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	<title>Comments on: African fractals</title>
	<atom:link href="http://www.ethanzuckerman.com/blog/2007/06/05/african-fractals/feed/" rel="self" type="application/rss+xml" />
	<link>http://www.ethanzuckerman.com/blog/2007/06/05/african-fractals/</link>
	<description>EthanZ's musings on Africa, media and international development</description>
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		<title>By: milo gardbner</title>
		<link>http://www.ethanzuckerman.com/blog/2007/06/05/african-fractals/comment-page-1/#comment-2658938</link>
		<dc:creator>milo gardbner</dc:creator>
		<pubDate>Fri, 09 Dec 2011 17:37:22 +0000</pubDate>
		<guid isPermaLink="false">http://www.ethanzuckerman.com/blog/?p=1469#comment-2658938</guid>
		<description>My interest in the topic dates to three time periods:


1. Had African fractal villages been common before 5,000years ago, the myth of Egyptian base 10 being created from the merger of Egyptian base 2 and base 5 cultures (Upper and Lower Egypt), about the time of the birth of hieroglyphic writing takes on a special meaning. Egyptian scribes would have understood infinite math aspects of its Eye of Horus 1 = 1/2 + 1/4 + 1/16 + 1.32 + 1/64 + ...

This possible historical event saw Pharaoh adopting the binary side of African fractal villages as a metaphor for eternity ... further encoded in the Book of the Dead.

2. Had African fractal villages been first created after contact with Egyptian Old Kingdom lovers of the Eye of Horus myth, another type of historical event would have taken place. Book of the Dead connections to eternity would have been modified by African village to infinite binary family line bisections (from 3,000 BCE to 2050 BCE)

3. Had African fractal villages been first been created after contact with Egyptian Middle Kingdom, New Kingdom, Demotic and more recent Egyptian cultures (from 2050 BCE to 800 AD) the infinite series aspect would have been modified by considering Egyptian finite arithmetic. Egyptian, Greek and medieval scribes considered infinite binary series family statements ... as Archimedes wrote down the first calculus ,,, stated the problem of an area of a parabola by a 1/4 geometric series, one-phase of the Eye of Horus:

4A/3 = A + A/4 + A/16 + A/64 + ...

and looked for a finite series solution, reported by Archimedes

4A/3 = A + A/4 + A/12

with the later not being reported in African villages. Africans seemed not to go beyond family. Abstract mathematical aspects arrive in other ways.</description>
		<content:encoded><![CDATA[<p>My interest in the topic dates to three time periods:</p>
<p>1. Had African fractal villages been common before 5,000years ago, the myth of Egyptian base 10 being created from the merger of Egyptian base 2 and base 5 cultures (Upper and Lower Egypt), about the time of the birth of hieroglyphic writing takes on a special meaning. Egyptian scribes would have understood infinite math aspects of its Eye of Horus 1 = 1/2 + 1/4 + 1/16 + 1.32 + 1/64 + &#8230;</p>
<p>This possible historical event saw Pharaoh adopting the binary side of African fractal villages as a metaphor for eternity &#8230; further encoded in the Book of the Dead.</p>
<p>2. Had African fractal villages been first created after contact with Egyptian Old Kingdom lovers of the Eye of Horus myth, another type of historical event would have taken place. Book of the Dead connections to eternity would have been modified by African village to infinite binary family line bisections (from 3,000 BCE to 2050 BCE)</p>
<p>3. Had African fractal villages been first been created after contact with Egyptian Middle Kingdom, New Kingdom, Demotic and more recent Egyptian cultures (from 2050 BCE to 800 AD) the infinite series aspect would have been modified by considering Egyptian finite arithmetic. Egyptian, Greek and medieval scribes considered infinite binary series family statements &#8230; as Archimedes wrote down the first calculus ,,, stated the problem of an area of a parabola by a 1/4 geometric series, one-phase of the Eye of Horus:</p>
<p>4A/3 = A + A/4 + A/16 + A/64 + &#8230;</p>
<p>and looked for a finite series solution, reported by Archimedes</p>
<p>4A/3 = A + A/4 + A/12</p>
<p>with the later not being reported in African villages. Africans seemed not to go beyond family. Abstract mathematical aspects arrive in other ways.</p>
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		<title>By: reni(g)2</title>
		<link>http://www.ethanzuckerman.com/blog/2007/06/05/african-fractals/comment-page-1/#comment-2658460</link>
		<dc:creator>reni(g)2</dc:creator>
		<pubDate>Mon, 21 Nov 2011 22:32:49 +0000</pubDate>
		<guid isPermaLink="false">http://www.ethanzuckerman.com/blog/?p=1469#comment-2658460</guid>
		<description>So are African&#039;s the stalk or the tip in the fractal of life?</description>
		<content:encoded><![CDATA[<p>So are African&#8217;s the stalk or the tip in the fractal of life?</p>
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		<title>By: reni(g)2</title>
		<link>http://www.ethanzuckerman.com/blog/2007/06/05/african-fractals/comment-page-1/#comment-2658459</link>
		<dc:creator>reni(g)2</dc:creator>
		<pubDate>Mon, 21 Nov 2011 22:30:05 +0000</pubDate>
		<guid isPermaLink="false">http://www.ethanzuckerman.com/blog/?p=1469#comment-2658459</guid>
		<description>Damn. This is the reason all people are primitive. &quot;We did this first&quot; arguments stunts growth. Far as I&#039;m concerned people didn&#039;t discover shit. They just sampled the order of life. Calculus is based on this logic. Anyone comfortable with themselves does not need to make enemies unnecessarily. To clarify my point here&#039;s a quote from Eglash.

