Like if you came from Ken Wheeler's proof of the divided line: phi is to 1 as 1 is to 1/phi.. this geometry gives the pythagorean pentagram and illustrates the angles between the oxygen and hydrogen atoms in the water molecule, which is the visible/physical/material/antenna for "the good" that all life follows.. there is no mysticism about sacred geometry..
For me it was the other way around. This got me interested in Ken's triangle. But yeah they're both correct. He's using Thales Theorm Ken uses the Pythagorean Theorm. One deals with circles to prove right angles the other does not. Both ideas are synthesized in Euclid's Elements with the 1st postulate constructing a equilateral triangle from the two points and 1 vertice of two circles. It's interesting to note. Artificial Intelligence from Google's Gemini using quantum computers from Google HQ at the Googleplex in Mountain View California agrees with both Proffesor Swearagen and Philosopher Wheeler's understanding. In that a ≠ Divided Line ÷ again into = porportions. Does in fact = Φ/φ (uppercase Phi lower case phi) The greek letter assigned to the golden ratio. And the first letter in Φιλοσοφία or φιλοσοφία phi-los-so-phi-A or "philosophy" ..... 🤔... wtf... did I just write? ....🤣... Lol Anyways it's a WILD ASS rabbit hole! Between those two. And why they are both correct in thier perspectives. They just came to the same answer using different paths. Thales's Theorm alone cannot construct a equilateral 🜂 with a ⭕. Pythagoras's can construct an equilateral 🜂 without a circle ⭕. But Euclid's 1st postulate can construct an equilateral ⎊ using 2 ⭕s 😊 And finally there's Sir Roger Penrose's impossible ⟁. Which apparently has quite a lot too say about this phenomena! 😆 Enjoy the ride! The road to understanding this stuff is a life long journey. Which in the end is its own reward!
Great lecture. At 49:37, Professor Swearengen mentions a contradiction or hang-up within the analogy of the divided line. I watched this video at night. The next morning, when I woke up, in a sort of heureka moment, I found a solution to the contradiction: GC = CH means that understanding equals material objects (not only quantitatively, but also qualitatively). How can this be? The modern word for that would be "embodied cognition". In other words: "OBJECT-BOUND UNDERSTANDING". It means that "understanding" is always bound to and represented in "material objects". The simplest example would be a textbook. It is a material object which represents understanding. Without understanding, there would be no textbook; and without a textbook, there would be no understanding. More generally speaking, our whole process of understanding is bound to our process of interacting with material objects, and material objects only exist insofar as we have an understanding of them. Material objects and understanding arise simultaneously through the interplay between body and mind. Ironically, the video description itself talks about "The Socratic Philosophy of Science Embodied" in the devided line. Professor Swearengen solves the contradiction implicitly by embodying his understanding of the divided line in his whiteboard drawings. When I was a seminar teacher myself, I embodied Plato's allegory of the cave in a series of interrelated optical experiments. By doing this, I came to the (embodied) understanding that the allegory of the cave works like the Golden Ratio played out fractally. I did NOT know then that the allegory of the cave was related to the analogy of the divided line. Today, it all makes sense, since the Golden Ratio is just a special case of the divided line. It just proves to me that Plato's allegory of the cave is really an analogy that works, and refers to something beyond itself, just like the divided line can be thought of as part of a longer divided line.
You are onto something. Are you familiar with the work of Ken wheeler? He’s a Neoplatonist and metaphysician. He speaks several dead languages as well. He has a TH-cam channel- Theoria Apophasis
@@spaceantelope1Using Thales Theorm from Euclid's Elements creates a golden triangle (acute Isoceles) by dividing the radius by Φ in a semicircle. Copying it to the other side? Into a full circle creates Ken's 108 36 36 gnomon golden triangle. (Obtuse Isoceles)That you are talking about.
This is one of the best lectures I have ever seen in person or in online video. What a superb job on behalf of the professor. I really wish the guy in the blue dress shirt would have spent less time asking questions and just focused on the message the lecture was trying to deliver. He was harmful to the quality of this presentation.
I don't think this interaction was unhelpful at all. They actually showed the importance of dialogue (the dialectical approach) to learning something that Plato sets up in the Republic.
@@fionamacdonald8363 unfortunately it’s a matter of opinion I suppose. The back and forth was very distracting. It seemed like he was trying to prove some level of understanding on the subject but his dialogue seemed irrelevant most of the time.
