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Newtonian Aristotelian physics

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    Science & Education 2 : 345- 362 , 1993 . 1993 Kluwer Academic Publishers. Printed in the Netherlands,N e w t o n i a n i n M i n d b u t A r i s t o t e l i a n a t H e a r t

    M A U R I C E G . E B I S O NConsultant in Physics, Institute of Physics, 47 Belgrave Square, London SW IX 8QX,EnglandA B S T R A C T : T h i s a r ti c le d i s cu s se s s o m e c o r e f e a t u r e s o f A r i s t o t e li a n p h y s ic s , a n d l o o k s a tt h e i r t ra n s f o r m a t i o n b y f i rs t G a l i l e o , a n d t h e n N e w t o n . I t s h o w s h o w t h e A r i s t o t e li a n v ie ww a s r o o t e d i n c o m m o n s e n s e , a n d i n d i c a t e s w h y t h i s i s t h e r e a s o n t h a t s u c h u n d e r s t a n d i n g sp r o v e s o r e s i s t a n t t o p h y s i c s i n s t r u c t i o n . S o m e s u g g e s t i o n s a r e m a d e f o r g u i d i n g e f f e c t i v ep e d a g o g y .

    M o r e o v e r , m e c h a n i c s is t o p h y s i c s w h a t t h e s k e l e t o n is t o t h e h u m a n f i g u r e - a t fi r stg l a n c e i t m a y a p p e a r s t i f f , c o l d , a n d s o m e w h a t g h a s t l y , b u t e v e n a f t e r a b r i e f s t u d y o f i t sf u n c t i o n s o n e e x p e r i e n c e s w i t h m o u n t i n g e x c i t e m e n t t h e d i s c o v e r y o f a n a s t o n i s h i n g l yb e a u t i f u l d e s i g n , o f a s t r u c t u r e t h a t is in g e n i o u s l y c o m p l e x , y e t s o s i m p l e a s t o b e a l m o s ti n e v i t a b l e . ( G e r a l d H o l t o n , Introduction to Concepts and Theories In Science)M e c h a n i c s is o n e o f t h e b r a n c h e s o f p h y s i cs i n w h i c h t h e n u m b e r o f p r i n c i p le s is a t o n c ev e r y f e w a n d v e r y r ic h i n u se f u l c o n s e q u e n c e s . O n t h e o t h e r h a n d , t h e r e a r e f e w s c ie n c e sw h i c h h a v e r e q u i r e d s o m u c h t h o u g h t - t h e c o n q u e s t o f a fe w a x io m s h a s t a k e n m o r et h a n 2 0 0 0 y e a rs . ( R e n e D u g a s , A History of Mechanics)A l t h o u g h i t i s u n s a f e t o r e a d l o g i c a l n e c e s s i t y i n t o p a r t i c u l a r h i s t o r i c a l d e v e l o p m e n t s , t h es p e ci a l p o s i t io n o c c u p i e d b y m e c h a n i c s a m o n g s t t h e o t h e r b r a n c h e s o f p h y si c s a n d n a t u r a ls c i e n c e m u s t b e e m p h a s i s e d , f o r i t w a s t h i s s p e c i a l p o s i t i o n t h a t m a d e i t t h e s t a r t i n g p o i n to f m o d e r n s c i e n ce . ( S . S a m b u r s k y , The Physical World of the Greeks)T h e r e i s , i n n a t u r e , p e r h a p s n o t h i n g o l d e r t h a n m o t i o n , c o n c e r n i n g w h i c h t h e b o o k sw r i t t e n b y p h i l o s o p h e r s a r e n e i t h e r f e w n o r s m a l l ; n e v e r t h e l e s s I h a v e d i s c o v e r e d b ye x p e r i m e n t s o m e p r o p e r t i e s o f i t w h i c h a r e w o r t h k n o w i n g a n d w h i c h h a v e n o t h i t h e r t ob e e n e i t h e r o b s e r v e d o r d e m o n s t r a t e d . ( G a l i l e o G a l i l e i , Dialogues Concerning Two NewSciences)O f t h e i n t el l e c tu a l h u r d l e s w h i c h th e h u m a n m i n d h a s c o n f r o n t e d a n d h a s o v e r c o m e i nt h e l a s t f i ft e e n h u n d r e d y e a rs , t h e o n e w h i c h s e e m s t o m e t o h a v e b e e n t h e m o s t a m a z i n gi n c h a r a c t e r a n d t h e m o s t s t u p e n d o u s i n t h e s c o p e o f i t s c o n s e q u e n c e s i s th e o n e r e l a t i n g t ot h e p r o b l e m o f m o t i o n . ( H e r b e r t B u t t e r fi e l d , The Origins of Modern Science: 1300-1800)I n t h e B e g i n n i n g w as M e c h a n i c s . ( M a x y o n L a n e , History o f Physics)I o f f e r t h i s w o r k a s t h e m a t h e m a t i c a l p r i n c i p l e s o f p h i l o s o p h y , f o r t h e w h o l e b u r d e n o fp h i l o s o p h y s e e m s t o c o n s i s t i n t h is - f r o m t h e p h e n o m e n a o f m o t i o n s t o i n v e s t ig a t e t h ef o rc e s o f n a t u r e , a n d t h e n f r o m t h e s e f o r ce s t o d e m o n s t r a t e t h e o t h e r p h e n o m e n a . ( I s aa cN e w t o n , P r e f a c e t o t h e Principia)

    I N T R O D U C T I O N

    M e c h a n i c s , b o t h h i s t o r i c a l l y a n d l o g i c a l l y , r e p r e s e n t s t h e f o u n d a t i o n o fp h y s i c s a n d t h e k e y t o p i c i n m e c h a n i c s i s t h e s t u d y o f m o t i o n b e c a u s ef r o m e a r l y t i m e s s c i e n t i s t s h a v e h e e d e d t h e a x i o m :

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    346 MAURICE G. EBISONignorato motu, ignoratur natura.

    The motion of heavenly bodies was one of the first pre-occupations ofhuman thought in the great civilisations of Egypt and Babylon. For exam-ple, in Egypt the changing seasons were related to the rising of certainprominent stars. In Babylon the observation of eclipses played a vital rolein astronomy. From the beginning of the second millenium the positionsof heavenly bodies was systematically recorded and from about 600 B.C.Babylonian astronomers used the records to develop highly complex andamazingly accurate mathematical methods of describing the motions ofthe heavenly bodies to predict eclipses. Their methods, however, remainedessentially empirical and it was left to the Greeks to begin the developmentof a rational structure.Whilst the Greeks successfully developed the principles of statics thoseof dynamics were obscured by incorrect concepts until the end of theMiddle Ages. There then followed the rapid development of dynamics inthe hands of Kepler, Galileo, Descartes, and Newton and the codificationof its laws by mathematicians such as Euler, Lagrange and Laplace. Sosuccessful was the process that by the end of the n ineteenth century therewas a general belief that the structure was complete and perfect. But thisbelief was shattered by the appearance of two supreme but unforeseendevelopments of classical mechanics - relativistic mechanics and wavemechanics.Whilst our main concern will be almost exclusively with dynamics it isinteresting to recall that Archimedes was able to construct a rationalscheme for statics which became the most complete branch of ancientmathematical physics and reached a standard which was not approachedin other sciences.The first of his works On the Equ i l ibr ium o f P lanes dealswith the statics of rigid bodies in a way reminiscent of a geometry text-book. His second, On Floa ting Bod ies , laid the foundations of hydrostat-ics.

    GREEK DYNAMICSWhereas Archimedes' work in statics has been of lasting value the workof the Greeks in dynamics was not anywhere near as successful. Neverthe-less we need to consider it because it was based on the ideas of Aristotle,who exerted vast influence on views of the physical universe for sixtygenerations. No other personality in science had so deep and long-lastingeffect on subsequent thought. His dynamics is the key to understandinghow physics developed in the Middle Ages and thus to an understandingof the difficulties which modern science initially had to face.

