Thursday, May 10, 2007
Wednesday, May 09, 2007
Science Vs Religion
I love it when athiests try to dismiss Christian beliefs as being nothing more than unscientific theories and assumptions. This attitude belies the fact that mathematics is every bit as filled with theories that are assumed to be true as is religion. I realize Christians have God on their side and don't need reason or logic to defend their beliefs, but I thought I'd take a shot at it anyway.
Strong evidence of similarities between science and the triumvirate of monotheistic religions (Judaism, Christianity and Islam) is found in Principia Mathematica. For those of you not in the know, this work was Alfred Whitehead and Bertrand Russell's ambitious attempt to reduce all of number theory (note that word there -- theory) to a formal, axiomatic system. Its whole foundation is a few simple axioms that are almost indesputible. (Note the emphasis there: ALMOST indesputible.)
If Principia Mathematica is analogous with Judaism, then Gödel's incompleteness theorem is Christianity. It uses that old mathematical trick of proof by assuming the opposite of everything and then finding a contradition. In theology I think they call it "paradox". Whatever the case, Gödel's theorem, like Russell and Whitehead's Principia Mathematica is still theory.
Douglas Hofstadter (author of Gödel, Escher, Bach) is the Johnny-come-lately like the prophet Muhammad and his Islam. The coincidences just keep piling up when we discover that Hofstadter called his version of Gödel's theorem Typographical Number Theory or TNT for short. Like Principia Mathematica and Gödel's theorem, one first has to assume TNT works. You only have to look to the bombings of the US Embassies in Kenya and Tanzania or that of the 1993 bombing of the World Trade Center to see how easy it is to assume TNT works.
As in theology, TNT has its own set of rules. "Axiom Strings" sure sounds like more fun than "Commandments", but they are essentially the same thing. However, people are more likely to turn to religion than mathematics because "Thou Shalt Not Kill" is a fuck of a lot easier to comprehend than "Axiom 5: Aa:Aa':(a*Sa')=((a*a')+a)".
It should also be noted that both Gödel and Hofstadter, taking a leaf out of God's Own Book, also created plenty of "fake rules" just to throw people off the scent of the truth. Hofstadter even called his false rule "Sentence G" undoubtedly in reference to The Almighty which is translated into his TNT theory as:
"This statement is not a theorem of TNT."
Now, ask yourself this question: is Sentence G true or false?
If Sentence G is false, then it is a theorem of TNT. Then we have a valid theorem which is false, and the whole system falls apart.
So it must be true. But if it is true, then it is not a theorem of TNT. Which means that Sentence G is true, but it is not provable within TNT. That is Gödel's "incompleteness." He showed that TNT, although it may be perfectly consistent and always correct, cannot possibly prove every true statement about number theory; there is always something which is true, which the system cannot prove.
Sounds a hell of a lot like religion to me!
It would be nice to think that Art came along to provide some kind of Trinity Balance to Mathematics and Religion. Alas, early artists (after a few millenia noodling images of dancing bison in wet mud on cave walls) were more compelled to paint pictures of the Virgin Mary nursing the infant Jesus in swaddling clothes than they ever were inclined to depict Number Theory -- not even in plain charcoal etchings!
Strong evidence of similarities between science and the triumvirate of monotheistic religions (Judaism, Christianity and Islam) is found in Principia Mathematica. For those of you not in the know, this work was Alfred Whitehead and Bertrand Russell's ambitious attempt to reduce all of number theory (note that word there -- theory) to a formal, axiomatic system. Its whole foundation is a few simple axioms that are almost indesputible. (Note the emphasis there: ALMOST indesputible.)
If Principia Mathematica is analogous with Judaism, then Gödel's incompleteness theorem is Christianity. It uses that old mathematical trick of proof by assuming the opposite of everything and then finding a contradition. In theology I think they call it "paradox". Whatever the case, Gödel's theorem, like Russell and Whitehead's Principia Mathematica is still theory.
Douglas Hofstadter (author of Gödel, Escher, Bach) is the Johnny-come-lately like the prophet Muhammad and his Islam. The coincidences just keep piling up when we discover that Hofstadter called his version of Gödel's theorem Typographical Number Theory or TNT for short. Like Principia Mathematica and Gödel's theorem, one first has to assume TNT works. You only have to look to the bombings of the US Embassies in Kenya and Tanzania or that of the 1993 bombing of the World Trade Center to see how easy it is to assume TNT works.
As in theology, TNT has its own set of rules. "Axiom Strings" sure sounds like more fun than "Commandments", but they are essentially the same thing. However, people are more likely to turn to religion than mathematics because "Thou Shalt Not Kill" is a fuck of a lot easier to comprehend than "Axiom 5: Aa:Aa':(a*Sa')=((a*a')+a)".
It should also be noted that both Gödel and Hofstadter, taking a leaf out of God's Own Book, also created plenty of "fake rules" just to throw people off the scent of the truth. Hofstadter even called his false rule "Sentence G" undoubtedly in reference to The Almighty which is translated into his TNT theory as:
"This statement is not a theorem of TNT."
Now, ask yourself this question: is Sentence G true or false?
If Sentence G is false, then it is a theorem of TNT. Then we have a valid theorem which is false, and the whole system falls apart.
So it must be true. But if it is true, then it is not a theorem of TNT. Which means that Sentence G is true, but it is not provable within TNT. That is Gödel's "incompleteness." He showed that TNT, although it may be perfectly consistent and always correct, cannot possibly prove every true statement about number theory; there is always something which is true, which the system cannot prove.
Sounds a hell of a lot like religion to me!
It would be nice to think that Art came along to provide some kind of Trinity Balance to Mathematics and Religion. Alas, early artists (after a few millenia noodling images of dancing bison in wet mud on cave walls) were more compelled to paint pictures of the Virgin Mary nursing the infant Jesus in swaddling clothes than they ever were inclined to depict Number Theory -- not even in plain charcoal etchings!
Labels: Humor, Non-fiction