OrthodoxChristianity.net
October 30, 2014, 09:58:36 AM *
Welcome, Guest. Please login or register.

Login with username, password and session length
News: Reminder: No political discussions in the public fora.  If you do not have access to the private Politics Forum, please send a PM to Fr. George.
 
   Home   Help Calendar Contact Treasury Tags Login Register  
Pages: 1   Go Down
  Print  
Author Topic: Any Mathematicians or Scientists in the Crowd? - Need help  (Read 1072 times) Average Rating: 0
0 Members and 1 Guest are viewing this topic.
Brian
Member
***
Offline Offline

Posts: 128


« on: July 01, 2006, 05:05:36 AM »

I am currently learning about Godel's Incompleteness Theorems and would like to check that my understanding is correct, and discuss the real world implications that follow.  Does anyone here have enough understanding of his work or of formal maths or logic to carry on a productive discussion?  I am especially interested in gaining a deeper understanding of what I think are the implications for science, religion, and AI programming, not just for maths.
Logged
Αριστοκλής
Merarches
***********
Offline Offline

Faith: Orthodox Catholic
Jurisdiction: American Carpatho-Russian Orthodox Diocese
Posts: 10,026


« Reply #1 on: July 01, 2006, 05:09:52 AM »

Try sending member Keble a PM; I think he can help if he has time.
Logged

"Religion is a neurobiological illness and Orthodoxy is its cure." - Fr. John S. Romanides
GiC
Resident Atheist
Site Supporter
Merarches
*****
Offline Offline

Faith: Mathematician
Posts: 9,490



« Reply #2 on: July 01, 2006, 05:49:57 AM »

I am currently learning about Godel's Incompleteness Theorems and would like to check that my understanding is correct, and discuss the real world implications that follow.ÂÂ  Does anyone here have enough understanding of his work or of formal maths or logic to carry on a productive discussion?ÂÂ  I am especially interested in gaining a deeper understanding of what I think are the implications for science, religion, and AI programming, not just for maths.

Ultimately, I believe that the Incompleteness Theorem must be viewed as a corollary to Computability Theory, for while the Incompleteness Theorem came first, it was only a specific instance within Turing and Church's Computability Theory which can apply the principles of the Incompleteness beyond Number Theory to all other fields of Mathematics and Computer Science. Essentially the Incompleteness theorem can logically be derived from the halting problem. I dont know what your experience with Computation and Complexity theory is, but this site offers a good introduction:

http://plato.stanford.edu/entries/computability/

As far as discussing the theory, I can give it a go, I will confess that my Computability theory is a bit rusty as I haven't used it in a few years, but it would do me good to brush up on it anyway (but I must warn you, while I always prefered computability theory, I was always much better at complexity theory). However, I dont know how popular this type of conversation would be, I tried to introduce a few class mates at Holy Cross to the Subject of Computability, but the usual conclusion to this introduction was a mocking of my textbook for it's claim to be entirely self-contained, requiring no prior knowledge -- which was technically true, but extensive mathematical experience is generally required to realize this.

If you simply want to discuss the incompleteness theorem in laymans terms and apply them to non-mathematical situatoins, that's pretty straightforward, the logical conclusion is relativism, but if you want to actually make progress I would really suggest the conversation centre around Computability.

As for a discussion of science, religion, etc. appart from mathematics, this quite confuses me. Did not Pythagoras teach us that 'Number is the ruler of forms and ideas and the cause of gods and demons;' then again, he also didn't believe in irrational numbers.

In any case, if you want to discuss something, shoot; no need to ask permission.
« Last Edit: July 01, 2006, 05:50:30 AM by greekischristian » Logged

"The liberties of people never were, nor ever will be, secure, when the transactions of their rulers may be concealed from them." -- Patrick Henry
Brian
Member
***
Offline Offline

Posts: 128


« Reply #3 on: July 02, 2006, 07:55:19 AM »

[quote author=Αριστοκλής link=topic=9402.msg126298#msg126298 date=1151744992]
Try sending member Keble a PM; I think he can help if he has time.
[/quote]

Thank you for the reference. Smiley
Logged
EkhristosAnesti
'I will say of the Lord, "He is my refuge and my fortress; My God, in Him I will trust."' - Psalm 91:2
Archon
********
Offline Offline

Faith: Oriental Orthodox
Posts: 2,743


Pope St Kyrillos VI


« Reply #4 on: July 02, 2006, 08:07:43 AM »

lol GiC just got barred.
Logged

No longer an active member of this forum. Sincerest apologies to anyone who has taken offence to anything posted in youthful ignorance or negligence prior to my leaving this forum - October, 2012.

"Philosophy is the imitation by a man of what is better, according to what is possible" - St Severus
Brian
Member
***
Offline Offline

Posts: 128


« Reply #5 on: July 02, 2006, 08:42:13 AM »

what? he did?  for what?
Logged
Fr. George
formerly "Cleveland"
Administrator
Stratopedarches
*******
Offline Offline

Faith: Orthodox (Catholic) Christian
Jurisdiction: GOA - Metropolis of Pittsburgh
Posts: 20,094


May the Lord bless you and keep you always!


« Reply #6 on: July 02, 2006, 08:02:16 PM »

He didn't really get barred; EA is mocking GiC's interest in the subject matter.
Logged

"The man who doesn't read good books has no advantage over the one who can't read them." Mark Twain
---------------------
Ordained on 17 & 18-Oct 2009. Please forgive me if earlier posts are poorly worded or incorrect in any way.
Tags:
Pages: 1   Go Up
  Print  
 
Jump to:  

Powered by MySQL Powered by PHP Powered by SMF 1.1.18 | SMF © 2013, Simple Machines Valid XHTML 1.0! Valid CSS!
Page created in 0.061 seconds with 33 queries.