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    N E W T O N I A N IN M I ND B U T A R I S T O T E L I A N A T H E A R T 3 47ARISTOTLE ON MOTIONI n h is t h e o r y o f m o t i o n A r i s t o t l e d i s ti n g ui s h es t h r e e t y p e s o f m o t i o n b u to n l y t w o o f t h e m a r e s i g n i f ic a n t f o r p h y s i c s . T h e f ir st o f t h e s e i s natura lm o t i o n w h i c h is f o l lo w e d b y b o d i e s u n d e r t h e i n f l u e n c e o f f o r c e s f o u n dw i t h i n th e b o d y i ts e lf . T h r e e f o r m s o f n a t u r a l m o t i o n c a n b e o b s e r v e d .T h e r e i s t h e d o w n w a r d fa ll o f h e a v y b o d i e s a n d t h e u p w a r d m o t i o n o fl ig h t b o d i e s l ik e s m o k e a n d f i re . W h e n t h e r e a r e n o e x t e r n a l o b s t a c le s t ot h e m o t i o n , b o d i e s s e e k t h e i r o w n ' n a t u r a l p l a c e ' . F o r h e a v y b o d i e s th isis t h e c e n t r e o f t h e e a r t h w h i l s t f o r f ir e , f o r e x a m p l e , i t is a s p h e r i c a l s h e l lj u s t b e l o w t h e f ir st o f t h e c e l e s t i a l s p h e r i c a l s h e ll s . T h e t h i r d t y p e o fn a t u r a l m o t i o n is th e r o t a t i o n o f h e a v e n l y b o d i e s . T h i s a l so r e su l ts f r o mi n t e r n a l f o r c e s b u t d i ff e rs f r o m t h e t e r r e s t r i a l m o t i o n s i n b e i n g e t e r n a l a n du n c h a n g e a b l e . T h e o t h e r c a t e g o r y o f m o t i o n s ig n if ic a n t f o r p h y s ic s isf o r c e d m o t i o n w h i c h i s t h e m o t i o n o f a n o b j e c t w h i c h is n o t t o w a r d i t sn a t u r a l p l a c e . S u c h m o t i o n i s a l w a y s c a u s e d b y a n e x t e r n a l f o r c e a n d a st h e f o r c e in c r e a s e s t h e s p e e d ( n o t e , sp eed n o t a c c e l e r a t i o n ) o f t h e m o t i o ni n c re a s e s . W h e n t h e f o r c e is r e m o v e d t h e m o t i o n m u s t s t o p . T h i s t h e o r yis in a c c o r d w i t h o u r e v e r y d a y e x p e r i e n c e s o f s h i ft in g o b j e c t s s u c h a s t a b l e sa n d d e s k s a c r o s s t h e f l o o r .

    S o all m o t i o n r e q u i r e d a m o v i n g f o r c e , e i t h e r in t e r n a l o r e x t e r n a l , a n dt h e A r i s t o t e l i a n d o c t r i n e o f i n e r t i a w a s a d o c t r i n e o f r e s t . I t w a s m o t i o n ,n o t r e s t , th a t h a d a l w a y s t o b e e x p l a i n e d ; t h e m o d e r n r e c o g n i t i o n o fi n e r ti a l m o t i o n a s t h e u n i f o r m a n d s t ra i g h t fi n e m o t i o n o f a b o d y w i t h o u tt h e a c t i o n o f f o r c e w a s c o m p l e t e l y a l i e n t o A r i s t o t l e . F o r h i m , w h e r e v e rm o t i o n e x i s t e d a n d n o m a t t e r h o w l o n g i t h a d e x i s t e d , a f o r c e h a d s o m e -h o w t o b e i n t r o d u c e d t o a c c o u n t f o r it .

    ARISTOTLE'S MOD EL OF TH E UNIVERSEA r i s t o t l e i n c o r p o r a t e d h i s b a s ic i de a s o n m o t i o n i n t o a m o d e l o f t h eu n i v e r s e . W i t h t h e e a r t h a s a f ix e d s p h e r e a t t h e c e n t r e h e d i v i d e d hi su n i v e r s e i n t o a s u b - l u n a r , o r t e r r e s t r i a l r e g i o n a n d a c e l e s t ia l r e g i o n . A l lt e r re s t r i a l m a t t e r w a s c o m p o s e d o f o n e o r m o r e o f f o u r e l e m e n t s , earth,water, air a n d f ire a n d e a c h e l e m e n t h a d i ts n a t u r a l p la c e i n t h e f o r m o fc o n c e n t r i c s p h e r e s s t ar t in g w i t h e a r t h a n d w i t h s u cc e s si v e s u r r o u n d i n gs p h e r e s o f w a t e r , a i r, a n d f ir e . In a c t u a l f a c t , t h e e l e m e n t s a n d b o d i e sm a d e u p o f t h e m a r e c o n s t a n t l y b e i n g s h i ft e d fr o m t h e i r n a t u r a l p o s i t i o nsb y t h e a p p l i c a t i o n o f a fo r c e . A n e l e m e n t r e si st s d i s p l a c e m e n t b u t o n c ed i s p l a c e d i t s e e k s t o r e t u r n t o i t s n a t u r a l p o s i t i o n b y t h e s h o r t e s t p o s s i b l ep a t h . S o fi re w o u l d t e n d t o r is e t h r o u g h A i r a n d A i r t h r o u g h W a t e r ,w h e r e a s E a r t h w o u l d t e n d t o fa ll t h r o u g h b o t h A i r a n d W a t e r . T h e a c t u a lm o v e m e n t o f a n y re a l o b je c t w o u l d d e p e n d b o t h o n t h e m i x t u r e o f t h ef o u r e l e m e n t s m a k i n g i t u p a n d w h e r e i t w a s i n r e l a t i o n t o i t s n a t u r a lp l ac e . A g o o d d e a l o f c o m m o n s e n s e e x p e r i e n c e s u p p o r t e d t h is v i e w . F o r

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    348

    /M A U R I C E G . E B I S O N

    ~ Primum M obile

    Diagram of medieval conce pt of wo rld structure.

    e x a m p l e , W a t e r b u b b l e s u p t h r o u g h t h e E a r t h i n s p ri n gs . W h e n s u ff ic i en tf ir e is a d d e d t o W a t e r , b y h e a t i n g i t , t h e r e s u l ti n g m i x t u r e o f e l e m e n t s ,w h i c h w e n o w c a l l s t e a m , r i s e s t h r o u g h t h e A i r .I n t h e c e l e s t i a l r e g i o n b o d i e s , s u c h a s s t a r s a n d p l a n e t s , w e r e s u p p o s e dt o m o v e in a f a r si m p l e r m a n n e r t h a n o b j e c t s n e a r t h e E a r t h . T h e c e l e st ia lb o d i e s w e r e b e l i e v e d n o t t o c o n ta i n a n y o f t h e f o u r o r d i n a r y e l e m e n t s b u ti n s t ead co n s i s t ed s o l e l y o f a f if th e l em en t ca l l ed ether ( in l a t e r t i m es ca l l edth e quintessence f r o m quinta essentia t h e " f i f t h e s s e n c e " ) . T h e n a t u r a lm o t i o n o f t h e s e b o d i e s w a s n e i t h e r r i s in g n o r f a ll in g , b u t e n d l e s s r e v o l u t i o ni n ci rc l es a r o u n d t h e c e n t r e o f t h e u n i v e r s e - t h e c e n t r e o f t h e e a r t h .C e l e s t i a l b o d i e s , a l t h o u g h m o v i n g , w e r e t h u s a t a l l t i m e s i n t h e i r n a t u r a lp l a c e s a n d t h i s s e t t h e m a b s o l u t e l y a p a r t f r o m o b j e c t s i n t h e t e r r e s t r i a lr e g io n w h i c h m o v e d i n n a t u ra l m o t i o n o n l y w h e n t h e y r e t u r n e d t o t h ei rn a t u r a l p l a c e s f r o m w h i c h t h e y h a d b e e n d i s p l a c e d .

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    N E W T O N I A N IN M I ND B U T A R I S T O T E L I A N A T H E A R T 3 49AREAS OF DIFFICULTYT h o u g h t h e t h e o r y s e e m e d t o e m b r a c e a v e r y w i d e ra n g e o f p h e n o m e n at h e r e w e r e , o f c o u r s e , o n e o r t w o a r e a s o f d if fi c ul ty . F o r e x a m p l e , i f as t o n e i s t h r o w n i t i s n o t e a s y t o a c c o u n t f o r it s m o t i o n o n c e i t h a s l e f t t h eh a n d f o r t h e s t o n e ' s i n t e r n a l f o r c e c o u l d o n l y m a k e i t m o v e i n i t s n a t u r a lm o t i o n v e r t i c a ll y d o w n w a r d s . I t m i g h t b e s a id , h o w e v e r , t h a t t h e t h e o r yg a i n e d s t r e n g t h f r o m t h e i n g e n u i t y w h i c h A r i s t o t e l i a n s d i s p l a y e d in b r in g -i n g t h e d i f f ic u l t c a s e s w i t h i n t h e g e n e r a l s w e e p o f t h e s c h e m e . I n t h e c a s eo f th e t h r o w n s t o n e t h e c o n t i n u e d f o r w a r d m o t i o n w a s e x p l a i n e d a s b e i n gd u e t o t h e c o m m o t i o n o f . t h e a i r w h i c h t h e in i t ia l m o v e m e n t o f t h e h a n dh a d p r o d u c e d a n d t h is w a s p a s s e d f r o m l a y e r t o n e i g h b o u r i n g l a y e r . Inp a r t i c u l a r , t h e m o t i o n c o n t i n u e d b e c a u s e a i r in f r o n t o f t h e s t o n e w a sc o m p r e s s e d a n d r u s h e d r o u n d t o th e b a c k t o p r e v e n t t h e v a c u u m t h a t o nn o a c c o u n t c o u l d b e a l l o w e d t o f o r m . A s e c o n d d i ff ic u l t y w a s t h a t f a l li n gb o d i e s w e r e s e e n t o a c c e l e r a t e . T h i s w a s e x p l a i n e d b y s a y in g t h a t t h e ym o v e d m o r e j u b i la n t ly a s t h e y n e a r e d t h e i r n a t u r a l p l a ce .

