Pure Reflection & Diagonalization [Supplement to a talk at NASS]
John Bovavisibility
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This paper investigates the concept of pure reflection and diagonalization through the lens of phenomenological philosophy. It critiques certain philosophies, notably empirico-criticism and psychologism, highlighting Husserl's assertion regarding consciousness and its relationship with the external world. The text explores different kinds of reflection and their implications for understanding intentional states and presents an analogy between the physical and mental realms, challenging the notion of psychophysical laws.
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❙❛rtr❡ ❆❢t❡r ❇❛❞✐♦✉✿ P✉r❡ ❘❡✢❡❝t✐♦♥ ❛♥❞ ❉✐❛❣♦♥❛❧✐③❛t✐♦♥ ✭❙✉♣♣❧❡♠❡♥t✮
◆♦rt❤ ❆♠❡r✐❝❛♥ ❙❛rtr❡ ❙♦❝✐❡t② ✭◆❆❙❙✮
❉✐✈❡rs❡ ▲✐♥❡❛❣❡s ♦❢ ❊①✐st❡♥t✐❛❧✐s♠✱ ❙t✳ ▲♦✉✐s✱ ▼❖✳ ❏✉♥❡ ✷✵✱ ✷✵✶✹
✶
❏✳ ❇♦✈❛
✶✳
❆ ❦♥♦t ♦❢ ❝♦♥st❛t✐✈❡s ❛♥❞ ♣❡r❢♦r♠❛t✐✈❡s ❛❧✇❛②s ❝❤❛r❛❝t❡r✐st✐❝ ♦❢ ❙❛rtr❡✬s ♣✉r❡ r❡✢❡❝t✐♦♥✳
❙❛rtr❡✱ ✏ ❆
❋✉♥❞❛♠❡♥t❛❧ ■❞❡❛ ♦❢ ❍✉ss❡r❧✬s P❤❡♥♦♠❡♥♦❧♦❣②✿ ■♥t❡♥t✐♦♥❛❧✐t②✑ ✳ tr✳ ❏✳ P✳ ❋❡❧❧✳
❆❣❛✐♥st t❤❡ ❞✐❣❡st✐✈❡ ♣❤✐❧♦s♦♣❤② ♦❢ ❡♠♣✐r✐❝♦✲❝r✐t✐❝✐s♠✱ ♦❢ ♥❡♦✲❑❛♥t✐❛♥✐s♠✱ ❛❣❛✐♥st ❛❧❧ ✏ ♣s②❝❤♦❧♦✲
❣✐s♠✱✑ ❍✉ss❡r❧ ♣❡rs✐st❡♥t❧② ❛✣r♠❡❞ t❤❛t ♦♥❡ ❝❛♥♥♦t ❞✐ss♦❧✈❡ t❤✐♥❣s ✐♥ ❝♦♥s❝✐♦✉s♥❡ss✳ ❨♦✉ s❡❡ t❤✐s
tr❡❡✱ t♦ ❜❡ s✉r❡✳ ❇✉t ②♦✉ s❡❡ ✐t ❥✉st ✇❤❡r❡ ✐t ✐s✿ ❛t t❤❡ s✐❞❡ ♦❢ t❤❡ r♦❛❞✱ ✐♥ t❤❡ ♠✐❞st ♦❢ t❤❡ ❞✉st✱
❛❧♦♥❡ ❛♥❞ ✇r✐t❤✐♥❣ ✐♥ t❤❡ ❤❡❛t✱ ❡✐❣❤t ♠✐❧❡s ❢r♦♠ t❤❡ ▼❡❞✐t❡rr❛♥❡❛♥ ❝♦❛st✳ ■t ❝♦✉❧❞ ♥♦t ❡♥t❡r ✐♥t♦
②♦✉r ❝♦♥s❝✐♦✉s♥❡ss✱ ❢♦r ✐t ✐s ♥♦t ♦❢ t❤❡ s❛♠❡ ♥❛t✉r❡ ❛s ❝♦♥s❝✐♦✉s♥❡ss✳ ❖♥❡ ✐s ♣❡r❤❛♣s r❡♠✐♥❞❡❞ ♦❢
❇❡r❣s♦♥ ❛♥❞ t❤❡ ✜rst ❝❤❛♣t❡r ♦❢ ▼❛tt❡r ❛♥❞ ▼❡♠♦r②✳ ❇✉t ❍✉ss❡r❧ ✐s ♥♦t ❛ r❡❛❧✐st✿ t❤✐s tr❡❡ ♦♥ ✐ts
❜✐t ♦❢ ♣❛r❝❤❡❞ ❡❛rt❤ ✐s ♥♦t ❛♥ ❛❜s♦❧✉t❡ t❤❛t ✇♦✉❧❞ s✉❜s❡q✉❡♥t❧② ❡♥t❡r ✐♥t♦ ❝♦♠♠✉♥✐❝❛t✐♦♥ ✇✐t❤
