x P R E F A C E
Einstein's genera l relativit y implie s th e existenc e o f gravitationa l waves . Th e
theory predicts that suc h waves might b e created b y gigantic gravitational disasters .
In th e cas e o f a collaps e o f a pai r o f binar y stars , thes e wave s woul d b e frequenc y
modulated signals , als o named chirps . Ther e is no doubt tha t detectin g such signal s
relies o n describin g an d analyzin g oscillatin g patterns . Thi s importan t topi c i s
discussed i n Chapte r 3 .
The unity betwee n our three chapters is now clear. Beyon d Fourier analysi s an d
its variants, new tools are available. Thes e tools help in understanding an d modelin g
oscillating patterns . Suc h pattern s ar e presen t i n man y natura l images . The y
help i n explainin g nonlinea r evolutions . The y ar e pivota l i n chirp s an d frequenc y
modulated signals .
Let m e expres s my dee p thank s t o th e Departmen t o f Mathematic s o f Rutger s
University. I wa s prou d an d happ y t o giv e thes e thre e Jacquelin e Lewi s Lectures .
Richard Fal k an d hi s colleague s hav e bee n kin d an d helpful .
This book is not a treatise bu t rathe r a n expanded versio n of my informal talks .
It i s not a textbook . Instea d i t i s aime d a t describin g a scientifi c vision .
Am I th e sol e write r o f thi s book ? Thi s i s no t clea r sinc e mos t o f th e fin e
results whic h wil l b e describe d o r prove d belon g t o m y student s o r m y colleagues .
Moreover th e 'gran d unification ' whic h i s unveile d i n thi s essay ca n b e trace d bac k
to a program whic h wa s launched i n the earl y fortie s b y the 'Institut e fo r th e Unit y
of Science ' (se e Sectio n 2 , Chapte r 1).
Let m e than k Alber t Cohe n an d hi s collaborator s fo r lettin g m e includ e som e
still unpublishe d materia l an d fo r hi s encouraging remarks . Naok i Sait o read a first
version o f thi s boo k an d suggeste d man y improvements . Th e anonymou s refere e
was kin d an d helpful .
I woul d lik e t o dedicat e my wor k t o Jacquelin e Lewis . Le t m e als o remembe r
Alberto Calderon . I mis s s o muc h ou r endles s discussion s abou t mathematics ,
literature an d politic s i n Argentina .
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