@@JoshsDigitalinteractions I think what he said about images being partial representations of the higher forms or truth is a good way of putting it; they are proportionally less real.
The divided line has the proportions of the Pythagorean pentagram(108,32,32) which displays perfect incommensurability and fractality aswell as 1:Phi ratio.
Wouldn't it be the case that iif the original ratio was different from used in the video, the whole analogy of their interelationship would still work hence the specific ratio was never mentioned i.e. if there were less people trapped at the bottom of the line then there would be more at the top.
@@anthonygarnett8374 something felt off while I was watching this and I finally figured out what it was. I think segment Ag = shadows Gc = puppets Ch = shadows and reflections of objects outside the cave, and Hb = the objects outside of the cave. Anyway, the medieval philosophers stated that the curriculum for HB was theology, because they equated the form of the good with the subject of their theological studies.
If you copy the semi circle to the other side. Ken's 108 36 36 "gnomon" triangle shows up as an Obtuse Isoceles. Remember he's using Thales right angle theorm from Euclid's Elements. Which constructs a 36 72 72 "golden" triangle which is an Acute Isoceles.
Blue shirt and his ego!!!! He just couldn't quite grasp what the lecturer was saying at the highest level, and even more than that didn't want to grasp it and got defensive about it. The lecturer was on an elevated plane than blue shirt on this occasion. And in fact was a nice demonstration of what Socrates was driving at!!!
The girl that asks about the Arbitrary Ratio after he just spent half an hour describing how that is arbitrary is hilarious. No offense to her, but wow, that's what you got from that?? Lol are there distances in this metaphysical to phenomenal world. 🤣 like that F'ing matters at all.
Like if you came from Ken Wheeler's proof of the divided line: phi is to 1 as 1 is to 1/phi.. this geometry gives the pythagorean pentagram and illustrates the angles between the oxygen and hydrogen atoms in the water molecule, which is the visible/physical/material/antenna for "the good" that all life follows.. there is no mysticism about sacred geometry..
For me it was the other way around. This got me interested in Ken's triangle. But yeah they're both correct. He's using Thales Theorm Ken uses the Pythagorean Theorm. One deals with circles to prove right angles the other does not. Both ideas are synthesized in Euclid's Elements with the 1st postulate constructing a equilateral triangle from the two points and 1 vertice of two circles.
It's interesting to note. Artificial Intelligence from Google's Gemini using quantum computers from Google HQ at the Googleplex in Mountain View California agrees with both Proffesor Swearagen and Philosopher Wheeler's understanding. In that a ≠ Divided Line ÷ again into = porportions. Does in fact = Φ/φ (uppercase Phi lower case phi) The greek letter assigned to the golden ratio. And the first letter in Φιλοσοφία or φιλοσοφία phi-los-so-phi-A or "philosophy" ..... 🤔... wtf... did I just write? ....🤣... Lol
Anyways it's a WILD ASS rabbit hole! Between those two. And why they are both correct in thier perspectives. They just came to the same answer using different paths.
Thales's Theorm alone cannot construct a equilateral 🜂 with a ⭕. Pythagoras's can construct an equilateral 🜂 without a circle ⭕.
But Euclid's 1st postulate can construct an equilateral ⎊ using 2 ⭕s 😊
And finally there's Sir Roger Penrose's impossible ⟁. Which apparently has quite a lot too say about this phenomena! 😆
Enjoy the ride! The road to understanding this stuff is a life long journey. Which in the end is its own reward!
Great lecture.
At 49:37, Professor Swearengen mentions a contradiction or hang-up within the analogy of the divided line.
I watched this video at night. The next morning, when I woke up, in a sort of heureka moment, I found a solution to the contradiction:
GC = CH means that understanding equals material objects (not only quantitatively, but also qualitatively). How can this be?
The modern word for that would be "embodied cognition". In other words: "OBJECT-BOUND UNDERSTANDING".
It means that "understanding" is always bound to and represented in "material objects".
The simplest example would be a textbook. It is a material object which represents understanding. Without understanding, there would be no textbook; and without a textbook, there would be no understanding.
More generally speaking, our whole process of understanding is bound to our process of interacting with material objects, and material objects only exist insofar as we have an understanding of them. Material objects and understanding arise simultaneously through the interplay between body and mind.
Ironically, the video description itself talks about "The Socratic Philosophy of Science Embodied" in the devided line.
Professor Swearengen solves the contradiction implicitly by embodying his understanding of the divided line in his whiteboard drawings.