♠❡✳ ❈♦♥s❝✐♦✉s♥❡ss ❛♥❞ t❤❡ ✇♦r❧❞ ❛r❡ ❣✐✈❡♥ ❛t ♦♥❡ str♦❦❡✿ ❡ss❡♥t✐❛❧❧② ❡①t❡r♥❛❧ t♦ ❝♦♥s❝✐♦✉s♥❡ss✱
t❤❡ ✇♦r❧❞ ✐s ♥❡✈❡rt❤❡❧❡ss ❡ss❡♥t✐❛❧❧② r❡❧❛t✐✈❡ t♦ ❝♦♥s❝✐♦✉s♥❡ss✳ ❍✉ss❡r❧ s❡❡s ❝♦♥s❝✐♦✉s♥❡ss ❛s ❛♥
✐rr❡❞✉❝✐❜❧❡ ❢❛❝t t❤❛t ♥♦ ♣❤②s✐❝❛❧ ✐♠❛❣❡ ❝❛♥ ❛❝❝♦✉♥t ❢♦r✳ ❊①❝❡♣t ♣❡r❤❛♣s t❤❡ q✉✐❝❦✱ ♦❜s❝✉r❡ ✐♠❛❣❡
♦❢ ❛ ❜✉rst✳ ❚♦ ❦♥♦✇ ✐s t♦ ✏ ❜✉rst t♦✇❛r❞✱✑ t♦ t❡❛r ♦♥❡s❡❧❢ ♦✉t ♦❢ t❤❡ ♠♦✐st ❣❛str✐❝ ✐♥t✐♠❛❝②✱ ✈❡❡r✐♥❣
♦✉t t❤❡r❡ ❜❡②♦♥❞ ♦♥❡s❡❧❢✱ ♦✉t t❤❡r❡ ♥❡❛r t❤❡ tr❡❡ ❛♥❞ ②❡t ❜❡②♦♥❞ ✐t✱ ❢♦r t❤❡ tr❡❡ ❡s❝❛♣❡s ♠❡ ❛♥❞
r❡♣✉❧s❡s ♠❡✱ ❛♥❞ ■ ❝❛♥ ♥♦ ♠♦r❡ ❧♦s❡ ♠②s❡❧❢ ✐♥ t❤❡ tr❡❡ t❤❛♥ ✐t ❝❛♥ ❞✐ss♦❧✈❡ ✐ts❡❧❢ ✐♥ ♠❡✳ ■ ❛♠
❜❡②♦♥❞ ✐t❀ ✐t ✐s ❜❡②♦♥❞ ♠❡✳
❉♦ ②♦✉ r❡❝♦❣♥✐③❡ ✐♥ t❤✐s ❞❡s❝r✐♣t✐♦♥ ②♦✉r ♦✇♥ ❝✐r❝✉♠st❛♥❝❡s ❛♥❞ ②♦✉r ♦✇♥ ✐♠♣r❡ss✐♦♥❄
❨♦✉
❝❡rt❛✐♥❧② ❦♥❡✇ t❤❛t t❤❡ tr❡❡ ✇❛s ♥♦t ②♦✉✱ t❤❛t ②♦✉ ❝♦✉❧❞ ♥♦t ♠❛❦❡ ✐t ❡♥t❡r ②♦✉r ❞❛r❦ st♦♠❛❝❤
❛♥❞ t❤❛t ❦♥♦✇❧❡❞❣❡ ❝♦✉❧❞ ♥♦t✱ ✇✐t❤♦✉t ❞✐s❤♦♥❡st②✱ ❜❡ ❝♦♠♣❛r❡❞ t♦ ♣♦ss❡ss✐♦♥✳
❝♦♥s❝✐♦✉s♥❡ss ✐s ♣✉r✐✜❡❞✱ ✐t ✐s ❝❧❡❛r ❛s ❛ str♦♥❣ ✇✐♥❞✳
❆❧❧ ❛t ♦♥❝❡✱
❚❤❡r❡ ✐s ♥♦t❤✐♥❣ ✐♥ ✐t ❜✉t ❛ ♠♦✈❡♠❡♥t
♦❢ ✢❡❡✐♥❣ ✐ts❡❧❢✱ ❛ s❧✐❞✐♥❣ ❜❡②♦♥❞ ✐ts❡❧❢✳ ■❢✱ ✐♠♣♦ss✐❜❧❡ t❤♦✉❣❤ ✐t ♠❛② ❜❡✱ ②♦✉ ❝♦✉❧❞ ❡♥t❡r ✏✐♥t♦✑
❝♦♥s❝✐♦✉s♥❡ss✱ ②♦✉ ✇♦✉❧❞ ❜❡ s❡✐③❡❞ ❜② ❛ ✇❤✐r❧✇✐♥❞ ❛♥❞ t❤r♦✇♥ ❜❛❝❦ ♦✉ts✐❞❡✱ ✐♥ t❤❡ t❤✐❝❦ ♦❢ t❤❡
❞✉st✱ ♥❡❛r t❤❡ tr❡❡✱ ❢♦r ❝♦♥s❝✐♦✉s♥❡ss ❤❛s ♥♦ ✏✐♥s✐❞❡✑✳
Pr❡❝✐s❡❧② t❤✐s ❜❡✐♥❣✲❜❡②♦♥❞✲✐ts❡❧❢✱ t❤✐s
❛❜s♦❧✉t❡ ✢✐❣❤t✱ t❤✐s r❡❢✉s❛❧ t♦ ❜❡ ❛ s✉❜st❛♥❝❡ ✐s ✇❤❛t ♠❛❦❡s ✐t ❜❡ ❛ ❝♦♥s❝✐♦✉s♥❡ss✳
✷✳ ❍✉ss❡r❧✬s ❛❝❦♥♦✇❧❡❞❣♠❡♥t ♦❢ r❡✢❡❝t✐♦♥✬s ♥❡❡❞ ❢♦r ❛ s❝❤❡♠❡ ✐♥❞❡①✐♥❣ ❛♥❞ ❞❡✐♥❞❡①✐♥❣ ✐♥t❡♥t✐♦♥❛❧ st❛t❡s✿
✷
■❞❡❛s ✶✱ ➓✶✵✶ ❈❤❛r❛❝t❡r✐st✐❝s ♦❢ ❧❡✈❡❧s✳ ❉✐✛❡r❡♥t s♦rts ♦❢ ✏r❡✢❡❝t✐♦♥s✑✳ tr✳ ❋✳ ❑❡rst❡♥ ✭✷✹✼✲✹✽✮✳
■t ✐s ❝❧❡❛r t❤❛t ✐♥ ❛❧❧ t❤♦s❡ ❦✐♥❞s ♦❢ ❤✐❡r❛r❝❤✐❝❛❧ str✉❝t✉r❡s ✇❤✐❝❤ ❝♦♥t❛✐♥ r❡✐t❡r❛t❡❞ ♣r❡s❡♥t✐❛t✐♦♥✲
♠♦❞✐✜❝❛t✐♦♥s ✐♥ t❤❡✐r ♠❡♠❜❡rs✱ ♥♦❡♠❛s ✇✐t❤ ❛ ❝♦rr❡s♣♦♥❞✐♥❣ ❤✐❡r❛r❝❤✐❝❛❧ ❢♦r♠❛t✐♦♥ ❛r❡ ❝♦♥st✐✲
t✉t❡❞✳ ■♥ t❤❡ ❝♦♥s❝✐♦✉s♥❡ss ♦❢ ❛ ❞❡♣✐❝t✉r✐♥❣ ❛t t❤❡ s❡❝♦♥❞ ❧❡✈❡❧ ❛ ✏♣✐❝t✉r❡✑ ✐♥ ✐ts❡❧❢ ✐s ❝❤❛r❛❝t❡r✐③❡❞