    N o w i t is i m p o r t a n t t o a p p r e c i a t e t h a t t h e A r i s t o t e l ia n t e a c h i n g o nm o t i o n h a d g r e a t p s y c h o l o g i c a l s t r e n g t h . T h e r e w a s a v e r y c lo s e in t e r -l o c k i n g o f o b s e r v a t i o n s a n d e x p l a n a t i o n s w h i c h c o v e r e d , w i t h o u t t o o m u c hd i ff ic u l ty , a n i m m e n s e r a n g e o f c as e s w h i c h w e r e a c c e ss i bl e t o o b s e r v a t i o n sa t t h a t t i m e . I n a d d i t i o n , t h e t h e o r y o f m o t i o n w a s f u r t h e r b u t t r e s s e d b yb e i n g a p a r t o f a m u c h w i d e r s y s t e m t h a t w a s a n i n t e l le c t u a l tour de forcei n it s l o g i c a l c o h e r e n c e . I t is n o t s u r p r i s i n g , t h e r e f o r e , t h a t i t p r o v e de x t r e m e l y d if fi c ul t f o r t h e h u m a n m i n d t o e s c a p e f r o m i ts g r ip .

    SHOULD ARISTOTLE HAV E ANTICIPATED NEW TON?I t is b o r d e r i n g o n t h e a b s u r d t o s u g g e st t h a t i f o n l y A r i s t o t le h a d l o o k e da t t h i ng s m o r e c l o s e ly h e w o u l d h a v e b e a t e n N e w t o n b y s o m e t w o t h o us -a n d y e a r s i n p u t t i n g f o r w a r d t h e m o d e r n v i e w o f i n e r ti a l m o t i o n t h a tb o d i e s c o n t i n u e i n a s t a t e o f r e s t o r i n m o t i o n a l o n g a s t r a i g h t li n e u n le s sa c t e d u p o n b y a n e x t e r n a l f o r c e . I t is in f a c t e x t r e m e l y d if fi cu l t t o e s c a p ef r o m t h e A r i s t o t e l i a n s c h e m e b y o b s e r v a t i o n a l o n e . F o r e x a m p l e , i t iss o m e t i m e s s u g g e s t e d t h a t m o d e r n s c i e n c e s t a r t e d w h e n G a l i l e o o b s e r v e de x p e r i m e n t a l l y th a t t w o b o d i e s o f u n e q u a l w e i g h t re l e a s e d f r o m t h e t o po f t h e L e a n i n g T o w e r o f P i s a, s t r u c k t h e g r o u n d a t e x a c t ly t h e s a m e t i m e .A s i d e f r o m t h e p o i n t t h a t i t is u n l i k e l y t h a t t h i s p a r t i c u l a r e x p e r i m e n t w a se v e r p e r f o r m e d b y G a l i l e o , t h e f a c t is t h a t i n th e e v e r y d a y w o r l d s o m eh e a v y b o d i e s d o f al l f a s t e r t h a n s o m e l i g h t e r o n e s .I t w a s n a t u r a l f o r A r i s t o te l i a n s t o f o c u s o n b o d i e s f a i li ng t h r o u g h ar e si s ti v e m e d i u m s u c h a s a i r o r w a t e r f o r t hi s is th e k i n d o f m o t i o n t h a tw e c o m m o n l y o b s e rv e . T h e r e s i s ta n c e o f t h e m e d i u m c o u l d ex p l ai n inq u a l i t a ti v e t e r m s w h y , f o r e x a m p l e , a l e a f f al ls m o r e s lo w l y t h a n a b o u l d e r .A r i s t o t e l i a n s w o u l d h a v e c o n s i d e r e d u n r e s i s te d m o t i o n a s a n u n r e a li s t i c

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    3 5 0 M A U R I C E G . E B I S O Na b s t r a c t i o n . I n d e e d A r i s t o t l e h i m s e l f d i d e x p li c it ly a r g u e t h a t i n a v a c u u m ,w h e r e t h e r e s i st a n c e to m o t i o n w o u l d b e z e r o , all b o d i e s w o u ld m o v e w i t ht h e s a m e s p e e d a n d h e t o o k t h i s a s a p i e c e o f e v i d e n c e th a t a v a c u u mc o u l d n o t e x i s t .A r i s t o t l e a n d h is s u c c e ss o r s d i d n o t o b s e r v e l es s t h a n , s a y , G a l i l e o ;r a t h e r t h e y v i e w e d t h in g s f r o m a d i f f e r e n t s t a n d - p o i n t a n d t h is w a s n o tb e c a u s e t h e y w e r e l e ss i n te l li g e n t b u t s im p l y b e c a u s e t h e r a t h e r m o r eq u a n t i t a t i v e a p p r o a c h o f G a l i l e o w a s i r r e l e v a n t t o t h e i r w o r l d - v i e w . F o rt h e m i t w a s n o t s u f fi c ie n t t h a t a t h e o r y s h o u l d m e r e l y d e s c r i b e a n d p r e d i c tt h e f a c ts o f o b s e r v a t i o n ; i t m u s t , a b o v e a ll , g i v e t h e m m e a n i n g i n a m u c hw i d e r s e n s e b y s h o w i n g t h e f a c ts t o b e c o n s i s t e n t w i t h a n d p a r t o f ac o m p l e t e p h i l o s o p h ic a l s y s t em . T o t h e A r i s to t e l i a n o f t h e l a t e s i x te e n t hc e n t u r y th e t h e o r y b a s e d u p o n e l e m e n t s a n d n a t u r a l m o t i o n w a s p h i lo -sophica l ly t r u e , c l e a r a n d c e r t a i n , p r e c i s e l y b e c a u s e i t w a s p a r t o f a s at is fy -i n g o v e r a l l s c h e m e w h i c h r e a c h e d a c r os s m a n y f ie ld s o f s t u d y . I n h i s v i e wt h e t h e o r y c o u l d n o t b e a b a n d o n e d s im p l y b e c a u s e t h e d e t a i l e d m o t i o n o ft w o w e i g ht s d r o p p e d f r o m a t o w e r a p p e a r e d n o t t o b e i n ac c o r d w i t ht h e s c h e m e w h i c h w a s s o m u c h g r a n d e r t h a n a n i n s i g n i f i c a n t a r t i f i c i a l' e x p e r i m e n t ' .

    THE NEED FOR A TRANSPOSITION WITHIN THE M INDW h a t w a s n e e d e d w a s a t r an s p o s i t io n w i th i n th e m i n d o f th e o b s e r v e r ; inr e a l li fe w e s im p l y d o n o t h a v e p e r f e c t l y s m o o t h s p h e r e s m o v i n g o np e r f e c t l y s m o o t h h o r i z o n t a l p la n e s n o r d o w e s e e o r d i n a r y o b j e c ts c o n t in u -i n g f o r e v e r in r e c t i li n e a r m o t i o n i n e m p t y s p a c e . T h e r e a l g e n i u s o f G a l i -l e o , o f c o u r s e , w a s t h a t i t o c c u r r e d t o h i m to imagine s u c h o b j e c t s a sg e o m e t r i c a l e n t it ie s m o v i n g i n a n i d e a l w o r l d . H i s i m p o r t a n t c o n t r i b u t i o nt o p h y s i c s , i n th e f i r st i n s t a n c e a t l e a s t , w a s n o t i n p r o d u c i n g f r e s h o b s e r -v a t i o n s o r n e w e v i d e n c e b u t r a t h e r i n c o n v i n c i n g p e o p l e t h a t a tr a n s p o s i -t i o n w i t h i n t h e m i n d w a s n e e d e d . T h i s i s a l w a y s a s u p r e m e l y d i f fi cu l t t a s kb e c a u s e n o m e n t a l a c ti v it y is h a r d e r t h a n b e i n g a s k e d t o h a n d l e t h e s a m es e t o f d a t a w i t h i n a c o m p l e t e l y d i f f e r e n t f r a m e w o r k . Y e t i t is a ls o as u p r e m e l y i m p o r t a n t t a s k b e c a u s e s c ie n c e is m u c h m o r e t h a n l o t s o f fa c tsf i tt e d i n t o a p r e - d e t e r m i n e d p a t t e r n . I t i n v o l v e s t h e a t t e m p t t o f a s h i o n as y s t e m w h i c h w i ll r e l a t e a n d o r d e r t h e s e f a ct s .

