Valheru
08 Jun 2009, 09:27 AM
WARNING: Massive Spoiler Ahead
To those of you who have read Carl Sagan's novel Contact will recall that, towards the end, during Ellie's discussion with the E.T.I. avatar, she directs a question of what fills THEM with religious/numinous awe.
The answer she is given is that, if one divides a circle's circumference with its diameter, the result is a value that she is already familiar with: π. What fills THEM with awe, is that if you calculate the fractional digits long and deep enough, the digit series switches to a massive run of ones and zeros that is statistically anomalous. In other words, there is a message "hidden" inside the mantissa of π, not unlike the message sent to Earth that allowed us to build "The Machine" in the first place.
The ETI is somewhat cryptic about the discovery, merely stating that they are "working on it".
When Ellie returns to Earth, and the entire project is discredited, she "hermits" herself to the Project Argus Radio installation, and works on algorithms to calculate the mantissa of π. Watched all the time, she smuggles copies of the program out to Palmer Joss, who has it implemented and whereby the "message" hidden is finally "cracked".
As it turns out, the message is encoded in "eleventary" (base 11) :D, and plotting the bits on a square grid draws a perfect circle. The idea is that the universe is designed, seeing as π is a fundamental "magic number" that is integral (sorry) to the universe itself. That it contains a message itself implies that our universe is intentional and "designed", and that the message itself is a message from a pantheistic "god".
Spoiler semi-ends
Now, I've never read any commentary of Mr. Sagan on this little piece, but this punch-line of the novel filled me with a bit of disappointment. My gut feel is that pi being a non-irrational-perhaps-non-infinite (at the very least in base 10 or 11) is highly unlikely. That it contains a message - even less likely.
What I can grok though, is how the mathematical magic of pi's relation to "circularity" might create a sort of echo when you attempt to represent it with digits. Anybody who has used a HEX editor and looked at the raw data behind graphics might understand what I'm trying to convey - there is a suggestion of the end product even though it's not the representation of the end product at all.
My feeling is that Mr. Sagan is multiplying entities, despite the beauty and elegance of the rest of the book. Is it plausible that our universe is intentional and designed? Certainly it is, but then it's subject to the same creaçionista implosion of logic - i.e. who designed the designer, and so on
To me... any "intentionality" to our universe is implicit, not explicit, which would otherwise make the word "intentional" a non sequitur.
To end off, I'd like to share this little entry of the Jargon File (http://catb.org/jargon/html/index.html), which is an entry to the IOCC (International Obfuscated C Code Contest). The IOCCC is a competition amongst hackers to create the most elegant-yet-hard-to-understand program in C. This particular entry is deep, dark, black voodoo magic. It calculates the value of π as a return value by looking at its own surface area. The larger you make the "program", the more accurate the return value is. The program instructions are in the shape of a circle. In other words... a circle encodes a value, and yet a series of digits encode the circle... and the value of pi...... :argh:
Behold:
#define _ -F<00||--F-OO--;
int F=00,OO=00;main(){F_OO();printf("%1.3f\n",4.*-F/OO/OO);}F_OO()
{
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}
To those of you who have read Carl Sagan's novel Contact will recall that, towards the end, during Ellie's discussion with the E.T.I. avatar, she directs a question of what fills THEM with religious/numinous awe.
The answer she is given is that, if one divides a circle's circumference with its diameter, the result is a value that she is already familiar with: π. What fills THEM with awe, is that if you calculate the fractional digits long and deep enough, the digit series switches to a massive run of ones and zeros that is statistically anomalous. In other words, there is a message "hidden" inside the mantissa of π, not unlike the message sent to Earth that allowed us to build "The Machine" in the first place.
The ETI is somewhat cryptic about the discovery, merely stating that they are "working on it".
When Ellie returns to Earth, and the entire project is discredited, she "hermits" herself to the Project Argus Radio installation, and works on algorithms to calculate the mantissa of π. Watched all the time, she smuggles copies of the program out to Palmer Joss, who has it implemented and whereby the "message" hidden is finally "cracked".
As it turns out, the message is encoded in "eleventary" (base 11) :D, and plotting the bits on a square grid draws a perfect circle. The idea is that the universe is designed, seeing as π is a fundamental "magic number" that is integral (sorry) to the universe itself. That it contains a message itself implies that our universe is intentional and "designed", and that the message itself is a message from a pantheistic "god".
Spoiler semi-ends
Now, I've never read any commentary of Mr. Sagan on this little piece, but this punch-line of the novel filled me with a bit of disappointment. My gut feel is that pi being a non-irrational-perhaps-non-infinite (at the very least in base 10 or 11) is highly unlikely. That it contains a message - even less likely.
What I can grok though, is how the mathematical magic of pi's relation to "circularity" might create a sort of echo when you attempt to represent it with digits. Anybody who has used a HEX editor and looked at the raw data behind graphics might understand what I'm trying to convey - there is a suggestion of the end product even though it's not the representation of the end product at all.
My feeling is that Mr. Sagan is multiplying entities, despite the beauty and elegance of the rest of the book. Is it plausible that our universe is intentional and designed? Certainly it is, but then it's subject to the same creaçionista implosion of logic - i.e. who designed the designer, and so on
To me... any "intentionality" to our universe is implicit, not explicit, which would otherwise make the word "intentional" a non sequitur.
To end off, I'd like to share this little entry of the Jargon File (http://catb.org/jargon/html/index.html), which is an entry to the IOCC (International Obfuscated C Code Contest). The IOCCC is a competition amongst hackers to create the most elegant-yet-hard-to-understand program in C. This particular entry is deep, dark, black voodoo magic. It calculates the value of π as a return value by looking at its own surface area. The larger you make the "program", the more accurate the return value is. The program instructions are in the shape of a circle. In other words... a circle encodes a value, and yet a series of digits encode the circle... and the value of pi...... :argh:
Behold:
#define _ -F<00||--F-OO--;
int F=00,OO=00;main(){F_OO();printf("%1.3f\n",4.*-F/OO/OO);}F_OO()
{
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}