LECTURE 2: REPRESENTATION

1. WHY ARE REPRESENTATIONS NEEDED?

2. DIGITAL REPRESENTATION

3. GEOGRAPHIC REPRESENTATION

4. THE FUNDAMENTAL PROBLEM

5. OBJECTS AND FIELDS

How do we know what we know?

The human senses

sight

visible spectrum
line of sight

horizon at ~10km
visibility 100km

sound

audible spectrum

50Hz to 15KHz

range 100m

taste
touch
smell

text
speech
maps
photographs
radio, TV
Internet
databases

500,000,000 sq km

on average 100 sq m is sensed directly at any time
p=100/500,000,000,000,000=.0000000000002

extend that through migration, travel

5 billion years

we live through 70
p=70/5,000,000,000=.000000014

we know almost nothing about the surface of the Earth via our senses

decide where to go as tourists, shoppers
run large corporations
manage agriculture, forestry
choose where to live

what is communicated is a representation of the real thing

Locations in time and space reduced to a few straight lines

what would more detail show?
representations always simplify the real world

the real world is infinitely complex
representations reduce information to manageable volume

in the human mind, in memory and reasoning
in speech
in written text
in photographs
in digital databases
in GIS

to communicate
to go beyond the space-time limits of our senses
to deal with an infinitely complex world

Much human communication is now digital

sent through a "pipe" that can transmit only 0s and 1s
stored on devices that can store only 0s and 1s
processed as 0s and 1s

text in email, word processors
voice in telephone
music on CD
DVD, digital TV
FAX

Digital

from "digit" meaning finger
a character in a counting system
how many symbols?

0 thru 9
0 and 1
the binary system

to all intents and purposes "digital"="binary"
how to express knowledge exclusively in 0s and 1s?

how to describe what we know about the world in 0s and 1s?
the fundamental question of data modeling for GIS

analog

information expressed by scaling quantities
good for quantitative information
a paper map is analog

the world is scaled to a miniature representation
representative fraction is key, e.g. 1:24,000

digital

information expressed by symbols
there must be a coding scheme to express the representation in symbols
sender and receiver must agree on the scheme

what does scale mean?

same for all kinds of information

same technology whatever the content
"a bag of bits"
massive economies of scale
miniaturization

text

ASCII code
one code per character

A = 65, B = 66, etc.

26 letters plus common symbols
originally 128, extended to 256
8 binary digits (one byte) per character

images

JPEG, TIFF, GIF, BMP, ...

music

MIDI, MP3

FAX

CCITT

maps, geographic information

GIS data models and structures

ASCII

eight bits per character
names, text annotation

integer

3 bits per decimal digit
n bits give 2ⁿ options

it takes about 3 times as many binary digits to express a number

16 or 32 bits per whole number (short, long integer)

-32767 to +32767
-2 billion to +2 billion

float (single precision)

1 sign bit
7 exponent bits (-63 to +63)
24 mantissa bits (8 significant digits)

double precision

1 sign bit
7 exponent bits
56 mantissa bits (18 significant digits)

what might you need to know to 18 significant digits?

BLOB

binary large object
e.g. image

01000001010101000101010001000001
01000011010010110101000001000101
01000001010100100100110001001000
01000001010100100100001001001111
01010010

What if you had to send a message to outer space?

the Voyager message

How efficient is the channel of communication?

is there information that can't be expressed

text omits gesture, pronunciation, voice inflection

can "duh" be written in text?

what are the limits of a GIS as a communication channel?

what information about a place can't be expressed in GIS?

what if the sender and receiver can't understand each other?

different language
different alphabet
different GIS
interoperability

Geographic information

information about some place on the surface of the Earth

or near the surface
at some point in time

one of the earliest forms of shared information

hunters and gatherers reporting back to the band
"there's good hunting near the old tree"
early stick maps for navigation in the Pacific
drawings on cave walls

storing on paper

the printing press in the 15th Century
information accessible to all
shared knowledge as a human community asset
Prince Henry the Navigator, 1394-1460

The Internet

massive new capability for sharing, communicating geographic information

in digital form

The atom of geographic information

<location, time, attribute>

it's cold today in Ottawa
at 45 North, 75 East at 12 noon EST the temperature was -10 Celsius

general methods for describing location

everyone around the world understands latitude and longitude

similarly for time

attributes must also be generally understood

"cold" is subjective and relative
-10 Celsius is generally understood
did Hugh Grant climb a hill or a mountain?