&quot;Creating a body of mathematics is about intellectual labor, not some kind of transcendental revelation. There are plenty of important components of European fractal geometry that are missing from the African version,&quot; Eglash said.

This obviously was said not offend his fellow European mathematicians and scholars. 


On the other hand, Eglash maintained, his work does show that African mathematics is much more complex than previously thought.

This obviously was said not to offend [any deeper] the African&#039;s who&#039;s work he was so astonished by.

Sorta like throwing them an extra ishango bone. 
&quot;That&#039;s a pretty decent idea, while not a complete concept we see you though.&quot;
 
Africans cheer with joy, &quot;we somebody! :)&quot;

Modern civilization is fucking sick. Epic.

Also since transcendence has no point in logical science I guess inspiration is irrelevant too.</description>
		<content:encoded><![CDATA[<p>Damn. This is the reason all people are primitive. &#8220;We did this first&#8221; arguments stunts growth. Far as I&#8217;m concerned people didn&#8217;t discover shit. They just sampled the order of life. Calculus is based on this logic. Anyone comfortable with themselves does not need to make enemies unnecessarily. To clarify my point here&#8217;s a quote from Eglash.</p>
<p>&#8220;Creating a body of mathematics is about intellectual labor, not some kind of transcendental revelation. There are plenty of important components of European fractal geometry that are missing from the African version,&#8221; Eglash said.</p>
<p>This obviously was said not offend his fellow European mathematicians and scholars. </p>
<p>On the other hand, Eglash maintained, his work does show that African mathematics is much more complex than previously thought.</p>
<p>This obviously was said not to offend [any deeper] the African&#8217;s who&#8217;s work he was so astonished by.</p>
<p>Sorta like throwing them an extra ishango bone.<br />
&#8220;That&#8217;s a pretty decent idea, while not a complete concept we see you though.&#8221;</p>
<p>Africans cheer with joy, &#8220;we somebody! :)&#8221;</p>
<p>Modern civilization is fucking sick. Epic.</p>
<p>Also since transcendence has no point in logical science I guess inspiration is irrelevant too.</p>
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		<title>By: michael carson</title>
		<link>http://www.ethanzuckerman.com/blog/2007/06/05/african-fractals/comment-page-1/#comment-1997260</link>
		<dc:creator>michael carson</dc:creator>
		<pubDate>Sat, 10 Apr 2010 03:34:06 +0000</pubDate>
		<guid isPermaLink="false">http://www.ethanzuckerman.com/blog/?p=1469#comment-1997260</guid>
		<description>i think thats so very true,also when i look at tv history chanel i always see them try to pass off roman mumification as ancient when they know egyptians with the right hand over the left are the real egytian mummies.</description>
		<content:encoded><![CDATA[<p>i think thats so very true,also when i look at tv history chanel i always see them try to pass off roman mumification as ancient when they know egyptians with the right hand over the left are the real egytian mummies.</p>
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		<title>By: yogourt</title>
		<link>http://www.ethanzuckerman.com/blog/2007/06/05/african-fractals/comment-page-1/#comment-1991782</link>
		<dc:creator>yogourt</dc:creator>
		<pubDate>Tue, 06 Apr 2010 09:50:05 +0000</pubDate>
		<guid isPermaLink="false">http://www.ethanzuckerman.com/blog/?p=1469#comment-1991782</guid>
