7.2
                          The Time Dimension

                                   by
                          Prof J. A. Finnegan
                      Computer Science Department
                        Oceanview University, KS
INTRODUCTION

Let D be the number of dimensions of our world.  In other worlds 
D may have other values.

Most engineers believe that D=3.  Modern physicists (especially
at Caltech) know that D=13.

Edwin Abbott in his book Flatland (circa 1880) starts with D=1
and proves that D=D+1.

The mathematicians, and only the mathematicians, know that the true
value of D is D=N.  Note that there is no conflict between D=N and
D=D+1.

Experimental results, by earthlings, show beyond a shadow of a doubt,
that power density decreases, as a function of the range R, as R^(-2),
which (if the conservation laws are to be believed) proves that D=3.

D=3 leads to the well known equation:

	(1)	x^2+y^2+z^2 = (Vt)^2

where V is the speed of signal propagation.  For example, V=~1.0 Mach
for sound.  For light V=1 MegaMach, aka c.

Since light is lighter (pun intended, sorry) than sound, and since it
does not (for all practical purposes) depend on temperature, humidity
and the like, we use here V=c.

Eq.(1) could be written as:

	(2)	x^2+y^2+z^2-(Vt)^2 = x^2+y^2+z^2+(iVt)^2 = 0

This suggests that T=iVt is just another dimension as x, y, and z are.
We let T represent this dimension, aka the "Fourth Dimension" ("fourth"
is "(D+1)th"), or just T for short.

The Vt is the spatial component of T.  The i in T=iVt is there to
remind us that this dimension is imaginary.


EVENTS

Events tend to move along the T axis at the constant speed of Q (for
"quick").  In several experiments Q was clocked roughly at
(7.001+/-0.025) days/week.  It is possible that there are worlds where
Q is different (e.g., 5 days/week).  As verified by the geographers who
visited there, Q=1day/month on moon, whereas on earth it is much faster,
Q=(29.5+/-1.6)days/month.

More examples of events are holidays, birthdays, Xmases, sunsets,
sunrises, noons, midnights, and some deadlines (but not all of them).

As the number of candles on birthday cakes reminds us, time keeps moving
forward (i.e., Q>0).  The non-linearity of this motion is the subject of
this document.

Let an observer be located at the origin facing the direction of +T
noticing how all events pass by him/her at the velocity of Q.  Actually
their velocity is -Q.  The observer sees, through his windshield, the
future events (with T>0) as they get closer and look bigger (following
the laws of perspective geometry).

As an event moves from the future, the T>0 sub-space to the past, the
T<0 sub-space, a few very interesting and unpredicted things happen.
The past events, as seen through the rear view mirror, get further and
look smaller (following the same laws of perspective geometry).

The first question that most observers ask is "Who moves? I think that I
am fixed and they move relative to me, but it may be that they are fixed
and I move relative to them".  Observers who do not ask this question
(or equivalent) are disqualified and are assigned to verify other
domains of physics.

Let P(t) be the position of an event at time t.  In a perfect linear
world the following holds for all events

	(3)	P(t) = P(0) - Qt

But is it so in practice?

Experimental evidence (using fMRI) shows that boring one-hour talks
seem to last forever, whereas interesting one-hour talks end prematurely
after what seems to be just a few moments.

The above data are supported by double-blind experiments where
subjects were chained to their seats and exposed to lectures by some
more-interesting and some less-interesting speakers.  All talks were of
exactly 55 minutes which was not known to the subjects who were asked to
estimate the length of each talk.  To our great surprise, the data show
no surprises, all was exactly as expected, which is a great surprise.

Deadlines have an interesting property, they jump in a discontinuous
manner from being too-early to work on, to being too-late to work on,
without ever being at just the right time to work on.  The only
explanation of this observation is based on the existence of tunnels
from T=too_early>0 to T=too_late<0, without access to the observer who
is stationary at T=0 which is the right time to work on it.  Continuity
is not a property of this theory.

Airlines also obey similar rules.  However, what passengers notice on
pleasant flights is not that Q is high, but that T is low, aka short
flight, (which is most welcome).  Unfortunately, the inverse is also
true, and unpleasant flights have low Q and high T, aka too long
flights.  It has been suggested that there may exist some disparity
between the number of pleasant and unpleasant flights.

What saves airlines from total confusion is that the ratio between
climbs and descents is 1:1 (on the average) for all practical purposes,
unlike bicycle riding where the ratio of up-hill to down-hill is about
10:1 which, by a strange coincedense, is also the headwind:tailwind
ratio.  By a clever use of gravity the airlines minimize the disparity
between the number of takeoffs and of landings.  When such disparity is
discovered it is typically front page news.

The thorough investigation of the Q motion reveals that what seems as
a uniform Q is actually a composition of two separate flows, a slow one
of desired events and a fast one of less (if at all) desired events.
The viscosity of time interacts with the desirability of events such
that desired events always lag behind the undesired ones.

This theory is supported by Prof Doug Adams who has reported that bad
news travels faster.  Unfortunately, so he reported, this news cannot
be used for propulsion because it is never welcome, anywhere.

The above applies to a wider scope than just events.  It applies also to
budgets, power consumption, performance, area used, etc.  It is not
uncommon to discover that the proposal-time estimates of the system
properties (taken at proposal time, T>0) exceed the measured properties
of the delivered system (aka actuals, taken at T<0)

This suggests that there may be, on some occasions, some disparity
between expectations and reality.


THE DISPARITY

Scientific observations have shown that many important events, such
as new year, do not happen everywhere at the same time.  There is some
theory explaining it using time zones, dateline, daylight saving and
standard time, leap years and leap centuries, and more terms that are
far beyond the reach of this document.

Bending the T=constant lines can simplify the situation.  Therefore,
it is left as an extra-credit task for the student to present the
simplified geometry of the (X,Y,Z,T) space, such that the important
events will have the same value of T, anywhere, regardless of their X
value (aka "east"), as X is quantized ("discretized") into time
zones.

The universe radiates heat which causes the world to shrink.  In order
to preserve momentum our world accelerates and spins faster which causes
increased friction, this is locally observed as "global warming".  This
acceleration is mathematically represented as dQ/dt>0 which is also
known as "the older one gets, the faster time flies".  Kids know that
it takes years from one summer vacation to the next, whereas parents
wonder why summer vacations are so frequent nowadays.


CONCLUSION

Time flies faster and faster.  dQ/dt>0 says it all.  

Some action is required ASAP to stop it, before it is too late.

We have never needed Al Gore as much we need him now.

[end]