Gödel - Revision history

Fractalguy: /* Gödel and Fractals */

2025-01-13T10:05:27Z

Gödel and Fractals

← Older revision		Revision as of 10:05, 13 January 2025
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	There is also the fact that all [[fractals]] are generated with [[recursive]], [[Self-reference\|self-referential]] [[Generating equation\|equations]], which is the same [[mathematical]] tool that Gödel used. It works on multiple levels!		There is also the fact that all [[fractals]] are generated with [[recursive]], [[Self-reference\|self-referential]] [[Generating equation\|equations]], which is the same [[mathematical]] tool that Gödel used. It works on multiple levels!

			Those who are nit-picky about the application of theories about formal [[logic]] systems to the domain of [[wikipedia:Empiricism\|empiricism]] should note that this is an [[allegory]] to show how the necessary incompleteness of our [[math]] is [[like]] the incompleteness of our models of [[reality]]. It's not to imply that Gödel's theory directly addresses questions of empirical knowledge. The [[idea]] is to draw parallels and [[connections]] in order to demonstrate that the principles of [[self-reference]] and infinite nuance are [[universal]].

	== Incomplete Videos ==		== Incomplete Videos ==

Fractalguy: /* Gödel and Fractals */

2025-01-03T00:11:41Z

Gödel and Fractals

← Older revision		Revision as of 00:11, 3 January 2025
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	The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors. Simple rules always break down, and we must consider all of the specifics in each edge case to determine the best course of action. No matter how many precedents are set, the Supreme Court will always have new cases to decide.		The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors. Simple rules always break down, and we must consider all of the specifics in each edge case to determine the best course of action. No matter how many precedents are set, the Supreme Court will always have new cases to decide.

	There is also the fact that all [[fractals]] are generated with [[Self-reference\|self-referential]] [[Generating equation\|equations]], which is the same [[mathematical]] tool that Gödel used. It works on multiple levels!		There is also the fact that all [[fractals]] are generated with [[recursive]], [[Self-reference\|self-referential]] [[Generating equation\|equations]], which is the same [[mathematical]] tool that Gödel used. It works on multiple levels!

	== Incomplete Videos ==		== Incomplete Videos ==

Fractalguy at 19:05, 2 January 2025

2025-01-02T19:05:30Z

← Older revision		Revision as of 19:05, 2 January 2025
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	[[File:Escher-drawing-hands.jpg\|thumb\|Escher uses [[self-reference]] extensively in his [[art]]]][[wikipedia:Kurt_Gödel\|Godel's]] [[wikipedia:Gödel's_incompleteness_theorems\|incompleteness theorems]] are fundamental to understanding the limits of [[scientific]] and [[mathematical]] knowledge and the power of [[self-reference]]. <blockquote>''"It was something to be expected that sooner or later my proof will be made useful for religion, since that is doubtless also justified in a certain sense."'' -[[wikipedia:Kurt_Gödel\|Kurt Gödel]]</blockquote>It proves the Taoist saying by demonstrating that we can never universally determine what is true using the [[language]] of [[mathematics]].<blockquote>''The tao that can be described is not the eternal Tao.''		[[File:Escher-drawing-hands.jpg\|thumb\|Escher uses [[self-reference]] extensively in his [[art]]]][[wikipedia:Kurt_Gödel\|Godel's]] [[wikipedia:Gödel's_incompleteness_theorems\|incompleteness theorems]] are fundamental to understanding the limits of [[scientific]] and [[mathematical]] knowledge and the power of [[self-reference]]. <blockquote>''"It was something to be expected that sooner or later my proof will be made useful for religion, since that is doubtless also justified in a certain sense."'' -[[wikipedia:Kurt_Gödel\|Kurt Gödel]]</blockquote>It proves the Taoist saying by demonstrating that we can never universally determine what is [[true]] using the [[language]] of [[mathematics]].<blockquote>''The tao that can be described is not the eternal Tao.''

