The City of Wood

Steven Tripp

Center for Language Research

University of Aizu

The Spatial Representation of Knowledge

• Gärdenfors, P., Conceptual spaces: The geometry of thought.: MIT Press, Cambridge, 2000.

• Fauconnier, G., Mappings in thought and language. Cambridge University Press, Cambridge, 1997.

• Fauconnier, G., Mental Spaces. Cambridge University Press, Cambridge, 1994.

Gärdenfors

• Theory of Conceptual Spaces

• Domains: spatial, color, kinship, sound, etc.

• Quality Dimensions: temperature, weight, hardness, pitch, height, etc.– Distance=similarity– Discrete dimensions: species, kinship

Discrete Dimensions

Cow Horse

Mammals Reptiles Fish

Animals

Taste Quality Space

• Tastes are combinations of three primaries

• Tastes can only be represented on planes.

Saline

SweetSour

Bitter

Multidimensional Scaling

• MDS

• Dimension Reduction

• Stress function measures misfit between data and reduced space

• No guarantee that the dimensions have a psychological interpretation

MDS Mammals

• Perceived similarities

• Experts

Up/Dn C/CC L/R Speed

Spin

Home

Rock

Clip

Zoom

Help Color Mouse Box Iter Undo

Raccoon

KangarooKoala

Lion

Ferret

Opossum

Dim1Dim2

Dim3

MDS Mammals

• Perceived similarities

• Novices

Up/Dn C/CC L/R Speed

Spin

Home

Rock

Clip

Zoom

Help Color Mouse Box Iter Undo

Rabbit

PlatypusBeaver

Kangaroo

Hedgehog

Manatee

Dim1

Dim2

Dim3

Domain

• A set of integral (correlated) dimensions

• Separable dimensions (color and weight)

• A conceptual space is a set of correlated domains

• A property is a region of a domain

Three Levels of Representation

• Symbolic (names and rules)

• Conceptual (maps)

• Associationist (paths)

• Problem: How should concepts be modeled?

Fauconnier’s Mental Spaces

• Cognitive Linguistics– Language is a set of instructions for

constructing interconnected domains

• Mappings– Analogy (computer virus)– New conceptual structure ( a new virus)– Projected Structure (disinfectant)– Blending (both computers and organisms)

Domains

• Different domains (beliefs, images, couterfactuals, scenarios, etc.) have similar structures.

• A limited set of principles allow structure projection between domains.

Space Projection

• Maybe Romeo is in love with Juliet.

• Maybe signals a possibility space

b

b’

Base Space B

New Space M

a

a’

A: name RomeoB: name Juliet

love a’b’

relative

I

I

WordNet

• G. Miller (Magic Number 7±2)• Hierarchically linked dictionary• http://www.cogsci.princeton.edu/~wn/• Nine starters• { entity, something, (anything having existence (living or nonliving)) }• { psychological_feature, (a feature of the mental life of a living organism) }• { abstraction, (a general concept formed by extracting common features from specific

examples) }• { state, (the way something is with respect to its main attributes; ") }• { event, (something that happens at a given place and time) }• { act, human_action, human_activity, (something that people do or cause to happen) }• { group, grouping, (any number of entities (members) considered as a unit) }• { possession, (anything owned or possessed) }• { phenomenon, (any state or process known through the senses rather than by intuition or

reasoning) }

Kinds of Nouns

• Table 1 List of 25 unique beginners for WordNet nouns

{act, action, activity {natural object

{animal, fauna {natural phenomenon

{artifact {person, human being

{attribute, property {plant, flora

{body, corpus {possession

{cognition, knowledge {process

{communication {quantity, amount

{event, happening {relation

{feeling, emotion {shape

{food {state, condition

{group, collection {substance

{location, place {time

{motive

Sample Hierarchy

• Oak• Sense 1• oak -- (the hard durable wood of any oak; used especially for furniture and flooring)• => wood -- (the hard fibrous lignified substance under the bark of trees)• => plant material -- (material derived from plants)• => material, stuff -- (the tangible substance that goes into the makeup of a physical object; "coal is a hard black

material"; "wheat is the stuff they use to make bread")• => substance, matter -- (that which has mass and occupies space; "an atom is the smallest indivisible unit of

matter")• => object, physical object -- (a physical (tangible and visible) entity; "it was full of rackets, balls and other

objects")• => entity, something -- (anything having existence (living or nonliving))

