 
...or How 40 purses can buy you swift precise Navigation
to anywhere on the Globe.
Copyright- Kimball J Thurlow 2002 This article is not to be reproduced
in any form without the written permission of Kimball J Thurlow.
 Why magic Carpet GPS?
I have coined this term to describe the Garmin
GPSMAP196 series, because it puts me in mind of a machine that
can magically transport a traveller from one point to another,
regardless of his mode of travel. This GPS combines all the massed
functionality of panel-mounted aviation GPS, and the auto route
calculating functions of in-car navigation. As well, it can read
marine charts to assist navigation of vessels through charted waters.
And it can also be used as a hand-held GPS. Then it begs the question
of where companies like Garmin can take us with this technology,
in the next generation?
GPS in modern times, helps ordinary people
to arrive at any destination without any seeming effort. Effortless
travel intrigued the ancients,
and the story of one such achievement, has come to us through
the annals known as the "Arabian Nights".
Firstly, let us acknowledge the contribution made by the Arab peoples
in long ago times (along with Egyptians BC, and Chinese and Western
cultures AD), in the arts of mathematics, astronomy and terrestrial
measurement, all of which are the basis for our space and geomatic
sciences.
|
This picture shows a typical Turkish kilim,
or flat woven carpet.
Carpets, whether knotted or flat woven (kilim) are very
practical home makers, particularly where temperature
fluctuations between day and night, summer and winter
may vary greatly. In regions such as Turkey, Arabia,
and central Asia, woven carpets were extensively used,
and became both practical and art objects, by covering
the floors, and sometimes walls and doorways. The carpets
are always hand made of wool or sometimes cotton, with
occasional additions of silk. The flat woven kilims which
are frequently embroidered are used as blankets, curtains,
and covers over sofas or as cushion covers.
With acknowledgement to
Ülkü Bates,
Ph.D., Professor of
Art History, Hunter College, New York City
|
Carpet Weaving
My article is going to mix a little home science with a
little myth, and hopefully raise a good story, which may
prove true; at the least entertaining.
Transport from one place to another geographically, has
always been fraught by danger. Partly because of natural
obstacles (rivers, hills) and also because of unfriendly
peoples (and animals) by whom you have to pass (including
brigands and robbers). But there is the other problem, of
which way and how far, and how not to get lost. And from
ancient times this has been done by knowing the lie of the
land in your own locality, but also by other means for further
afield.
Firstly, it becomes known by experience, and from what your
father told you, that to reach Zee, you walk one half a day
toward the rising sun, then another half a day with the sun
in front of you, then later over your left shoulder. By night
fall you should reach Zee. {This is the time method; you
could also use the number of paces (= distance), but counting
becomes tedious}
Desirably, this instruction can be written down for absorption
by others. One of the easiest ways to do this is graphically,
and what better method than a piece of cloth, which you weave
in your own home from local fibres. The woof thread runs
one way in the weaving shuttle, and the warf thread runs
the other. So you have a piece of cloth with a natural check
pattern, which can easily represent both direction and distance.
The woof can represent the direction to the rising sun, and
the warf can represent the direction to the noon sun (at
right angles to the woof of course). Each thread of the weave
can represent a distance. Perfect.
|
Arabian Science
When faced with distance and direction problems in the treatise
above, it becomes useful to understand the size of the globe on which
we live. For example, the length of a shadow in Brisbane on a certain
day and time, will differ in length from a shadow in Sydney, and
from Melbourne. Differences in shadow lengths will be proportional
to the distances between cities. By building up a table of shadow
lengths and distances, we could become rather expert at knowing how
far to go to a destination. Similarly we can actually determine how
far you are from the equator, and so on. Way back in AD820, Caliph
Al-Mamun in Arabia, observed these principles, and actually managed
to calculate the size of our globe. (As did
Ptolemy in 110BC, Reference:Introduction to Geodesy, The History
and Concepts of Modern Geodesy, by James R Smith, publ John Wiley
and Sons, Inc)
Arabian Nights
At the same time as this scientific publicity, Arabian scribes were
putting pen to paper to preserve stories from the region. These are
still very well known and popular, and include the tales of Sindbad,
and Scheherazade. (With
acknowledgement to John
Crocker, expert in matters relating to
the ancient Arab writings and cultures. )
The first identifiable written version of the Arabian Nights seems
to have been a book of Persian tales called Hazar Afsanah (A
Thousand Legends), translated into Arabic around A.D. 850. The Arab
writer Al-Mas'oodi (who died in A.D. 956) refers to this book, and
reveals that it is known as Alf Layla (A Thousand Nights).