	''The name that can be spoken is not the eternal Name''		''The name that can be spoken is not the eternal Name''

Fractalguy at 19:04, 2 January 2025

2025-01-02T19:04:46Z

← Older revision		Revision as of 19:04, 2 January 2025
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	[[File:Escher-drawing-hands.jpg\|thumb\|Escher uses [[self-reference]] extensively in his [[art]]]][[wikipedia:Kurt_Gödel\|Godel's]] [[wikipedia:Gödel's_incompleteness_theorems\|incompleteness theorems]] are fundamental to understanding the limits of [[scientific]] and [[mathematical]] knowledge and the power of [[self-reference]]. <blockquote>''"It was something to be expected that sooner or later my proof will be made useful for religion, since that is doubtless also justified in a certain sense."'' -Kurt Gödel</blockquote>It proves the Taoist saying by demonstrating that we can never universally determine what is true using the [[language]] of [[mathematics]].<blockquote>''The tao that can be described is not the eternal Tao.''		[[File:Escher-drawing-hands.jpg\|thumb\|Escher uses [[self-reference]] extensively in his [[art]]]][[wikipedia:Kurt_Gödel\|Godel's]] [[wikipedia:Gödel's_incompleteness_theorems\|incompleteness theorems]] are fundamental to understanding the limits of [[scientific]] and [[mathematical]] knowledge and the power of [[self-reference]]. <blockquote>''"It was something to be expected that sooner or later my proof will be made useful for religion, since that is doubtless also justified in a certain sense."'' -[[wikipedia:Kurt_Gödel\|Kurt Gödel]]</blockquote>It proves the Taoist saying by demonstrating that we can never universally determine what is true using the [[language]] of [[mathematics]].<blockquote>''The tao that can be described is not the eternal Tao.''

	''The name that can be spoken is not the eternal Name''		''The name that can be spoken is not the eternal Name''

	-Lao Tzu</blockquote>[[wikipedia:Gödel,_Escher,_Bach\|Gödel, Escher, Bach]] should be considered [[required reading]] for a full understanding of [[metaculture]].		-[[wikipedia:Laozi\|Lao Tzu]]</blockquote>[[wikipedia:Gödel,_Escher,_Bach\|Gödel, Escher, Bach]] should be considered [[required reading]] for a full understanding of [[metaculture]].

	[[Special:WhatLinksHere/Gödel\|View All References to Self-Reference]]		[[Special:WhatLinksHere/Gödel\|View All References to Self-Reference]]

Fractalguy at 23:23, 29 December 2024

2024-12-29T23:23:01Z

← Older revision		Revision as of 23:23, 29 December 2024
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	[[File:Escher-drawing-hands.jpg\|thumb\|Escher uses [[self-reference]] extensively in his [[art]]]][[wikipedia:Kurt_Gödel\|Godel's]] [[wikipedia:Gödel's_incompleteness_theorems\|incompleteness theorems]] are fundamental to understanding the limits of [[scientific]] and [[mathematical]] knowledge and the power of [[self-reference]]. <blockquote>''"It was something to be expected that sooner or later my proof will be made useful for religion, since that is doubtless also justified in a certain sense."'' -Kurt Gödel</blockquote>It proves the Taoist saying by demonstrating that we can never universally determine what is true using the language of [[mathematics]].<blockquote>''The tao that can be described is not the eternal Tao.''		[[File:Escher-drawing-hands.jpg\|thumb\|Escher uses [[self-reference]] extensively in his [[art]]]][[wikipedia:Kurt_Gödel\|Godel's]] [[wikipedia:Gödel's_incompleteness_theorems\|incompleteness theorems]] are fundamental to understanding the limits of [[scientific]] and [[mathematical]] knowledge and the power of [[self-reference]]. <blockquote>''"It was something to be expected that sooner or later my proof will be made useful for religion, since that is doubtless also justified in a certain sense."'' -Kurt Gödel</blockquote>It proves the Taoist saying by demonstrating that we can never universally determine what is true using the [[language]] of [[mathematics]].<blockquote>''The tao that can be described is not the eternal Tao.''

	''The name that can be spoken is not the eternal Name''		''The name that can be spoken is not the eternal Name''

Fractalguy: /* Gödel and Fractals */

2024-12-29T11:02:17Z

Gödel and Fractals

← Older revision		Revision as of 11:02, 29 December 2024
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	Visualizing it this way, it becomes clear that why [[truth]] is such a slippery concept. On the macro scale, obvious truths and falsehoods can be clearly identified. But as soon as you start looking at the edge cases, and considering more and more [[Complexity\|complex]] variables, simple theories and models break down, and we need to revise them to get a more accurate, higher resolution picture of [[reality]].		Visualizing it this way, it becomes clear that why [[truth]] is such a slippery concept. On the macro scale, obvious truths and falsehoods can be clearly identified. But as soon as you start looking at the edge cases, and considering more and more [[Complexity\|complex]] variables, simple theories and models break down, and we need to revise them to get a more accurate, higher resolution picture of [[reality]].