    GALILEO CRITICISES ARISTOTLEA l t h o u g h t h e A r i s to t e l ia n s y s t em w a s s u b j e c t, o f c o u r s e , t o a g o o d d e a lo f c ri t ic a l a n a l y s i s o v e r t h e y e a r s w i t h r e g a r d t o c e r t a i n d e t a i l s it w a s , b ya n d l a r g e , t h e s y s t e m t h a t G a l i l e o w a s t a u g h t a t t h e U n i v e r s i t y o f P i s a.I n d e e d h e s t a r t e d h is s c ie n ti fi c c a r e e r i n t h e w a y t h a t w a s c u s t o m a r y a tt h a t t i m e , b y a n n o t a t i n g A r i s t o t l e ' s De Caelo . N e v e r t h e l e s s , h e w a s n o t

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    N E W T O N I A N IN M IN D B U T A R I S T O T E L I A N A T H E A R T 351l o n g i n c a u s in g a s c a n d al b y p e r f o r m i n g e x p e r i m e n t s o n t h e m o t i o n o ft e r re s t r ia l o b j ec t s . R e a s o n i n g f r o m t h e r e s u lt s o f t h e s e e x p e r i m e n t s , h ew a s a b l e t o p o i n t o u t e r r o r s a n d m i s c o n c e p t i o n s i n t h e A r i s t o t e l i a n i d e a so n m o t i o n , p a r t i c u l a r ly i n t h e f r e e f a ll o f o b j e c t s , in p r o j e c t i l e m o t i o n a n di n t h e c o n c e p t s o f ' n a t u r a l ' a n d ' v i o l e n t ' m o t i o n t h e m s e l v e s a n d i n sod o i n g h e l a id t h e b a s is f o r m o d e r n k i n e m a t i c s .

    THE IMPORTANCE OF ANALYSISA n o t h e r f e a t u r e o f t h e g e n iu s o f G a l i le o w a s t h a t h e r e a l i s e d th a t a ne x p e r i m e n t a l r e s u l t h a d t o b e v e r y c a r e fu l l y a n a l y s e d i f i t w a s t o f o r m t h eb a s is f o r a t h e o r y - a c a su a l f ir st g l a n c e w a s n o t e n o u g h . S o i f d i f f e r e n tb o d i e s a r e r e l e a s e d s i m u l t a n e o u s ly t o f a ll f r e e l y f r o m t h e t o p o f a t o w e ra n d d o not a r r i v e a t e x a c t l y t h e s a m e i n s t a n t a t t h e b o t t o m , t h i s o n c a r e f u lc o n s i d e r a t i o n t u r n s o u t t o b e f a r le s s s i g n if ic a n t t h a n t h e f a c t th a t t h e yvery nearly d o a r r i v e a t t h e s a m e i n s t a n t . I n a v a c u u m t h e t i m e s o f f a llwould b e e q u a l . A f o c u s o n t h is c o n c e p t i o n i s f r u i tf u l b e c a u s e i t r e g a r d st h e f a i lu r e o f p r e c i s e l y s im u l t a n e o u s a r r iv a l s a s a minor d i s c r e p a n c y in s t e a do f a major f a c t r e q u i r i n g e x p l a n a t i o n i n t e r m s o f r e s i s t e d m o t i o n a n d i tm a r k s a fu n d a m e n t a l l y d i f f e r e n t v i e w p o i n t f r o m t h a t o f t h e A r i s t o te l ia n s .I n G a l i l e o ' s t i m e , o f c o u r s e , a v a c u u m w a s a n u n a t t a i n a b l e i d e a l i s a t io nb u t G a l i l e o s h o w e d t h a t a n a n a l y s is a r is i n g f r o m t h i s i d e a l is a t i o n w a sc a p a b l e o f g i v in g a n e w a n d m o r e f r u i tf u l u n d e r s t a n d i n g o f t h e r e a l w o r l d .I n e x a m i n i n g G a l i l e o ' s a t t i t u d e t o e x p e r i m e n t s G e r a l d H o l t o n r e m i n d s u so f t h e o l d q u i p :

    Science has grown almost more by w hat it has learned to ignore than by w hat it has hadto take into account

    THE SEARCH FOR UNDERLYING SIMPLICITYG a l i l e o ' s t h e o r y i s m o r e u s e f u l th a n A r i s t o t l e ' s t o t h e p r o g r e s s o f p h y s i c snot s o m u c h b e c a u s e i t r e p r e s e n t s o b s e r v a t i o n a l e x p e r i e n c e m o r e p e r f e c t l yb u t r a t h e r b e c a u s e i t r e a c h e s b e h i n d a n y s u p e r f i c i a l r e g u l a r i t y s h o w n b yt h e s e n s e s t o a u n d e r l y i n g b u t h i d d e n a s p e c t o f t h e w a y i n w h i c h t h e w o r l dw o r k s . T h i s is a r e c u r r i n g t h e m e i n s c i e n c e - t h e n e e d t o s e a r c h b e h i n dt h e i m m e d i a t e c o n f u s i o n o f a p p e a r a n c e s f o r a n u n d e r l y i n g s i m p li ci ty ex -p r e s s i b l e in m a t h e m a t i c a l l aw s . I n t h is p a r t i c u l a r w o r k o f G a l i l e o it w a se a s i e r t o c o u n t e r a c t th e A r i s t o t e l i a n h y p o t h e s i s t h a t s p e e d o f fa ll is p r o -p o r t i o n a l t o w e i g h t b y r e a s o n i n g i n a t h o u g h t e x p e r i m e n t t h a n b y p e r f o r -m i n g e x t e n s iv e e x p e r i m e n t s w h i c h a t t h a t t i m e w o u l d n o t h a v e b e e n w h o l l yc o n v i n c i n g . I t w o u l d h a v e b e e n f u ti le t o e x p e c t to g e t t o t h e c o r r e c t re s u l tb y u si n g th e o b s e r v a t i o n a l m e t h o d s a n d t h e t e ch n i c a l e q u i p m e n t t h e n

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    3 5 2 M A U R I C E G . E B I S O N

    Fo r each angle, the acceleration was found to be constant.

    a v a i la b l e . I n s t e a d , e v e r y t h i n g d e p e n d e d o n G a l i l e o ' s a b il it y t o ' t h i n k a w a y 't h e a i r a n d i ts e f f e c t s o n f r e e f a ll .

    RIGOROUS TREATMENT OF M OTIONI n d e a l i n g w i t h t h e m o t i o n o f f r e e l y f a ll in g b o d i e s G a l i l e o h a d a la r g e ro v e r a l l p l a n i n m i n d . T h i s w a s t o p r o d u c e a r i g o r o u s , m a t h e m a t i c a l a n dg e n e r a l t r e a t m e n t o f t h e m o t i o n o f o b je c ts . H e b e g i n s b y m a k i n g t w od i s t in c t s u g g e s ti o n s . T h e f ir st is t h a t ' u n i f o r m a c c e l e r a t i o n ' i s t o b e d e f i n e da s e q u a l c h a n g e s i n s p e e d A v i n e q u a l t imes At. N o w G a l i l e o k n e w f r o mh i s e a r l y s t r u g g l e s w i t h t h e c o n c e p t o f a c c e l e r a t i o n t h a t i t w a s f a r f r o mo b v i o u s t h a t t h i s i s t h e on ly p o s s i b l e d e f i n i t i o n . H e c o u l d h a v e c h o s e ne q u a l s p e e d c h a n g e s A v i n e q u a l distances As. The c h o i c e s i m p l y t u r n e do n w h i ch d e f i n it io n t u r n e d o u t t o b e t h e m o r e usefu l i n d e s c r i b i n g r e a l ,o b s e r v a b l e m o t i o n s i n n a t u r e . T h e s e c o n d s u g g e s t i o n is t h a t b o d i e s a c t u a l lydo f a ll w i t h u n i f o r m a c c e l e r a t i o n . T h i s w a s a p u r e h y p o t h e s i s f r o m w h i c hh e d e d u c e d s o m e c o n s e q u e n c e s w h i c h c o u ld b e t e s t e d e x p e r im e n t a l l y .T h i s w a s n o t e a s y b e c a u s e w i t h t h e i n s t r u m e n t s a v a i l ab l e t o h i m a t t h a tt i m e i t w a s n o t p o s s i b l e t o p e r f o r m t h e t e st s o n f r e e l y f a ll in g b o d i e sdirectly. G a l i l e o t h e r e f o r e a r g u e d t h a t h is h y p o t h e s i s w o u l d b e c o n f i r m e di t i t w e r e t o b e s u c c e s s f u l i n d e s c ri b i n g a n o t h e r k i n d o f m o t i o n r e l a t e d t of r e e f a l l - t h e r o l l in g o f a b a l l d o w n a n i n c l i n e d p l a n e .

