relationships** that involve Pi would still exist whether humans were around or not, but there would be no encoding of anything in that (or in any other such infinite string), it would simply be a case of chaos and absence of chaos (or order if you will) existing in the same universe.

A computer programmer encodes a set of instructions into a formal program. But the actual physical form of the program is either symbols of some arbitrary shape inscribed by the programmer in ink on paper or perhaps various kinds of arbitrary patterns of pixels on a computer screen stored as other arbitrary electronic states in a memory chip. The encoding is not in the symbols, not even in the pattern of those sets of symbols; it is in the human mind that runs the whole show and actively employs those otherwiuse inert meaningless patterns to accomplish some task. The only encoding is the human invention of transforming certain kinds of symbols or pixel patterns into other kinds of electronic states in order to ultimately accomplish some useful task.

Encoding is strictly a human endeavour. The symbols are merely human inventions used as tools to accomplish that function.

Pete B