	Consider [[wikipedia:Newton's_laws_of_motion\|Newtonian]] [[physics]] versus [[wikipedia:Theory_of_relativity\|Relativity]]. Newton's laws of motion predicted the behavior of [[matter]] at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our [[fractal]] picture of [[reality]], revealing new, complex patterns that were not visible with Newton. [[Quantum mechanics]] further enhanced the picture, allowing us to model the behavior of subatomic particles. However, the more we learn about the [[complexity]] of the [[universe]], the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered.		Consider [[wikipedia:Newton's_laws_of_motion\|Newtonian]] [[physics]] versus [[wikipedia:Theory_of_relativity\|Relativity]]. Newton's laws of motion predicted the behavior of [[matter]] at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our [[fractal]] picture of [[reality]], revealing new, complex patterns that were not visible with Newton. [[Quantum mechanics]] further enhanced the picture, allowing us to model the behavior of subatomic particles. However, the more we learn about the [[complexity]] of the [[universe]], the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered. Even if it isn't [[literally]] infinite, it's big enough to be effectively so.

	Gödel proved that [[universal]] objective [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].		Gödel proved that [[universal]] objective [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].

Fractalguy: /* Gödel and Fractals */

2024-12-20T18:45:57Z

Gödel and Fractals

← Older revision		Revision as of 18:45, 20 December 2024
Line 15:		Line 15:
	Consider [[wikipedia:Newton's_laws_of_motion\|Newtonian]] [[physics]] versus [[wikipedia:Theory_of_relativity\|Relativity]]. Newton's laws of motion predicted the behavior of [[matter]] at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our [[fractal]] picture of [[reality]], revealing new, complex patterns that were not visible with Newton. [[Quantum mechanics]] further enhanced the picture, allowing us to model the behavior of subatomic particles. However, the more we learn about the [[complexity]] of the [[universe]], the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered.		Consider [[wikipedia:Newton's_laws_of_motion\|Newtonian]] [[physics]] versus [[wikipedia:Theory_of_relativity\|Relativity]]. Newton's laws of motion predicted the behavior of [[matter]] at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our [[fractal]] picture of [[reality]], revealing new, complex patterns that were not visible with Newton. [[Quantum mechanics]] further enhanced the picture, allowing us to model the behavior of subatomic particles. However, the more we learn about the [[complexity]] of the [[universe]], the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered.

	Gödel proved that [[universal]] [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].		Gödel proved that [[universal]] objective [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].

	The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors. Simple rules always break down, and we must consider all of the specifics in each edge case to determine the best course of action. No matter how many precedents are set, the Supreme Court will always have new cases to decide.		The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors. Simple rules always break down, and we must consider all of the specifics in each edge case to determine the best course of action. No matter how many precedents are set, the Supreme Court will always have new cases to decide.

Fractalguy: /* Gödel and Fractals */

2024-12-18T14:00:06Z

Gödel and Fractals

← Older revision		Revision as of 14:00, 18 December 2024
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	Gödel proved that [[universal]] [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].		Gödel proved that [[universal]] [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].

	The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors.		The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors. Simple rules always break down, and we must consider all of the specifics in each edge case to determine the best course of action. No matter how many precedents are set, the Supreme Court will always have new cases to decide.

	There is also the fact that all [[fractals]] are generated with [[Self-reference\|self-referential]] [[Generating equation\|equations]], which is the same [[mathematical]] tool that Gödel used. It works on multiple levels!		There is also the fact that all [[fractals]] are generated with [[Self-reference\|self-referential]] [[Generating equation\|equations]], which is the same [[mathematical]] tool that Gödel used. It works on multiple levels!

Fractalguy: /* Incomplete Videos */

2024-12-18T13:54:13Z

Incomplete Videos

← Older revision		Revision as of 13:54, 18 December 2024
Line 35:		Line 35:
	<br>		<br>
	{{#ev:youtube\|https://www.youtube.com/watch?v=lfXxzAVtdpU\|\|center\|Doug Hofstadter - Reflections on AI\|frame}}		{{#ev:youtube\|https://www.youtube.com/watch?v=lfXxzAVtdpU\|\|center\|Doug Hofstadter - Reflections on AI\|frame}}
	<br>		<br>Many science fiction stories have used Gödel's technique to short-circuit machines that operate on [[logic]].
	{{#ev:youtube\|https://www.youtube.com/watch?v=YbHtzqCge_8\|\|center\|Kirk, Spock, Scotty, and McCoy Outwit the Androids\|frame}}		{{#ev:youtube\|https://www.youtube.com/watch?v=YbHtzqCge_8\|\|center\|Kirk, Spock, Scotty, and McCoy Outwit the Androids\|frame}}
	<br>		<br>
	{{#ev:youtube\|https://www.youtube.com/watch?v=ddbxFi3-UO4\|\|center\|Bach "Little" Fugue in G Minor\|frame}}		{{#ev:youtube\|https://www.youtube.com/watch?v=ddbxFi3-UO4\|\|center\|Bach "Little" Fugue in G Minor\|frame}}