• Sense 2• oak, oak tree -- (a deciduous tree of the genus Quercus; has acorns and lobed leaves; "great oaks grow from little

acorns")• => tree -- (a tall perennial woody plant having a main trunk and branches forming a distinct elevated crown;

includes both gymnosperms and angiosperms)• => woody plant, ligneous plant -- (a plant having hard lignified tissues or woody parts especially stems)• => vascular plant, tracheophyte -- (green plant having a vascular system: ferns, gymnosperms, angiosperms)• => plant, flora, plant life -- (a living organism lacking the power of locomotion)• => life form, organism, being, living thing -- (any living entity)• => entity, something -- (anything having existence (living or nonliving))

Meronyms of Oak Tree

• oak, oak tree -- (a deciduous tree of the genus Quercus; has acorns and lobed leaves; "great oaks grow from little acorns")

– HAS SUBSTANCE: oak -- (the hard durable wood of any oak; used especially for furniture and flooring)

– HAS PART: acorn -- (fruit of the oak tree: a smooth thin-walled nut in a woody cup-shaped base)

• HAS PART: cupule, acorn cup -- (cup-shaped structure of hardened bracts at the base of an acorn)

• => tree -- (a tall perennial woody plant having a main trunk and branches forming a distinct elevated crown; includes both gymnosperms and angiosperms)

– HAS SUBSTANCE: sapwood -- (newly formed outer wood lying between the cambium and the heartwood of a tree or woody plant; usually light colored; active in water conduction)

– HAS SUBSTANCE: heartwood, duramen -- (the older inactive central wood of a tree or woody plant; usually darker and denser than the surrounding sapwood)

– HAS PART: stump, tree stump -- (the base part of a tree that remains standing after the tree has been felled)

– HAS PART: crown, capitulum, treetop -- (the upper branches and leaves of a tree)

– HAS PART: tree branch -- (a branch arising from the trunk or a bough of a tree)

– HAS PART: trunk, tree trunk, bole -- (the main stem of a tree; usually covered with bark; the bole is usually the part that is commercially useful for lumber)

• HAS PART: bark -- (tough protective covering of the woody stems and roots of trees and other woody plants)

The Image of the City

• Kevin Lynch, 1960• Interviews about

mental maps• Features

– Paths

– Edges

– Districts

– Nodes

– Landmarks

Map

Tokyo Subway

Wood Samples

Wood Classification

Wood Identification

Primary Color

Whitish Yellowish Purplish orcrimson

Reddish or pinkish Brownish Blackish orgreyish

Rings Distinct ash lacewoodplane

padouk agba afrormosia

maple, bird'seye

oak bubinga cedar, western red cedar of lebanon

pine,poderosa

cherry

elm

iroko

oak, brown

teak

walnut, blackamerican

walnut, circassian

Obscure Poplar zebrawood purpleheart mahogony, african walnut,australian ebony

Avodire antiaris beech paldao

sycamoremaple

birch mahogony,honduras

lime pearwood

satinwood

Navigation

• Animal Navigation

• Complex and Varied

• Two General Types– Egocentric (path, homing, DR)– Allocentric (Cognitive Maps)

• Novel routes

• Short Cuts

• Multiple starting points

Brain Studies

• Hippocampus

• Episodic Memory (egocentric?)

• Semantic memory (allocentric?)

• Brain damage– Damage to the hippocampus causes loss of

navigational ability in rodents and birds– Damage in humans causes anterograde amnesia

Navigation In Information Space

P.P. Maglio and T. Matlock, The Conceptual Structure of Information Space, in A.J. Munro, K. Höök, and D. Benyon, eds., Social Navigation of Information Space, Springer, London, 1999.

People using internet browsers conceive of cognitive space as physical space and construct cognitive maps of that space.

Senses of Wood

lignin

meronymsubstance

plant material

underbrushtree

meronymmember

forest

fingerholethumbhole

bellmouthpiece

meronympart

woodwind golf club

Wood

Hyponyms of Wood

pineoak...

many more

plant

groveold growth

second growth

forest

fluteclarinet

woodwind golf

Wood

Hypernyms of Wood

wood

plant material

material

substance

woodwind

wind instrument

musical instrument

instrument

device

wood

golf club

golf equipment

sports equipment

equipment

instrumentality

artifact

Object

Entity

Treemaps

Shneiderman, B. (2000). Treemaps for Space Constrained Visualization of Hierarchies, http://www.cs.umd.edu/hcil/treemaps/.

The Problem

• Representing Information Visually

• Two-dimensional interface

• Lack of space and resolution

• Visual complexity is no solution

TreeMap Structure

• Representing:• Hierarchy• Values

Disk Contents

Stock Market data

Sports Statistics

Decision-Making Tool

Curriculum Structure

• Major and Minor Topics

• Time Structure (weekly schedule)

• Difficulty

• Test Weight

• Minutes of Lecture

• Other?

Semantic Navigator

Semantic Navigator

Semantic Hierarchy