❛s ❛ ♣✐❝t✉r❡ ❛t t❤❡ s❡❝♦♥❞ ❧❡✈❡❧✱ ❛s ♣✐❝t✉r❡ ♦❢ ❛ ♣✐❝t✉r❡✳ ■❢ ✇❡ r❡❝❛❧❧ ❤♦✇ ②❡st❡r❞❛② ✇❡ r❡♠❡♠❜❡r❡❞
❛ ❝❤✐❧❞❤♦♦❞ ❡①♣❡r✐❡♥❝❡✱ t❤❡♥ t❤❡ ♥♦❡♠❛✱ ✏❝❤✐❧❞❤♦♦❞ ❡①♣❡r✐❡♥❝❡✑✱ ✐♥ ✐ts❡❧❢ ❤❛s ❛ ❝❤❛r❛❝t❡r✐③❛t✐♦♥
❛s s♦♠❡t❤✐♥❣ r❡♠❡♠❜❡r❡❞ ❛t t❤❡ s❡❝♦♥❞ ❧❡✈❡❧✳ ❚❤✉s ✐♥ ❣❡♥❡r❛❧✿
❚♦ ❡✈❡r② ♥♦❡♠❛t✐❝ ❧❡✈❡❧ t❤❡r❡ ❜❡❧♦♥❣s ❛ ❝❤❛r❛❝t❡r✐st✐❝ ❛♣♣r♦♣r✐❛t❡ t♦ t❤❛t ❧❡✈❡❧ ❛s ❛ ❦✐♥❞ ♦❢ ✐♥❞❡①
✇✐t❤ ✇❤✐❝❤ ❡❛❝❤ t❤✐♥❣ ❝❤❛r❛❝t❡r✐③❡❞ ♠❛♥✐❢❡sts ✐ts❡❧❢ ❛s ❜❡❧♦♥❣✐♥❣ t♦ ✐ts ❧❡✈❡❧
✇❤❡t❤❡r ✐t ✇♦✉❧❞
♦t❤❡r✇✐s❡ ❜❡ ❛ ♣r✐♠❛r② ♦❜❥❡❝t ♦r ♦♥❡ ❧②✐♥❣ ✐♥ s♦♠❡ ❧✐♥❡ ♦r ♦t❤❡r ♦❢ t❤❡ r❡✢❡❝t✐✈❡ r❡❣❛r❞✳ ❋♦r ✐♥❞❡❡❞
t♦ ❡✈❡r② ❧❡✈❡❧ ❜❡❧♦♥❣ ♣♦ss✐❜❧❡ r❡✢❡❝t✐♦♥s ❛t t❤❛t ❧❡✈❡❧✱ s♦ t❤❛t✱ ❡✳❣✳✱ ✇✐t❤ r❡s♣❡❝t t♦ r❡♠❡♠❜❡r❡❞
t❤✐♥❣s ❛t t❤❡ s❡❝♦♥❞ ❧❡✈❡❧ ♦❢ r❡♠❡♠❜❡r✐♥❣✱ ❁t❤❡r❡ ❛r❡❃ r❡✢❡❝t✐♦♥s ♦♥ ♣❡r❝❡✐✈✐♥❣s ♦❢ ❥✉st t❤❡s❡
t❤✐♥❣s ❜❡❧♦♥❣✐♥❣ t♦ t❤❡ s❛♠❡ ❧❡✈❡❧ ✭t❤✉s ♣r❡s❡♥t✐❛t❡❞ ❛t t❤❡ s❡❝♦♥❞ ❧❡✈❡❧✮✳
❋✉rt❤❡r♠♦r❡✿ ❡❛❝❤ ♥♦❡♠❛t✐❝ ❧❡✈❡❧ ✐s ❛♥ ✏♦❜❥❡❝t✐✈❛t✐♦♥✑ ✏ ♦❢ ✑ t❤❡ ❞❛t❛ ♦❢ t❤❡ ❢♦❧❧♦✇✐♥❣ ❁❧❡✈❡❧❃✳
✏ ❖❜❥❡❝t✐✈❛t✐♦♥ ✑ ❞♦❡s ♥♦t s✐❣♥✐❢② ❤❡r❡✱ ❤♦✇❡✈❡r✱ t❤❡ ♦❜❥❡❝t✐✈❛t✐♦♥✲♣r♦❝❡ss✱ ❛♥❞ t❤❡ ✏♦❢ ✑ ❞♦❡s ♥♦t
❡①♣r❡ss ❤❡r❡ t❤❡ r❡❧❛t✐♦♥ ♦❢ ❝♦♥s❝✐♦✉s♥❡ss ❛♥❞ t❤❡ ❖❜❥❡❝t ♦❢ ❝♦♥s❝✐♦✉s♥❡ss✳ ■t ✐s✱ ❛s ✐t ✇❡r❡✱ ❛
✶ ▲❛st
✷ ❚❤✐s
❛♥❞ ■ts
♠♦❞✐✜❡❞ ❏✉♥❡ ✷✽✱ ✷✵✶✹✳ ❆✉t❤♦r ❡♠❛✐❧ s✉♥②❛t❛✐✈❛r✉♣❛♠❅ ❣♠❛✐❧✳ ❝♦♠
❢❛♠♦✉s t❡①t ❤❛s ♣r♦✈♦❦❡❞ ❞✐s❝✉ss✐♦♥ ✐♥✱ ❛♠♦♥❣ ♠❛♥② ♦t❤❡rs✱ ❉❡rr✐❞❛✬s ❱♦✐❝❡
◆❡✉tr❛❧✐③❛t✐♦♥✳
✶
❛♥❞ P❤❡♥♦♠❡♥♦♥✱ ❛♥❞ ❇r❛✐♥❛r❞✬s ❇❡❧✐❡❢
♥♦❡♠❛t✐❝ ✐♥ ❝♦♥tr❛st t♦ ❛ ♥♦❡t✐❝ ✐♥t❡♥t✐♦♥❛❧✐t②✳✸
❚❤❡ ❧❛tt❡r ✐♥❝❧✉❞❡s ✐♥ ✐ts❡❧❢ t❤❡ ❢♦r♠❡r ❛s ✐ts
❝♦♥s❝✐♦✉s♥❡ss✲❝♦rr❡❧❛t❡✱ ❛♥❞ ✐ts ✐♥t❡♥t✐♦♥❛❧✐t②✱ ✐♥ ❛ ❝❡rt❛✐♥ ✇❛②✱ ❣♦❡s ❝❧❡❛r t❤r♦✉❣❤ t❤❡ ❧✐♥❡ ♦❢
♥♦❡♠❛t✐❝ ✐♥t❡♥t✐♦♥❛❧✐t②✳
❚❤✐s ✇✐❧❧ ❜❡❝♦♠❡ ♠♦r❡ ❞✐st✐♥❝t ✇❤❡♥ ✇❡ ❛❧❧♦✇ t❤❡ ❊❣♦✬s ❛tt❡♥t✐✈❡ r❡❣❛r❞ t♦ ❜❡ ❞✐r❡❝t❡❞ t♦
t❤r♦✉❣❤ t❤❡
❧❡✈❡❧ ❃ ❜❡②♦♥❞
s❤✐❢t ❢r♦♠ ❧❡✈❡❧
t❤❡ ❝♦♥s❝✐♦✉s♥❡ss ♦❢ s♦♠❡t❤✐♥❣ ♦❜❥❡❝t✐✈❡✳ ❚❤❡ ❁❊❣♦✬s r❡❣❛r❞❃ t❤❡♥ ❣♦❡s str❛✐❣❤t
