Over lunch with tweewo today.
I went into my usual pattern of starting to tell a story, and then interrupting myself to explain why I couldn't ever tell a story right off, and as a result, lengthening the time I needed to tell the story. Tweewo called it my opposite paradox. lol.
Tweewo also made an interesting analogy of how a 3-dimensional ball would appear passing through a 2-dimensional Flatworld. He said that Flatlanders would see a dot expanding outwards to become a circle, which would shrink back into a dot and disappear as the ball passed through. He then went on to say that in our 3-dimensional world, Time is like our 4th dimension; and like the Flatlanders who were incapable of understanding the passage of the ball, we were incapable of understanding the passage of Time.
I know, some folks' lunchtime conversations are other people's lectures. ;)
I went into my usual pattern of starting to tell a story, and then interrupting myself to explain why I couldn't ever tell a story right off, and as a result, lengthening the time I needed to tell the story. Tweewo called it my opposite paradox. lol.
Tweewo also made an interesting analogy of how a 3-dimensional ball would appear passing through a 2-dimensional Flatworld. He said that Flatlanders would see a dot expanding outwards to become a circle, which would shrink back into a dot and disappear as the ball passed through. He then went on to say that in our 3-dimensional world, Time is like our 4th dimension; and like the Flatlanders who were incapable of understanding the passage of the ball, we were incapable of understanding the passage of Time.
I know, some folks' lunchtime conversations are other people's lectures. ;)
4 Comments:
this just reminded me of flatland... been trying to read for months...
By
Anonymous, at 10:13 PM
From the point of view of someone who is not on the plane of Flatworld, they would see a dot becoming a circle and back to a dot. But to somebody who is in Flatworld what is seen is a dot becoming a line segment becoming a dot again.
Time isn't exactly our 4th dimension. We live in 3+1 dimensions. There's a Euclidean metric on the three space dimensions and the time dimension is coupled only through the Minkowski metric.
By
Anonymous, at 11:09 AM
But what is a line segment for somebody who lives on Flatworld? In fact, it's a hypersurface that may not have a meaningful analogy in three dimensions.
Question: do you need an infinity of observers on Flatworld to confirm that the passing sphere shows as a circle? My gut says yes, but my heart says no.
By
Anonymous, at 6:42 PM
1963 #3: Tales of the Uncanny "It Came From Higher Space!" (Image Comics, June 1993)
written by Alan Moore (who else)
Along the way a 4-D villain wrecks havok with the Hypernaut (who lives aboard a Penrose triangle shaped satellite), in a way that intelligently illustrates the fourth dimension (with many 4-D effects accomplished by treating the 2-D panels in an Escher-like way), and with the Hypernaut defeating the villain by exploiting his own 3-D nature.
Elsewhere in the series are also graphs explaining time travel, a remarkable example of Galilean relativity, and left-right reversals.
The fake fan letters in the back include one complaining about an inaccuracy in the Hypernaut's math, which gets a weaselly response.
http://math.cofc.edu/faculty/kasman/mathfict/mfview.php?callnumber=mf430
By
Anonymous, at 6:20 PM
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