Benoit Mandelbrot 1924 - 2010

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Offline Jehovajah

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« on: September 15, 2017, 10:07:00 AM »

http://M.youtube.com/watch?v=0ABtOHVhr6E

The first of a series I intend to post in commemoration .
Enjoy xxx

Linkback: https://fractalforums.org/discuss-fractalforums/5/benoit-mandelbrot-1924-2010/312/

Offline Fraktalist

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« Reply #1 on: September 15, 2017, 08:33:33 PM »
great series, can recommend!
Good to see them on youtube now.

here's the full mandelbrot playlist:
https://www.youtube.com/watch?v=0ABtOHVhr6E&list=PLVV0r6CmEsFwl4HlrIKxKmdpBAGYJ9AbR
(Jehovajah, I'll edit this link out if you wanted to post them one by one)

Offline Jehovajah

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« Reply #2 on: September 16, 2017, 12:12:13 AM »
@Frank Fraktalist
Not a problem! I will still post individual videos with comments to keep the topic live .

Offline Softology

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« Reply #3 on: September 16, 2017, 10:28:11 AM »
I wish that had been 1 single movie.  Downloading all 144 parts for offline viewing was a tedious process.

Here are another two good Mandelbrot videos...



Jason

Offline Sockratease

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« Reply #4 on: September 17, 2017, 10:59:36 AM »
I wish that had been 1 single movie.  Downloading all 144 parts for offline viewing was a tedious process....

You should have asked if there was an easier way!

Just copy this link - https://www.youtube.com/watch?v=0ABtOHVhr6E&list=PLVV0r6CmEsFwl4HlrIKxKmdpBAGYJ9AbR - into a free program called jDownloader and it will grab the complete playlist and download all 144 parts automatically to a single folder in 1 click  :peace:
Study stupidity, kids. It's not getting smarter out there - Frank Zappa

Offline Softology

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« Reply #5 on: September 17, 2017, 11:03:17 PM »
a free program called jDownloader and it will grab the complete playlist and download all 144 parts automatically to a single folder in 1 click

Thanks for the tip.  That will help next time I face the same issue.

Offline Jehovajah

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« Reply #6 on: September 23, 2017, 05:59:48 PM »

http://m.youtube.com/watch?v=qhbuKbxJsk8
The circle, and rotational dynamics are crucial to interpreting some of the images generated by a fractal generator, especially when you encounter the so called imaginary magnitudes.

Try to rid your mind of centuries of confusion about imaginary magnitudes and realise they are arc lengths and associated chords, dynamically constituting a rotation. Because circles are scale free they are absolutely fundamental to grasping why deep zooms can be rendered . The absolute and relative variations in plotted positions under the Mandelbrot iteration show the structural integrity of our numeral multiplication ( duplication of forms) systems and the geometric relation of factors and factorisation particularly in the circle and sphere. Mathlogger does a nice introduction to the dynamics and colouring of the Mandelbrot and Buddhabrot set.

Offline Jehovajah

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« Reply #7 on: October 12, 2017, 11:57:17 AM »
http://m.youtube.com/watch?v=Jv7xBxRQips


Here Benoit discusses the range of fractal geometry having previously laid out his view of it as an intermediary theory. Its status as a topic on academia is tenuous, as Benoit relates, but he worked all his life to make it stick around by making it useful. Classifying chaos as he does reminds me of the reaction to Cantors classification of infinity, which of course I do not subscribe to as far as I understand it.

Offline Jehovajah

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« Reply #8 on: October 12, 2017, 01:14:38 PM »
http:/m./youtube.com/watch?v=2s90McQ9YfY
The Ecole Normale view of Euclid was tainted by Legendres legendary work on Geometry. In fact LeGendre received his training via the Aristitelian Islamic Scholars, which made a fresh study of the Stoikeia almost impossible.
The Stoikia , popularly ascribed to Euclid is a more complex document  than a book written by an erudite scholar. He in fact belonged to the extant Pythagorean school as did Eudoxus and qualified as dud Eudoxus under the Pythagorean Scholarship. He was a Mathematikos, accepted among the Mathematikoi as an equal, well versed in the Pythagorean discourse. Plato, and definitely Aristotle were not!

Euclids Pythagorean outpost in Alexandria therefore established Pythagorean scholarship and principles in the cultural centre of the Greek empire. The Pythagoreans had been driven out to settle in Southern Italy, prior to Euclid.

The influence of the Pythagoreans spread from Italy via rich patrons( Plato being one) to various centres throughout the empire. However when the Greek empire was on the rise Aristotle achieved a position of dominance under Phillip and Akdxandria nd all but buried the Pythagorean schools influence. Aristotle presented the Pythagorean scholasticism as flawed and static, whereas in fact the schools principles were extremely utilitarian and dynamic.

It is perhaps much later in the 1800's when Prussian scholars analysed the texts of the Euclidean Stoikeia found in the Italian vaults in Rome that differences were found but not understood.

However Newton, who through Barrow and Wallis had access to these documents understood the dynamic nature of them almost in a dream. That dream was of the dynamic creative point or seemeiaoon. This is an indicator. Originally it would be a stick or pointed object for pointing, today we use laser pointers. It would also be used to draw lines in the ground or in the air.
A pointer is that which has no part! Literally it conducts the perception dynamically along, around objects that do have parts or extension. A point is not an object for analysis, but to direct perception of what needs to be analysed or what needs to be synthesised.

Thus when Mathematicians claim Euclid was limited or wrong, they in fact betray their ignorance of the Stoikia and the Pythagorean school of thought.

Iteration is fundamental to the Stoikeia, both as counting and as mosaic construction, including the Arithmoi. When Eudoxus in book5 discourses on Logoi he introduces the Skesis and the Kinesis involved in their development ( pelikotes ) , the static or held form and the kinetic form .
The Logos and Analogos process for multiple form comparison breathes dynamic ruled change.

Here then Benoit refers not to the insufficiency of Euclid, but the terror of Academics to continue to explore the dynamic nature around them because the forms were irregular, rough and developmentally not Skesis, that is handlable by a quick eye and a sketch . Today we can use very fast photography to capture the development of dynamic change. We can see the iteration of form in minute femto second time slots . We can trace the development of chaotic vibrations in detail.

Fractal geometry dealt with these extreme behaviours from a visual geometrical approach concentrating on self similarity, almost self similarity on the way to some limit, but not aiming to reach that limit. It was not about the destination, but the views on the journey!

Chaos and nonlinear dynamics now become defineable ? Randomness, stochastic, teleological, statistical all become categories. The Global wildness becomes not a terror , but a signal that we have reached our current limit of discernment, but their still exists hope of pushing the dynamic boundary a bit further back! We can not say we have the set of all sets that exclude themselves if it does not include itself ! We can not construct or evaluate such a set with a static boundary ! We have to recognise the nonsense of thinking we can do all, or preside over all, and humbly enjoy the view of the fractal beauty of consciousness

http://m.youtube.com/watch?v=JG3V9KkkE3U

« Last Edit: October 12, 2017, 02:38:53 PM by Jehovajah »


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