The Greek philosopher Plato is well known for his allegories and metaphors. Of particular interest is his Allegory of the Cave, which appeared in The Republic, written around 380AD. In it, Plato describes a group of prisoners which are chained to a wall within a cave, and have been all of their lives. They have no direct interaction with the world outside of the cave. They only know of the world via shadows that are cast on the wall opposite of them. For the prisoners, the shadows are their reality. Though you and I know the shadows are only a very low-resolution representation of that reality.

Theoretical physicist Steven Weinberg, a Nobel Prize winner who works out of the University of Texas in Austin, once likened himself to a prisoner in Plato’s cave. We are forever chained to this cave by the limitations in measurements we can make and experiments we can perform. All that we can know are shadows of the reality that exists in the sub-atomic world. We can see the shadowy figures lurking in our math and as wisps of misty vapor trails in our cloud chambers. We attempt to pierce the veil with the power of our imagination and draw nifty looking charts and animations depicting what our mind’s eye thinks it can see. But in the end, we are all trapped in a cave… staring at shadows. Reflections of a reality we can never truly know.

Sounds like Steven Weinberg's problem to me.

" All that we can know are shadows of the reality that exists in the sub-atomic world " Same as the other side of the spectrum...Deep Space. The very large and the very small are indeed a mystery.

Flatland: A Romance of Many Dimensions

https://en.wikipedia.org/wiki/Flatland

Is there a particular episode in that adventure that came to mind? Perhaps visiting the line?

Folks might enjoy the the allegories in The Republic presented before the one about the cave.

Magicfish, this is an interesting allegory and one I like to roll around my mind. Dimentions, if we lived in a world of two dimentions, what would an apple look like? Certainly we could not see it as an apple, lacking the ability and knowledge of the third dimention, so, perhaps we could prove it exists using mathematics or a two dimention version of physics, or we may even be able to see a vague shape or shadow. The point is we'd never truly be able to "see" the apple without knowledge of a third dimention, and a way to transition to a three dimentional reality. How is that achieved? Could it be death? Is dying our way to transition to the fourth dimention? What would the fourth dimention be? Time? Light? Energy? Gotta admit this is waaaay more fun to contemplate when stoned.

"Every man takes the limits of his own field of vision for the limits of the world" - Schopenhauer

I'm so glad I am not smart enough to pretend to be this smart.

@ Danny!

In words of one syllable: Yes! Me too!

BTW Bill: "dimensions" is spelled with an "S" (dimenSions). But then, how should I know? I've never been stoned.

Exactly! Excellent quote.

Field of Vision ... An invisible hole in the middle, all tingly around the periphery and lots of negotiating between the eyes. Stranger than Escher.

We're still learning...evolving.
What we can truly know is not known.

Weinberg should have more confidence in us.

You don't know what you don't know if you don't know it.

? shadow of the divided line?

Weinberg didn't lack confidence in us.

Let's make it much simpler and go with a sphere with a white interior and red surface layer. It gets strange when you look at a two dimensional slice when the sphere rotates about various axes. For example: consider the cross section (in the plane of the circle) of the sphere as it rotates about an axis which passes through a point on the "visible" circumference. What would a circle make of that?

If you want "troublesome" - consider the circle as having a differential thickness in three dimensions. Now look at neighboring planes and what kind of thing it might be to get that circle to move between planes.

The more we find out, the more we realize how little we know.

Danny and Dick, does this help?

If it requires my being smart or thinking probably not.

You're not alone, LOL. I destroyed countless brain cells in my wicked youth.