- published: 14 Dec 2016
- views: 2853
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Math isn’t perfect, and math can prove it. In this video, we dive into Gödel’s incompleteness theorems, and what they mean for math.
Created by: Cory Chang
Produced by: Vivian Liu
Special thanks to Ryan O’Donnell, associate professor at Carnegie Mellon University (http://www.cs.cmu.edu/~odonnell/).
Twitter: https://twitter.com/UBehavior
—
Extra Resources:
Ryan O’Donnell’s slide deck: http://www.cs.cmu.edu/~aada/courses/15251s16/www/slides/15251-s16-lecture16.pdf
Wikipedia Entry: https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems
Axiomatic Systems: https://en.wikipedia.org/wiki/Axiomatic_system
Peano Axioms: https://en.wikipedia.org/wiki/Peano_axioms
Principle of Explosion: https://en.wikipedia.org/wiki/Principle_of_explosion
Picture credits:
http://www.wallpapervortex.com/wallpaper-15925_shadow_of_the_colossus.html
http://nomads-sotc-blog.blogspot.com/2011/08/colossi-sizes.html
http://nomads-sotc-blog.blogspot.com/2011/07/5th-colossus.html
https://www.wired.com/2015/07/sorry-perfect-lego-brick-may-never-eco-friendly/
https://i.ytimg.com/vi/TZJByZjfNwM/maxresdefault.jpg
http://disney.wikia.com/wiki/Yoda
http://fictionalcharacterbattles.wikia.com/wiki/Darth_Vader
https://www.spriters-resource.com/mobile/robouniatk/sheet/51416/
http://clipart-library.com/image_gallery/2180.png
In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox. Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so, Gödel changed the way we understand what mathematics is, and the implications of his work in physics and philosophy take us to the very edge of what we can know. Melvyn Bragg discusses Gödel’s Incompleteness Theorems with Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.
This is from a BBC program called In Our Time.
- published: 02 Nov 2016
- views: 4058
Kurt Godel: The World's Most Incredible Mind.
"Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel
Kurt Godel (1931) proved two important things about any axiomatic system rich enough to include all of number theory.
1) You'll never be able to prove every true result..... you'll never be able to prove every result that is true in your system.
2) Godel also proved that one of the results that you can never prove is the result that says that the system is consistent. More precisely: You cannot prove the consistency of any mathematical system rich enough to include the known theory of numbers.
Hence, any consistent mathematical system that is rich enough to include number theory is inherently incomplete.
Second, one of the propositions whose truth or falsity cannot be proved within the system is precisely the proposition that states that the system is consistent. "
What Godel's proof means, then, is that we can't prove that arithmetic—let alone any more-complicated system—is consistent.
For 2000 years, mathematics has been the model—the subject—that convinces us that certainty is possible. Yet Now there's no certainty anywhere—not even in mathematics.
More...
http://teachingcompany.12.forumer.com/viewtopic.php?t=2327
Goedel's Ontological Proof.
For those interested in a discussion of Goedel's reasoning for God, then I suggest starting with this heavily annotated work, which I recently stumbled upon.
www.scribd.com/doc/95364925/Goedel-s-God-Proof-Annotated-Version
"It's not that God is subject to the Freedom Proof or the Doubt Proof.
According to Gödel, He's not. But we have to be, or else we are not free. So
our truth game with God turns into something like Feynman had described.
Feynman's Gods, every time physicists think they have the rules of the game
figured out, throw in a new wrinkle. They let people like Feynman make
progress, but if the Feynmans of the world learn too much, physics will stop
being the joy and challenge that it is. The Gods don't let that happen.
Gödel's God has to be very careful about how he lets our universe unfold.
If the world becomes totally controllable and comprehensible, we'll be God.
God does not object to that. In fact, according to Gödel, that is our destiny.
But it is also the end of us as free human beings. And human freedom is an
essential part of the beauty of God's universe."
~ page 251
- published: 18 Oct 2011
- views: 215046
A brief bio of Kurt Gödel from :-
The Limits of Understanding - World Science Festival
https://www.youtube.com/watch?v=DfY-DRsE86s
- published: 02 Jan 2015
- views: 21198
A short mind-bending trip through the wonderful world of Mathematical Paradoxes: An examination of some recent work on paradoxes by the Austrian-American Mathematician Kurt Gödel. You can watch the full lecture by Professor Tony Mann here: http://www.gresham.ac.uk/lectures-and-events/this-lecture-will-surprise-you-when-logic-is-illogical
- published: 21 Feb 2015
- views: 26860
En mathématiques, il existera toujours des choses vraies, mais indémontrables. Merci Kurt Gödel...