Suppose we could capture it all

complete representation of the planet
past, present, and future
a "mirror world"

“Imagine, for example, a young child going to a Digital Earth exhibit at a local museum. After donning a head-mounted display, she sees Earth as it appears from space. Using a data glove, she zooms in, using higher and higher levels of resolution, to see continents, then regions, countries, cities, and finally individual houses, trees, and other natural and man-made objects. Having found an area of the planet she is interested in exploring, she takes the equivalent of a ‘magic carpet ride’ through a 3-D visualization of the terrain. Of course, terrain is only one of the numerous kinds of data with which she can interact. Using the system’s voice recognition capabilities, she is able to request information on land cover, distribution of plant and animal species, real-time weather, roads, political boundaries, and population. She can also visualize the environmental information that she and other students all over the world have collected as part of the GLOBE project. This information can be seamlessly fused with the digital map or terrain data. She can get more information on many of the objects she sees by using her data glove to click on a hyperlink. To prepare for her family’s vacation to Yellowstone National Park, for example, she plans the perfect hike to the geysers, bison, and bighorn sheep that she has just read about. In fact, she can follow the trail visually from start to finish before she ever leaves the museum in her hometown.
She is not limited to moving through space, but can also travel through time. After taking a virtual field-trip to Paris to visit the Louvre, she moves backward in time to learn about French history, perusing digitized maps overlaid on the surface of the Digital Earth, newsreel footage, oral history, newspapers and other primary sources. She sends some of this information to her personal e-mail address to study later. The time-line, which stretches off in the distance, can be set for days, years, centuries, or even geological epochs, for those occasions when she wants to learn more about dinosaurs.” (U.S. Vice President Al Gore, in a speech written for presentation at the California Science Museum, Los Angeles, January 1998)

How many atoms are there?

an infinite number
to make a two-word description of every sq km on the planet would require 10 Gigabytes
to store one number for every sq m on the planet would require 1 Petabyte

that's too many for any system
how to limit?

ignore the water

that's 2/3 of the planet

one temperature for all of Ottawa

one number for an entire polygon

sample the space

only measure at weather stations
because temperature varies slowly

all geographic data miss detail

all are uncertain to some degree

there are many ways of doing this
a GIS user must make choices
GIS designers must allow for many options
geographic description is complex

The most important of the options

how we think about the world

points, lines, areas (or volumes) having known properties

littering an otherwise empty space

can be manipulated/edited

can be found in the real world

may overlap

can be counted

how many people living in Santa Barbara?
how many vehicles in California?
how many trees growing on the UCSB campus?
how many lakes are there in Minnesota?
how many mountains in Scotland over 3000 ft?
how many clouds in the sky?
how many cities over 1 million population?
how many atmospheric lows in the northern hemisphere today?

represent as shapefiles

things it's worth measuring at every location on the planet

temperature
soil pH
soil type
land cover type
elevation
rainfall
ownership

each of these variables has one value everywhere

variable is a function of location

field = a way of conceiving of geography as a set of variables each having one value at every location on the planet

z = f(x,y,z,t)

represent one variable as:

polygons
raster
TIN
sample points
contours

number of such objects is property of the representation, not the phenomenon

cannot be manipulated

cannot overlap

how many are there?

fronts, highs, lows, or pressure surfaces?

fields are more associated with science

Ontology: the study of the basic elements of description

"what we tell about"
discrete objects and fields are two different ontologies