		<description>TruthTeller is right Mark. Ancient greeks were black. (greek statues in museums with caucasoid facial features are fake). As a matter of fact , blacks invented everything. music is just a detail really. Blacks invented western civilisation too. and all the most important scientific discoveries in human history were discovered by black slaves (white slave owners took all the credit for these inventions)...Most ironic of all , the very language you&#039;re speaking (english) was also invented by blacks.</description>
		<content:encoded><![CDATA[<p>TruthTeller is right Mark. Ancient greeks were black. (greek statues in museums with caucasoid facial features are fake). As a matter of fact , blacks invented everything. music is just a detail really. Blacks invented western civilisation too. and all the most important scientific discoveries in human history were discovered by black slaves (white slave owners took all the credit for these inventions)&#8230;Most ironic of all , the very language you&#8217;re speaking (english) was also invented by blacks.</p>
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		<title>By: Tj</title>
		<link>http://www.ethanzuckerman.com/blog/2007/06/05/african-fractals/comment-page-1/#comment-1955634</link>
		<dc:creator>Tj</dc:creator>
		<pubDate>Tue, 09 Mar 2010 15:48:59 +0000</pubDate>
		<guid isPermaLink="false">http://www.ethanzuckerman.com/blog/?p=1469#comment-1955634</guid>
		<description>Well said Truthteller, we should all do our own research and stop relying on what we&#039;ve been told.</description>
		<content:encoded><![CDATA[<p>Well said Truthteller, we should all do our own research and stop relying on what we&#8217;ve been told.</p>
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		<title>By: TruthTeller</title>
		<link>http://www.ethanzuckerman.com/blog/2007/06/05/african-fractals/comment-page-1/#comment-1532725</link>
		<dc:creator>TruthTeller</dc:creator>
		<pubDate>Sun, 26 Apr 2009 15:11:24 +0000</pubDate>
		<guid isPermaLink="false">http://www.ethanzuckerman.com/blog/?p=1469#comment-1532725</guid>
		<description>Mark, you are wrong. Ancient Greeks were not Whites. In fact, there is no scientific record every published in history which claims Ancient Greeks were Whites. Ancient Greece an Ancient Kemetian (Ancient Egyptian) colony and was inhabited by the same race of people (Black Africans) as those in Ancient Kemet. Furthermore, the first time White-Europe ever heard of the Ancient Greeks was from the Arabs (who know they were Black African). Most of the history you were taught was created in the mid-1700&#039;s and 1800&#039;s.</description>
		<content:encoded><![CDATA[<p>Mark, you are wrong. Ancient Greeks were not Whites. In fact, there is no scientific record every published in history which claims Ancient Greeks were Whites. Ancient Greece an Ancient Kemetian (Ancient Egyptian) colony and was inhabited by the same race of people (Black Africans) as those in Ancient Kemet. Furthermore, the first time White-Europe ever heard of the Ancient Greeks was from the Arabs (who know they were Black African). Most of the history you were taught was created in the mid-1700&#8242;s and 1800&#8242;s.</p>
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		<title>By: Chris</title>
		<link>http://www.ethanzuckerman.com/blog/2007/06/05/african-fractals/comment-page-1/#comment-1238247</link>
		<dc:creator>Chris</dc:creator>
		<pubDate>Sat, 11 Oct 2008 16:15:00 +0000</pubDate>
		<guid isPermaLink="false">http://www.ethanzuckerman.com/blog/?p=1469#comment-1238247</guid>
		<description>I thought the ancient Greek&#039;s were aknowledged to have taken their music theory from the Eygptian / Sumerians?   Pythagorus studied in Eygpt, and there is no evidence that he even came up with the material credited to him (emerging as written records at least 600 years after his death, at much the same time as the Christian Bible).  Music Theory was later edited by the Christians for their own purposes, and as a result, the origin of modes has been completely lost.  