Sur mon blog, le billet qui accompagne la vidéo : https://sciencetonnante.wordpress.com/2016/12/09/theoreme-godel/ Vous y trouverez beaucoup de précisions et de compléments.
La vidéo de Passe-Science : https://www.youtube.com/watch?v=SBwupYwDgHg
Me soutenir sur Tipeee : http://www.tipeee.com/science-etonnante
Mon livre : http://science-etonnante.com/livre.html
Facebook : http://www.facebook.com/sciencetonnante
Twitter : http://www.twitter.com/dlouapre
Abonnez-vous : https://www.youtube.com/scienceetonnante
- published: 09 Dec 2016
- views: 17360
Gödel´s theorem easy. El teorema de Gödel explicado de forma fácil.
- published: 19 May 2016
- views: 13411
An explication of Gödel Numbers, Free Variables, Arithmatization, Substitution, and Arithmoquining. This covers some of the basics for Gödel's incompleteness theorem, and Tarski's Theorem on the Indefinability of Truth.
- published: 27 Mar 2016
- views: 2664
Kurt Gödel
Kurt Friedrich Gödel (/ˈkɜːrt ˈɡɜːrdəl/;German: [ˈkʊʁt ˈɡøːdəl]; April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher. Considered with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell,A. N. Whitehead, and David Hilbert were pioneering the use of logic and set theory to understand the foundations of mathematics.
Gödel published his two incompleteness theorems in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The first incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.
This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Kurt_Gödel
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
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6:55Math's Existential Crisis (Gödel's Incompleteness Theorems)
Math's Existential Crisis (Gödel's Incompleteness Theorems)Math's Existential Crisis (Gödel's Incompleteness Theorems)
Math isn’t perfect, and math can prove it. In this video, we dive into Gödel’s incompleteness theorems, and what they mean for math. Created by: Cory Chang Produced by: Vivian Liu Special thanks to Ryan O’Donnell, associate professor at Carnegie Mellon University (http://www.cs.cmu.edu/~odonnell/). Twitter: https://twitter.com/UBehavior — Extra Resources: Ryan O’Donnell’s slide deck: http://www.cs.cmu.edu/~aada/courses/15251s16/www/slides/15251-s16-lecture16.pdf Wikipedia Entry: https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems Axiomatic Systems: https://en.wikipedia.org/wiki/Axiomatic_system Peano Axioms: https://en.wikipedia.org/wiki/Peano_axioms Principle of Explosion: https://en.wikipedia.org/wiki/Principle_of_explosion Picture credits: http://www.wallpapervortex.com/wallpaper-15925_shadow_of_the_colossus.html http://nomads-sotc-blog.blogspot.com/2011/08/colossi-sizes.html http://nomads-sotc-blog.blogspot.com/2011/07/5th-colossus.html https://www.wired.com/2015/07/sorry-perfect-lego-brick-may-never-eco-friendly/ https://i.ytimg.com/vi/TZJByZjfNwM/maxresdefault.jpg http://disney.wikia.com/wiki/Yoda http://fictionalcharacterbattles.wikia.com/wiki/Darth_Vader https://www.spriters-resource.com/mobile/robouniatk/sheet/51416/ http://clipart-library.com/image_gallery/2180.png -
41:58Gödel's Incompleteness Theorems (BBC's In Our Time)
Gödel's Incompleteness Theorems (BBC's In Our Time)Gödel's Incompleteness Theorems (BBC's In Our Time)
In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox. Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so, Gödel changed the way we understand what mathematics is, and the implications of his work in physics and philosophy take us to the very edge of what we can know. Melvyn Bragg discusses Gödel’s Incompleteness Theorems with Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol. This is from a BBC program called In Our Time. -
15:00Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)
Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)
