WorLd Of Consciousness

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    A Course in

    ConsciousnessPart 1: Quantum theory and consciousness

    Part 2: The metaphysics of nonduality

    Part 3: The end of sufferingand the discovery of our true nature

    Stanley Sobotta!meritus Professor of Physics

    "niversity of #irginiaCharlottesville$ #A 22%&'(')1'

    Permission is granted to copy and distribute freely* Changes in content are not permitted* Please cite this+ebsite ,http:--faculty*virginia*edu-consciousness .*

    /mportant: 0ecause this course maes many statements$ the reader might thin that itcomprises a ne+ belief system$ either to be adopted or reected* o+ever$ that is not myintention nor is it the intention of the sages of nonduality +ho are uoted anddiscussed* 0eliefs are not understanding in themselves((they can actually beobstructions to understanding* 0ecause 4eality cannot be described in +ords$ the

    +ords are meant to be used as pointers to 4eality rather than as descriptors of 4eality*ence$ this is a course in seeing$ not in believing*

    0

    http://faculty.virginia.edu/consciousnesshttp://faculty.virginia.edu/consciousness
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    Table of contents

    (With last update date)

    Summary: A Dialogue in Consciousness (March 13, 011)

    !ore"ord(August 13, 00#)

    Part 1* Quantum theory and consciousness$re%ace to part 1(April 1, 000)

    Chapter 1& 'he three maor metaphysical philosophies(Septemer *, 010) 1&1& 'he assumption o% oecti+e reality, a necessity %or sur+i+al and %or science 1&& Materialism (pure oecti+ity): the philosophy that all is matter, or at least, all isgo+erned y physical la" 1&3& Cartesian dualism (oecti+ity plus suecti+ity): the philosophy that oth matter and

    mind are primary and irreducile 1&-& .dealism (pure suecti+ity): the philosophy that consciousness is all and all isconsciousness

    1&/& 'he teaching o% nonduality 1&& 'he distinction et"een Consciousness, A"areness, and mind 1&*& What is eality notChapter & Classical physics %rom 2e"ton to instein(4ctoer 11, 010) &1& 'he scienti%ic method && 2e"ton5s la"s and determinism &3& 'hermodynamics and statistical mechanics6 entropy and the direction o% time

    &-& lectromagnetism &/& Wa+es && elati+ityChapter 3& 7uantum physics %rom $lanc8 and instein to 9ohr, eisenerg, de 9roglie, andSchr;dinger(4ctoer 1, 010) 3&1& 'he eginning o%

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    Chapter /& Conscious mind and %ree "ill(4ct& 1, 010) /&1& What are the characteristics o% conscious mind /&& =traordinary ailities o% the mind /&3& 'he unity o% the human mind /&-& >nconscious %unctioning o% the rain /&/& .s there a test %or consciousness

    /&& Can a machine e conscious /&*& What seem to e the e%%ects o% consciousness /&B& When and ho" does a child egin to percei+e oects /& 'he e=periments o% iet, et al&, and their implication %or %ree "ill /&10& 9rain imaging e=periments on %ree "ill

    /&11& !ree "ill as the possiility o% alternati+e action /&1& 'he origin o% the elie% in %ree "ill /&13& .s %ree "ill necessary %or our happiness /&1-& !reedom as suecti+ity /&1/& .% there is no %ree "ill, ho" do things happen /&1& Speculations on the %uture in deterministic and proailistic uni+erses

    Chapter & What does

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    Chapter B& 'ranscendental realms(!eruary 0, 010) B&1& Similarities et"een the di%%erent transcendental realms B&& 'he meanings o% the transcendental realms

    Chapter #& $ercei+ing and conceptualiFing (March 13, 011)

    #&1& A re+ie" o% the physics #&& What is the percei+ed #&3& Who is the percei+er #&-& Many minds, one A"areness #&/& 4ecti%ication, the ody@mind organism, and the primacy o% the concept o% memory

    #&& 'he hard prolem in consciousness scienceChapter 10& 'he teaching o% nonduality(4ctoer 1-, 00*) 10&1& 'he metaphysics o% nonduality 10&& 'he practices 10&3& 'he paths

    10&-& Aout death 10&/& Summary diagram

    Chapter 11& 'he %unctioning o% the mind(April *, 010) 11&1& 'he nature o% duality 11&& 'he appearance o% sentience "ithin Consciousness 11&3& Mani%estation: 'he %irst le+el o% identi%ication 11&-& 4ecti%ication: 'he second le+el o% identi%ication 11&/& 4"nership: 'he third le+el o% identi%ication 11&& $olar pairs, separation, and su%%ering 11&*& 'he +ictimG+ictimiFer polar pair 11&B& Sin, guilt, and shame@@monstrosities o% mind 11& 'he thin8ing mind and the "or8ing mind 11&10& Summing up& & &