The following scene from the story of 'Prince Ahmed and the Fairy
Pari Banou' is set in Bisnagar, the ancient Hindu capital city of
southern India; the story has three sons compete for the hand of
a princess. The successful suitor will prove his worth, by presenting
the princess's guardian with a marvel, more fantastic than the others.
Our interest lies with Prince Houssain, the eldest of the three.
"After Prince Houssain had run through
that division, street by street, his thoughts fully employed on
the riches he had seen,
he was very much tired; which a merchant perceiving, civilly invited
him to sit down in his shop, and he accepted of it; but had not been
sat down long, before he saw a crier pass by with a piece of tapestry
on his arm, about six foot square, and cried it at thirty purses.
The prince called to the crier, and asked him to see the tapestry,
which seemed to him to be valued at an exorbitant price, not only
for the size of it, but for the meanness of the stuff. When he had
examined it well, he told the crier, that he could not comprehend
how so small a piece of tapestry, and of so indifferent appearance,
could be set at so high a price. The crier, who took him for a merchant,
replied, If this price seems so extravagant to you, your amazement
will be greater, when I tell you I have orders to raise it to forty
purses, and not to part with it under. Certainly, answered Prince
Houssain, it must have something very extraordinary in it, which
I know nothing of. You have guessed it, sir, replied the crier, and
will own it, when you come to know, that whoever sits on this piece
of tapestry may be transported in an instant where-ever he desires
to be, without being stopped by any obstacle."
And so Prince Houssain was short of forty purses, but possibly betrothed
to a beautiful princess.
Carpets tell a Story
.... he could not comprehend how so small a piece
of tapestry, and of so indifferent appearance, could be set at
so high a price......
We assume that myths have some origin in fact. Is it possible that
Prince Houssain was handed a carpet that was simply a map, which
enabled him to traverse the land speedily and effectively? A
map made from tapestry, where each woof and warf is a representation
of a real place, or road or some physical geographic attribute,
may not appear particularly attractive, especially to the trained
symmetrical eye. But if it can direct you certainly to any place
in the habitable world, then it is a marvel that has no price.
Imagine this piece. Small colured threads represent towns and
streets, different colours woven in lines represent roads or
byways, and so on
The concept of the woven carpet, is exactly the same as our modern
mapping grid systems. Each thread in the carpet represents a
distance in either the north (south) or east (west) direction.
Due to continual refinement in our measurement of the globe (particularly
over the last 200 years), we now rely not only on maps, but on
satellite pathed navigation systems, that actually use the same
grid system. Our modern geographic location systems use grids
that can be theoretically represented to millimetres, and regularly
do so in practice to 1cm, by surveying quality GPS.
But of course one has to learn the method and use of the map. We
learn in school, about compass points, north south east and west,
about distance and measurement. And applyng that knowledge to
reading a map, has long been the subject of dispute between husband
and wife. Is it easier to point the map in the direction of travel,
or line it up with the north point? The answer depends on your
spatial understanding. So I doubt if there is a right or wrong
way. The human brain is certainly smart when absorbing the streets,
and possble routes on an urban map. But as soon as you start
to travel, what seemed like a logical sequence of turns, becomes
mixed up in street signage, traffic hazards, and intersections
that suddenly seem larger or more important than they did on
the map, and so on. But enter mathematics and computers, and
we find they can certainly make it easier for us.