    GALILEO AND INCLINED PLANESA b a ll w a s r o ll e d d o w n a g r o o v e d p l a n k l i n ed w i th s m o o t h p a r c h m e n t a n dh e l d a t d i f f e r e n t in c l in a t io n s . T h e t i m i n g w a s d o n e w i t h a s im p l e w a t e rd o c k . O f c o u r s e , e v e n i n th e s e d i l u t e d g ra v i ty e x p e r i m e n t s i t w a s n o tp o s s i b l e t o t e s t directly w h e t h e r A v / A t i s c o n s t a n t , b e c a u s e t h i s n e e d e dd i r e ct m e a s u r e m e n t s o f i n s ta n t a n e o u s v e lo c i ti e s. B y a n i n g e n i o u s a r g u -m e n t G a l i l e o w a s a b l e t o s h o w t h a t fo r uni fo rmly accelerated mo t ion fr omrest the distance travelled is pro po rtion al to the square o f the t ime. T h i sw a s t h e r e s u l t o b t a i n e d f r o m t h e e x p e r i m e n t s .

    B y e x t r a p o l a t i o n ( o f t e n v e r y d a n g e r o u s ! ) f r o m t h e s m a l l a n g le i n cl in a -

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    N E W T O N I A N I N M I N D B U T A R I S T O T E L I A N A T H E A R T 353

    J

    G a l i l e o ' s e x t r a p o l a t i o n .

    t i o n s t o s t e e p e r a n d s t e e p e r o n e s u p t o n i n e t y d e g r e e s G a l i l e o a r g u e d t h a ti n ver t i ca l f al l b o d i e s w o u l d m o v e w i t h u n i f o r m a c c e l e r a t i o n .

    I t is n o t d i ff ic u l t, o f c o u r s e , t o c r i t ic i s e G a l i l e o ' s a r g u m e n t . F o r e x a m p l e ,i f t h e r u n w a y i s t i l t e d m o r e a n d m o r e t o w a r d s t h e v e r t ic a l , t h e b a l l w i lls t a r t t o s l i p a s w e l l a s r o l l a n d t h e s i m p l e t h e o r e t i c a l r e l a t i o n s h i p w i l l n ol o n g e r h o l d .

    I t is n o t c l e a r w h e t h e r G a l i l e o a c t u a l l y d id a l l t h e e x p e r i m e n t s h i m s e l fo r w h e t h e r h e w a s q u o t i n g f r o m t h e w o r k o f e a r l ie r in v e s t ig a t o rs . I n a n yc a se , b y t h e . v e r y n a t u r e o f t h e e x p e r i m e n t s t h e m e a s u r e m e n t s w e r e v e r ya p p r o x i m a t e . T h i s d i d n o t w o r r y G a l i l e o s i n c e h e w a s a l r ea d y c o n v i n c e dt h a t h e k n e w t h e c o r r e c t la w .

    G a l i l eo w e n t o n t o gu e s s t h a t i f a b a l l ro l l s d o w n a n i n c l i n e , A , a n d u pa n o t h e r c o n n e c t e d i n c l i n e , B , i t w i ll r o l l u p t o t h e o r i g i n a l h e i g h t a n d t h i sw o u l d b e t r u e f o r a n o t h e r i n i ti a l i n c l i n e , A ' , o f t h e s a m e v e r t i c a l h e i g h t ,h ( s e e d i a g r a m o n n e x t p a g e ) .

    F r i c t i o n , o f c o u r s e , p r e v e n t e d a s a t i s fa c t o r y d e m o n s t r a t i o n o f th is i d e ab u t G a l i l e o u s e d a j u d i c io u s m i x t u r e o f e x p e r i m e n t a n d t h i n k i n g - h eh a d a g e n i u s f o r m a k i n g i n t ui t iv e g u e s se s o n t h e b a si s o f a p p r o x i m a t ee x p e r i m e n t a l r e s u l t s .O n e i n t e r e s t i ng f u r t h e r d e v e l o p m e n t o c c u r r e d to G a l i l eo . H e a s k e dh i m s e l f w h a t w o u l d h a p p e n i f s l op e B w a s m a d e m o r e a n d m o r e s h al lo wu n t i l in t h e e x t r e m e c a s e i t w a s h o r i z o n t a l ( B ' ) . I n t h a t c a s e , G a l i l e oa r g u e d , t h e b a l l w o u l d c o n t i n u e a l o n g t h e h o r i z o n t a l s u r fa c e f o r e v e r.N o w a t f i rs t s ig h t th i s i d e a m i g h t a p p e a r t o c o n t a i n t h e e s s e n c e o f N e w t o n ' s

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    354 M A U R I C E G . E B I S O N

    Galileo's guess on 'ideal' dow nhill-uphill mo tion.

    B

    Galileo's thought experiment.

    Earth

    Galileo's 'horizontal' plane.

    F i r s t L a w o f M o t i o n . B u t i t w a s o n l y t h e f ir st s t e p t o w a r d s a f ul l u n d e r -s t a n d i n g o f t h e c o n c e p t o f i n e r ti a b e c a u s e f o r G a l i l e o a h o r i z o n t a l p l a n ew a s o n e f o r w h i c h e v e r y p o i n t w a s e q m d i s t a n t f r o m t h e c e n t r e o f t h eE a r t h , t h a t i s , i t w a s a k i n d o f s p h e r i c a l s h e l l p a r a l l e l t o t h e E a r t h ' ss u r f a c e .

    S o t h e p e r p e t u a l circular m o t i o n o f c e le s t i a l b o d i e s w h i c h d o m i n a t e dG r e e k t h o u g h t s t il l g o v e r n e d G a l i l e o ' s w o r l d p i c t u r e . F o r h i m c i r c u la rm o t i o n w a s the n a t u r a l m o t i o n w h i c h d i d n o t n e e d t o b e e x p l a i n e d .

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    N E W T O N I A N I N M I N D B U T A R I S T O T E L I A N A T H E A R T 355T H E P R OB L EM O F I N E R T I A L M O T IO NI n fa c t t he p r o b l e m o f i ne r t ia l m o t i o n o n l y b e c a m e m a n a g e a b l e w h e n m e nc o u ld b e i n d u c e d t o c h a n g e t h e i r f u n d a m e n t a l v i e w o f space. T h e m o d e mv i e w o f i n e r t i a l m o t i o n a s a p p l y i n g t o a b o d y m o v i n g p e r p e t u a l l y i n as t r a i g h t l in e t o i n fi n it y i n th e a b s e n c e o f e x t e r n a l f o r c e s is n o t o n e t h a tc o u l d a r is e f r o m e x p e r i m e n t . I t d e p e n d s o n a c e r ta i n k n a c k o f lo o k i n g a tt h in g s . F i r s t, t o s e e b o d i e s a s b e in g , f o r t hi s p u r p o s e , p u r e l y g e o m e t r i c a l ,t h a t is , t h e m o t i o n a s b e i n g i n d e p e n d e n t o f t h e n a t u r e o f t h e b o d y .S e c o n d l y , t o s e e th e s p a c e t h r o u g h w h i c h t h e b o d i e s a r e m o v i n g a s b e i n ge m p t y a n d n e u t r a l . F o r A r i s to t e l ia n s b o t h i d e a s w o u l d h a v e s e e m e d u t t e r lyi n c o n c e iv a b l e . A s w e h a v e s e e n , t h e m o t i o n o f b o d i e s w a s d e p e n d e n tu p o n t h e i r n a t u r e a n d a l s o c e r ta i n d i r e c t io n s i n s p a c e h a d t o b e r e g a r d e di n a p r e f e r e n t i a l w a y i n th e s e n s e t h a t c e r t a i n p a r t s o f th e u n i v e r s e e x e r t e ds p e c i a l a t t r a c t i v e f o r c e s . G a l i l e o e s c a p e d f r o m t h e f ir st o f t h e s e c o n s t r a i n -in g c o n c e p t s b u t w a s u n a b l e t o e s c a p e f r o m t h e s e c o n d b y r e a c h i n g af u ll r e a l i s a t io n o f c o m p l e t e l y e m p t y , u t t e r l y d i r e c ti o n l e ss a n d n e u t r a l ,E u c l i d e a n s p a c e .

