I LOVE Sagan's analogy because it makes it so easy to understand the idea of why we have trouble seeing/experiencing other dimensions. (And listening to him talk just cracks me up.) The video started all kinds of quantum wanderings in my head. I intended to blog about my mental musings, but Mark gave me the perfect opportunity to post them first on Facebook by making his status read: [Insert Profound Thought Here]. I obliged with what was forming in my head, and accordingly he replied with his own thoughts and questions.
The odd part is that after I submitted my second long post in response to his counterpoints, Facebook lost the entire thread. It wouldn't let me post any more comments and even the ones that appeared previously are not viewable. I had no trouble viewing or posting on anyone else's page, but this particular conversation was OVER. I dunno if I blew Facebook's brain or the aliens were like, "Oh no you didn't!" but the entire discussion is gone.
However... smart pirates have backups. :) Yarrrr. Internet gremlins be damned! Since I was going to blog about it anyway, I was saving the convo elsewhere, so the following is the discussion we were having...
Him: Status: [INSERT PROFOUND THOUGHT]
Me: Ok... if Carl Sagan can hold up a clear plastic cube and create a shadow of it on paper thus illustrating how 3D becomes 2D; then he shows us a clear plastic 3D representation of a tesseract and says that's like a shadow of 4D becoming 3D; and if the 3rd dimension is defined as the directions of back/forth, up/down, side/side, and the fourth dimension is measured as adding the element of time to the 3D directions, then considering all that should the element added to 3D to create 4D actually NOT be time, but "within/without" instead (I mean look at how the "shadow" of a tesseract looks - one cube within another), and if so, how do we measure "within/without?" By an emotional scale? Is that profound enough for you?
Him: I don't believe time was considered one of the dimensions in a tesseract, however. It's four spatial dimensions that it represents. The questions is, if there are more than three spatial dimensions, how many objects that are four dimensional (+) intersect our three dimensions and defy explanation by their behavior because we are unaware of the activities taking place in the other spatial dimension for them?
Me: That's what I'm saying - time SHOULDNT be considered in measuring or describing a tesseract (because what is describing something in our world besides measuring it?). Time is always considered in measuring distance (distance = the time it takes to get from A to B, yes?) and MATHEMATIC tesseracts involve measurements of distance through the spatial relationships of one cube to another. If the distances of the vertices are not all equal then it's not a tesseract but some other poly-shape, right? So time is involved in some way through the measurement of distance when describing that particular form mathematically. But since (as Ray said) time is only a human thing then it only exists in the dimension WE live in - the 3rd dimension, yes? Generally, we cannot extract ourselves from the use of time/distance as a measurement of our world. Just like a 2D creature could not imagine up/down as a direction in their world. So in order to properly describe a form that lives in a dimension outside of our own, should we not remove time as a means of measurement? (Oh yes, I want to delete math from the equation - what a surprise. haha) Perhaps things in the fourth dimension are measured on some kind of emotional relation scale and what WE see as a tesseract here in this dimension is only a 3D representation of it just like a drawing of a cube is a 2D representation of the real cube in 3D. The trouble for us is comprehending how to measure or describe a form without a scale we're familiar with. Even when we say "on an emotional scale, how do you feel?" we tend towards numbers (like 1 being I feel icky and 10 being I feel great) because distance and numbers and time is what we use to measure and describe the 3rd dimension. I think this is why yogis can do what we would consider "magic" - their relational thinking involves different kinds of spacial relationships - they do not bind themselves to the means of measurement of the 3rd dimension like most of the rest of us do. It's all in how you THINK about it. Your perspective. Hence, my idea of measuring with emotions, not math. Geez, I'm not even sure I understand all that now. haha
You know what's really sad is that spell check on FB can't recognize the words "mathematics" or "tesseract." (Or "vertices" for that matter.) You'd think this site was built by 20-somethings... oh wait...
Him: I forgot how integrally time figures into distance equations... yeah. Without the time it takes to get "there," "here" and "there" have no meaning since you are everywhere all at once.
Me: And to answer your second question about how many objects intersect our three dimensions and defy explanation by their behavior... I'd guess somewhere just under 7 billion and counting. :)