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Kurt Gödel
I don't think that Gödel proved that 2+2 <> 4. He proved that any system sufficiently complex could not be both complete and consistent. It used to be believed (as per the Shrödinger article) that if we knew the the initial conditions of a system and we knew all of the rules determining the system, that we could then perfectly predict everything about the system at any moment in the future. (This assumes of course that the system was deterministic.) We believed that the universe was understandable, that it was deterministic, that it was causal, that it was logical. But ... weird stuff was happening ... things that contradicted basic assumptions - some of them assumptions so basic that few, if any, had ever thought to question them.
Gauss, Bolyai, et. al., showed that despite supposed proof by Kant to the contary, that one could develop a consistent geometry replacing Euclid's fifth postulate with something inconsistent with it.
Cantor showed that not all infinities are equal, some infinities are bigger than others.
Michelson and Morley show that there is no ether ... but if there is no ether, through what do light waves travel? How can you have a wave without a medium?
Russell and Whitehead spent years in a thought-provoking, but failed attempt at showing that mathematics could be derived from logic.
A patent clerk publishes a paper in Annalen der Physik that in a very few paragraphs (and if I recall correctly not a single reference) questions our ideas about simultaneity and absoluteness. The speed of light does not depend on the speed of the source or the reciever. It's absolute (in a vacuum). [A common layman's MIS-understanding is that Einstein said "everthing is relative."] In any case, what he actually proposes violates our classical assumption that velocity vectors are additive.
Said clerk had previously published a paper in same journal explaining that in addition to obvious wave properties, light also exhibits some particle properties (waited for De Broglie, Germer, et al to 'reconcile').
Heisenberg states remarkable conclusion that we can't perfectly know position AND momentum of a particle, not because we have bad eyes, or faulty equipment, but because of a fundamental aspect of nature - when we look at something (measure it), we change it. We can know these things, but only within the constraints of the uncertainty relation.
Bohr and others advance the copenhagen interpretation (which I don't understand and I don't even remember what I read about it) and Schrodinger graciously volunteers his cat for an experiment to show the aburdity of this view.
While the feline is in the box, she's out of the bag. Mystics the world over use this knowledge as final proof of what they've always believed - that there is no objective reality. (No idea how they get there from here, and I don't understand this stuff well enough to argue the point - but I have a strong suspicion that these guys are misinterpreting things.)
Godel develops his incompleteness theorem. Even if you knew all the rules of a sufficiently complex system, you STILL couldn't prove that all the true statements are true. If you could magically find another true statement and at it to the list of axioms, you still would YET be true statements that couldn't be proved to be so.
It's not easy for me to recognize one thing or person that is more important than the others in the demolition of the classical view (although I, too, have a soft place for Godel.) Each of these is a pretty startling development - even now.
k
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old hand
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> isn't that Kurt Gödel? as in Gödel, Escher, and Bach?
Spell dyslexia for me there, eation. [sic]
Thanks for the explanation FallibleFiend. I didn't mean to suggest that Kurt proved that 2+2 didn't equal 4, more that, as far as I know, maths was coming to recognize this possibility (or truth?) at about this time.
Can you, at the risk of p-ing off InselPeter, also explain these new theories regarding the speed of light as not being the 'speed limit' for the universe?
The orignality of any idea is directly proportionate to the knowledge of the audience.
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"Can you, at the risk of p-ing off InselPeter, also explain these new theories regarding the speed of light as not being the 'speed limit' for the universe?"
I'm afraid not. It's way outside my area of expertise - in fact, all of this is (well, except for the Goedel stuff, which is almost comprehensible).
I work with a crapload of PhDs in various fields, though, and I sent a query to one of my buds several months back asking about this and recieved no reply. He got his physics degree from BU about a million years ago, so he's kinduva curmudgeony, old fart, and usually busy, but sometimes he'll give me the time of day. (Actually, he's a really nice - crotchety - guy, but he's pretty busy.)
I recall an article I read decades ago about a model of tachyon, tardyon, and photon universes. Tachyon is FTL, Tardyon is STL (slower than light). Each universe is tardyon wrt itself, but tachyon with respect to the other universe. After I read the article (smithsonian? SciAm?), I wasn't sure whether this was just a curiosity derived from a mathematical excursion, or something someone was seriously proposing. I pretty much forgot about it till a few months ago when I read about the experiment where the guys had apparently achieved FTL communication - a clear violation (FTL is not impossible, according to Martin Gardner, it's FTL with transfer of information that's impossible). However, I don't think the experimenters themselves believe they (Wang, et. al.) achieved FTL communication. If I recall, they were very skeptical and seemed to indicate it was some sort of artifact of their experimental design. Really, I didn't understand this very well when I read it, and my memory sucks, so it's anybody's guess what they really meant. If you look for it, you might be able to find it on the web. Maybe you can make more sense of it than I could. (I can't find my old email to my friend on it.)
Just as an aside (and not as a jab or anything) - aren't you at university? That's a great time to make friends with people all over campus. People dog the "old boy network" and it does have a lot of potential for abuse, but it's also an extremely valuable thing - not just professionally, but on a personal level. Not a lecture or anything. Not even advice, really. Just a stating my own experience.
good luck,
k
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Pooh-Bah
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The final arguments:
Reader Query of Cecil, the doyen of a scientific newsgroup I've long since lost track of:
Cecil, you're my final hope
Of finding out the true Straight Dope
For I have been reading of Schrodinger's cat
But none of my cats are at all like that.
This unusual animal (so it is said)
Is simultaneously live and dead!
What I don't understand is just why he
Can't be one or the other, unquestionably.