Kurt Godel: The World's Most Incredible Mind. "Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel Kurt Godel (1931) proved two important things about any axiomatic system rich enough to include all of number theory. 1) You'll never be able to prove every true result..... you'll never be able to prove every result that is true in your system. 2) Godel also proved that one of the results that you can never prove is the result that says that the system is consistent. More precisely: You cannot prove the consistency of any mathematical system rich enough to include the known theory of numbers. Hence, any consistent mathematical system that is rich enough to include number theory is inherently incomplete. Second, one of the propositions whose truth or falsity cannot be proved within the system is precisely the proposition that states that the system is consistent. " What Godel's proof means, then, is that we can't prove that arithmetic—let alone any more-complicated system—is consistent. For 2000 years, mathematics has been the model—the subject—that convinces us that certainty is possible. Yet Now there's no certainty anywhere—not even in mathematics. More... http://teachingcompany.12.forumer.com/viewtopic.php?t=2327 Goedel's Ontological Proof. For those interested in a discussion of Goedel's reasoning for God, then I suggest starting with this heavily annotated work, which I recently stumbled upon. www.scribd.com/doc/95364925/Goedel-s-God-Proof-Annotated-Version "It's not that God is subject to the Freedom Proof or the Doubt Proof. According to Gödel, He's not. But we have to be, or else we are not free. So our truth game with God turns into something like Feynman had described. Feynman's Gods, every time physicists think they have the rules of the game figured out, throw in a new wrinkle. They let people like Feynman make progress, but if the Feynmans of the world learn too much, physics will stop being the joy and challenge that it is. The Gods don't let that happen. Gödel's God has to be very careful about how he lets our universe unfold. If the world becomes totally controllable and comprehensible, we'll be God. God does not object to that. In fact, according to Gödel, that is our destiny. But it is also the end of us as free human beings. And human freedom is an essential part of the beauty of God's universe." ~ page 251 -
3:50Hitler against Godel's Theorem
Hitler against Godel's TheoremHitler against Godel's Theorem
Hitler faces the awful truth: arithmetic is incomplete. -
1:02:34MIT Godel Escher Bach Lecture 1
MIT Godel Escher Bach Lecture 1MIT Godel Escher Bach Lecture 1
-
3:38Kurt Gödel - from the Limits of understanding
Kurt Gödel - from the Limits of understandingKurt Gödel - from the Limits of understanding
A brief bio of Kurt Gödel from :- The Limits of Understanding - World Science Festival https://www.youtube.com/watch?v=DfY-DRsE86s -
6:22Gödel's Incompleteness Theorem - Professor Tony Mann
Gödel's Incompleteness Theorem - Professor Tony MannGödel's Incompleteness Theorem - Professor Tony Mann
A short mind-bending trip through the wonderful world of Mathematical Paradoxes: An examination of some recent work on paradoxes by the Austrian-American Mathematician Kurt Gödel. You can watch the full lecture by Professor Tony Mann here: http://www.gresham.ac.uk/lectures-and-events/this-lecture-will-surprise-you-when-logic-is-illogical -
18:28Les théorèmes d'incomplétude de Gödel — Science étonnante #37
Les théorèmes d'incomplétude de Gödel — Science étonnante #37Les théorèmes d'incomplétude de Gödel — Science étonnante #37
En mathématiques, il existera toujours des choses vraies, mais indémontrables. Merci Kurt Gödel... Sur mon blog, le billet qui accompagne la vidéo : https://sciencetonnante.wordpress.com/2016/12/09/theoreme-godel/ Vous y trouverez beaucoup de précisions et de compléments. La vidéo de Passe-Science : https://www.youtube.com/watch?v=SBwupYwDgHg Me soutenir sur Tipeee : http://www.tipeee.com/science-etonnante Mon livre : http://science-etonnante.com/livre.html Facebook : http://www.facebook.com/sciencetonnante Twitter : http://www.twitter.com/dlouapre Abonnez-vous : https://www.youtube.com/scienceetonnante -
3:01El Teorema de Gödel por fin Explicado Fácilmente
El Teorema de Gödel por fin Explicado FácilmenteEl Teorema de Gödel por fin Explicado Fácilmente
Gödel´s theorem easy. El teorema de Gödel explicado de forma fácil. -
15:04What is a Gödel Number? (Arithmatization)
What is a Gödel Number? (Arithmatization)What is a Gödel Number? (Arithmatization)
An explication of Gödel Numbers, Free Variables, Arithmatization, Substitution, and Arithmoquining. This covers some of the basics for Gödel's incompleteness theorem, and Tarski's Theorem on the Indefinability of Truth.
