Speaking as someone whose job often includes working out geometric figures in four-dimensional space, I find it charming that some very smart folks believe it to be beyond human imagination. I'm not going to tell them, though; I'd rather leave them some mystery. God set a good example by not revealing everything.
@Jonathan - specific ability varies very widely among humans.
Lewis could not pass the 'basic' mathematics required for university entrance (usually done age 16) despite at least three attempts for which he was individuall tutored - yet he got three first class Oxford degrees (two in classics, which was the most elite humanities degree in the whole world at that time).
Lewis was only allowed to attend Oxford because as an ex-army veteran he was allowed an exemption.
So Lewis displayed very wide divergences in specific cognitive aptitudes - and indeed this is probably the usual pattern among people of very high intelligence: that the intelligence is relatively specialized (more so than used to be considered the case in the past).
Some musicians can perform feats which strike non-musicians or moderate musicians as uncanny, superhuman: I used to know (mostly via close friends) a great musician called Dennis Matthews -
http://en.wikipedia.org/wiki/Denis_Matthews
Who would - for pleasure - sit and read full scores of - say - Beethoven symphonies; hearing them performed in his head...
His musical memory was prodigious also, and he could recall full score concertos (for example) and play them from memory while simultaneously performing a piano reduction (i.e. reducing the dozen or more lines of orchestral music to the two hands on a piano).
But this kind of thing is not *that* unusual among top musucians, there are probably hundreds in the UK who could do something similar (e.g church organists who can transpose and improvise pastiche Bach fugues). What made Matthews into a top (British) soloist was his musicality - phrasing, architectural structuring etc. and not his technique.
All this quite aside from the fact that the mechanical business of playing complex music on the piano is itself an amazing physical achievement - far, far beyond most people.
On the other hand, some people clearly *cannot* do these high order things but don't let-on: there are plenty of physicists (the vast majority of physicists) who do not remotely *understand* quantum theory or relativity - they just know the rules and do the maths...
30 September 2011 at 10:41
Kristor said...
It is important to bear in mind always that the geometrical representation of time as a fourth dimension (in effect) of space is an abstraction, that enables us to think about it more easily; while useful, it bears the same relation to the reality of time as a subway map does to the reality of London. The temptation to think of time as *really* extending into the future like a line one extends from left to right on a sheet of paper is very strong; but it is not warranted.
Geometic figures in four-dimensional space are unimaginable, but they are conceivable, which I take it is the author's point: "I can work with the figures easily enough, but not visualize them - it can't be done." I beg your pardon if I have misunderstood you, but images and concepts --- and imagining and conceiving --- are very different things.
30 September 2011 at 19:02
chebek said...
i thought all you had to do to visualize the 4th dimension is imagine something moving.
15 October 2011 at 22:53
*
I already knew, from his incomplete story The Dark Tower that Lewis had read JW Dunne - and this was also an interest of Tolkien's, and probably the subject of Inklings discussion.
I have found further evidence of critical engagement with JW Dunne's ideas, and of Lewis's interest in Time in a collection of short memoirs and pieces about Lewis, recommended me by commenter Dale (thanks).
The discussion described below was more than a decade after the Inklings Thursday evening meetings had ceased - indicating a prolonged interest in Time on the part of Lewis, even after he had ceased to meet Tolkien regularly.
*
From We Remember CS Lewis edited by David Graham, 2001.
From the chapter by Daniel Morris - Encounter in a Two-Bit Pub. Describing a conversation between Graham and Lewis in 1959. This passage derives from a letter written shortly after the conversation.
*
Then he asked me what I was doing in England. Thence to mathematics, biochemistry, and the fourth dimension.
He was much interested in the latter, and wanted to know if I knew of Hinton's ideas, including the one that with enough practice you can actually visualize the fourth dimension.
I said that with all my practice, I can work with the figures easily enough, but not visualize them - it can't be done.
He was insisting that the whole idea is pure imagination (he's read Hinton and Dunne and Ouspenski and Abbot) like the square root of minus one. And I wasn't willing to make it that imaginary, considering curvature of space, for example, which seems to be experimentally true - and meaningless, unless the universe really is four dimensional.
He went into Dunne a good bit (that is, JW Dunne: An experiment in time, published in 1925) and he doesn't see (neither do I) why Dunne had to postulate an infinity of times at right angles to one another. Two times would cover he whole thing. Granted, that leaves a mystery as to what makes the thing run, but Dunne simply puts that off at infinity.
And thence to previsions, and to extrasensory perception, and predestination (...)
In the course of our talk about Dunne, and such, he said it was a shame we couldn't control the rate of flow of time.
As it was, the clock was rapidly moving on towards half past seven, and the end of this delightful talk he was having with me.
"JW Dunne and CS Lewis"
5 Comments -
Speaking as someone whose job often includes working out geometric figures in four-dimensional space, I find it charming that some very smart folks believe it to be beyond human imagination. I'm not going to tell them, though; I'd rather leave them some mystery. God set a good example by not revealing everything.
30 September 2011 at 09:36
@Jonathan - specific ability varies very widely among humans.
Lewis could not pass the 'basic' mathematics required for university entrance (usually done age 16) despite at least three attempts for which he was individuall tutored - yet he got three first class Oxford degrees (two in classics, which was the most elite humanities degree in the whole world at that time).
Lewis was only allowed to attend Oxford because as an ex-army veteran he was allowed an exemption.
So Lewis displayed very wide divergences in specific cognitive aptitudes - and indeed this is probably the usual pattern among people of very high intelligence: that the intelligence is relatively specialized (more so than used to be considered the case in the past).
Some musicians can perform feats which strike non-musicians or moderate musicians as uncanny, superhuman: I used to know (mostly via close friends) a great musician called Dennis Matthews -
http://en.wikipedia.org/wiki/Denis_Matthews
Who would - for pleasure - sit and read full scores of - say - Beethoven symphonies; hearing them performed in his head...
His musical memory was prodigious also, and he could recall full score concertos (for example) and play them from memory while simultaneously performing a piano reduction (i.e. reducing the dozen or more lines of orchestral music to the two hands on a piano).
But this kind of thing is not *that* unusual among top musucians, there are probably hundreds in the UK who could do something similar (e.g church organists who can transpose and improvise pastiche Bach fugues). What made Matthews into a top (British) soloist was his musicality - phrasing, architectural structuring etc. and not his technique.
All this quite aside from the fact that the mechanical business of playing complex music on the piano is itself an amazing physical achievement - far, far beyond most people.
On the other hand, some people clearly *cannot* do these high order things but don't let-on: there are plenty of physicists (the vast majority of physicists) who do not remotely *understand* quantum theory or relativity - they just know the rules and do the maths...
30 September 2011 at 10:41
It is important to bear in mind always that the geometrical representation of time as a fourth dimension (in effect) of space is an abstraction, that enables us to think about it more easily; while useful, it bears the same relation to the reality of time as a subway map does to the reality of London. The temptation to think of time as *really* extending into the future like a line one extends from left to right on a sheet of paper is very strong; but it is not warranted.
30 September 2011 at 17:39
Jonathan,
Geometic figures in four-dimensional space are unimaginable, but they are conceivable, which I take it is the author's point: "I can work with the figures easily enough, but not visualize them - it can't be done." I beg your pardon if I have misunderstood you, but images and concepts --- and imagining and conceiving --- are very different things.
30 September 2011 at 19:02
i thought all you had to do to visualize the 4th dimension is imagine something moving.
15 October 2011 at 22:53