    Chapter 1& Space, time, causality, and destiny(March -, 010) 1&1& 'he concepts o% space and time 1&& Speculations on the concepts o% nonlocality in time and space 1&3& 'he concept o% causality 1&-& 'he nature o% la"s 1&/& 'he concept o% destiny and od?s Will 1&& We are already here no" 1&*& Maya, the di+ine hypnosis

    Chapter 13& Some use%ul metaphors(2o+emer 1, 00#) 13&1& 'he dream 13&& 'he mo+ie 13&3& 'he puppet and the root 13&-& 'he shado" 13&/& 'he ocean 13&& 'he thorns 13&*& lectricity and the appliance

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    13&B& 'he gold oect 13& 'he dust in a light eam 13&10& 'he mirror 13&11& 'he sna8e and the rope 13&1& 'he mirage 13&13& 'he pot and the space in "hich it e=ists

    Chapter 1-& eligion, elie%, and nonduality(2o+emer 13, 00#) 1-&1& 'he di%%erence et"een religion and nonduality 1-&& eligion as the elie% in a dualistic od 1-&3& A nondualistic +ie" o% od 1-&-& eligion as the elie% in oecti+e reality 1-&/& 9uddhism@@religion or not 1-&& Hipassana meditation 1-&*& Ien 1-&B& 4ther nondual teachings

    Chapter 1/& !ree "ill and responsiility(June *, 00*)

    Chapter 1& o+e see8ing .tsel% (April 1, 010) 1&1& 2ondualistic +s& dualistic lo+e 1&& Sel%@hatred and sel%@lo+e 1&3& A%%irmation as sel%@lo+e practice 1&-& !looding oursel+es and others "ith light 1&/& 'onglen practicePart 3* The end of suffering and the discovery of our true nature$re%ace to part 3(2o+emer 1B, 00#)

    Chapter 1*& o" to li+e one5s li%e (April 1, 010) 1*&1& 'he prolems "ith reading the scriptures 1*&& +erything happens y itsel% 1*&3& Meaning and purpose in li%e 1*&-& 'he "ill to li+eGthe "ish to die

    1*&/& .% su%%ering is to end, spiritual practice usually happens %irst 1*&& 'he rarity o% enlightenment 1*&*& o" is peace realiFed 1*&B& An e=ploration o% non+olitional li+ing (1##3), y alen Sharp

    Chapter 1B& $ractices and teachers(August *, 010)

    1B&1& Why practice 1B&& 'he importance o% eing a"are 1B&3& Some sages and the practices they teach 1B&-& Who or "hat is it that practices 1B&/& Some possily help%ul tips 1B&& Some o% the contemporary sages o% nonduality

    Chapter 1#& Surrender, mantra, and trust (Decemer , 00#) 1#&1& Surrender and mantra practice

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    1#&& amesh?s teaching on surrender 1#&3& 'rusting A"areness

    Chapter 0& >nderstanding y direct seeing(Decemer , 00#) 0&1& 'he role o% concepts in Ad+aita 0&& What is direct seeing

    0&3& 'he use o% direct seeing to disidenti%y %rom the E.E@doer 0&-& 'he use o% direct seeing to disidenti%y %rom EmineE 0&/& 9ecause there is no E.E, there is no other

    Chapter 1& esistance, clinging, and acceptance (August , 010) 1&1& What are resistance and clinging 1&& epression o% emotions creates physical illness 1&3& esistance, desireG%ear, attachmentGa+ersion 1&-& What is Acceptance 1&/& When resistance ends, li%e ecomes stress@%ree

    Chapter & Disidenti%ication %rom attachment and a+ersion (January , 010)Chapter 3& Disidenti%ication through in

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    c& Without thoughts, there are no oects (e&g&, in dreamless sleep, under anesthesia,or in samadhi) ecause, y de%inition, an oect is the thought o% it&d& eality is not a thought& ather, .t is asence o% separation&