-
Math's Existential Crisis (Gödel's Incompleteness Theorems)
Math isn’t perfect, and math can prove it. In this video, we dive into Gödel’s incompleteness theorems, and what they mean for math. Created by: Cory Chang Produced by: Vivian Liu Special thanks to Ryan O’Donnell, associate professor at Carnegie Mellon University (http://www.cs.cmu.edu/~odonnell/). Twitter: https://twitter.com/UBehavior — Extra Resources: Ryan O’Donnell’s slide deck: http://www.cs.cmu.edu/~aada/courses/15251s16/www/slides/15251-s16-lecture16.pdf Wikipedia Entry: https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems Axiomatic Systems: https://en.wikipedia.org/wiki/Axiomatic_system Peano Axioms: https://en.wikipedia.org/wiki/Peano_axioms Principle of Explosion: https://en.wikipedia.org/wiki/Principle_of_explosion Picture credits: http://www.wallpapervortex.co...
published: 14 Dec 2016 -
Gödel's Incompleteness Theorems (BBC's In Our Time)
In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox. Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so, Gödel changed the way we understand what mathematics is, and ...
published: 02 Nov 2016 -
Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)
Kurt Godel: The World's Most Incredible Mind. "Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel Kurt Godel (1931) proved two important things about any axiomatic system rich enough to include all of number theory. 1) You'll never be able to prove every true result..... you'll never be able to prove every result that is true in your system. 2) Godel also proved that one of the results that you can never prove is the result that says that the system is consistent. More precisely: You cannot prove the consistency of any mathematical system rich enough to include the known theory of numbers. Hence, any consistent mathematical system that is rich enough to include number theory is inherently incomplete. Second, one of the propositions wh...
published: 18 Oct 2011 -
Hitler against Godel's Theorem
Hitler faces the awful truth: arithmetic is incomplete.
published: 04 May 2014 -
MIT Godel Escher Bach Lecture 1
published: 02 Dec 2012 -
Kurt Gödel - from the Limits of understanding
A brief bio of Kurt Gödel from :- The Limits of Understanding - World Science Festival https://www.youtube.com/watch?v=DfY-DRsE86s
published: 02 Jan 2015 -
Gödel's Incompleteness Theorem - Professor Tony Mann
A short mind-bending trip through the wonderful world of Mathematical Paradoxes: An examination of some recent work on paradoxes by the Austrian-American Mathematician Kurt Gödel. You can watch the full lecture by Professor Tony Mann here: http://www.gresham.ac.uk/lectures-and-events/this-lecture-will-surprise-you-when-logic-is-illogical
published: 21 Feb 2015 -
Les théorèmes d'incomplétude de Gödel — Science étonnante #37
En mathématiques, il existera toujours des choses vraies, mais indémontrables. Merci Kurt Gödel... Sur mon blog, le billet qui accompagne la vidéo : https://sciencetonnante.wordpress.com/2016/12/09/theoreme-godel/ Vous y trouverez beaucoup de précisions et de compléments. La vidéo de Passe-Science : https://www.youtube.com/watch?v=SBwupYwDgHg Me soutenir sur Tipeee : http://www.tipeee.com/science-etonnante Mon livre : http://science-etonnante.com/livre.html Facebook : http://www.facebook.com/sciencetonnante Twitter : http://www.twitter.com/dlouapre Abonnez-vous : https://www.youtube.com/scienceetonnante
published: 09 Dec 2016 -
El Teorema de Gödel por fin Explicado Fácilmente
Gödel´s theorem easy. El teorema de Gödel explicado de forma fácil.
published: 19 May 2016 -
What is a Gödel Number? (Arithmatization)
An explication of Gödel Numbers, Free Variables, Arithmatization, Substitution, and Arithmoquining. This covers some of the basics for Gödel's incompleteness theorem, and Tarski's Theorem on the Indefinability of Truth.
published: 27 Mar 2016
Math's Existential Crisis (Gödel's Incompleteness Theorems)
- Order: Reorder
- Duration: 6:55
- Updated: 14 Dec 2016
- views: 2853
Math isn’t perfect, and math can prove it. In this video, we dive into Gödel’s incompleteness theorems, and what they mean for math.
Created by: Cory Chang
Pro...
Math isn’t perfect, and math can prove it. In this video, we dive into Gödel’s incompleteness theorems, and what they mean for math.
Created by: Cory Chang
Produced by: Vivian Liu
Special thanks to Ryan O’Donnell, associate professor at Carnegie Mellon University (http://www.cs.cmu.edu/~odonnell/).
