1
Networks
1.1 Countrie s o f th e insec t world . Imagin e a worl d populate d b y semi -
intelligent insects . Th e worl d o f the insect s i s divided int o smal l countries , eac h
country consistin g o f a fe w citie s connecte d b y dar k narro w tunnels . I n th e
course o f thei r wor k an d leisur e th e insect s slowl y wal k thes e tunnels , an d b y
the tim e the y reac h adulthoo d al l insect s kno w ho w thei r country' s citie s ar e
connected. I f an insec t need s to trave l fro m on e city to another , an d thos e citie s
are directl y connected , the n th e connectin g tunne l i s taken . Mayb e th e rout e
could b e shortene d b y takin g tw o shor t tunnel s throug h anothe r city , bu t th e
insects ar e onl y semi-intelligent , s o thi s possibilit y neve r occur s t o them . An d
the insect s ar e poo r a t measurin g distances , s o the y probabl y couldn' t identif y
a shorte r rout e eve n i t the y looke d fo r it . Lif e o n th e insec t worl d i s cal m an d
uneventful, th e citizen s blissfull y bumpin g alon g i n th e dark , performin g thei r
chores wit h cal m inefficiency .
Let's tak e a close r loo k a t th e worl d o f th e insects . Her e ar e tw o insec t
countries:
Our vie w from th e 'outside ' provide s u s wit h a complet e pictur e o f bot h coun -
tries. Th e insect s ar e confine d t o th e citie s an d tunnels , s o the y mus t expen d
more effor t t o ge t a n accurat e vie w o f th e layout . Suppos e tha t communicatio n
between insec t countrie s take s plac e b y radio. Citizen s fro m th e abov e countrie s
were talking , an d the y bega n t o wonde r i f thei r tw o countrie s ar e th e same .
How ca n the y determin e tha t thei r countrie s hav e differen t layouts ? Firs t the y
observe tha t bot h countrie s hav e fou r citie s and fou r mai n tunnels . S o far, thei r
countries appea r similar . The n on e says , "W e hav e a cit y wit h jus t on e tun -
nel leadin g t o it. " Th e othe r on e says , "AHA ! Al l ou r citie s hav e tw o tunnel s
connected t o them , s o our countrie s ar e no t se t u p th e sam e way. "
1
http://dx.doi.org/10.1090/mawrld/006/01
Previous Page Next Page