♥♦❡♠❛t❛ ♦❢ t❤❡ s❡q✉❡♥❝❡ ♦❢ ❧❡✈❡❧s
✉♥t✐❧ ✐t ❛rr✐✈❡s ❛t t❤❡
❖❜❥❡❝t ♦❢ t❤❡ ✉❧t✐♠❛t❡
❁
✇❤✐❝❤ ✐t ❝❛♥♥♦t ❣♦✱ ❜✉t ✉♣♦♥ ✇❤✐❝❤✱ ✐♥st❡❛❞✱ ✐t ✜①❡s✳ ❚❤❡ r❡❣❛r❞ ❝❛♥✱ ❤♦✇❡✈❡r✱
t♦ ❧❡✈❡❧✱
❛♥❞ ✐♥st❡❛❞ ♦❢ ❣♦✐♥❣ t❤r♦✉❣❤ ❛❧❧ ♦❢ t❤❡♠ ✐t ✐s r❛t❤❡r ❞✐r❡❝t❡❞ t♦ t❤❡ ❞❛t❛ ♦❢ t❤❛t ❧❡✈❡❧
✉♣♦♥ ✇❤✐❝❤ ✐t ✜①❡s❀ ✐t ❁❝❛♥ ❞♦ t❤✐s❃ ❡✐t❤❡r ✐♥ ❛ ✏
r❡❣❛r❞✳
str❛✐❣❤t❢♦r✇❛r❞ ✑
♦r ✐♥ ❛
r❡✢❡❝t✐✈❡ ❞✐r❡❝t✐♦♥ ♦❢
■♥ t❤❡ ♣r❡✈✐♦✉s ❡①❛♠♣❧❡✿ t❤❡ r❡❣❛r❞ ❝❛♥ r❡♠❛✐♥ ❛t t❤❡ ❧❡✈❡❧ ♦❢ t❤❡ ❉r❡s❞❡♥ ●❛❧❧❡r②
✏r❡♠❡♠❜❡r✐♥❣❧②✑
✇❡ ✇❛❧❦ t❤r♦✉❣❤ t❤❡ ●❛❧❧❡r② ✐♥ ❉r❡s❞❡♥✳ ❚❤❡♥ ✇❡ ❝❛♥✱ ❛❣❛✐♥ ✇✐t❤✐♥ ♠❡♠♦r②✱ ❧✐✈❡ ✐♥ t❤❡ ♦❜s❡r✈❛✲
t✐♦♥ ♦❢ ♣✐❝t✉r❡s ❛♥❞ ✜♥❞ ♦✉rs❡❧✈❡s ✐♥ t❤❡ ✇♦r❧❞ ♦❢ ♣✐❝t✉r❡s✳ ❆❢t❡r t❤✐s✱ ❛❞✈❡rt❡❞ t♦ t❤❡ ❣❛❧❧❡r② ♦❢
♣❛✐♥t✐♥❣s ✐♥ ♣✐❝t✉r❡ ❝♦♥s❝✐♦✉s♥❡ss ♦❢ t❤❡ s❡❝♦♥❞ ❧❡✈❡❧✱ ✇❡ ❧♦♦❦ ❛t t❤❡ ♣✐❝t✉r❡s t❤❡♠s❡❧✈❡s❀ ♦r ✇❡
r❡✢❡❝t ❤✐❡r❛r❝❤✐❝❛❧❧② ✉♣♦♥ t❤❡ ♥♦❡s❡s✱ ❡t❝✳
✹ ❚❤✐s ♠✉❧t✐♣❧✐❝✐t② ♦❢ ♣♦ss✐❜❧❡ ❞✐r❡❝t✐♦♥s ♦❢ t❤❡ r❡❣❛r❞
❡ss❡♥t✐❛❧❧② ❜❡❧♦♥❣s t♦ t❤❡ ♠✉❧t✐♣❧✐❝✐t② ♦❢ ✐♥t❡♥t✐♦♥❛❧✐t✐❡s r❡❧❛t❡❞ t♦ ❛♥❞ ❢♦✉♥❞❡❞ ✐♥ ♦♥❡ ❛♥♦t❤❡r❀
❛♥❞ ✐♥ ✇❤❛t ❢♦❧❧♦✇s ✇❡ ✇✐❧❧ ❜❡❝♦♠❡ ❛❝q✉❛✐♥t❡❞
❛♥❞ ✇❤❡r❡✈❡r ✇❡ ✜♥❞ ❛♥❛❧♦❣♦✉s r❡❧❛t✐♦♥s❤✐♣s
✇✐t❤ ♠❛♥② ❞✐✛❡r❡♥t ❦✐♥❞s
❛♥❛❧♦❣♦✉s
♣♦ss✐❜✐❧✐t✐❡s ♦❢ ❝❤❛♥❣✐♥❣ r❡✢❡❝t✐♦♥
❛r❡ ❜r♦✉❣❤t ♦✉t✳
■t ♥❡❡❞ ♥♦t ❜❡ s❛✐❞ t❤❛t t❤❡s❡ r❡❧❛t✐♦♥s r❡q✉✐r❡ s❝✐❡♥t✐✜❝❛❧❧② ❞❡t❛✐❧❡❞ ❡①♣❧♦r❛t✐♦♥s ✇✐t❤ r❡s♣❡❝t t♦
✺
t❤❡✐r ❡ss❡♥❝❡✳
✸✳
❖♥❡ ♣❛rt✐❝✉❧❛r❧② ♣♦✐♥t❡❞ ❢♦r♠✉❧❛t✐♦♥ ♦❢ t❤❡ ❞✐❧❡♠♠❛ ♦❢ r❡✢❡❝t✐♦♥✿ ❙❛rtr❡✱
❇❡✐♥❣ ❛♥❞ ◆♦t❤✐♥❣♥❡ss✱
tr✳
❍❛③❡❧ ❇❛r♥❡s ✭✷✶✸✲✶✹✮
❍❡r❡ ♦♥❝❡ ❛❣❛✐♥ ✇❡ ♠❡❡t t❤❛t t②♣❡ ♦❢ ❜❡✐♥❣ ✇❤✐❝❤ ❞❡✜♥❡s t❤❡ ❢♦r✲✐ts❡❧❢✿ r❡✢❡❝t✐♦♥✖✐❢ ✐t ✐s t♦ ❜❡
❛♣♦❞✐❝t✐❝ ❡✈✐❞❡♥❝❡✖❞❡♠❛♥❞s t❤❛t t❤❡ r❡✢❡❝t✐✈❡
❜❡
t❤❛t ✇❤✐❝❤ ✐s r❡✢❡❝t❡❞✲♦♥✳ ❇✉t t♦ t❤❡ ❡①t❡♥t
t❤❛t r❡✢❡❝t✐♦♥ ✐s ❦♥♦✇❧❡❞❣❡✱ t❤❡ r❡✢❡❝t❡❞✲♦♥ ♠✉st ♥❡❝❡ss❛r✐❧② ❜❡ t❤❡
♦❜❥❡❝t
❢♦r t❤❡ r❡✢❡❝t✐✈❡❀ ❛♥❞
t❤✐s ✐♠♣❧✐❡s ❛ s❡♣❛r❛t✐♦♥ ♦❢ ❜❡✐♥❣✳ ❚❤✉s ✐t ✐s ♥❡❝❡ss❛r② t❤❛t t❤❡ r❡✢❡❝t✐✈❡ s✐♠✉❧t❛♥❡♦✉s❧② ❜❡ ❛♥❞