Twitter: https://twitter.com/UBehavior
—
Extra Resources:
Ryan O’Donnell’s slide deck: http://www.cs.cmu.edu/~aada/courses/15251s16/www/slides/15251-s16-lecture16.pdf
Wikipedia Entry: https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems
Axiomatic Systems: https://en.wikipedia.org/wiki/Axiomatic_system
Peano Axioms: https://en.wikipedia.org/wiki/Peano_axioms
Principle of Explosion: https://en.wikipedia.org/wiki/Principle_of_explosion
Picture credits:
http://www.wallpapervortex.com/wallpaper-15925_shadow_of_the_colossus.html
http://nomads-sotc-blog.blogspot.com/2011/08/colossi-sizes.html
http://nomads-sotc-blog.blogspot.com/2011/07/5th-colossus.html
https://www.wired.com/2015/07/sorry-perfect-lego-brick-may-never-eco-friendly/
https://i.ytimg.com/vi/TZJByZjfNwM/maxresdefault.jpg
http://disney.wikia.com/wiki/Yoda
http://fictionalcharacterbattles.wikia.com/wiki/Darth_Vader
https://www.spriters-resource.com/mobile/robouniatk/sheet/51416/
http://clipart-library.com/image_gallery/2180.png
https://wn.com/Math's_Existential_Crisis_(Gödel's_Incompleteness_Theorems)
Math isn’t perfect, and math can prove it. In this video, we dive into Gödel’s incompleteness theorems, and what they mean for math.
Created by: Cory Chang
Produced by: Vivian Liu
Special thanks to Ryan O’Donnell, associate professor at Carnegie Mellon University (http://www.cs.cmu.edu/~odonnell/).
Twitter: https://twitter.com/UBehavior
—
Extra Resources:
Ryan O’Donnell’s slide deck: http://www.cs.cmu.edu/~aada/courses/15251s16/www/slides/15251-s16-lecture16.pdf
Wikipedia Entry: https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems
Axiomatic Systems: https://en.wikipedia.org/wiki/Axiomatic_system
Peano Axioms: https://en.wikipedia.org/wiki/Peano_axioms
Principle of Explosion: https://en.wikipedia.org/wiki/Principle_of_explosion
Picture credits:
http://www.wallpapervortex.com/wallpaper-15925_shadow_of_the_colossus.html
http://nomads-sotc-blog.blogspot.com/2011/08/colossi-sizes.html
http://nomads-sotc-blog.blogspot.com/2011/07/5th-colossus.html
https://www.wired.com/2015/07/sorry-perfect-lego-brick-may-never-eco-friendly/
https://i.ytimg.com/vi/TZJByZjfNwM/maxresdefault.jpg
http://disney.wikia.com/wiki/Yoda
http://fictionalcharacterbattles.wikia.com/wiki/Darth_Vader
https://www.spriters-resource.com/mobile/robouniatk/sheet/51416/
http://clipart-library.com/image_gallery/2180.png
- published: 14 Dec 2016
- views: 2853
Gödel's Incompleteness Theorems (BBC's In Our Time)
- Order: Reorder
- Duration: 41:58
- Updated: 02 Nov 2016
- views: 4058
In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundatio...
In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox. Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so, Gödel changed the way we understand what mathematics is, and the implications of his work in physics and philosophy take us to the very edge of what we can know. Melvyn Bragg discusses Gödel’s Incompleteness Theorems with Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.
This is from a BBC program called In Our Time.
https://wn.com/Gödel's_Incompleteness_Theorems_(Bbc's_In_Our_Time)
In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox. Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so, Gödel changed the way we understand what mathematics is, and the implications of his work in physics and philosophy take us to the very edge of what we can know. Melvyn Bragg discusses Gödel’s Incompleteness Theorems with Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.
This is from a BBC program called In Our Time.
- published: 02 Nov 2016
- views: 4058
Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)
- Order: Reorder
- Duration: 15:00
- Updated: 18 Oct 2011
- views: 215046
Kurt Godel: The World's Most Incredible Mind.
"Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel
Kurt Godel...
Kurt Godel: The World's Most Incredible Mind.
"Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel
Kurt Godel (1931) proved two important things about any axiomatic system rich enough to include all of number theory.
1) You'll never be able to prove every true result..... you'll never be able to prove every result that is true in your system.
2) Godel also proved that one of the results that you can never prove is the result that says that the system is consistent. More precisely: You cannot prove the consistency of any mathematical system rich enough to include the known theory of numbers.
Hence, any consistent mathematical system that is rich enough to include number theory is inherently incomplete.
Second, one of the propositions whose truth or falsity cannot be proved within the system is precisely the proposition that states that the system is consistent. "
What Godel's proof means, then, is that we can't prove that arithmetic—let alone any more-complicated system—is consistent.
For 2000 years, mathematics has been the model—the subject—that convinces us that certainty is possible. Yet Now there's no certainty anywhere—not even in mathematics.
More...
http://teachingcompany.12.forumer.com/viewtopic.php?t=2327
Goedel's Ontological Proof.