    T h e c o n c e p t o f i n e r t i a l m o t i o n is n o t j u s t a d e ta i l o f a w o r l d - p i c t u r e -i t is o n e o f th e e s s e n t i a l f o u n d a t i o n s o f a s y s t e m . T h e c h a n g e f r o m t h eA r i s t o t e l ia n i d e a o f i n e rt ia l m o t i o n p r o b a b l y r e p r e s e n t s the m o s t i m p o r t a n te l e m e n t i n t h e t r a n s i t i o n f r o m a n c i e n t a n d m e d i e v a l s c ie n c e t o cl as s ic a ls c ie n c e. T h e r e c a n b e n o d o u b t t h a t th is t r e m e n d o u s c h a n g e w a s l a rg e l yi n i ti a t e d b y G a l i l e o b u t i t n e e d e d N e w t o n t o s e t t h e s e a l f i na l l y b y h iss y s t e m a t i s a t i o n o f m e c h a n i c s .

    KINEMATICS AND DYNAM ICSB e c a u s e o f t h e s u c c es s w i t h w h i c h G a l i l e o h a d i n v e s t i g a t e d m a n y s p e c i a lt o p i c s i n m e c h a n i c s a n d h a d d e v e l o p e d e f f e c t iv e s c h e m e s f o r s a y i n g howo b j e c t s m o v e ( k i n e m a t i c s ) , N e w t o n w a s a b l e t o t u r n h i s a t t e n t i o n t o t h eq u e s t i o n o f why o b j e c t s m o v e a s t h e y d o ( d y n a m i c s ) . I n o n e s e n s e , o fc o u r s e ' w h y ' q u e s t i o n s a r e e x t r e m e l y d if fi cu l t [ i m p o s s i b le ( ? ) ] to a n s w e r .T h i s h a s b e e n n e a t l y p u t b y F e y n m a n :

    W hat makes planets go round the su n? At the time of Kepler some people answered thisproblem b y saying that there were angels behind them beating their wings and pushingthe planets around an orbit . . .Th e an swer is not far from the truth. The only difference is that ange ls sit in a differentdirection and their w ings push inwa rds (The Character of Physical Law)

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    356 M AUR I C E G. EB I S ON

    NEWTON'S METHODS

    I t is n o t i n t h e d e e p l y m e t a p h y s i c a l s e n s e t h a t w e t a l k a b o u t N e w t o nt a c k li n g ' w h y ' q u e s t i o n s b u t r a t h e r t o e m p h a s i s e t h a t w h a t l a y at t h e h e a r to f hi s a p p r o a c h w a s n o t s o m u c h h o w o b j e c ts m o v e p e r s e b u t w h a t c a u s e st h e m t o m o v e i n th e w a y t h a t t h e y d o . I n h is w o r k o n m e c h a n i c s N e w t o na d o p t s a c o n s is t e nt m e t h o d g o v e r n e d b y a n u m b e r o f ru le s :1. T o a s s u m e a s f e w c a u s e s as p o s s i b l e in e x p l a i n i n g a p a r t i c u l a r p h e n o m e -

    n o n .2 . T o r e l a t e a s c o m p l e t e l y a s p o s s ib l e a n a l o g o u s e f f e c ts t o t h e s a m e c a u s e .3 . T o e x t e n d t o a ll b o d i e s t h e p r o p e r t i e s o n w h i c h i t is p o s s ib l e t o m a k e

    e x p e r i m e n t s .4 . T o c o n s i d e r e v e r y p r o p o s i t i o n o b t a i n e d b y i n d u c t i o n f r o m o b s e r v e dp h e n o m e n a t o b e va l i d u n t i l a n e w p h e n o m e n o n i s o b s e r v e d w h i ch

    c o n t r a d i c t s o r l i m i t s t h e p r o p o s i t i o n .E s s e n t i a l l y t h e t a s k t h a t f a c e d N e w t o n w a s t o s y s t e m a t i se a m a s s o f

    a c c u m u l a t e d k n o w l e d g e t h a t s t i l l h a d a f r a g m e n t a r y a n d c o n f u s e d c h a r a c -t e r . I t h a s b e e n s u g g e s t e d t h a t in m e c h a n i c s N e w t o n f a c e d th e s a m e s o r to f p r o b l e m a s P a s c a l i n h y d r o st a t i c s w h o b y t h e e n u n c i a t i o n o f a si n gl eu n i v e r s a l p r in c i p l e ( t h e e q u a l i t y o f p r e s s u r e i n e v e r y d i r e c t i o n a t a p o i n ti n a l i q u id ) s u c c e e d e d i n s y s t e m a t i z i n g a w h o l e b r a n c h o f s c i e n c e . B u td e a r l y N e w t o n ' s p r o b l e m in m e c h a n i c s w a s v e r y m u c h m o r e d if fi cu lt d u et o t h e m u c h g r e a t e r g e n e r a l i t y o f th e s u b je c t .

    A s w e h a v e s e e n , s c ie n ti s ts h a d f r o m e a r l y t i m e s s p e c u l a t e d a b o u tm o t i o n u n d e r t h e i n f l u e n c e o f i n t e r n a l o r e x t e r n a l f o r c e s . In o r d e r t o d ot hi s it w a s n e c e s s a r y , o f c o u r s e , t o e m p l o y s p e ci a li st t e r m s . N o w o n e o ft h e p e r e n n i a l d i ff ic u l t ie s f a c e d b y p h y s ic s is th a t , m o r e t h a n a n y o t h e rb r a n c h o f s c ie n c e , i t u s e s t e r m s w h i c h a ls o o c c u r i n e v e r y d a y l a n g u a g e .T h i s c a n g i v e a q u i t e s p u r i o u s f e e l i n g o f c o n f i d e n c e in t h e c l a r it y o f t h em e a n i n g t o b e a t t a c h e d t o t e r m s ( j u st th i n k o f t h e d i f f e r e n c e i n th em e a n i n g s o f w o r d s s u c h as v e l o c i t y , p o w e r a n d e n e r g y n o w a d a y s w h e nt h e y a r e u s e d s t ri c tl y i n p h ys i cs o r m o r e l o o s e l y in o r d i n a r y s p e e c h ) .C o m m o n l y u s e d w o r d s s uc h as gr av i t y , f o r c e , r e s i s t anc e , t e nde nc i e s , i m -p e t u s , q u a n t i ty o f m o t i o n a n d s o o n w e r e u s e d i n t h e e a r l y s p e c u la t i o n sa b o u t m o t i o n a n d t h e s e t u r n e d o u t t o b e i n su f fi c ie n t ly s h a r p l y d e fi n e d t ob e u s e f u l i n s c i e n t i f i c d i s c u s s i o n s .

    S o o n e o f N e w t o n ' s i m p o r t a n t t a sk s w a s to a t t e m p t t o i n t r o d u c e s o m es o r t o f o r d e r i n t h e c h a o s o f t e rm s . P e r h a p s t h e b e s t m e t h o d w o u l d h a v eb e e n t o m a k e a c o m p l e t e l y cl e a n b r e a k a n d u s e a n e n t i r e ly n e w s e t o ft e r m s n o t d r a w n f r o m c o m m o n u s a g e . H o w e v e r , t hi s is n e v e r e a s y b e c a u s ea n y r e f o r m e r o r r e v o l u t i o n a r y w h o w i s h e s to r e o r g a n i s e a s y s t e m h a sn e v e r t h e l e s s b e e n b r o u g h t u p w i t h i n i t a n d c a n n o t h e l p b e i n g i n f l u e n c e db y it s t e r m s a n d i t s c o n c e p t s . N o o n e i s e v e r r a d i ca l e n o u g h i n re f o r m a t i o n ,t e n d i n g t o p r e s e r v e t h e m o r e f a m i l ia r th i n gs w h i c h a r e o f t e n p r e c i s e lyt h o s e w h i c h m o s t n e e d r e c o n s t r u c t i o n . P a r t i c u l a rl y in t h e c a s e o f te r m i n o l -

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    N E W T O N I A N I N M I N D B U T A R I S T O T E L I A N A T H E A R T 3 5 7

    [A] [g]inertial mo tion for Galileo [A] and New ton [B].

    o g y , t h e w o r s t p o s s ib l e c o n f u s i o n a r i se s w h e n o l d t e r m s a r e u s e d f o r n e wi d e a s .