♥♦t ❜❡ t❤❡ r❡✢❡❝t❡❞✲♦♥✳ ❲❡ ❤❛✈❡ ❛❧r❡❛❞② ❞✐s❝♦✈❡r❡❞ t❤✐s ♦♥t♦❧♦❣✐❝❛❧ str✉❝t✉r❡ ❛t t❤❡ ❤❡❛rt ♦❢ t❤❡
❢♦r✲✐ts❡❧❢✳ ❇✉t t❤❡♥ ✐t ❞✐❞ ♥♦t ❤❛✈❡ ❛t ❛❧❧ t❤❡ s❛♠❡ ♠❡❛♥✐♥❣✳ ■♥ ❢❛❝t ✐t s✉♣♣♦s❡❞ ✐♥ t❤❡ t✇♦ t❡r♠s
✏r❡✢❡❝t❡❞ ❛♥❞ r❡✢❡❝t✐♥❣✑ ❛ r❛❞✐❝❛❧
❯♥s❡❧❜stä♥❞✐❣❦❡✐t
♦♥ t❤❡ ♣❛rt ♦❢ t❤❡ s✉❣❣❡st❡❞ ❞✉❛❧✐t②❀ t❤❛t
✐s✱ s✉❝❤ ❛♥ ✐♥❛❜✐❧✐t② ♦♥ t❤❡ ♣❛rt ♦❢ t❤❡ t❡r♠s t♦ ❜❡ ♣♦s✐t❡❞ s❡♣❛r❛t❡❧② t❤❛t t❤❡ ❞✉❛❧✐t② r❡♠❛✐♥❡❞
♣❡r♣❡t✉❛❧❧② ❡✈❛♥❡s❝❡♥t ❛♥❞ ❡❛❝❤ t❡r♠✱ ✇❤✐❧❡ ♣♦s✐t✐♥❣ ✐ts❡❧❢ ❢♦r t❤❡ ♦t❤❡r
✹✳ ❚r✐❛❞✐❝ s②♥t❤❡s✐s ♦❢ ❛❝❝❡ss♦r② r❡✢❡❝t✐♦♥✿
■❜✐❞✳
❜❡❝❛♠❡
t❤❡ ♦t❤❡r✳
✷✷✹
❚❤❡ ♠❡❛♥✐♥❣ ♦❢ r❡✢❡❝t✐♦♥ ✐s✳✳✳✐ts ❜❡✐♥❣✲❢♦r✳✳✳ ❚❤✐s ♠❡❛♥s t❤❛t t❤r❡❡ ❢♦r♠s ❡①✐st ✐♥ ✐♠♣✉r❡ r❡✢❡❝✲
t✐♦♥✿ t❤❡ r❡✢❡❝t✐✈❡✱ t❤❡ r❡✢❡❝t❡❞✲♦♥✱ ❛♥❞ ❛♥ ✐♥✲✐ts❡❧❢ ✇❤✐❝❤ t❤❡ r❡✢❡❝t✐✈❡ ❤❛s t♦ ❜❡ ✐♥ s♦ ❢❛r ❛s
t❤✐s ✐♥✲✐ts❡❧❢ ✇♦✉❧❞ ❜❡ t❤❡ r❡✢❡❝t❡❞✲♦♥✱ ❛♥ ✐♥✲✐ts❡❧❢ ✇❤✐❝❤ ✐s ♥♦t❤✐♥❣ ♦t❤❡r t❤❛♥ t❤❡ ❋♦r ♦❢ t❤❡
r❡✢❡❝t✐✈❡ ♣❤❡♥♦♠❡♥♦♥✳ ✭✷✷✹✮
✺✳ ❙❛rtr❡ ♦♥ ❍❡❣❡❧✿
■❜✐❞✳
❋♦♦t♥♦t❡ ✾
❲❡ ✜♥❞ ❤❡r❡ ❛❣❛✐♥ t❤❛t ✏❞✐✈✐s✐♦♥ ♦❢ t❤❡ ❡q✉❛❧ t♦ ✐ts❡❧❢ ✑ ✇❤✐❝❤ ❍❡❣❡❧ ♠❛❦❡s t❤❡ ♣❡❝✉❧✐❛r tr❛✐t
❇✉t t❤✐s ❞✐✈✐s✐♦♥ ✐♥st❡❛❞ ♦❢ ❧❡❛❞✐♥❣ t♦ ❛ ❤✐❣❤❡r ✐♥t❡❣r❛t✐♦♥✱ ❛s ✐♥ t❤❡ P❤❡✲
♥♦♠❡♥♦❧♦❣② ♦❢ ▼✐♥❞✱ ♦♥❧② ♠❛❦❡s ❞❡❡♣❡r ❛♥❞ ♠♦r❡ ✐rr❡♠❡❞✐❛❜❧❡ t❤❡ ♥♦t❤✐♥❣♥❡ss ✇❤✐❝❤ s❡♣❛r❛t❡s
♦❢ ❝♦♥s❝✐♦✉s♥❡ss✳
❝♦♥s❝✐♦✉s♥❡ss ❢r♦♠ ✐ts❡❧❢✳ ❈♦♥s❝✐♦✉s♥❡ss ✐s ❍❡❣❡❧✐❛♥✱ ❜✉t ✐t ✐s ❍❡❣❡❧✬s ❣r❡❛t❡st ✐❧❧✉s✐♦♥✳
✸ ❍✉ss❡r❧✬s
♠❛r❣✐♥❛❧ ❝♦♠♠❡♥t ✐♥ ❈♦♣② ❆✿ ✏❉✉❜✐♦✉s✱ ❛♥❞ t♦ ❜❡ ♠♦r❡ ♣r❡❝✐s❡❧② ❝❤❛r❛❝t❡r✐③❡❞ ❛s ❛ r❡❧❛t✐✈❡ ✇❛② ♦❢ s♣❡❛❦✐♥❣✑
✭❚r❛♥s❧❛t♦r✬s ♥♦t❡✳✮
✹ ❍✉ss❡r❧✬s ♠❛r❣✐♥❛❧ ♥♦t❡ t♦ t❤❡ ✜♥❛❧ ❝❧❛✉s❡ ✐♥ ❝♦♣② ❉✿ ✏❄✑ ✭❚r❛♥s❧❛t♦r✬s ♥♦t❡✳✮
✺ ▼✐❝r♦❧❡①✐❝♦♥ ❢♦r ♠❡t❛❧♦❣✐❝❛❧ ♠❛r❦✉♣✿ ❛♥❛❧♦❣②✱ ❛❞✈❡rt✐♥❣✱ ❝❤❛r❛❝t❡r✐st✐❝✱ ❝♦rr❡❧❛t✐♦♥✴❝♦rr❡s♣♦♥❞❡♥❝❡✱
❞✐r❡❝t✐♦♥ ♦❢ r❡❣❛r❞✱
✜①✐♥❣✱ ❤✐❡r❛r❝❤✐❝❛❧ str✉❝t✉r❡✱ ✐♥❞❡①✱ ❧✐✈✐♥❣✱ ♠✉❧t✐♣❧✐❝✐t②✱ ♥♦❡♠❛t✐❝ ✐♥t❡♥t✐♦♥❛❧✐t②✱ ♥♦❡♠❛t✐❝ ❧❡✈❡❧✱ ♦❜❥❡❝t✐✈❛t✐♦♥✱ ♣✐❝t✉r❡✲❛s✲