My future now hangs in between eigenstates.
In one I'm enlightened, the other I ain't.
If you understand, Cecil, then show me the way
And rescue my psyche from quantum decay.
But if this queer thing has perplexed even you,
Then I will and won't see you in Schrodinger's zoo.
-Randy F., Chicago
Cecil's Reply:
Schrodinger, Erwin! Professor of Physics!
Wrote daring equations! Confounded his critics!
(Not bad, eh? Don't worry. This part of the verse
Starts off pretty good, but it gets a lot worse.)
Win saw that the theory that Newton'd invented
By Einstein's discov'ries had been badly dented.
What now? wailed his colleagues. Said Erwin, "Don't panic,
No grease monkey I, but a quantum mechanic.
Consider electrons. Now, these teeny articles
Are sometimes like waves, and then sometimes like particles.
If that's not confusing, the nuclear dance
Of electrons and suchlike is governed by chance!
No sweat, though - my theory permits us to judge
Where some of 'em is and the rest of 'em was."
Not everyone bought this. It threatened to wreck
The comforting linkage of cause and effect.
E'en Einstein had doubts, and so Schrodinger tried
To tell him what quantum mechanics implied.
Said Win to Al, "Brother, suppose we've a cat,
And inside a tube we have put that cat at -
Along with a solitaire deck and some Fritos,
A bottle of Night Train, a couple of mosquitoes
(Or something else rhyming) and, oh, if you got 'em,
One vial prussic acid, one decaying ottom
Or atom - whatever - but when it emits,
A trigger device blasts the vial to bits
Which snuffs our poor kitty. The odds of this crime
Are 50 to 50 per hour each time.
The cylinder's sealed. The hour's passed away. Is
Our pussy still purring - or pushing up daisies?
Now, you'd say the cat either lives or it don't
But quantum mechanics is stubborn and won't.
Statistically speaking, the cat (goes the joke),
Is half a cat breathing and half a cat croaked.
To some this may seem a ridiculous split,
But quantum mechanics must answer, 'Tough shit.
We may not know much, but one thing's fo,sho':
There's things in the cosmos that we cannot know.
Shine light on electrons - you'll cause them to swerve.
The act of observing disturbs the observed -
Which ruins the test. But then if there's no testing
To see if a particle's moving or resting
Why try to conjecture? Pure useless endeavor!
We know probability - certainty, never.'
The effect of this notion? I very much fear
'Twill make doubtful all things that were formerly clear.
Till soon the cat doctors will say in reports,
'We've just flipped a coin and we've learned he's a corpse.'"
So said Herr Erwin. Quoth Albert, "You're nuts.
God doesn't play dice with the universe, putz.
I'll prove it!" he said, and the Lord knows he tried -
In vain - until fin'ly he more or less died.
Win spoke at the funeral: "Listen, dear friends,
Sweet Al was my buddy. I must make amends.
Though he doubted my theory, I'll say of this saint:
Ten-to-one he's in heaven - but five bucks says he ain't."
- Pfranz
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Carpal Tunnel
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haha! that's terrific. thanks for sharing. 
formerly known as etaoin...
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The following has been circulating over the net for a couple decades at least.
UNIFIED FIELD THEORY by TIM JOSEPH
In the beginning there was Aristotle,
At objects at rest tended to remain at rest,
And objects in motion tended to come to rest,
And soon everything was at rest,
And God saw that it was boring.
Then God created Newton,
And objects at rest tended to remain at rest,
But objects in motion tended to remain in motion,
And energy was conserved and momentum was conserved
and matter was conserved,
And God saw that it was conservative.
Then God created Einstein,
And everything was relative,
And fast things became short,
And straight things became curved,
And the universe was filled with inertial frames,
And God saw that it was relatively general, but some
of it was especially relative.
Then God created Bohr,
And there was the principle,
And the principle was quantum,
And all things were quantified,
But some things were still relative,
And God saw that it was confusing.
Then God was going to create Ferguson,
And Ferguson would have unified,
And he would have fielded a theory,
And all would have been one,
But it was the seventh day,
And God rested,
And objects at rest tend to remain at rest.
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Carpal Tunnel
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UNIFIED FIELD THEORY by TIM JOSEPH
So nice to see this actually credited. Tim Joseph is the Chairman of the Tompkins County Board of Representatives, the group whose twice-monthly meetings I do camera for. There are many copies floating around the web uncredited. He'll be interested in seeing that his spelling of Furgeson has been "corrected". I asked him about that once and he had some reason for the spelling he used but I forget what it was. Looks like there's two days missing.
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UNIFIED FIELD THEORY by TIM JOSEPH
Crediting was an accident. The site I snagged it from happened to include it.
First time I ever saw it was on crinkled old paper (that green and white striped stuff) hanging up in the Engineering Computer Lab (ECL) in the basement of Speed School (U of Louisville) - just about two decades ago. It was hanging next to the 6 phases of an engineering project (1. enthusiasm, 2. disillusionment, 3. Panic, 4. search for the guilty, 5. punish the innocent, 6. praise and honors for the non-participants - no attribution because I don't know where it originated).
I remember this was some of the first stuff I ever saw just hanging up on a wall at college and thought college guys must be the smartest people in the world to think such clever thoughts.
k
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Carpal Tunnel
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Crediting was an accident. The site I snagged it from happened to include it.
Huh?
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Carpal Tunnel
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Huh?It's all over the place. Apparently first publication was in Analog about 20 yrs ago. Google unified furgeson. There's even a German transltion out there. Credited. http://www.borsche.de/borsche/inhalte/furge.htmThe Zeit link at the bottom of the page seems to be broken.
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