    I t c o u l d b e s a id t h a t i n o n e s e n s e N e w t o n d i d n o t h a v e t h e i d e a l s c ie n ti fi cp e r s o n a l i t y t o s u c c e e d co m p l e t e l y i n t h i s p a r t i c u l a r t a s k . H e h a d a r a r em i n d o f g r e a t c r e a t i v e b r il l ia n c e w h i c h w a s a b l e t o f o r m u l a t e o r i g i n a l a n de l e g a n t p r o o f s o v e r a v a s t r a n g e o f to p i c s b u t i t w a s n o t w e l l s u it e d t o t h ep a t i e n t w o r k r e q u i r e d t o a x i o m a t i s e a s u b j e c t a n d s o m e t i m e s h is w r i ti n g sl a c k e d t h e c a r e f u l d e f i n i ti o n o f t e r m s . N e v e r t h e l e s s , h i s a x i o m a t i c s y s t e md i d p r o v i d e t h e v e r y t h in g t h a t h a d a lw a y s b e e n l a ck i n g p r e v i o u s ly ina n c i e n t m e c h a n i c s a n d i n th i s w a y h e l a i d d o w n a f ir m f o u n d a t i o n f o rf u t u r e d e v e l o p m e n t s . F u r t h e r m o r e , i t is i m p o r t a n t t o a p p r e c i a t e t h a t a x io -m a t i z a t i o n , w h i ls t v i ta l i n l ay i n g f o u n d a t i o n s , is o n l y o n e a s p e c t o f t h ec o n t r i b u t i o n t h a t a g e n i u s c a n m a k e t o t h e d e v e l o p m e n t o f h is s u b je c t.T h e e f f ic a c y o f t h e m e t h o d s w h i c h h e d e v e l o p s , w h i c h c a n b e r e p r e s e n t e da s t h e b u i l d i n g o f t h e s u p e r s t r u c t u r e , n e e d a l s o to b e c o n s i d e r e d . I n t h i sa r e a t h e r e c a n b e n o d o u b t i n g N e w t o n ' s u n i v e r s a l g e n i u s .

    NEWTON'S LAWS OF MOTION

    N e w t o n ' s s c h e m e f o r d y n a m i c s is e s s en t ia l ly s u m m e d u p in h is t h r e e l a w so f m o t i o n . I n t h e F i r s t L a w w e f i n a ll y a r r i v e a t a s a ti s f a c to r y qual i ta t iveu n d e r s t a n d i n g o f in e r t i a ( t h e t e n d e n c y o f a o b j e c t t o m a i n t a i n i t s s t a te o fr e s t o r u n i f o r m m o t i o n i n a s t r a i g h t l i n e ) a s a b a s i c i n h e r e n t p r o p e r t y o fa l l o b j e c t s .

    I t is a c o m p l e t e l y g e n e r a l l a w w h i c h e m p h a s i s e s t h a t a s in g le s c h e m e i sa p p l i c a b l e t o m o t i o n a n y w h e r e i n t h e u n i v e r s e . I t is t h e v e r y f ir s t o c c a s i o ni n t h e h i s t o r y o f p h y s i c s w h e n n o d i s t in c t i o n is m a d e b e t w e e n t h e t e r r e s t r i a la n d c e l e s t i a l d o m a i n s .

    I n h is S e c o n d L a w w e f in a ll y r e a c h t h e e x p l a n a t i o n o f a c c e l e r a t io n a n da quan t i ta t i ve r e l a t i o n s h i p b e t w e e n i n e r t i a a n d f o r c e . [ I t is i n t e r e s t i n g t o

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    3 5 8 M A U R I C E G . EB I S O Nr e m e m b e r t h a t N e w t o n d i d n o t e x p r e s s t h i s a s F = m a = m ( d v / d t ) b u te s s e n t i a l l y i n t h e f o r m F A t = m A v , t h a t is , h e s p o k e o f " c h a n g e o f ' m o -t i o n ' " ( = m o m e n t u m ) a n d r e l a t e d th is t o th e v a l u e o f f o r c e x t im e ] .

    N e w t o n ' s T h i r d L a w w a s h i gh l y o r i gi n a l a n d i t c o m p l e t e d h is g e n e r a lt r e a t m e n t o f th e c o n c e p t o f f o r c e b y e x p la i n in g t h a t e v e r y f o r c e h a s i t sm i r r o r i m a g e t w i n . A c o n s e q u e n c e o f t h is la w is th a t a s o l i t a r y p a r t i c l ec a n b y i ts e lf n e i th e r e x e r t n o r e x p e r i e n c e a n y f o r c e . F o r c e s a r is e o n l yf r o m t h e i n t e r a c t i o n o f t w o e n t i t ie s . W e m a y e l e c t t o c a ll o n e f o r c e ' a c t i o n 'a n d t h e o t h e r ' r e a c ti o n ' b u t t h e n a m i n g is a rb i t ra r y . T h e y a r e r e l a t e d i nt h e s a m e w a y a s c r e d i t a n d d e b i t : t h e o n e i s i m p o s s i b l e w i t h o u t t h e o t h e r .A c t i o n a n d r e a c t io n a r e e q u a l in m a g n i t u d e b u t o p p o s i t e in d i r ec t io n . A n yc a u s a l c o n n e c t i o n w e i n t r o d u c e is a rt if ic ia l. M o s t i m p o r t a n t o f a ll is t h a tt h e y h a p p e n r e s p e c t iv e l y t o t w o d i f f e r e n t e n t i t i e s .

    THE WOR K OF KEPLER

    W e m u s t l o o k b r i ef l y a t N e w t o n ' s c o n t r i b u t i o n t o t h e t h e o r y o f g ra v it y .B y t h e e n d o f th e s i x t e e n th c e n t u r y t h e r e w e r e t w o p r o b l e m s c o n c e r n e dw i t h th e m o t i o n o f c e le s ti al b o d i e s t h a t w e r e b e c o m i n g m o r e a n d m o r ea c u t e . B a s i c a l ly t h e s e p r o b l e m s w e r e :

    W h a t f o r c e k e e p s c e l es t ia l b o d i e s in m o t i o n ?H o w a r e c e l e s ti a l b o d i e s h e l d i n t h e i r o r b i ts ?

    T h e o l d v i e w t h a t b o t h q u e s t i o n s c o u l d b e s a t i s fa c t o r il y a n s w e r e d b ya t t a c h i n g t h e c e l e s t i a l b o d i e s t o l a r g e c r y s t a l l i n e s p h e r e s w a s i n c r e a s i n g l yb e i n g r e g a r d e d a s s u s p e c t . W e c a n n o t d e a l e v e n i n o u t l i n e w i t h all t h ec o n t ri b u ti o n s m a d e p r i o r to N e w t o n b u t m e n t i o n m u s t b e m a d e o f t h eg r e a t a s t r o n o m e r K e p l e r . H e c o n f i n e d h is s u g g e st io n s o n g r a v it y t o t h es o l a r s y s t e m s i n c e h e r e g a r d e d t h e f i x e d s t ar s a s b e i n g s o d i f f e r e n t f r o mt e r re s t r ia l b o d ie s t h a t t h e y h a d n o g r a v it y . H e k n e w n o t h i n g o f th e m o d e r ni d e a o f i n e r t ia a n d s u g g e s te d t h a t t h e p l a n e t s n e e d e d a f o r c e t o p u s h t h e mr o u n d t h e i r o r b it s . T h i s f o r c e r e a c h e d o u t f r o m t h e s u n a n d m o v e d r o u n dw i t h t h e s u n ' s r o t a t i o n s o s w e e p i n g t h e p l a n e t a l o n g l i k e a b r o o m s w e e p sa p e b b l e a l o n g a r o a d . T h e e s s e n t i a l f e a t u r e w a s t h e r o t a t i o n o f t h e s u n .I f t h e s u n d i d n o t r o t a t e o n i ts a xi s, h e s a id , t h e e a r t h w o u l d n o t r e v o l v er o u n d i t a n d s i m i la r ly if t h e e a r t h d i d n o t r o t a t e o n i ts a xi s, t h e m o o n i nt u r n w o u l d n o t r e v o l v e r o u n d t h e e a r t h . K e p l e r d o e s n o t s u g g es t a ni n v e r s e - s q u a r e l a w , f o r h i s f o r c e d i d n o t r a d i a t e i n a ll d i r e c t i o n s b u ts t r e a m e d o u t f r o m t h e s u n o n l y a l o n g th e p l a n e o f t h e p l a n e t 's o r b i t . I na s e n s e th e f o r c e h a d t o ' k n o w ' w h e r e t o f in d it s o b j e c t a n d t h is w a s o n eo f th e o b j e c ti o n s o f t e n m a d e t o t h e i d e a o f a tt r a c ti o n a c ro s s e m p t y s p a c e.

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    N E WT O N I A N I N MI N D BU T A RI ST O T E L I A N A T H E A RT 359

    ~ . . . ~ . . , . . . . . . . , , . . . , . , . . . . . , . . .

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    Sun

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    Kepler' s gravitational theory for the so lar system. This is perhaps a classical example of areasonable answer to questions which have been expressed in the wrong way.

    NEWTON AND GRAVITATION

    Newton's superb contribution to the answering of both of the abovequestions was made only after a remarkable and protracted intellectualstruggle.This was the Law of Universal Gravitation derived essentially byasking the question in the right way, namely, what prevents the planetfrom moving in a straight line?