♣✐❝t✉r❡✱ ♣✐❝t✉r❡✲❝♦♥s❝✐♦✉s♥❡ss✱ ♣✐❝t✉r❡✲♦❢✲❛✲♣✐❝t✉r❡✱ ♣♦ss✐❜✐❧✐t❡s ♦❢ ❝❤❛♥❣✐♥❣ r❡✢❡❝t✐♦♥✱ r❡❣❛r❞✱ s❡❡✐♥❣✲❛s✱ s❤✐❢t ❢r♦♠ ❧❡✈❡❧ t♦
❧❡✈❡❧✱ ✉❧t✐♠❛t❡ ❧❡✈❡❧✱ ✇♦r❧❞ ♦❢ ♣✐❝t✉r❡s
✷
✻✳ ❚❡tr❛❞✐❝ ❞✐s❥✉♥❝t✐✈❡ s②♥t❤❡s✐s ♦❢ ♣✉r✐❢②✐♥❣ r❡✢❡❝t✐♦♥✿ ❙❛rtr❡✱
◆♦t❡❜♦♦❦s ❢♦r ❛♥ ❊t❤✐❝s✱ tr✳
❉❛✈✐❞ P❡❧❧❛✉❡r
✭✹✼✸✲✹✮ ✭❊♠♣❤❛s✐s ❛❞❞❡❞✱ tr❛♥s❧❛t✐♦♥ r❡✈✐s❡❞✳✮
❚❤❡ ❛♣♣❡❛r❛♥❝❡ ♦❢ ♣✉r❡ r❡✢❡❝t✐♦♥ ❝♦♥st✐t✉t❡s ❛♥♦t❤❡r t②♣❡ ♦❢ ❡①✐st❡♥❝❡ ✐♥ ✇❤✐❝❤ t❤❡ ♣r♦❥❡❝t
❛s ♣✉r❡ ❡①✐st❡♥❝❡✱ ✇❤♦s❡ ❞✐♠❡♥s✐♦♥ ✐s ♥♦♥t❤❡t✐❝ ❝♦♥s❝✐♦✉s♥❡ss ✭♦❢ ✮ s❡❧❢✱ ✐s ❛t t❤❡ s❛♠❡ t✐♠❡
t❤❡♠❛t✐③❡❞ ❛♥❞ ❝❛❧❧❡❞ ✐♥t♦ q✉❡st✐♦♥ ✇✐t❤✐♥ t❤❡ ❞❡t♦t❛❧✐③❡❞ r❡✢❡❝t❡❞✴r❡✢❡❝t✐♥❣ ✉♥✐t②✳✳✳ ❚❤❡ ♠♦❞✲
✐✜❝❛t✐♦♥s ❜r♦✉❣❤t ❛❜♦✉t ❜② ♥♦♥❛❝❝❡ss♦r② r❡✢❡❝t✐♦♥ ✭✇❤✐❝❤ ✐s ♥♦t ❛ ❢♦r♠ ♦❢ ❝♦♥t❡♠♣❧❛t✐♦♥ ❜✉t
✐s ✐ts❡❧❢ ❛ ♣r♦❥❡❝t✮ ❛r❡ t❤❡ ❢♦❧❧♦✇✐♥❣✿ ❆ ♥❡✇✱ ✏ ❛✉t❤❡♥t✐❝✱✑ ✇❛② ♦❢ ❜❡✐♥❣ ♦♥❡s❡❧❢ ❛♥❞ ❢♦r ♦♥❡s❡❧❢✱
❚❤✐s ✇❛② ♦❢ ❜❡✐♥❣ ❤❛s ❢♦✉r t❡r♠s
t❤✐s t✐♠❡✿ r❡✢❡❝t❡❞ ✭r❡✢❡❝t✐♦♥✴r❡✢❡❝t✐♥❣✮✱ r❡✢❡❝t✐✈❡ ✭❬r❡✢❡❝t✐♦♥❪✴r❡✢❡❝t✐♥❣✮✳ ❬❈❡tt❡
♠❛♥✐èr❡ ❞✬êtr❡ ❡st à q✉❛tr❡ t❡r♠❡s ❝❡tt❡ ❢♦✐s✿ ré✢é❝❤✐ ✭r❡✢❡t✲r❡✢ét❛♥t✮✱ ré✢❡①✐❢ ✭r❡✢❡t✲r❡✢ét❛♥t✮✳❪
✇❤✐❝❤ tr❛♥s❝❡♥❞s t❤❡ ❞✐❛❧❡❝t✐❝ ♦❢ s✐♥❝❡r✐t② ❛♥❞ ❜❛❞ ❢❛✐t❤✳
❆ t❤❡♠❛t✐❝ ❣r❛s♣✐♥❣ ♦❢ ❢r❡❡❞♦♠✱ ♦❢ ❣r❛t✉✐t②✱ ♦❢ ✉♥❥✉st✐✜❛❜✐❧✐t②✳
❆ ♥❡✇ r❡❧❛t✐♦♥ ♦❢ ♠❛♥ t♦ ❤✐s
♣r♦❥❡❝t✿ ❤❡ ✐s ❜♦t❤ ✐♥s✐❞❡ ❛♥❞ ♦✉ts✐❞❡✳❬❚❪❤❡s❡ t❤r❡❡ ❝❤❛r❛❝t❡r✐st✐❝s✳✳✳❡♥t❛✐❧ ❛ ♠♦❞✐✜❝❛t✐♦♥ ♦❢ ♠②
♣r♦❥❡❝t✳
✼✳ ❇❡❛✉✈♦✐r✿
❋♦r❝❡ ♦❢ ❈✐r❝✉♠st❛♥❝❡
✏❲❤❛t ❞♦ ②♦✉ t❤✐♥❦ ❛❜♦✉t ②♦✉rs❡❧❢✱ ▼♦♥s✐❡✉r ❙❛rtr❡❄✑ ♦♥❡ ❣✐r❧ ❛s❦❡❞ ❛t t❤❡ ❡♥❞ ♦❢ ❛ ❧❡❝t✉r❡✳ ✏■
❞♦♥✬t ❦♥♦✇✱✑ ❤❡ ❛♥s✇❡r❡❞ ✇✐t❤ ❛ ❧❛✉❣❤✱ ✏■✬✈❡ ♥❡✈❡r ♠❡t ♠②s❡❧❢✳✑
✏❖❤✦ ❍♦✇ s❛❞ ❢♦r ②♦✉✦✑
s❤❡
❝r✐❡❞ ✐♠♣✉❧s✐✈❡❧②✳
✽✳ ❈❛❧❡❜ ❍❡❧❞t✿ ✏❆❝❝❡ss♦r② ❛♥❞ ◆♦♥✲❆❝❝❡ss♦r② ❆♣♣r♦♣r✐❛t✐♦♥✿ ❙❛rtr❡ ❛♥❞ t❤❡ ◆❡✉r♦♣s②❝❤♦❧♦❣② ♦❢ ▼❡♠♦r②✑
❞✐✛❡r❡♥❝❡ ❀
❖♥❧② ❛ ♥♦♥✲❛❝❝❡ss♦r② ❛♣♣r♦♣r✐❛t✐♦♥ ♣r❡s❡r✈❡s t❤❡ t❤♦✉❣❤t ♦❢ ❇❡✐♥❣ ✐♥ ✐ts ❛❜s♦❧✉t❡
♦♥❧② ❛ ♣✉r✐✜❡❞ r❡✢❡❝t✐♦♥ ❛s ❛ ✬❦❛t❤❛rt✐❝✬ ✬❧✐❣❤t❬♥❪✐♥❣ ✐♥t✉✐t✐♦♥✬ ♦❢ ♣r❡s❡♥❝❡ ❛♣♣r❡❤❡♥❞s ❇❡✐♥❣
✐♥ ✐ts ♥♦✈❡❧t② ❛♥❞ ❡✈❛♥❡s❝❡♥❝❡✳