Shortest Path Algorithms
Computing has enabled continuous calculations
that in practice, could never have been done by hand. One such
calculation is the
shortest path algorithm, a mathematical method used to calculate
the "least cost" from one point to another. "Least
cost" may refer to shortest distance, lowest fare, least
energy, or any other parameter. So the algorithm could be applied
to design of electronic circuitry, water reticulation, or any
application requiring travel of any particle or substance in
the MOST effective manner.
The algorithm reduces the problem to a graphical one. In applying
it to travel geographically, the required solution may be the
shortest, or the quickest. Either method uses the same basic
graphical sequencing, with slightly different attributes on the
possible path.
The mathematical terms for a position, or destination, is a vertex
(a layman's term may be a node). Edges are the lines or routes
connecting those nodes (another term for this could be a vector).
In order to find the shortest path from a position, to a destination
(a vertex), it is necessary to find the shortest path from that
position to every other adjacent vertex, that may create a path
to that destination. In turn, the shortest path vertex then becomes
the basis of a search for the shortest path to every adjacent
vertex, that may create a path to the destination, and so on.
Dijkstra's algorithm (named after Edsger
Dijkstra, see below ) sequentially queries each adjacent
node for least cost (or distance or time), until it arrives at
a single complete solution for the best path through adjacent
nodes to a destination.
(Reference: Data Structures and Algorithms,
Bruno R Preiss, John Wiley and Sons Inc, 1999.)
Smart Mapping
And so to a conclusion, for now. The knowledge that computers can
find a quicker route is not much comfort without a practical
advantage for us. Companies like TeleAtlas (tools for computer
mapping) have contributed, and Sensis (through their Whereis
Navigation subsidiary), have already completed substantial detail
for Australian highways, roads and streets, and applied the shortest
path algorithms to benefit end-users.
The computing ability of even a small hand-held GPS is a marvel.
Combine that with the the ability to calculate street by street
to a destination, and show you on a moving map screen is perfect.
And this is what our Magic Carpet GPS can do. As well as give
us the runway length and direction of the nearest airport. Which
is great if you're an aviator. All of the GPS we supply, are
Magic Carpet things in a way. And when you see the top of the
range StreetPilot3, which also speaks to you (street by street,
turn by turn), then you know you really have secured some very
powerful mapping technology, in concert with global positioning
technology. If that adds up to less frustration, less fuel burnt,
and time saved, it will be money well spent.
We do not promise you the hand of a princess, or even a prince,
but we can help when it comes to spending 40 purses on some really
useful stuff like GPS.
Smart mapping
available now!
Edsger
Dijkstra, and some computing examples of the algorithm, with
acknowledgment to University of Western Australia
At this link you will find an example of a Dijkstra's Algorithm Animation,
written by Mervyn Ng and Woi Ang.
Edsger Dijkstra (1930-2002) made many more contributions to computer science
than the algorithm that is named after him. Dijkstra was a prodigious writer.
His entire collection of over thirteen hundred written works was digitally
scanned and is accessible at http://www.cs.utexas.edu/users/EWD.
He also corresponded regularly with hundreds of friends and colleagues over
the years --not by email but by conventional post. He strenuously preferred
the fountain pen to the computer in producing his scholarly output and letters.
Edsger Dijkstra passed away in August 2002, and you will find an obituary published
by the University of Texas at http://www.cs.utexas.edu/users/UTCS/notices/dijkstra/ewdobit.html.
Further reading:
Welcome to Stammtisch Beau Fleuve! Alfred M. Kriman
A multidisciplinary collaboration for Communication, Research,
and Lunch.
http://www.plexoft.com/SBF/index.html
http://www.plexoft.com/SBF/W.html
"warp
The multiple threads in a loom, transverse to which the shuttle is passed (the
thread on the shuttle is the weave). I'm tired right now. If anyone has the
energy, let me know if that's right. "
Note from Kimball Thurlow:
I have found in various manuals and references, that woven material is described
as having
a warf and a weave, or
warf and or the woof, or as above
a warp.
|
Johnny Appleseed GPS