Professor J. A. Finnegan

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]
 

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

The idea of communication by light over long distances (aka optical
tele-communication) is not new.  Fires lit on chains of mountain tops
and ship-to-ship light signaling are examples for early open-space
optical communication systems.  What is new is the ability to divert
the light to flow in fibers.  New is also the fast modulation of light
with information.

The basic idea is simple, using light reduces latency because light
travels fast.

The HISTORY of PHOTONIC COMMUNICATION

The use of light for signaling is a striking example of the true
American innovation.  It dates back about four thousand years to the
native American Indian tribes that used smoke signals to communicate
over long distances (essentially the first packet-based communication).

Thet achieved a data rate of many seconds per bit after an initial
packet pre-amble of about 30 minutes - to start the fire.

There was some independent work on the European continent about a
thousand years later when the Greeks used their shiny shields as
modulators to bounce sun-light to their generals during battle.

After their patent has expired the same idea was copied by the active
sun-collection farms which may be found today in California.

However, this was short-distance communication and quite unreliable
(to be precise, reliable optical communications were short-lived).

Unfortunately, the rate of innovation of light-based signaling in the
Americas was reduced drastically over the next several millenia because
most of the native American Indian engineers were killed by the
settling European engineers in an early example of predatory business
practices.

COMMUNICATION APPLICATIONS

In modern digital binary communication the only symbols are 0 and 1.
Light represents the 1s and 0s are represented by darkness.  In order
to reduce skew it is very important to minimize the disparity between
the speed of light (SoL) and the speed of darkness (SoD).

Since SoL, in vacuum, is the fastest speed that physics allows, SoD

		

Professor J. A. Finnegan was born in Oceanview, Kansas.

After receiving his MS degree in Engineering from Oceanview University
he joined the ADP (now IT) department of the First National Bank of
Oceanview.  His many innovations and the numerous technical papers which
he published in the scientific literature while working at FNBO earned
him the admiration of all his peers.

After several years at FNBO he returned to his alma mater to continue
his scientific pursuits.  He graduated in the top 90% of his class.

After receiving his PhD he joined the Computer Science faculty at
Oceanview University.

Computer communication, artificial intelligence, and VLSI are only a few
of the many scientific areas that he actively investigates.

It came as no surprise that he has won a highly acclaimed knowledge
competition, as indicated by a pin that he often wears on the lapel of
his suits.

Professor Finnegan contributes regularly to many technical
publications and conferences.

In 1987 he became a bona fide associate member of the International Flat
Earth Society.

While on sabbatical leaves from his home institute in Oceanview he used
to work at USC/ISI with Danny Cohen and Jon Postel but recently, due to
global warming, he works with the scientists of Sun Laboratory in
northern California, where the weather is better.

[end]

             The VLSI Approach to Computational Complexity
			 Professor J. Finnegan
				    
		    University of Oceanview, Kansas
		(Formerly with the DP department of the
		   First National Bank of Oceanview)

The rapid advance of VLSI and the trend toward the decrease of the
geometrical feature size, through the submicron and the subnano to
the subpico, and beyond, have dramatically reduced the cost of VLSI
circuitry. As a result, many traditionally unsolvable problems can
now (or will in the near future) be easily implemented using VLSI
technology.

For example, consider the traveling salesman problem, where the
optimal sequence of N nodes ("cities") has to be found. Instead of
applying sophisticated mathematical tools that require investment
in human thinking, which because of the rising cost of labor is
economically unattractive, VLSI technology can be applied to construct
a simple machine that will solve the problem!

The traveling salesman problem is considered difficult because of
the requirement of finding the best route out of N! possible ones.
A conventional single processor would require O(N!) time, but with
clever use of VLSI technology this problem can easily be solved in
polynomial time!

The solution is obtained with a simple VLSI array having only N!
processors. Each processor is dedicated to a single possible route
that corresponds to a certain permutation of the set [1,2,3...N]. 
The time to load the distance matrix and to select the shortest route(s)
is only polynomial in N. Since the evaluation of each route is linear in
N, the entire system solves the problem in just polynomial time!  Q.E.D.

Readers familiar only with conventional computer architecture may
wrongly suspect that the communication between all of these processors
is too expensive (in area). However, with the use of wireless
communication this problem is easily solved without the traditional,
conventional area penalty. If the system fails to obtain from the FCC
the required permit to operate in a reasonable domain of the frequency
spectrum, it is always possible to use microlasers and picolasers for
communicating either through a light-conducting substrate
(e.g. sapphire) or through a convex light-reflecting surface mounted
parallel to the device. The CSMA/CD (Carrier Sense Multiple Access,
with Collision Detection) communication technology, developed in the
early seventies, may be found to be most helpful for these applications.

If it is necessary to solve a problem with a larger N than the one
for which the system was initially designed, one can simply design
another system for that particular value of N, or even a larger
one, in anticipation of future requirements. The advancement of
VLSI technology makes this iterative process feasible and attractive.

This approach is not new. In the early eighties many researchers
discovered the possibility of accelerating the solution of many
NP-complete problems by a simple application of systems with an
exponential number of processors.

Even earlier, in the late seventies many scientists discovered that
problems with polynomial complexity could also be solved in lower time
(than the complexity) by using a number of processors which is also a
polynomial function of the problem size, typically of a lower
degree. NxN matrix multiplication by systems with N^2 processors used
to be a very popular topic for conversations and conference papers, even
though less popular among system builders. The requirement of dealing
with variable N was (we believe) handled by the simple P/O technique,
namely, buying a new system for any other value of N, whenever needed.

According to the most popular model of those days, the cost of VLSI
processors decreases exponentially. Hence the application of an
exponential number of processors does not cause any cost increase,
and the application of only a polynomial number of processors results
in a substantial cost saving!! The fact that the former exponential
decrease refers to calendar time and the latter to problem size
probably has no bearing on this discussion and should be ignored.

The famous Moore model of exponential cost decrease was based on
plotting the time trend (as has been observed in the past) on
semilogarithmic scale. For that reason this model failed to predict
the present as seen today. Had the same observations been plotted on
a simple linear scale, it would be obvious that the cost of VLSI
processors is already (or about to be) negative. This must be the
case, or else there is no way to explain why so many researchers
design systems with an exponential number of processors and compete
for solving the same problem with more processors.


CONCLUSIONS

- With the rapid advances of VLSI technology anything is possible.
- The more VLSI processors in a system, the better the paper.

======================================================================


This paper has been published as "A VLSI Approach to Computational 
Complexity (by Professor J. Finnegan)", in "VLSI, Systems and
Computation", edited by H. T. Kung, Bob Sproull, and Guy Steele, 
Computer Science Press, 1981, pp. 124-125.


[end]

Papers of special scientific interest:

• Advanced Applications of Photonics
  
• The Fourth Dimension
• VLSI Approach to Complexity