Also Pythagorus was also supposed to have had a thing for the number 4, and squares, which must have horrified him when they found the circle of fifths gave a diminished 7th in relation to this number/ shape (and doubtless led to some swift revision of the theory in order to maintain the integrity of his philosophy).  Overall i have to confer with Bernie that Music Theory is most likely African or Middle Eastern in origin ... although since the library at Alexandria was burnt down, and the dark ages sort to redefine written history as we know it, maybe we will never know for sure...over to Mark to refute this ... (although i will say now that stating that the Greek came up with the theory independantly of the Sumerians, about 2000 years of the facts is unprovable, and highly unlikely, given we still use Sumerian Clocks)...maybe it&#039;s best to aknowledge that it&#039;s not currently possible to be sure of any of the &quot;facts&quot;? ...</description>
		<content:encoded><![CDATA[<p>I thought the ancient Greek&#8217;s were aknowledged to have taken their music theory from the Eygptian / Sumerians?   Pythagorus studied in Eygpt, and there is no evidence that he even came up with the material credited to him (emerging as written records at least 600 years after his death, at much the same time as the Christian Bible).  Music Theory was later edited by the Christians for their own purposes, and as a result, the origin of modes has been completely lost.  </p>
<p>Also Pythagorus was also supposed to have had a thing for the number 4, and squares, which must have horrified him when they found the circle of fifths gave a diminished 7th in relation to this number/ shape (and doubtless led to some swift revision of the theory in order to maintain the integrity of his philosophy).  Overall i have to confer with Bernie that Music Theory is most likely African or Middle Eastern in origin &#8230; although since the library at Alexandria was burnt down, and the dark ages sort to redefine written history as we know it, maybe we will never know for sure&#8230;over to Mark to refute this &#8230; (although i will say now that stating that the Greek came up with the theory independantly of the Sumerians, about 2000 years of the facts is unprovable, and highly unlikely, given we still use Sumerian Clocks)&#8230;maybe it&#8217;s best to aknowledge that it&#8217;s not currently possible to be sure of any of the &#8220;facts&#8221;? &#8230;</p>
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		<title>By: Mark</title>
		<link>http://www.ethanzuckerman.com/blog/2007/06/05/african-fractals/comment-page-1/#comment-1130595</link>
		<dc:creator>Mark</dc:creator>
		<pubDate>Fri, 01 Aug 2008 13:55:17 +0000</pubDate>
		<guid isPermaLink="false">http://www.ethanzuckerman.com/blog/?p=1469#comment-1130595</guid>
		<description>Music theory is based on musical modes of the ancient Greeks, which were Caucasoid people. The modes are Ionian (Major scale), Aeolian (minor scale), Locrian (diminished scale), and the rest are categorized into the Major type (Lydian and Mixolydian) and the minor type (Dorian and Phrygian) by the Tonic (1st), Mediant (3rd), and Dominant (5th) degrees of the modes.

The Blues scale is an added Diminished 5th or Augmented 4th (enharmonic) note (the blue note) to the Major and minor pentatonic scales, which take particular notes from the Major (Ionian) and minor (Aeolian) scales.

Classical music often used the Harmonic and Melodic minor scales. The former is an augmentation of the 7th (leading tone) degree by one half-step (semitone), and the latter is the same but with an augmented 6th (submediant) degree. Both scales are variations of the minor scale (Aeolian).