    2* 6hat is meant by true and untrue concepts7

    a& A elie% is a concept "hich contains the concept o% attachment&& A elie% that cannot e +eri%ied y direct seeing is al"ays suect to attac8 y acounter@elie%& 'here%ore, it must e constantly rein%orced y repetition o% the elie%&c& Since eality is asence o% separation, .t cannot e percei+ed& 'here%ore, conceptscannot descrie eality (ut they can e true, see g and h elo")&d& =ample: A material oect y de%inition is separate %rom other material oects&'here%ore, material oects are not real& 'he elie% that material oects are real isconstantly rein%orced y materialistic culture, and is sustained only y a %ailure to seethe distinction et"een oects and eality&e& Although concepts cannot descrie eality, they can point to eality&%& A pointer is an in+itation to see directly the distinction et"een an oect and eality&

    g& .% a concept asserts or implies the reality o% any oect, it is untrue& .% it negates thereality o% an oect, it is true (ut not a description o% eality)& A true concept can e ause%ul pointer to eality&h& =ample: 'he concept that material oects are not real is true, and is a pointer toeality&

    3* 6hat is the +orld ,the universe.7

    a& 'he "orld (the uni+erse) is the collection o% oects consisting o% the ody@mind andall other oects& 'he "orld appears to e=ist in time and space&& o"e+er, time and space are nothing ut concepts& 'hey are not real&

    c& 'ime is the concept o% change& Since all oects change, all oects are temporalconcepts&d& Space is the concept o% e=tension (siFe and shape)& Since all oects are e=tended inspace, all oects are spatial concepts&

    '* 6hat are polar$ or dual$ pairs of concepts7

    a& 'hought al"ays results in inseparale pairs o% concepts (dual pairs) ecause e+erythought has an opposite&& eality is apparently split into dual pairs y thought& o"e+er, no thought is real sinceeality cannot e split&c& 'he result o% apparently splitting eality into dual pairs o% concepts is called duality&d& 'he t"o concepts o% a pair are al"ays inseparale ecause the merger o% theopposites "ill cancel the pair&e& =ample: [email protected] is a dual pair o% concepts& .% the E.E and [email protected] merge, neitherconcept remains&

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    8* 6hat is A+areness-Presence7

    a& A"arenessG$resence is not a concept or oect& .t is "hat is a"are o% all conceptsand oects&& .t does not change and .t has no e=tension so .t is time@less and space@less&c& o"e+er, .t is said to e space@li8e ecause all concepts and oects are said to

    appear in .t&d& 'he terms KA"arenessG$resenceL and KealityL are e

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    1&* 6hat is the true nature of all obects7

    a& All apparent oects arise in A"arenessG$resence&& 9ecause physical space and time are apparent oects, they also arise in

    A"arenessG$resence&c& 2o apparent oect is separate %rom A"arenessG$resence& 'hus, all apparent oects

    consist o% A"arenessG$resence&d& 4ects are not real as oects ut they are real as A"arenessG$resence&e& A"arenessG$resence "elcomesGlo+es all apparent oects that appear in .t&

    11* 6hat is the personal sense of doership7

    a& Along "ith illusory E.E@oect, arises also the sense o% personal doership&& o"e+er, since there is no E.E@oect, there is no doer, no thin8er, no chooser, and nooser+er&c& 'here%ore, E"eE ha+e no control& 'hus, "hate+er happens, happens& Whate+erdoesn?t happen, doesn?t happen&

    12* /f there is no doer$ ho+ do things happen7

    a& +erything that happens is only an arising in A"arenessG$resence&& 4nly one arising is present at any moment& 2o other arisings are e+er present toa%%ect the arising that is present&c& Since no arising is present to a%%ect the arising that is present, there can e no la" o%cause@and@e%%ect&d& 'he concept o% causality, i&e&, that one e+ent causes another e+ent, is only an arisingin A"arenessG$resence&e& Since causality is only a concept, E.E can ne+er do anything&

    %& 9ecause E.E can do nothing, neither can E.E choose& 'hus, %ree "ill is nothing ut anempty concept&

    13* 6hat is suffering7

    a& 'he %eeling o% eing separate is an arising that carries "ith it a sense o% shame %or%eeling isolated, alienated, lonely, and disconnected&& 'he sense o% %ree "ill is an arising that carries "ith it the %eeling o% personalresponsiility %or EmyE past and EmyE %uture&c& 'he sense o% personal responsiility is an arising that carries "ith it guilt and regret%or EmyE past and "orry and an=iety %or EmyE %uture&

    1'* 6hat is a+aening ,enlightenment.7

    a& A"a8ening is the realiFation that . am not separate and . ha+e ne+er een separate&'here%ore there is no shame&& A"a8ening carries "ith it the realiFation that . do nothing and . ha+e ne+er doneanything& 'here%ore, there is no regret, guilt, "orry, or an=iety&c& A"a8ening is the a"areness that eality, "hich is "hat . am, has ne+er eena%%ected y any concepts&

    B

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    d& A"a8ening is the a"areness that my true nature includes a sense o%WelcomingGo+e&