    One of Newton's aims when developing his gravitational theory was toput forward an alternative to the vortex theory used by Descartes whohad produced a world-system by starting with only matter and motionand working deductively. This world-system was very attractive to manyscientists and continued to be so for many years. There can be no doubtthat Newton owed a considerable intellectual debt to Descartes whichunfortunately he never publicly acknowledged. Newton showed mathema-tically that the vortices could not sensibly account for the observed motionof planets or comets and that if space was indeed composed of matterdense enough to push planets along their paths by the whirling of vorticesthen it would also act as a resistive medium which would slow down allmovements in the universe. By using the idea of action at a distanceNewton at one stroke dest royed two grand Aristoteli an principles - first,the view that a vacuum was impossible and second, the view that objectscould only influence one another if they actually touched. Newton's theorydid not gain immediate and complete acceptance being severely criticised,for example, by Huygens and Leibnitz. But eventually it triumphed andin retrospect it can be seen as one of the great culminating points in thehistory of thought.

    So in outline we have traced a gradually evolving pattern with brilliantindividual contributions from great scientists such as Aristotle, Kepler,

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    360 MAURICE G. EBISONGalileo, Descartes and Newton. The process may be likened to the build-ing up of a jigsaw from pieces which can interlock to produce a recogni-sable picture if properly fitted together by someone of sufficient talent.For mechanics that someone was Newton but he did recognise the debtthat he owed his predecessors when he said that if he had seen furtherthan others

    It is by standing upon the shoulders of Giants.

    IMPLICATIONS FOR TEACHINGWhat lessons does this historical development of mechanics hold for ourteaching of the subject? I would like to suggest the following:1 . W e n eed t o r em em b er t h a t A r i s t o te l i a n i d ea s h a ve a d eep - r o o t eda p p e a lWe need to be aware that students bring to their study of physics acollection of proto-concepts formed from early commonsense experi-ences. Very commonly held pre-conceptions include the idea that continu-ing motion implies the presence of a force in the direction of the motionand that changes in the speed of an object can be accounted for by aforce that either 'dies out' or 'builds up'. Consider, for example, a boxbeing pulled across a horizontal floor with a steady speed in a straightfine. The Newtonian commentator would suggest that the effort beingapplied by the person pulling the box is only to equalise and cancel thefrictional force between box and floor. The Aristotelian, on the otherhand, would explain that since the natural state of the box is rest, a forcehas to be supplied to the box in order to keep it in uniform motion.There is. of course, no dispute about the experimentally observed factsbut rather a difference in viewpoint and it is important for teachers toappreciate that the Aristotelian view in this case, as in many other con-texts, is closer to common-sense opinion. Since friction is never altogetherabsent in the everyday world and indeed is often a very real hindrance inmoving objects, it is natural that people develop early on in thei r lives theintuitive idea that a force is necessary 'to keep an object moving'.. It isinstructive to try problems similar to the ones below on students, eventhose who have studied a good deal of physics.2 . Th e de f in it ion o f term s is v i ta l ly imp or ta n tReturning to the example of the box being pulled across the floor, it isclear that the two observers are using the word f o r c e in two quite differentsenses. The Aristotelian uses intuitive ideas and seeks to define force as'the cause of continued motion'. The Newtonian attempts to turn awayfrom the human-centered viewpoint by considering the n e t force acting

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    N E W T O N I A N I N M I N D B U T A R I S T O T E L I A N A T H E A R T 361

    U s e a r r o w s t o r e p r e s e n t t h e f o r c e s a c t i n gon t h i s b l oc k a t r e s t o f t a b l e .

    S t one be i ng whi r l e d i n a hor i z on t a l c i r c l e .Dra w t he i n i t i a l t r a j e c t o ry i f t he s t r i ng i scut .

    nl

    B

    S h o w t o t a l f o r c e a t A a n d a t B . H o r i z o n t a l c u r v e d t u b e . W h a t t r a je c t o r yd o e s t h e b a l l f o ll o w o n l e a v i n g t h e t u b e ?

    Astronaut iny satellite

    ~ E a r t h ~

    A n y f o r c e s o n a s t r o n a u t ?A C

    C o i n t o s s e d f r o m A t o b e c a u g h t a t C .F o r c e w h e n a t B ?

    o n t h e o b j e c t ( t a k i n g i n t o a c c o u n t t h e v e c t o r n a t u r e o f f o rc e s ) . B u t t h i s isn o t a n a t u r a l t h i n g t o d o u n t i l a g o o d d e a l o f e x p e r i e n c e c o n v i n c e s y o ut h a t t h i s v i e w p o i n t i s, i n p r a c t i c e , m u c h t h e m o r e f r u i tf u l .

    F u r t h e r m o r e , w h e n d e a l i n g w i th t h e d e f i n i ti o n o f te r m s w e d o w e l l t or e m e m b e r h o w a b s t ra c t a r e s o m e o f t h e c o n c e p t s w e u s e i n p h y si cs . I f w er e c a l l t h e d i f f i c u l ty t h a t G a l i l e o , a s u p e r b p h y s i c i s t , h a d i n d e a l i n g w i t ha c c e l e r a ti o n w e m a y h a v e m o r e p a t i e n c e w i t h o u r s t u d e n ts .

    3 . I t i s i m p o r t a n t t o a s k t h e r i g h t q u e s t i o nI f w e r e ca l l t h e e x a m p l e o f K e p l e r a n d N e w t o n t h e v i ta l n e c e ss i ty o ff r a m i n g q u e s t i o n s i n th e r i g h t w a y ( p r e f e r a b l y i n a w a y t h a t f a c i l it a t e s t h eo b t a i n i n g o f a n a n s w e r ! ) is m a d e a b u n d a n t l y c l ea r . S o m a n y o t h e r s im i l ar

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    3 6 2 M A U R I C E G . E B I S O Ne x a m p l e s a r is e in t h e h i s t o r y o f p h y s i c s t h a t th e r e i s n o n e e d t o l a b o u rt h e p o i n t .

    C O N C L U S I O NT h e r e c a n b e li tt le d o u b t t h a t A r i s t o t e l i a n c o n c e p t s d o h a v e a s t r o n g h o l do n t h e w a y in w h ic h w e t h in k . K u h n i n h is b o o k T h e C o p e r n i c a n R e v o l u -t i o n w r i t e s a s f o l l o w s :

    Ari s to t l e was ab l e t o exp ress i n an abs t rac t and cons i s t en t manne r many spon taneouspe rcep t i ons o f t he un ive rse t ha t had ex i s t ed fo r cen tu r i e s be fo re he gave t hem a l og i ca lv e r b a l r a t i o n a l e . . , t h e o p i n io n s o f c h il d r en , o f t h e m e m b e r s o f p r im i t i v e t r ib e s , a n d o fmany non -wes t e rn peop l e s do pa ra l l e l h i s w i th su rp r i s i ng f requency .

    A n d a ll o f u s s ti ll t a l k a b o u t t h e s u n r i s i n g i n t h e m o r n i n g !

    R E F E R E N C E SBlanp ied , W . : 1969 , Physics: lts Structure and Evolution, Bla i sde l l , W a l tham, Massachuse t ts .Bu t t e r f i e ld , H . : 1965 , The Origins of Modern Science, B e l l & S o n s , L o n d o n .Caspe r , M. & Noer , R . J . : 1972 , Revolutions in Physics, N o r t o n , N e w Y o r k .C o o p e r , L . N . : 1 9 6 8 , An Introduction to the Meaning and Structure of Physics, H a r p e r &

    R o w , N e w Y o r k .D i c k s , D . R . : 1 9 7 0 , Early Greek Astronomy to Aristotle, T h a m e s & H u d s o n , L o n d o n .D i jk s t e rhu i s , E . J . : 1961 , The Mechanization of the World Picture, Cla rendon Press , Oxfo rd .Dugas, R. : 1957, A History of Mechanics, R o u t l e d g e & K e g a n P a u l , L o n d o n .Go ldbe rg , S . : 1984 , Understanding Relativity, C l a r e n d o n P r e s s , O x f o r d .Ho l ton , G . & Brush , S .G . : 1973 , Introduction to Concepts and Theories in Physical Science,

    Addi son -W es l ey , Read ing , Massachuse t t s .Kuhn , T .S . : 1957 , The Copernican Revolution, H a r v a r d U n i v e r s i t y P r e ss , C a m b r i d g e , M a s s a -chuset t s .Pede rsen , O . & Pih l , M. : 1974 , Early, Physics and Astronomy, M a c d o n a l d , L o n d o n .

    Sambursky , S. : 1956, The Physical World of the Greeks, R o u t l e d g e & K e g a n P a u l , L o n d o n .