Jazz uses chords like 9ths (2nd degree), 11ths (4th degree), 13ths (6th degree), diminished, and half diminished. As far as I know black people formulated the Blues and Jazz genres, but these genres are based on established music theory. Blues and Jazz are tritone heavy (Diminished 5th interval), which throughout much musical history has been shunned for its dissonant and evil sound. The diminished chord is also the tonic of the Locrian (diminished) mode, which was rarely used back then because of its anomalous sound. During the 18th century the Dimished 5th interval was called diabolus in musica. Times change and people become more open to different things. You can hear good examples of this from George Crumb&#039;s Black Angels and Heavy Metal music. Considering all of this, what was it that I didn&#039;t know, Bernie?</description>
		<content:encoded><![CDATA[<p>Music theory is based on musical modes of the ancient Greeks, which were Caucasoid people. The modes are Ionian (Major scale), Aeolian (minor scale), Locrian (diminished scale), and the rest are categorized into the Major type (Lydian and Mixolydian) and the minor type (Dorian and Phrygian) by the Tonic (1st), Mediant (3rd), and Dominant (5th) degrees of the modes.</p>
<p>The Blues scale is an added Diminished 5th or Augmented 4th (enharmonic) note (the blue note) to the Major and minor pentatonic scales, which take particular notes from the Major (Ionian) and minor (Aeolian) scales.</p>
<p>Classical music often used the Harmonic and Melodic minor scales. The former is an augmentation of the 7th (leading tone) degree by one half-step (semitone), and the latter is the same but with an augmented 6th (submediant) degree. Both scales are variations of the minor scale (Aeolian).</p>
<p>Jazz uses chords like 9ths (2nd degree), 11ths (4th degree), 13ths (6th degree), diminished, and half diminished. As far as I know black people formulated the Blues and Jazz genres, but these genres are based on established music theory. Blues and Jazz are tritone heavy (Diminished 5th interval), which throughout much musical history has been shunned for its dissonant and evil sound. The diminished chord is also the tonic of the Locrian (diminished) mode, which was rarely used back then because of its anomalous sound. During the 18th century the Dimished 5th interval was called diabolus in musica. Times change and people become more open to different things. You can hear good examples of this from George Crumb&#8217;s Black Angels and Heavy Metal music. Considering all of this, what was it that I didn&#8217;t know, Bernie?</p>
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		<title>By: Bernie</title>
		<link>http://www.ethanzuckerman.com/blog/2007/06/05/african-fractals/comment-page-1/#comment-1108086</link>
		<dc:creator>Bernie</dc:creator>
		<pubDate>Wed, 23 Jul 2008 07:56:46 +0000</pubDate>
		<guid isPermaLink="false">http://www.ethanzuckerman.com/blog/?p=1469#comment-1108086</guid>
		<description>Mark: 

Do you really think whites invented music theory?? I would love to see reference to support that crazy assertion. 

Last I checked blues, jazz and soul employed a completely different scaling system than European classical. A new form of theory evolved from African music, and this is based on pentatonic scaling. Indian music uses another scaling, for example. Whites did not invent either

In addition to this; if you were to take jazz theory in university you will find many important differences between it and classical theory.  Modern music is heavily based on African music theory, and the employment of the “blue notes” which derive from this theory.

Your hypothesis is absurd, and I suspect that you know absolutely nothing about music.

- Bernie</description>
		<content:encoded><![CDATA[<p>Mark: </p>
<p>Do you really think whites invented music theory?? I would love to see reference to support that crazy assertion. </p>
<p>Last I checked blues, jazz and soul employed a completely different scaling system than European classical. A new form of theory evolved from African music, and this is based on pentatonic scaling. Indian music uses another scaling, for example. Whites did not invent either</p>
<p>In addition to this; if you were to take jazz theory in university you will find many important differences between it and classical theory.  Modern music is heavily based on African music theory, and the employment of the “blue notes” which derive from this theory.</p>
<p>Your hypothesis is absurd, and I suspect that you know absolutely nothing about music.</p>
<p>- Bernie</p>
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