Fractalguy: /* Gödel and Fractals */

2024-12-18T13:52:35Z

Gödel and Fractals

← Older revision		Revision as of 13:52, 18 December 2024
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	== Gödel and Fractals ==		== Gödel and Fractals ==
	[[File:Mandelbrot Fractal Zoom.gif\|thumb\|Visualizing the implications of Gödel's incompleteness theorems]]		[[File:Mandelbrot Fractal Zoom.gif\|thumb\|Visualizing the implications of Gödel's incompleteness theorems]]
	The implications of Gödel are [[Metaphor\|metaphorically]] represented by the [[fractal]] boundary between the black and the color in the Mandelbrot set. Consider the black areas of the Mandelbrot to be the [[Truth]]--theories about the [[universe]] that can be proven, and are consistently true when tested. All of the colored areas are incorrect ideas--imprecise estimations that are often true in simple cases but break down when you consider more [[Complexity\|complex]] variables.		The implications of Gödel are [[Metaphor\|metaphorically]] and visually represented by the [[fractal]] boundary between the black and the color in the Mandelbrot set. Consider the black areas of the Mandelbrot to be the [[Truth]]--theories about the [[universe]] that can be proven, and are consistently true when tested. All of the colored areas are incorrect ideas--imprecise estimations that are often true in simple cases but break down when you consider more [[Complexity\|complex]] variables.

	Visualizing it this way, it becomes clear that why [[truth]] is such a slippery concept. On the macro scale, obvious truths and falsehoods can be clearly identified. But as soon as you start looking at the edge cases, and considering more and more [[Complexity\|complex]] variables, simple theories and models break down, and we need to revise them to get a more accurate, higher resolution picture of [[reality]].		Visualizing it this way, it becomes clear that why [[truth]] is such a slippery concept. On the macro scale, obvious truths and falsehoods can be clearly identified. But as soon as you start looking at the edge cases, and considering more and more [[Complexity\|complex]] variables, simple theories and models break down, and we need to revise them to get a more accurate, higher resolution picture of [[reality]].

	Consider [[wikipedia:Newton's_laws_of_motion\|Newtonian]] [[physics]] versus [[wikipedia:Theory_of_relativity\|Relativity]]. Newton's laws of motion predicted the behavior of [[matter]] at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our [[fractal]] picture of [[reality]], revealing new, complex patterns that were not visible with Newton. [[Quantum mechanics]] further enhanced the picture, allowing us to model the behavior of subatomic particles. ~~The~~ more we learn about the [[complexity]] of the [[universe]], the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered.		Consider [[wikipedia:Newton's_laws_of_motion\|Newtonian]] [[physics]] versus [[wikipedia:Theory_of_relativity\|Relativity]]. Newton's laws of motion predicted the behavior of [[matter]] at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our [[fractal]] picture of [[reality]], revealing new, complex patterns that were not visible with Newton. [[Quantum mechanics]] further enhanced the picture, allowing us to model the behavior of subatomic particles. However, the more we learn about the [[complexity]] of the [[universe]], the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered.

	Gödel proved that [[universal]] [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer approximations of the true [[laws of physics]].		Gödel proved that [[universal]] [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].

	The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors.		The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors.

			There is also the fact that all [[fractals]] are generated with [[Self-reference\|self-referential]] [[Generating equation\|equations]], which is the same [[mathematical]] tool that Gödel used. It works on multiple levels!

	== Incomplete Videos ==		== Incomplete Videos ==
	Here's ~~a basic~~ explanation of Gödel's incompleteness theorem ~~if such a thing exists~~.		Here's an incomplete explanation of Gödel's incompleteness theorem.