    18* 6hat can +e do to a+aen7

    a& Since direct seeing sho"s that there is no doer, there is nothing that the Eindi+idualE

    can do to a"a8en&& Since a"a8ening transcends time, no practice that occurs in time can ring aouta"a8ening& 'hus most practices do not ring aout a"a8ening&c& o"e+er, direct seeing can ring aout a"a8ening ecause direct seeing is timelessseeing&

    19* 5oes this mean that there is no hope for the sufferer7

    a& De%initely not& 'here are many practices that "ill lead to less su%%ering& o"e+er, li8eall other actions, they are ne+er done y a doer since there is no doer& 'here%ore, E"eEcannot do them& .% they happen, they happen& .% not, they don5t&

    & =ample: 'o see that there is no K.L, loo8 in"ard %or it and see that there is none& Seealso that e+erything that happens, including all thoughts and %eelings, happensspontaneously so there can e no doer&c& =ample: 'o see that no oect e=ists, loo8 and see that all oects are nothing utarisings in A"arenessG$resence& 'hen, loo8 and see that no oect could e+er ringEyouE peace& !inally, see that nothing can a%%ect ou "ho are

    A"arenessG$resenceG$resence .tsel%&

    1)* 6hat else can +e do7

    a& We can go in"ard and do"n"ard and %eel the reath& 'his ta8es us out o% the head

    and the thin8ing mind and puts us in the ody and the senses&& We can practice mind%ulness and see that our attachments and a+ersions are nothingut arisings in A"arenessG$resence&c& We can ecome a"are that all oects are nothing ut arisings in

    A"arenessG$resence and there%ore cannot a%%ect >s&d& We can see that there can e no su%%ering in pure A"arenessG$resence&e& We can trust A"arenessG$resence, "hich is our true nature&%& We can rest in A"arenessG$resence, "hich is our home&

    =ore+ord

    !rom 1## through 1##/, . taught se+eral seminars on reality and consciousness according toni+ersity o% Hirginia& 'hese seminarsattempted to outline in an understandale "ay to the nonscientist the reasons "hyconsciousness is a necessary part o% the most "idely accepted interpretations o%

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    !rom 1##/ through spring 00B, again %or the undergraduate nonscientist, . taught manyseminars on nonduality, or Ad+aita, eginning "ith the ao+e descried scienti%ic in%ormationas $art 1, %ollo"ing "ith se+eral speculati+e chapters on the metaphysics o% nonduality as $art, and concluding "ith the teachings o% se+eral contemporary nanis, or enlightened sages, as$art 3& Sages are not usually interested in teaching the principles o% nonduality in such asystematic, logical "ay since such a conceptual system can e a prison %or the mind, leading it

    to thin8 that it can transcend itsel% (escape %rom its sel%@imposed prison) merely y masteringthe system& 2e+ertheless, %or teaching purposes, . "rote a set o% notes %or these seminarsalso& 9eginning "ith %all 00*, . egan to teach the same course to senior citiFens and othercollege graduates also&. ha+e continually updated and re%ined these notes as my e=perience and insights ha+ee+ol+ed& My intent has een to present the teaching o% nonduality in a scienti%ically sound andlogically consistent, ut still readale, document& While there is little aout $art 1 that anyscientist "ould disagree "ith, gi+en enough time %or care%ul contemplation, there isconsiderale material in $arts and 3 that is in disagreement "ith "hat some sages say& 'hereason %or this di%%erence is that science deals entirely "ith concepts, "hich can e seen to e

    either sel%@consistent or not, and in agreement "ith oser+ations or not, "hile it is impossile%or a sage to use concepts to descrie eality, ecause eality transcends all concepts& .nscience, concepts are (or are not) truth, "hile in spiritual teachings, concepts can only epointers to eality& 'he sage uses concepts as tools to crac8 open the conceptual prisons in"hich "e li+e, ut then all o% those concepts must e thro"n a"ay or they ecome chains inour ondage& 2e+ertheless, there are many concepts in $arts and 3 that are susceptile to+eri%ication y direct oser+ation y those "ho thin8 they are still in prison, and these impartcredence to the rest o% the teaching&

    !or the reader "ho is not interested in

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    mani%ests the "orld& o"e+er, it cannot e the indi+idual consciousness o% the oser+er thatdoes this, ut it must e nonlocal, uni+ersal Consciousness&

    Chapter 1* The three maor metaphysical philosophies

    1*1* The assumption of obective reality$ a necessity for survival and for science7