❲❤✐❝❤ ✐s t♦ s❛② t❤❛t ♥♦♥✲❛❝❝❡ss♦r② ❛♣♣r♦♣r✐❛t✐♦♥s ❛r❡ t❤♦s❡
✇❤✐❝❤ ❝✉t ❛❝r♦ss ♣r❡✈✐♦✉s ❛♣♣r♦♣r✐❛t✐♦♥s✱ ✇❤✐❝❤ r❡✈❡❛❧ t❤❛t t❤❡ s✐t✉❛t✐♦♥ t❤❛t ♣r❡s❡♥ts ✐ts❡❧❢ ❞♦❡s
♥♦t ❝♦rr❡s♣♦♥❞ t♦ ❛♥② ♣❛st ❛♣♣r♦♣r✐❛t✐♦♥ ❛♥❞ ❛s s✉❝❤ ♥♦ ♦r❣❛♥✐③❛t✐♦♥ ♦❢ ♣❛st ❛♣♣r♦♣r✐❛t✐♦♥s
s✉✣❝✐❡♥t❧② r❡✲♣r❡s❡♥ts ❜❡✐♥❣ ❛s ❝♦❤❡r❡♥t❧② ❛s ✐t ♣r❡s❡♥ts ✐ts❡❧❢ ✐♥ t❤✐s ♥♦✈❡❧ s✐t✉❛t✐♦♥✳
❚❤✐s ✐s
✇❤② ♥♦♥✲❛❝❝❡ss♦r② ❛♣♣r♦♣r✐❛t✐♦♥s ❝❛♥ ❧❡❛❞ t♦ ♥♦✈❡❧ ♣❡rs♣❡❝t✐✈❡s ✇❤✐❝❤ ✐♥ t✉r♥ ✐♥✢✉❡♥❝❡ ❢✉t✉r❡
♦r❣❛♥✐③❛t✐♦♥s ♦❢ ♣❛st ❛♣♣r♦♣r✐❛t✐♦♥s✳ ❆ ♥♦♥✲❛❝❝❡ss♦r② r❡✢❡❝t✐♦♥✱ ❛s ❙❛rtr❡ s❛②s ✐♥ t❤❡
✏❛t ❧❡❛st ✐s✲❛♥❞✲✐s✲♥♦t ❛t t❤❡ s❛♠❡ t✐♠❡ t❤❡ r❡✢❡❝t❡❞✱ ✇❤❡r❡❛s ❛❝❝❡ss♦r② r❡✢❡❝t✐♦♥ ✐s
✇❛②
t❤❡ ❝♦♥st✐t✉t❡❞ ♥♦❡♠❛
◆♦t❡❜♦♦❦s✱
♥♦t ✐♥ ❛♥②
✳ ✭◆✱ ✹✼✷✲✹✼✸✮✱ ✇❤✐❝❤ ✐s t♦ s❛②✱ ❛ ♥♦♥✲❛❝❝❡ss♦r② r❡✢❡❝t✐♦♥ ❛❞❡q✉❛t❡❧②
❛♣♣r♦♣r✐❛t❡s ❇❡✐♥❣ ❜② ♠♦♠❡♥t❛r✐❧② ❝♦rr❡s♣♦♥❞✐♥❣ ✇✐t❤ t❤❡ ❜❡✐♥❣ ♦❢ t❤❡ ♥♦❡♠❛ ❛♥❞ r❡♥❞❡r✐♥❣
✐t ❝♦❤❡r❡♥t✱ ❜✉t ✐t ✐s ♥♦t ✐ts❡❧❢ ✐❞❡♥t✐✜❡❞ ✇✐t❤ ❇❡✐♥❣ s✐♥❝❡ t❤❡ ❞✉r❛t✐♦♥ ♦❢ ❝♦♥s❝✐♦✉s♥❡ss ❛♥❞ t❤❡
❞✉r❛t✐♦♥ ♦❢ t❤❡ ♥♦❡♠❛t✐❝ ❝♦rr❡❧❛t❡ ❛r❡ ❞✐st✐♥❝t❀ t❤❡② ✬❝♦❤❡r❡♥t❧② ❝♦rr❡s♣♦♥❞✬ ❢♦r ❛ ♠♦♠❡♥t✱ ❛♥❞
t❤❛t ✐s ❛❧❧✳
✾✳ ❚❤❡ ♥❡❡❞❡❞ ♦♥t♦❧♦❣✐❝❛❧ ❜❛s✐s✿ ❉❛✈✐❞s♦♥ ✏▼❡♥t❛❧ ❊✈❡♥ts✑ ✭✶✾✼✵✮
❆♥♦♠❛❧♦✉s ♠♦♥✐s♠ r❡s❡♠❜❧❡s ♠❛t❡r✐❛❧✐s♠ ✐♥ ✐ts ❝❧❛✐♠ t❤❛t ❛❧❧ ❡✈❡♥ts ❛r❡ ♣❤②s✐❝❛❧✱ ❜✉t r❡❥❡❝ts t❤❡
t❤❡s✐s✱ ✉s✉❛❧❧② ❝♦♥s✐❞❡r❡❞ ❡ss❡♥t✐❛❧ t♦ ♠❛t❡r✐❛❧✐s♠✱ t❤❛t ♠❡♥t❛❧ ♣❤❡♥♦♠❡♥❛ ❝❛♥ ❜❡ ❣✐✈❡♥ ♣✉r❡❧②
♣❤②s✐❝❛❧ ❡①♣❧❛♥❛t✐♦♥s✳✳✳
❆❧t❤♦✉❣❤ t❤❡ ♣♦s✐t✐♦♥ ■ ❞❡s❝r✐❜❡ ❞❡♥✐❡s t❤❡r❡ ❛r❡ ♣s②❝❤♦♣❤②s✐❝❛❧ ❧❛✇s✱ ✐t ✐s ❝♦♥s✐st❡♥t ✇✐t❤ t❤❡
✈✐❡✇ t❤❛t ♠❡♥t❛❧ ❝❤❛r❛❝t❡r✐st✐❝s ❛r❡ ✐♥ s♦♠❡ s❡♥s❡ ❞❡♣❡♥❞❡♥t✱ ♦r s✉♣❡r✈❡♥✐❡♥t✱ ♦♥ ♣❤②s✐❝❛❧ ❝❤❛r✲
❛❝t❡r✐st✐❝s✳ ❙✉❝❤ s✉♣❡r✈❡♥✐❡♥❝❡ ♠✐❣❤t ❜❡ t❛❦❡♥ t♦ ♠❡❛♥ t❤❛t t❤❡r❡ ❝❛♥♥♦t ❜❡ t✇♦ ❡✈❡♥ts ❛❧✐❦❡
✐♥ ❛❧❧ ♣❤②s✐❝❛❧ r❡s♣❡❝ts ❜✉t ❞✐✛❡r✐♥❣ ✐♥ s♦♠❡ ♠❡♥t❛❧ r❡s♣❡❝t✱ ♦r t❤❛t ❛♥ ♦❜❥❡❝t ❝❛♥♥♦t ❛❧t❡r ✐♥
s♦♠❡ ♠❡♥t❛❧ r❡s♣❡❝t ✇✐t❤♦✉t ❛❧t❡r✐♥❣ ✐♥ s♦♠❡ ♣❤②s✐❝❛❧ r❡s♣❡❝t✳ ❉❡♣❡♥❞❡♥❝❡ ♦r s✉♣❡r✈❡♥✐❡♥❝❡ ♦❢