When I was a seminar teacher myself, I embodied Plato's allegory of the cave in a series of interrelated optical experiments. By doing this, I came to the (embodied) understanding that the allegory of the cave works like the Golden Ratio played out fractally. I did NOT know then that the allegory of the cave was related to the analogy of the divided line.
Today, it all makes sense, since the Golden Ratio is just a special case of the divided line. It just proves to me that Plato's allegory of the cave is really an analogy that works, and refers to something beyond itself, just like the divided line can be thought of as part of a longer divided line.
You are onto something. Are you familiar with the work of Ken wheeler? He’s a Neoplatonist and metaphysician. He speaks several dead languages as well. He has a TH-cam channel- Theoria Apophasis
Yes I know Ken Wheeler's channel.@@spaceantelope1
@@spaceantelope1Using Thales Theorm from Euclid's Elements creates a golden triangle (acute Isoceles) by dividing the radius by Φ in a semicircle. Copying it to the other side? Into a full circle creates Ken's 108 36 36 gnomon golden triangle. (Obtuse Isoceles)That you are talking about.
This is one of the best lectures I have ever seen in person or in online video. What a superb job on behalf of the professor. I really wish the guy in the blue dress shirt would have spent less time asking questions and just focused on the message the lecture was trying to deliver. He was harmful to the quality of this presentation.
I don't think this interaction was unhelpful at all. They actually showed the importance of dialogue (the dialectical approach) to learning something that Plato sets up in the Republic.
@@fionamacdonald8363 unfortunately it’s a matter of opinion I suppose. The back and forth was very distracting. It seemed like he was trying to prove some level of understanding on the subject but his dialogue seemed irrelevant most of the time.
@@JoshsDigitalinteractions I think what he said about images being partial representations of the higher forms or truth is a good way of putting it; they are proportionally less real.
The divided line has the proportions of the Pythagorean pentagram(108,32,32) which displays perfect incommensurability and fractality aswell as 1:Phi ratio.
108, 36, 36*
alight wheeler
Bless you for teaching this knowledge to the public.
I've watched this a couple of times and will be watching again so interesting and clear thank you!
This is a excellent lecture and lecturer Thankyou.
Illustration is partially upside down.
Visual region is not bigger than intelligible realm.
Intelligible realm is Phi, 1, not 1, 1/Phi
Very nice explanation 👌🏻,, the best available on internet till today,,👌🏻👌🏻
Yeah. This was good.
Amazing. Absolutely amazing. Thank you!
that guy at 34:00 made a very good point
Great job... keep-up the good work A Love Supreme
13:33. Big - Big Thank you
Wouldn't it be the case that iif the original ratio was different from used in the video, the whole analogy of their interelationship would still work hence the specific ratio was never mentioned i.e. if there were less people trapped at the bottom of the line then there would be more at the top.
"You don't question the postulates," a big part of why I hated geometry
steady on there Bertrand Russell
@@anthonygarnett8374 I think that I'll be flattered by the comparison.
@@reveranttangent1771 ;)
@@anthonygarnett8374 😄
@@anthonygarnett8374 something felt off while I was watching this and I finally figured out what it was. I think segment
Ag = shadows
Gc = puppets
Ch = shadows and reflections of objects outside the cave, and
Hb = the objects outside of the cave.
Anyway, the medieval philosophers stated that the curriculum for HB was theology, because they equated the form of the good with the subject of their theological studies.
Blue shirt needs to stop trippin over the shape and get the deep knowledge.
47:28
The triangle is wrong. It’s 1:1:phi
dont look outside, look backward
This professor gets it wrong. There is a specific ratio. It’s 1, phi. Ken Wheeler gets it right
If you copy the semi circle to the other side. Ken's 108 36 36 "gnomon" triangle shows up as an Obtuse Isoceles. Remember he's using Thales right angle theorm from Euclid's Elements. Which constructs a 36 72 72 "golden" triangle which is an Acute Isoceles.
Blue shirt and his ego!!!! He just couldn't quite grasp what the lecturer was saying at the highest level, and even more than that didn't want to grasp it and got defensive about it. The lecturer was on an elevated plane than blue shirt on this occasion. And in fact was a nice demonstration of what Socrates was driving at!!!
The girl that asks about the Arbitrary Ratio after he just spent half an hour describing how that is arbitrary is hilarious. No offense to her, but wow, that's what you got from that?? Lol are there distances in this metaphysical to phenomenal world. 🤣 like that F'ing matters at all.
Moron. It's one of the key elements of the analogy.