• The apple﻿ is an asshole.

• Sagan's ability to explain higher concepts was marvelous.﻿

• But how was that shadow of a tesseract developed? From an imaginary perpendicular directional projection of a cube that constitutes a tesseract, how on earth did we derive its shadow? It seems even Sagan has failed to explain this to me. So far all the﻿ explanations I found were semantic and of little value. This too was that, even if slightly better worded.

• Wow, something that is such an amazing interesting subject you are saying you'd not want to learn more about because of poor sound quality from the 80s﻿ when this was recorded? You're fucked up bud.

• No, as Sagan says in this video, we can see a tesseract, but it figures in a third dimension. The same you can apply in a cube. When you see a cube﻿ in the 3 dimensions all the sides are equal, but when you draw it in a paper (second dimension material) it loses the proportionality. If we could see a tesseract in the fourth dimension, all the sides would be equal, but this doesn't happen when you see a tesseract in the third dimension.

• This is a serie taped in the 80's, no wonder there's a terrible﻿ sound.

• I have all Cosmos series on DVD, I bought them in 2006 and it's an amazing serie. The tesseract and 4th dimension are something that make me wonder why we are stuck in a 3rd world dimension, or how the 4th dimension works? Questions with﻿ no answers I guess...

• Yeah people sometimes go on about how he isnt smart and such, who cares how smart Carl Sagan is or isnt.

Whats amazing is his ability to simplify stuff. I mean if teachers in schools had this ability, learning would not only be easier﻿ but more fun.

• You just﻿ saw the shadow of the tesseract, duh. Weren't you even listening to Carl?

• If I am grasping this correctly, I think the best way to think about directions in the 4th dimension would﻿ be "inward and outward".

• my mind﻿ was just raped