	{{#ev:youtube\|https://www.youtube.com/watch?v=I4pQbo5MQOs\|\|center\|The Paradox at the Heart of Mathematics: Gödel's Incompleteness Theorem\|frame}}		{{#ev:youtube\|https://www.youtube.com/watch?v=I4pQbo5MQOs\|\|center\|The Paradox at the Heart of Mathematics: Gödel's Incompleteness Theorem\|frame}}

← Older revision		Revision as of 11:02, 29 December 2024
Line 13:		Line 13:
	Visualizing it this way, it becomes clear that why [[truth]] is such a slippery concept. On the macro scale, obvious truths and falsehoods can be clearly identified. But as soon as you start looking at the edge cases, and considering more and more [[Complexity\|complex]] variables, simple theories and models break down, and we need to revise them to get a more accurate, higher resolution picture of [[reality]].		Visualizing it this way, it becomes clear that why [[truth]] is such a slippery concept. On the macro scale, obvious truths and falsehoods can be clearly identified. But as soon as you start looking at the edge cases, and considering more and more [[Complexity\|complex]] variables, simple theories and models break down, and we need to revise them to get a more accurate, higher resolution picture of [[reality]].

	Consider [[wikipedia:Newton's_laws_of_motion\|Newtonian]] [[physics]] versus [[wikipedia:Theory_of_relativity\|Relativity]]. Newton's laws of motion predicted the behavior of [[matter]] at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our [[fractal]] picture of [[reality]], revealing new, complex patterns that were not visible with Newton. [[Quantum mechanics]] further enhanced the picture, allowing us to model the behavior of subatomic particles. However, the more we learn about the [[complexity]] of the [[universe]], the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered.		Consider [[wikipedia:Newton's_laws_of_motion\|Newtonian]] [[physics]] versus [[wikipedia:Theory_of_relativity\|Relativity]]. Newton's laws of motion predicted the behavior of [[matter]] at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our [[fractal]] picture of [[reality]], revealing new, complex patterns that were not visible with Newton. [[Quantum mechanics]] further enhanced the picture, allowing us to model the behavior of subatomic particles. However, the more we learn about the [[complexity]] of the [[universe]], the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered. Even if it isn't [[literally]] infinite, it's big enough to be effectively so.

	Gödel proved that [[universal]] objective [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].		Gödel proved that [[universal]] objective [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].

← Older revision		Revision as of 18:45, 20 December 2024
Line 15:		Line 15:
	Consider [[wikipedia:Newton's_laws_of_motion\|Newtonian]] [[physics]] versus [[wikipedia:Theory_of_relativity\|Relativity]]. Newton's laws of motion predicted the behavior of [[matter]] at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our [[fractal]] picture of [[reality]], revealing new, complex patterns that were not visible with Newton. [[Quantum mechanics]] further enhanced the picture, allowing us to model the behavior of subatomic particles. However, the more we learn about the [[complexity]] of the [[universe]], the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered.		Consider [[wikipedia:Newton's_laws_of_motion\|Newtonian]] [[physics]] versus [[wikipedia:Theory_of_relativity\|Relativity]]. Newton's laws of motion predicted the behavior of [[matter]] at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our [[fractal]] picture of [[reality]], revealing new, complex patterns that were not visible with Newton. [[Quantum mechanics]] further enhanced the picture, allowing us to model the behavior of subatomic particles. However, the more we learn about the [[complexity]] of the [[universe]], the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered.

	Gödel proved that [[universal]] [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].		Gödel proved that [[universal]] objective [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].

	The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors. Simple rules always break down, and we must consider all of the specifics in each edge case to determine the best course of action. No matter how many precedents are set, the Supreme Court will always have new cases to decide.		The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors. Simple rules always break down, and we must consider all of the specifics in each edge case to determine the best course of action. No matter how many precedents are set, the Supreme Court will always have new cases to decide.

← Older revision		Revision as of 14:00, 18 December 2024
Line 17:		Line 17:
	Gödel proved that [[universal]] [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].		Gödel proved that [[universal]] [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].

	The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors.		The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors. Simple rules always break down, and we must consider all of the specifics in each edge case to determine the best course of action. No matter how many precedents are set, the Supreme Court will always have new cases to decide.

	There is also the fact that all [[fractals]] are generated with [[Self-reference\|self-referential]] [[Generating equation\|equations]], which is the same [[mathematical]] tool that Gödel used. It works on multiple levels!		There is also the fact that all [[fractals]] are generated with [[Self-reference\|self-referential]] [[Generating equation\|equations]], which is the same [[mathematical]] tool that Gödel used. It works on multiple levels!

