On the previous page (probably relegated there by this very post) was a very lively discussion introduced by Zeus-Boy about the rationality of an afterlife. These are often fun and can be entertaining, but the everyone knows how the story will end.

From the Rennaissance up to the beginning of the twentieth century, history records the steady advancement of the rational mind - an advance that has overcome epic challenges on the frontiers of science, mathematics, and logic as well as the chaotic hordes of irrational dogmas. Over those centuries, religion has most often carried the banner of dogmatic inconsistency and large remnants of those forces remain. The battle on that front is not over.

But the twentieth century also revealed the formidable fortresses unassailable by rationality and impervious to logic. Legions of paradoxes oozed from the microcosm of quantum mechanics, vortexes of recursion sucked in the regiments of computation. But, in my mind, the Dark Lord of Logic was always Kurt Gödel who found the Achilles heel of rational thought.

I first encountered Gödel's work in Douglas Hofstadter's 'Godel, Escher, Bach' and I owe my carreer as an algorithmatist to the inspiration of that book. Gödel, arguably the most important logician of his time, explored and charted the limits of logic and will be remembered most for his Incompleteness Theorem. This theorem - now mathematically proven - essentially states that within any branch of mathematics, there will always remain propositions within the domain which cannot be proven by the rules and axioms of the domain itself. There is a good synopsis of it here, but for those who don't like links, I will summarize:

1. Someone introduces Gödel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.
2. Gödel reviews the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine.
3. Gödel writes the following sentence: "The machine constructed on the basis of the program P(UTM) will never say that this sentence is true." Call this sentence G for Gödel. Note that G is equivalent to: "UTM will never say G is true."
4. Gödel asks the UTM whether G is true or not.
5. If UTM says G is true, then "UTM will never say G is true" is false. If "UTM will never say G is true" is false, then G is false (since G = "UTM will never say G is true"). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.
6. So UTM will never say G is true and "UTM will never say G is true" is a true statement. So G is true (since G = "UTM will never say G is true").
7. "I know a truth that UTM can never utter," Gödel says. "I know that G is true. UTM is not truly universal."

However, the power of Gödel's Theorem is not that this is true, but, as Hofstadter championed - it is recursive. Expansion of the Universal Truth Machine only exposes more inconsistencies. We can see the limits of rationalism - there are truths that we can know, but never prove and there are truths that we can never know.

Just like the dogmas of religion, the days of rationalism are numbered. The writing is on the wall, written by the mathematicians and physicists who wielded its power. It is always the wizards, the alchemists, who first understand that the jig is up.

Gödel was born a Czech and lived in Vienna until the winds of Nazism blow him across the Atlantic to settle and grow - like so many of the other great minds of europe - in the academia of the United States. At Princeton, he became lasting friends with Albert Einstein, presenting him with paradoxical solutions to the Einstein's field equations of general relativity.

Late in his life, this most powerful engine of logic developed an obsessive fear of being poisoned - to the extent that he required his wife, Adele, to taste all of his food before he would eat. In 1977, Adele - a dancer before she married Kurt, was hospitalized for nearly six months.

Kurt Gödel, unable to eat without Adele, died of starvation In January of 1978 at the age of seventy-two weighing sixty-five pounds. This part I didn't know until today.

It seems to me that incompleteness has many meanings.

"We can construct paradoxes, therefore God exists."

Glad to see that Douglas H's book did some good for someone, in the sense of introducing you to Godel, not to Douglas H.

You know, I assume, that the book is generally dismissed as the work of a lightweight, to which I will add my own somewhat jaundiced opinion that it probably would never have seen the light of day had Douglas H's father not been who he was.

was the title of the post an invitation to take it personally. My apologies.

My use of the particular combination of punctuation marks in the subject line is meant to indicate my confusion at your reply.

Dougals H is something of an enigma for me. Did I every tell you about my 'Single's Bar Sorting on Commercial Applicatons Epiphany' and how it led to the development manager going off the deep end? Perhaps not. I met a student of Hofstadter when I was a headhunter. Fascinating kid. You know, theory is one thing, but it's popular mechanics that moves the masses. I'm juist sayin'.

His father? Jesus H, I hate Googling on the weekend.

"Reason is a wonderful servant, rationalism a terrible master."

In the domain of both rational and irrational, you choose to be the imaginary.

Good choice.

aka God?

Then God would be the Goliathe Killer David? aka King David clans

as Allah & Mohammud, Elijah, Jesus human clans too are creators of paradox? Thus man clan is ruled by God sons?

hmmm

"there are truths that we can never know" mean to you? Would it make the statement "humans can never understand the ways and purposes of God" true, assuming one posited the exisitence of God?

out of the strong came forth sweetness.

A happy Independence Day to you, too.

even if exclamatory, but allow me to observe that what I do is but to observe. Punctuation is for the punctual and I would rather be late than never

. Period

EOP.

I'm not promoting anything. I'm not hawking Stephen Hawking or anyone. If you find God in Godel, that is not my problemo. And if you think this response is incomplete, well, so do I. That's the point. Everyfuckinthing is incomplete. Does anything ever get done around here? So there.

1. From the Rennaissance up to the beginning of the twentieth century, history records the steady advancement of the rational mind

2. But the twentieth century also revealed the formidable fortresses unassailable by rationality and impervious to logic.

3. But, in my mind, the Dark Lord of Logic was always Kurt Gödel who found the Achilles heel of rational thought.

4. Just like the dogmas of religion, the days of rationalism are numbered. The writing is on the wall, written by the mathematicians and physicists who wielded its power. It is always the wizards, the alchemists, who first understand that the jig is up.

An interesting combination of germs of truth, with fairly deep exaggeration, and mild misunderstandings. Would it bother you much to find out - hypothetically - that you've based your career being inspired by misunderstanding the consequences of Godel and his theorem(s).

He said that because the subtlety of nature exceeds the subtlety of our senses, there is a structure "beneath" what we perceive that we will never grasp. He didn't reckon on the discovery of instruments that would (if properly used) vastly extend the human perceptual range. However, if Bacon could see what we do today, he would probably shrug and say, "Yeah, but so what? It's still tortoises all the way down, isn't it?"--merely having uncovered one level of subtlety doesn't prove that there isn't still another, and another, etc. If the history of science teaches us anything, it's that nature's always more subtle than we thought.