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flatland


A friend of mine recently came up with a good one: What does it look like, when a bowl travels through flatland?*´Flatland` is not only a term used within geographical or federal contexts, but a term used also in physics and philosophy as another word for the second dimension, simply.


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Well you´d see its shadow. 2-dimensionally.

Want to see a 3-dimensional shadow of a 4-dimensional object? There´s a mathematician who made an awesome scultpure representing such a shadow. Link

And here´s a flash animation of that sculpture.

found on boingboing

... Link

"Well you´d see its shadow. 2-dimensionally."

nope. try again. :-)

[I dont think, there are shadows at all in flatland.]

... Link

Hm..
Yesterday as I was trying to sleep I couldn´t help thinking about this question some more:
I put myself back into the time, when I had arts classes.

"Looking like something" implies that one can see an object. Seeing implies the 3rd dimension, since human perception is based on it. We can only see representations, i.e. "shadows" or "projections"
of an object other than 3 dimensional on a three dimensional object (a sculpture or a sheet of paper.)

So the bowl wouldn´t "look like something" at all, because seeing something is impossible when applying it in the second dimension. Only when transferred to a 3D model of the 2nd dimension (a sheet of paper, a monitor..), it would look like something. But then it would look like 2D geometrical form, a circle for example.

... Link

"I hope that was confusing enough."

not at all, look.

.."I thought to myself that what you´re doing when making a still life is projecting a 3D object on a 2D surface."

exactly.

"But as human perception is based on 3D, the 2D surface is only viewable on a 3 dimensional object, which the sheet of paper in fact is."

no. we indeed ARE able to think twodimensionally.
we think in Ableitungen--thats why we have so much difficulties in visualizing the fourth dimension, which has a different relation to the third dimension than the third dimension has to the second, u see?
connecting your example of drawing a Stilleben with the problem:
the difference is, the latter includes movement:
what does it look like, when a bowl travels through flatland. :-)

... Link

aaahm, movement. I´m a careless reader ;-)
hmm.. Well I think that would be a circle moving on a sheet of paper?

Maybe I don´t get the point. I´ll have to think of it again when trying to sleep.

Ps.: It seems I was editing my entry as you were typing your answer, so the quotes are different. Anyway, the point is the same.

... Link

"Maybe I don´t get the point."

you re almost done. ;-)

... Link


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