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Truth, Incompleteness and the Gödelian Way
New York Times ^ | 2005 | Edward Rothstein

Posted on 05/21/2005 2:42:12 AM PDT by infocats

Is there a more powerful modern Trinity? These reigning deities proclaim humanity's inability to thoroughly explain the world. They have been the touchstones of modernity, their presence an unwelcome burden at first, and later, in the name of postmodernism, welcome company.

Their rule has also been affirmed by their once-sworn enemy: science. Three major discoveries in the 20th century even took on their names. Albert Einstein's famous Theory (Relativity), Kurt Gödel's famous Theorem (Incompleteness) and Werner Heisenberg's famous Principle (Uncertainty) declared that, henceforth, even science would be postmodern.

(Excerpt) Read more at r-s-r.org ...


TOPICS: Philosophy
KEYWORDS: incompleteness; mathematics; relativity; uncertainty
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1 posted on 05/21/2005 2:42:12 AM PDT by infocats
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To: infocats
It adds little to the discussion but I recently finished a book titled "Uncle Petros and the Goldbach Conjecture"

It discusses, tangentially, the impact of Godel's theorem on mathematics. I had been aware of him since back in the '70's or '80's when Godel, Escher, Bach came out but didn't appreciate how profoundly he changed everything

2 posted on 05/21/2005 2:58:24 AM PDT by muir_redwoods (Free Sirhan Sirhan, after all, the bastard who killed Mary Jo Kopeckne is walking around free)
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To: muir_redwoods
It adds little to the discussion but I recently finished a book titled "Uncle Petros and the Goldbach Conjecture"

It discusses, tangentially, the impact of Godel's theorem on mathematics. I had been aware of him since back in the '70's or '80's when Godel, Escher, Bach came out but didn't appreciate how profoundly he changed everything.

Profound indeed! What Goedel demonstrated was that in any linear logical system (mathematics, law etc.), by using only the initial assumptions, laws, and understandings of that system, a point would be reached where the system would contrdict itself.

Only by resorting to a new law or understanding taken from outside the orignal rule set, could this contradiction (at least temporarily) be overcome.

3 posted on 05/21/2005 3:06:43 AM PDT by infocats
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To: infocats
contrdict -> contradict

orignal -> original

4 posted on 05/21/2005 3:09:03 AM PDT by infocats
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To: All

This is totally off topic, but this seems to be a thread where someone might know the answer. If F=ma then does this not state that there would be zero force if an object is not accelerating? But if a car is moving at a constant 60 mph (no acceleration) wouldn't it have a force were it to slam into me?


5 posted on 05/21/2005 3:16:58 AM PDT by Socratic (There are methods and meth-heads. Life is about choice.)
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To: Socratic
if a car is moving at a constant 60 mph (no acceleration) wouldn't it have a force were it to slam into me?

You are confusing force with energy.

F=ma where
m, the mass of the object
a, the acceleration

But E=mc**2 where
m, the mass of the object
c, this is what happens when you stand in the road.

c is squared because you would c stars 2 if you got hit by a car.

I hope this clears things up.


6 posted on 05/21/2005 3:30:15 AM PDT by Nick Danger (Honey, Intel wants to go outside)
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To: Socratic
This is totally off topic, but this seems to be a thread where someone might know the answer. If F=ma then does this not state that there would be zero force if an object is not accelerating? But if a car is moving at a constant 60 mph (no acceleration) wouldn't it have a force were it to slam into me?

YOU BETCHA!

What your forgetting is that when this hypothetical car slams into that hypothetical you, it will accelerate (negatively) and all that energy that went into accelerating it up to 60 MPH will be transmitted into YOU, as you slow the vehicle from 60 to zero, in a VERY short time (high acceleration rate).

The force that the car will impose upon your body will be sufficient to cause the rigid structures of your body to fracture and the soft structures to burst.

The force of transmitted to you by the car will cause your body to accelerate. Of course the part that is in contact with the car will accelerate faster than the parts that are not. As a result of this your arms might be torn from their sockets, shoes ripped from your feet, and watched thrown from your wrists.

What I am describing is entirely the result of the car's deceleration and transmittal of force (and energy to you). I have to tell you that only a fraction of the car's speed need be lost to cause all sorts of havoc and mayhem to your hypothetical body, due to the huge difference in mass between you and a car, as well as the energy associate with speed.

Good luck with your experimentation!

7 posted on 05/21/2005 3:32:49 AM PDT by John Valentine (Whoop dee doo)
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To: John Valentine

Ah, thanks. Potential energy is just that - potential until an interation occurs. It's the interaction which creates the transfer of energy and force.