For those interested in a discussion of Goedel's reasoning for God, then I suggest starting with this heavily annotated work, which I recently stumbled upon.
www.scribd.com/doc/95364925/Goedel-s-God-Proof-Annotated-Version
"It's not that God is subject to the Freedom Proof or the Doubt Proof.
According to Gödel, He's not. But we have to be, or else we are not free. So
our truth game with God turns into something like Feynman had described.
Feynman's Gods, every time physicists think they have the rules of the game
figured out, throw in a new wrinkle. They let people like Feynman make
progress, but if the Feynmans of the world learn too much, physics will stop
being the joy and challenge that it is. The Gods don't let that happen.
Gödel's God has to be very careful about how he lets our universe unfold.
If the world becomes totally controllable and comprehensible, we'll be God.
God does not object to that. In fact, according to Gödel, that is our destiny.
But it is also the end of us as free human beings. And human freedom is an
essential part of the beauty of God's universe."
~ page 251
https://wn.com/Kurt_Godel_The_World's_Most_Incredible_Mind_(Part_1_Of_3)
Kurt Godel: The World's Most Incredible Mind.
"Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel
Kurt Godel (1931) proved two important things about any axiomatic system rich enough to include all of number theory.
1) You'll never be able to prove every true result..... you'll never be able to prove every result that is true in your system.
2) Godel also proved that one of the results that you can never prove is the result that says that the system is consistent. More precisely: You cannot prove the consistency of any mathematical system rich enough to include the known theory of numbers.
Hence, any consistent mathematical system that is rich enough to include number theory is inherently incomplete.
Second, one of the propositions whose truth or falsity cannot be proved within the system is precisely the proposition that states that the system is consistent. "
What Godel's proof means, then, is that we can't prove that arithmetic—let alone any more-complicated system—is consistent.
For 2000 years, mathematics has been the model—the subject—that convinces us that certainty is possible. Yet Now there's no certainty anywhere—not even in mathematics.
More...
http://teachingcompany.12.forumer.com/viewtopic.php?t=2327
Goedel's Ontological Proof.
For those interested in a discussion of Goedel's reasoning for God, then I suggest starting with this heavily annotated work, which I recently stumbled upon.
www.scribd.com/doc/95364925/Goedel-s-God-Proof-Annotated-Version
"It's not that God is subject to the Freedom Proof or the Doubt Proof.
According to Gödel, He's not. But we have to be, or else we are not free. So
our truth game with God turns into something like Feynman had described.
Feynman's Gods, every time physicists think they have the rules of the game
figured out, throw in a new wrinkle. They let people like Feynman make
progress, but if the Feynmans of the world learn too much, physics will stop
being the joy and challenge that it is. The Gods don't let that happen.
Gödel's God has to be very careful about how he lets our universe unfold.
If the world becomes totally controllable and comprehensible, we'll be God.
God does not object to that. In fact, according to Gödel, that is our destiny.
But it is also the end of us as free human beings. And human freedom is an
essential part of the beauty of God's universe."
~ page 251
- published: 18 Oct 2011
- views: 215046
Hitler against Godel's Theorem
- Order: Reorder
- Duration: 3:50
- Updated: 04 May 2014
- views: 18322
Hitler faces the awful truth: arithmetic is incomplete.
Hitler faces the awful truth: arithmetic is incomplete.
https://wn.com/Hitler_Against_Godel's_Theorem
MIT Godel Escher Bach Lecture 1
- Order: Reorder
- Duration: 1:02:34
- Updated: 02 Dec 2012
- views: 152662
- published: 02 Dec 2012
- views: 152662
Kurt Gödel - from the Limits of understanding
- Order: Reorder
- Duration: 3:38
- Updated: 02 Jan 2015
- views: 21198
A brief bio of Kurt Gödel from :-
The Limits of Understanding - World Science Festival
https://www.youtube.com/watch?v=DfY-DRsE86s
A brief bio of Kurt Gödel from :-
The Limits of Understanding - World Science Festival
https://www.youtube.com/watch?v=DfY-DRsE86s
https://wn.com/Kurt_Gödel_From_The_Limits_Of_Understanding
A brief bio of Kurt Gödel from :-
The Limits of Understanding - World Science Festival
https://www.youtube.com/watch?v=DfY-DRsE86s
- published: 02 Jan 2015
- views: 21198
Gödel's Incompleteness Theorem - Professor Tony Mann
- Order: Reorder
- Duration: 6:22
- Updated: 21 Feb 2015
- views: 26860
A short mind-bending trip through the wonderful world of Mathematical Paradoxes: An examination of some recent work on paradoxes by the Austrian-American Mathem...