← Older revision		Revision as of 13:52, 18 December 2024
Line 9:		Line 9:
	== Gödel and Fractals ==		== Gödel and Fractals ==
	[[File:Mandelbrot Fractal Zoom.gif\|thumb\|Visualizing the implications of Gödel's incompleteness theorems]]		[[File:Mandelbrot Fractal Zoom.gif\|thumb\|Visualizing the implications of Gödel's incompleteness theorems]]
	The implications of Gödel are [[Metaphor\|metaphorically]] represented by the [[fractal]] boundary between the black and the color in the Mandelbrot set. Consider the black areas of the Mandelbrot to be the [[Truth]]--theories about the [[universe]] that can be proven, and are consistently true when tested. All of the colored areas are incorrect ideas--imprecise estimations that are often true in simple cases but break down when you consider more [[Complexity\|complex]] variables.		The implications of Gödel are [[Metaphor\|metaphorically]] and visually represented by the [[fractal]] boundary between the black and the color in the Mandelbrot set. Consider the black areas of the Mandelbrot to be the [[Truth]]--theories about the [[universe]] that can be proven, and are consistently true when tested. All of the colored areas are incorrect ideas--imprecise estimations that are often true in simple cases but break down when you consider more [[Complexity\|complex]] variables.

	Visualizing it this way, it becomes clear that why [[truth]] is such a slippery concept. On the macro scale, obvious truths and falsehoods can be clearly identified. But as soon as you start looking at the edge cases, and considering more and more [[Complexity\|complex]] variables, simple theories and models break down, and we need to revise them to get a more accurate, higher resolution picture of [[reality]].		Visualizing it this way, it becomes clear that why [[truth]] is such a slippery concept. On the macro scale, obvious truths and falsehoods can be clearly identified. But as soon as you start looking at the edge cases, and considering more and more [[Complexity\|complex]] variables, simple theories and models break down, and we need to revise them to get a more accurate, higher resolution picture of [[reality]].

	Consider [[wikipedia:Newton's_laws_of_motion\|Newtonian]] [[physics]] versus [[wikipedia:Theory_of_relativity\|Relativity]]. Newton's laws of motion predicted the behavior of [[matter]] at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our [[fractal]] picture of [[reality]], revealing new, complex patterns that were not visible with Newton. [[Quantum mechanics]] further enhanced the picture, allowing us to model the behavior of subatomic particles. ~~The~~ more we learn about the [[complexity]] of the [[universe]], the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered.		Consider [[wikipedia:Newton's_laws_of_motion\|Newtonian]] [[physics]] versus [[wikipedia:Theory_of_relativity\|Relativity]]. Newton's laws of motion predicted the behavior of [[matter]] at macro scales and low velocities, but began to give incorrect predictions at higher velocities and subatomic scales. Relativity allowed us to zoom in further on our [[fractal]] picture of [[reality]], revealing new, complex patterns that were not visible with Newton. [[Quantum mechanics]] further enhanced the picture, allowing us to model the behavior of subatomic particles. However, the more we learn about the [[complexity]] of the [[universe]], the more questions it raises. We realize that despite the accuracy of our models, there is an infinite amount of detail yet to be discovered.

	Gödel proved that [[universal]] [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer approximations of the true [[laws of physics]].		Gödel proved that [[universal]] [[truths]] are impossible. The [[truth]] is infinitely [[Complexity\|complex]], and [[science]] can only continue to refine our models to create closer and closer approximations of the true [[laws of physics]].

	The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors.		The same [[logic]] also applies to [[ethics]], which is why every "[[Moral absolutes\|moral absolute]]" has a thousand exceptions when you consider all the possible external factors.

			There is also the fact that all [[fractals]] are generated with [[Self-reference\|self-referential]] [[Generating equation\|equations]], which is the same [[mathematical]] tool that Gödel used. It works on multiple levels!

	== Incomplete Videos ==		== Incomplete Videos ==
	Here's ~~a basic~~ explanation of Gödel's incompleteness theorem ~~if such a thing exists~~.		Here's an incomplete explanation of Gödel's incompleteness theorem.

	{{#ev:youtube\|https://www.youtube.com/watch?v=I4pQbo5MQOs\|\|center\|The Paradox at the Heart of Mathematics: Gödel's Incompleteness Theorem\|frame}}		{{#ev:youtube\|https://www.youtube.com/watch?v=I4pQbo5MQOs\|\|center\|The Paradox at the Heart of Mathematics: Gödel's Incompleteness Theorem\|frame}}