t❤✐s ❦✐♥❞ ❞♦❡s ♥♦t ❡♥t❛✐❧ r❡❞✉❝✐❜✐❧✐t② t❤r♦✉❣❤ ❧❛✇ ♦r ❞❡✜♥✐t✐♦♥✿ ✐❢ ✐t ❞✐❞✱ ✇❡ ❝♦✉❧❞ r❡❞✉❝❡ ♠♦r❛❧
♣r♦♣❡rt✐❡s t♦ ❞❡s❝r✐♣t✐✈❡✱ ❛♥❞ t❤✐s t❤❡r❡ ✐s ❣♦♦❞ r❡❛s♦♥ t♦
❜❡❧✐❡✈❡
❝❛♥♥♦t ❜❡ ❞♦♥❡❀ ❛♥❞ ✇❡ ♠✐❣❤t
❜❡ ❛❜❧❡ t♦ r❡❞✉❝❡ tr✉t❤ ✐♥ ❛ ❢♦r♠❛❧ s②st❡♠ t♦ s②♥t❛❝t✐❝❛❧ ♣r♦♣❡rt✐❡s✱ ❛♥❞ t❤✐s ✇❡
❦♥♦✇
❝❛♥♥♦t ✐♥
❣❡♥❡r❛❧ ❜❡ ❞♦♥❡✳
❚❤✐s ❧❛st ❡①❛♠♣❧❡ ✐s ✐♥ ✉s❡❢✉❧ ❛♥❛❧♦❣② ✇✐t❤ t❤❡ s♦rt ♦❢ ❧❛✇❧❡ss ♠♦♥✐s♠ ✉♥❞❡r ❝♦♥s✐❞❡r❛t✐♦♥✳ ❚❤✐♥❦
♦❢ t❤❡ ♣❤②s✐❝❛❧ ✈♦❝❛❜✉❧❛r② ❛s t❤❡ ❡♥t✐r❡ ✈♦❝❛❜✉❧❛r② ♦❢ s♦♠❡ ❧❛♥❣✉❛❣❡ ▲ ✇✐t❤ r❡s♦✉r❝❡s ❛❞❡q✉❛t❡
✸
t♦ ❡①♣r❡ss ❛ ❝❡rt❛✐♥ ❛♠♦✉♥t ♦❢ ♠❛t❤❡♠❛t✐❝s✱ ❛♥❞ ✐ts ♦✇♥ s②♥t❛①✳ ▲✬ ✐s ▲ ❛✉❣♠❡♥t❡❞ ✇✐t❤ t❤❡
tr✉t❤ ♣r❡❞✐❝❛t❡ ✬tr✉❡✲✐♥✲▲✱✬ ✇❤✐❝❤ ✐s ✏♠❡♥t❛❧✳✑ ■♥ ▲ ✭❛♥❞ ❤❡♥❝❡ ▲✬✮ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ♣✐❝❦ ♦✉t✱ ✇✐t❤
❛ ❞❡✜♥✐t❡ ❞❡s❝r✐♣t✐♦♥ ♦r ♦♣❡♥ s❡♥t❡♥❝❡✱ ❡❛❝❤ s❡♥t❡♥❝❡ ✐♥ t❤❡ ❡①t❡♥s✐♦♥ ♦❢ t❤❡ tr✉t❤ ♣r❡❞✐❝❛t❡✱ ❜✉t
✐❢ ▲ ✐s ❝♦♥s✐st❡♥t t❤❡r❡ ❡①✐sts ♥♦ ♣r❡❞✐❝❛t❡ ♦❢ s②♥t❛① ✭♦❢ t❤❡ ✏♣❤②s✐❝❛❧✑ ✈♦❝❛❜✉❧❛r②✮✱ ♥♦ ♠❛tt❡r ❤♦✇
❝♦♠♣❧❡①✱ t❤❛t ❛♣♣❧✐❡s t♦ ❛❧❧ ❛♥❞ ♦♥❧② t❤❡ tr✉❡ s❡♥t❡♥❝❡s ♦❢ ▲✳ ❚❤❡r❡ ❝❛♥ ❜❡ ♥♦ ✏♣s②❝❤♦♣❤②s✐❝❛❧
❧❛✇✑ ✐♥ t❤❡ ❢♦r♠ ♦❢ ❛ ❜✐❝♦♥❞✐t✐♦♥❛❧✱ ✬✭① ✮
✭① ✐s tr✉❡✲✐♥✲▲ ✐❢ ❛♥❞ ♦♥❧② ✐❢ ① ✐s
φ✮✬ ✇❤❡r❡✱ ✬φ✬ ✐s r❡♣❧❛❝❡❞
❜② ❛ ✏♣❤②s✐❝❛❧✑ ♣r❡❞✐❝❛t❡ ✭❛ ♣r❡❞✐❝❛t❡ ♦❢ ▲✮✳ ❙✐♠✐❧❛r❧②✱ ✇❡ ❝❛♥ ♣✐❝❦ ♦✉t ❡❛❝❤ ♠❡♥t❛❧ ❡✈❡♥t ✉s✐♥❣
t❤❡ ♣❤②s✐❝❛❧ ✈♦❝❛❜✉❧❛r② ❛❧♦♥❡✱ ❜✉t ♥♦ ♣✉r❡❧② ♣❤②s✐❝❛❧ ♣r❡❞✐❝❛t❡✱ ♥♦ ♠❛tt❡r ❤♦✇ ❝♦♠♣❧❡①✱ ❤❛s✱ ❛s
❛ ♠❛tt❡r ♦❢ ❧❛✇✱ t❤❡ s❛♠❡ ❡①t❡♥s✐♦♥ ❛s ❛ ♠❡♥t❛❧ ♣r❡❞✐❝❛t❡✳✳✳
❚❤❡ ❛♥❛❧♦❣② ❥✉st ❜r✉✐t❡❞✱ ❜❡t✇❡❡♥ t❤❡ ♣❧❛❝❡ ♦❢ t❤❡ ♠❡♥t❛❧ ❛♠✐❞ t❤❡ ♣❤②s✐❝❛❧✱ ❛♥❞ t❤❡ ♣❧❛❝❡ ♦❢
t❤❡ s❡♠❛♥t✐❝❛❧ ✐♥ ❛ ✇♦r❧❞ ♦❢ s②♥t❛①✱ s❤♦✉❧❞ ♥♦t ❜❡ str❛✐♥❡❞✳
❨❡s ✐t s❤♦✉❧❞✦ ▲❡t✬s str❛✐♥ ✐t ❛♥❞ s❡❡ ✇❤❛t ❤❛♣♣❡♥s✳ ✭❖❤✱ ❛♥❞ ♥♦t❡ t❤❛t t❤❡ ♦♥t♦❧♦❣② ♦❢
❛♥ ❛♥♦♠❛❧♦✉s ♠♦♥✐s♠ ✐♥ t❤❡ str✐❝t s❡♥s❡ ❞❡r✐✈❛❜❧❡ ❢r♦♠ ❞✐❛❣♦♥❛❧✐③❛t✐♦♥✳✮ ❏✳
✹
❇❡✐♥❣ ❛♥❞ ❊✈❡♥t ✐s
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