A short mind-bending trip through the wonderful world of Mathematical Paradoxes: An examination of some recent work on paradoxes by the Austrian-American Mathematician Kurt Gödel. You can watch the full lecture by Professor Tony Mann here: http://www.gresham.ac.uk/lectures-and-events/this-lecture-will-surprise-you-when-logic-is-illogical
https://wn.com/Gödel's_Incompleteness_Theorem_Professor_Tony_Mann
A short mind-bending trip through the wonderful world of Mathematical Paradoxes: An examination of some recent work on paradoxes by the Austrian-American Mathematician Kurt Gödel. You can watch the full lecture by Professor Tony Mann here: http://www.gresham.ac.uk/lectures-and-events/this-lecture-will-surprise-you-when-logic-is-illogical
- published: 21 Feb 2015
- views: 26860
Les théorèmes d'incomplétude de Gödel — Science étonnante #37
- Order: Reorder
- Duration: 18:28
- Updated: 09 Dec 2016
- views: 17360
En mathématiques, il existera toujours des choses vraies, mais indémontrables. Merci Kurt Gödel...
Sur mon blog, le billet qui accompagne la vidéo : https://sc...
En mathématiques, il existera toujours des choses vraies, mais indémontrables. Merci Kurt Gödel...
Sur mon blog, le billet qui accompagne la vidéo : https://sciencetonnante.wordpress.com/2016/12/09/theoreme-godel/ Vous y trouverez beaucoup de précisions et de compléments.
La vidéo de Passe-Science : https://www.youtube.com/watch?v=SBwupYwDgHg
Me soutenir sur Tipeee : http://www.tipeee.com/science-etonnante
Mon livre : http://science-etonnante.com/livre.html
Facebook : http://www.facebook.com/sciencetonnante
Twitter : http://www.twitter.com/dlouapre
Abonnez-vous : https://www.youtube.com/scienceetonnante
https://wn.com/Les_Théorèmes_D'Incomplétude_De_GöDel_—_Science_Étonnante_37
En mathématiques, il existera toujours des choses vraies, mais indémontrables. Merci Kurt Gödel...
Sur mon blog, le billet qui accompagne la vidéo : https://sciencetonnante.wordpress.com/2016/12/09/theoreme-godel/ Vous y trouverez beaucoup de précisions et de compléments.
La vidéo de Passe-Science : https://www.youtube.com/watch?v=SBwupYwDgHg
Me soutenir sur Tipeee : http://www.tipeee.com/science-etonnante
Mon livre : http://science-etonnante.com/livre.html
Facebook : http://www.facebook.com/sciencetonnante
Twitter : http://www.twitter.com/dlouapre
Abonnez-vous : https://www.youtube.com/scienceetonnante
- published: 09 Dec 2016
- views: 17360
El Teorema de Gödel por fin Explicado Fácilmente
- Order: Reorder
- Duration: 3:01
- Updated: 19 May 2016
- views: 13411
Gödel´s theorem easy. El teorema de Gödel explicado de forma fácil.
Gödel´s theorem easy. El teorema de Gödel explicado de forma fácil.
https://wn.com/El_Teorema_De_Gödel_Por_Fin_Explicado_Fácilmente
Gödel´s theorem easy. El teorema de Gödel explicado de forma fácil.
- published: 19 May 2016
- views: 13411
What is a Gödel Number? (Arithmatization)
- Order: Reorder
- Duration: 15:04
- Updated: 27 Mar 2016
- views: 2664
An explication of Gödel Numbers, Free Variables, Arithmatization, Substitution, and Arithmoquining. This covers some of the basics for Gödel's incompleteness t...
An explication of Gödel Numbers, Free Variables, Arithmatization, Substitution, and Arithmoquining. This covers some of the basics for Gödel's incompleteness theorem, and Tarski's Theorem on the Indefinability of Truth.
https://wn.com/What_Is_A_Gödel_Number_(Arithmatization)
An explication of Gödel Numbers, Free Variables, Arithmatization, Substitution, and Arithmoquining. This covers some of the basics for Gödel's incompleteness theorem, and Tarski's Theorem on the Indefinability of Truth.
