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

## Friday, May 20, 2005

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## 1 comment:

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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