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..

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.

This is a excellent lecture and lecturer Thankyou.

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.

I've watched this a couple of times and will be watching again so interesting and clear thank you!

Bless you for teaching this knowledge to the public.

The divided line has the proportions of the Pythagorean pentagram(108,32,32) which displays perfect incommensurability and fractality aswell as 1:Phi ratio.

Amazing. Absolutely amazing. Thank you!

Very nice explanation 👌🏻,, the best available on internet till today,,👌🏻👌🏻

Great job... keep-up the good work A Love Supreme

Illustration is partially upside down. Visual region is not bigger than intelligible realm. Intelligible realm is Phi, 1, not 1, 1/Phi

that guy at 34:00 made a very good point

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.

47:28

Blue shirt needs to stop trippin over the shape and get the deep knowledge.

"You don't question the postulates," a big part of why I hated geometry

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

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.