- published: 27 Mar 2016
- views: 2664
- Playlist
- Chat
6:55
Math's Existential Crisis (Gödel's Incompleteness Theorems)
Math isn’t perfect, and math can prove it. In this video, we dive into Gödel’s incompleten...
published: 14 Dec 2016
Math's Existential Crisis (Gödel's Incompleteness Theorems)
Math's Existential Crisis (Gödel's Incompleteness Theorems)
- Report rights infringement
- published: 14 Dec 2016
- views: 2853
41:58
Gödel's Incompleteness Theorems (BBC's In Our Time)
In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope...
published: 02 Nov 2016
Gödel's Incompleteness Theorems (BBC's In Our Time)
Gödel's Incompleteness Theorems (BBC's In Our Time)
- Report rights infringement
- published: 02 Nov 2016
- views: 4058
15:00
Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)
Kurt Godel: The World's Most Incredible Mind.
"Either mathematics is too big for the huma...
published: 18 Oct 2011
Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)
Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)
- Report rights infringement
- published: 18 Oct 2011
- views: 215046
3:50
Hitler against Godel's Theorem
Hitler faces the awful truth: arithmetic is incomplete.
published: 04 May 2014
Hitler against Godel's Theorem
Hitler against Godel's Theorem
- Report rights infringement
- published: 04 May 2014
- views: 18322
1:02:34
MIT Godel Escher Bach Lecture 1
published: 02 Dec 2012
MIT Godel Escher Bach Lecture 1
MIT Godel Escher Bach Lecture 1
- Report rights infringement
- published: 02 Dec 2012
- views: 152662
3:38
Kurt Gödel - from the Limits of understanding
A brief bio of Kurt Gödel from :-
The Limits of Understanding - World Science Festival
htt...
published: 02 Jan 2015
Kurt Gödel - from the Limits of understanding
Kurt Gödel - from the Limits of understanding
- Report rights infringement
- published: 02 Jan 2015
- views: 21198
6:22
Gödel's Incompleteness Theorem - Professor Tony Mann
A short mind-bending trip through the wonderful world of Mathematical Paradoxes: An examin...
published: 21 Feb 2015
Gödel's Incompleteness Theorem - Professor Tony Mann
Gödel's Incompleteness Theorem - Professor Tony Mann
- Report rights infringement
- published: 21 Feb 2015
- views: 26860
18:28
Les théorèmes d'incomplétude de Gödel — Science étonnante #37
En mathématiques, il existera toujours des choses vraies, mais indémontrables. Merci Kurt ...
published: 09 Dec 2016
Les théorèmes d'incomplétude de Gödel — Science étonnante #37
Les théorèmes d'incomplétude de Gödel — Science étonnante #37
- Report rights infringement
- published: 09 Dec 2016
- views: 17360
3:01
El Teorema de Gödel por fin Explicado Fácilmente
Gödel´s theorem easy. El teorema de Gödel explicado de forma fácil.
published: 19 May 2016
El Teorema de Gödel por fin Explicado Fácilmente
El Teorema de Gödel por fin Explicado Fácilmente
- Report rights infringement
- published: 19 May 2016
- views: 13411
15:04
What is a Gödel Number? (Arithmatization)
An explication of Gödel Numbers, Free Variables, Arithmatization, Substitution, and Arithm...
published: 27 Mar 2016
What is a Gödel Number? (Arithmatization)
What is a Gödel Number? (Arithmatization)
- Report rights infringement
- published: 27 Mar 2016
- views: 2664
Math's Existential Crisis (Gödel's Incompleteness ...
Gödel's Incompleteness Theorems (BBC's In Our Time...
Kurt Godel: The World's Most Incredible Mind (Part...
Hitler against Godel's Theorem...
MIT Godel Escher Bach Lecture 1...
Kurt Gödel - from the Limits of understanding...
Gödel's Incompleteness Theorem - Professor Tony Ma...
Les théorèmes d'incomplétude de Gödel — Science é...
El Teorema de Gödel por fin Explicado Fácilmente...
What is a Gödel Number? (Arithmatization)...
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Lyrics list:lyrics
-
Go Quietly, Terra Naomi
-
Cocktail, Hysteric Blue
-
Cocktail, Vortex Of Clutter
Go Quietly
on the day you came to
did you know you had come
did you know why you came
could you feel where you're from
did you ask it out loud
when no one could hear you
did you cry all alone
when everyone feared you
i ask you this
mostly for me
cause people like us
can go quietly
when they told you to stop
did you want to keep going
when they pushed you to tears
could you feel the pain showing
did you know you were drifting
from the moment you drifted
and could you feel your heart shifting
before it had shifted,
i ask you this
mostly for me
cause people like us
can go quietly
i ask you this
mostly for me