8 posted on 05/21/2005 3:40:19 AM PDT by Socratic (There are methods and meth-heads. Life is about choice.)
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To: Nick Danger

Nick, you're in danger of many things, but clarification is not one of them. ;0)


9 posted on 05/21/2005 3:44:30 AM PDT by Socratic (There are methods and meth-heads. Life is about choice.)
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To: John Valentine
as you slow the vehicle from 60 to zero, in a VERY short time

no way. conservation of momentum. you will be flung at a sizable fraction of that 60 mph for a hundred feet or so (until you hit the ground and the law of friction takes over) but the car will scarcely lose velocity.

10 posted on 05/21/2005 3:48:33 AM PDT by The Red Zone (Florida, the sun-shame state and Georgia, the rotten peach, and Illinois the chicken injun.)
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To: infocats

Bump


11 posted on 05/21/2005 4:15:14 AM PDT by Archon of the East ("universal executive power of the law of nature")
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To: Nick Danger
I hope this clears things up.

Actually, it kind of leaves me lying in the road, bleeding :-)

12 posted on 05/21/2005 5:00:31 AM PDT by T'wit (The difference between death and taxes is that death doesn't get worse when Congress is in session.)
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To: infocats
a point would be reached where the system would contradict itself.

Not exactly. You can still have a consistent (non contradictory) system. What Goedel showed was that any such system would contains "undecidable" statements. In OTW, there will always be some statement S, that cannot be proven neither True nor False.

13 posted on 05/21/2005 5:18:03 AM PDT by beckaz (The facts of life are conservative. (Maggie Thatcher))
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To: infocats
Further discussion here:

http://www.freerepublic.com/focus/f-news/1343937/posts

14 posted on 05/21/2005 5:46:50 AM PDT by snarks_when_bored
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To: The Red Zone

That was obviously one of the senarios I had in mind, when I referred to a very small reduction in the velocity of the car.

The other scenario, where the cars velocity was reduced to zero in a very short time presupposed a solid brick wall immediately behind the experimenter. Now it is true that the brick wall would ultimately be responsible for the deceleration of the car (if it is possible to speak of a brick wall as "responsible") but the action-reaction of the car-wall combination wwould be mediated through and by the body of the experimenter.

Result: severe compression.


15 posted on 05/21/2005 6:06:07 AM PDT by John Valentine (Whoop dee doo)
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To: The Red Zone
...conservation of momentum. you will be flung at a sizable fraction of that 60 mph...

You will be flung at far greater than 60 mph, actually, but the poster is correct about conservation of momentum.

16 posted on 05/21/2005 10:25:44 AM PDT by MonroeDNA ("Eat my body, drink my blood." --Catholicism)
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To: MonroeDNA
("Eat my body, drink my blood." --Catholicism)

Don't forget: "Keep it up constantly" and that it's both a necessary and sufficient condition for eternal life!

(Which is why Protestants and evangelicals rightly view it as a spiritual activity that doesn't depend on a ceremony to make it happen)

17 posted on 05/21/2005 10:57:36 AM PDT by The Red Zone (Florida, the sun-shame state, and Illinois the chicken injun.)
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To: beckaz
a point would be reached where the system would contradict itself.

Not exactly. You can still have a consistent (non contradictory) system. What Goedel showed was that any such system would contains "undecidable" statements. In OTW, there will always be some statement S, that cannot be proven neither True nor False.

Hmmm. I'll have to research your assertion. Unfortunately, I already packed both my copy of Goedel's Proof and The World of Mathematics in preparation for a move to Albany.

18 posted on 05/21/2005 12:35:24 PM PDT by infocats
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To: Mitchell
“They have been the touchstones of modernity
their presence an unwelcome burden
at first
and later
in the name of postmodernism
welcome company."

“..henceforth
even science would be postmodern.”

Can someone tell me what postmodernism is??

It seems to be a word esteemed by sophisticated writers.
But yesterday
I even was surprised to see the straightforward writer
Victor Davis Hanson
using it.

Literally
it seems to me
that to be postmodern would be
to be living in the future.

Somehow I do not think that is the intended meaning.
19 posted on 05/21/2005 12:46:42 PM PDT by Allan
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To: infocats
Actually he showed it for the axioms of Peano arithmetic. It hasn't even been successfully extended to the axioms of set theory, let alone any formal system. Peano arithmetic is Turing complete, so it can emulate other systems up to the computable functions (all countable) - though that took Turing, not Godel, to show.
20 posted on 05/21/2005 12:52:39 PM PDT by JasonC
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