I was traveling through my world, gazing at the big sky surrounding me in it's clear blue. I reached towards the blue. As I did so I was able to reach through with my hands. I hoisted the rest of my body, half in the world I knew and half in the new space, through the blue. As the tips of my toes left the old familiar world behind it formed a bouncing ball. Simultaneously the new space opened up to be as large as what I believed my old world had been.
This is a true story that happened in a meditative trance. It got me to thinking ...
The concept of time can and is confusing. We believe it moves forward in a linear fashion, and therefore theoretically should be accessed backwards in the same way. I think that the problem is we forget that linear isn't just horizontal. It can be vertical. Often when peoples lives begin to 'feel' like they're in the groove ... or as some call it "in the flow" ... it's actually a vertical movement upwards. The problem with backwards is we aren't very good at that skill. Try walking around a room quickly. Now try walking around the same room backwards quickly. Even when we drive we never back up for long distances. If time can move vertically, perhaps when we move backwards it's too difficult to find a groove to stay in? Well, that's just my thought.
-Sophie Robertson
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as I understand it, linear time just means the way that we experience
things as happening in a particular sequence or order. Normally we feel
as though the past happens before the present, and the present before
the future. This is the way we tell stories. We start at the
beginning, and then work our way, event by event, towards the end. The
end is the future of the beginning, and the beginning is the past of the
end. First there was the Anglo-Saxon kings, and then William the
conqueror invaded in 1066 and took over, and now there are the Norman
kings, etc... You can think of history as a line of ordered "time"
along which all events are placed. One direction along the line is
further in the future, the other is further into the past, and we only
move in one direction along the line, away from the past and into the
future. Any event is some "point" on the line ( or if you want to talk
about events that lasted some time, you can think of small sections of
the line ).
Anglo-Saxons 1066 Normans
PAST >------->-------->-----X---------->--------> Future
Which direction does this line point? Does it have to go from left to
right? No, that's just a convention we have because we ( in the west )
read from left to right - it could just as easily be drawn as right to
left, or top to bottom. The direction or orientation isn't important,
its the ordered nature of events which is important. Just in the same
way that it doesn't matter what particular numbers we use for dates - we
could use the Julian calendar, or we could use the Hebrew calendar, and
give totally different year numbers to the same events - but so long as
all the events are ordered in this way then time is still "linear" -
that is, time is motion along this line ( or sequence ) of ordered
events. So in this sense being horizontal or vertical doesn't matter.
Normally we just live our lives with this kind of time as a basic
assumption - because it always seems to be correct. Events always "seem"
to occur in these ordered sequences. So often in science time is modeled
as being "one-dimensional" which is just another way of saying that it
is just on a line, where you can move forwards - and (maybe?) backwards.
Normal space is said to be 3-dimensional in that there are 3 independent
directions you can move ( length, width, height or north-south, east-
west, up-down ), lines which are perpendicular to each other represent
an "independent" direction - and so another "dimension". Picture a
rectangle:
--------
|\ |
| \ |
| \ |
| \ |
| \ |
| \|
--------
the reason we say that this picture is 2-dimensional is that you can
describe everything in it in terms of 2 separate directions ( and not
less than two ) there is the edge running along the bottom, and the
edge going up one side ( perpendicular to the bottom ). Each of the
other two edges is just the first edge shifted over a bit ( so they lie
in the same "direction" ). The diagonal which cuts across the rectangle
doesn't lie entirely in either direction - but it is a combination of
both:
|\
| \
| \
-----
| |\
| | \
| | \
---------
notice in the shape above, how for every three "dashes" down you go, the
diagonal line takes you 4 lines across (although the picture here isn't
quite perfect). You can see that if you continue the line down thee
more dashes, it moves the same amount over. So we can say that this
diagonal line is a "combination" with "fixed ratios" of moving 4 "units"
across for every 3 "units" down - and if we call the vertical direction
y, and the horizontal x then you get that this line is: 4x = 3y. Notice
though, that we write it like this just because we chose to name them
this way - it could just as easily have been 4y = 3x if we switched the
names around, or 4(jones) = 3(smith), or 4(horizontal) = 3(vertical);
the names are not important - its this particular relationship which is
important. Also if you rotated the picture, you could do exactly the
same thing - but you'd need to put x and y not as horizontal and
vertical, but some other lines pointing in different directions, so
there is something about all pictures like this which are
"fundamentally" 2-dimensional.
Anyway, this is all a long way of saying in pictures what we mean by
talking about "dimensions". If you have some "world" or "domain" in
which you can describe everything in terms of a single line, then you
say that that "domain" is 1-dimensional - if you need 2 lines then its
2-dimensional, etc.
In our normal way of thinking about things we say that because we can
explain all of history in terms of this one line or ordered events then
history and time is one-dimensional. However, we can't look at time and
examine it the way we can with space and shapes and geometry. We only
think of it that way because that's the way it "seems to us" because we
have memories (both in our heads, and in books, tapes, videos, etc.)
Some people have suggested that time may not really work like this - it
is not "fundamentally" along a line - but just that our experience of
time is this way. Maybe time is a 2-dimensional ( or 3,4,... ),
"world", where forwards and backwards (past/future) is just one possible
"direction" to travel, and that there is another possible direction.
Maybe there is something about our way of existing in this world that
makes us only travel in one direction, but it might be possible to
travel in others - or maybe we don't even travel in one straight linear
direction, but our minds are built to organize things such that it seems
as though we are.
So in this sense your question about horizontal and vertical would mean
something different - if you imagine that our "normal" experience of
time is linear like the line above ( and we'll call it horizontal for
the sake of argument ), then there might be another perpendicular
direction ( call it vertical ), which would allow us to move not
forwards or backwards, but upwards and downwards in time - or maybe
there are even more directions. So in this sense, your question means
something different. However, in the language that is normally used to
describe these things, the terms "linear" and "non-linear" are usually
used - because they have certain special meanings in math and geometry,
whereas "horizontal" and "vertical" don't. Einsteins theory of
relativity really challenges our notions of space and time, and puts
forward the notion that time and space are not the perfectly ordered
things we think they are, but are "bendy" and can be twisted and warped
by extreme forces.
But the question remains, what does all this "mean" - we have an
understanding of history as linear - and this seems to make sense, and
although we can speculate about other possible ways time might be
organized, we still need to know what this "means" in a more basic way.
What does it mean to say you're moving vertically in time? It can't
mean moving into the past or the future - because we've already decided
that that is "horizontal" movement - so what does "vertical" movement
mean? If you want to read more about all this, then Hawkins "Brief
history of time" is very good.
Anyway - sorry to blab so much - you just happened to tap into one of my
personal obsessions here. Its things like this that are exactly why I
like mathematics so much - because it challenges you to think in very
different ways about the world. As for summer school - I'm taking a
course on complex numbers - which are very strange things having to do
with adding a "real" number to an "imaginary" number - and there is a
whole branch of mathematics devoted to this study. It sounds like a big
waste of time working with "imaginary" numbers - but they are actually
very useful for a lot of applications. So I hope I've made it clear - I
know talking about lines and shapes and dimensions is pretty abstract,
but I don't think there is an easier way without leaving large parts
out.
Cheers,
Tristan
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