    'he assumption o% an e=ternal reality is the assumption that there is a real "orld that ise=ternal to our mind and senses, and that it e=ists "hether or not "e as oser+ers e=ist, and"hether or not "e are oser+ing it& .t is one "e all commonly ma8e "ithout e+en thin8ing aoutit& We assume the o%%ice and the computer in it are there a%ter "e lea+e "or8 at the end o% theday and "ill e there "hen "e arri+e at "or8 in the morning& When "e head home at the endo% the day, "e assume that our house or apartment "ill e there "hen "e arri+e, and that itcontinued to e there in our asence a%ter "e le%t in the morning& We assume that our %riends,relati+es, and ac

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    e+en though they are y necessity suecti+e, are considered to e oecti+e and %or thisreason, "e consider psychology to e an oecti+e science&

    'he concept o% oecti+e reality is also applied to the study o% history, "hich is thought to e amore@or@less accurate record o% past e+ents& .n order to e considered an oecti+e part o% therecord, e+ents must e agreed upon y historians& o"e+er, history is continually changing as

    ne" historical E%actsE appear, so history is only "hat "e thin8 it is at the present time& +en2apoleon is reputed to ha+e said, EWhat is history ut a %ale agreed uponE&

    What aout the person "ho oser+es hisGher o"n thoughts, %eelings, and sensorye=periences .n this case, the oser+ed reality is clearly not e=ternal, ut it still can ecommunicated and compared "ith similar internal oser+ations o% others, so, i% there isagreement, normally "e regard it to e oecti+e& !or e=ample, there is no di%%iculty "hen "ecompare the mental steps that "e go through "hile "or8ing the same math prolem, or e+en"hen "e compare our e=periences o% %ear, or red, i% "e are responding to the same Ee=ternalEstimuli& .% "e agree that "e are seeing or %eeling the same thing, then "e de%ine thesee=periences to e oecti+e ut not e=ternal&

    7uestion: .s there any "ay o% +eri%ying that your thoughts e=ist i% you are not oser+ingthem.% you elie+e they e=ist in your suconscious mind, ho" can you +eri%y that.% you cannot +eri%y it, "hy "ould you elie+e it

    /n fact$ all observations of so(called

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    that KnormalL minds can e really considered to e su%%ering %rom collecti+e delusion and thatall su%%ering, "hile KnormalL, is the result o% this delusion&

    Does the mind %unction "hen "e are not oser+ing it .n our e+eryday e=perience, the mind"ill sometimes appear to "or8 on a prolem unconsciously or suconsciously, i&e& "ithoutconscious a"areness, so that the solution later appears %ull@lo"n, seemingly in a %lash o%

    genius& o"e+er, this assumes that the mind is a real oect that can e=ist outside o%a"areness, i&e&, that it is oecti+ely real& (ater "e shall use a di%%erent de%inition %or the mind&)9ecause the suconscious and unconscious minds can ne+er e oser+ed directly, theire=istence can only e an assumption&

    9ecause all o% our e=periences are necessarily suecti+e, "e ha+e no means to get eyondthem to any 8ind o% oecti+e reality that might e=ist& 9ecause o% this, it is impossile %or anoecti+e reality to re+eal itsel% through any oser+ation& 'hus, the e=istence o% an oecti+ereality can ne+er e pro+ed and, e+en i% such an oecti+e reality e=isted, it could ne+er a%%ectany o% our oser+ations&

    7uestion: .s there any "ay o% +eri%ying that your %eelings e=ist i% you are notoser+ing them.% you elie+e they e=ist suconsciously, ho" can you +eri%y that.% you cannot, "hy "ould you elie+e it

    While "e may call it reality, e=ternal oecti+e reality is not reality at all& An assumption that yits +ery nature cannot e +eri%ied is not a physical assumption, ut is called a metaphysicalassumption& (Such an assumption can also e called an a=iom&) 'hus, the edroc8 o% allscience is not science at all ut is metaphysics 2ot only the nature o% science, ut also oure=perience o% li+ing, "ould e %undamentally changed i% this assumption "ere not made& aterin this course, "e shall discuss a teaching in "hich this assumption is not made and "hich

    gi+es us a radically di%%erent picture o% oursel+es and o% the "orld&

    13

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    'o leap or not to leapArt y Jolyon,"""&olyon&co&u8

    1*2* >aterialism ,pure obectivity.: The philosophy that all is matter$ or at least$ all isgoverned by physical la+

    'he earliest "ell@articulated philosophy o% materialism "as that o% Democritus (ree8philosopher, c& -0 @ c& 3*0 9C)& e postulated a "orld made up entirely o% hard, in+isile

    particles called atoms& 'hese atoms had shape, mass and motion, ut had no other

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    roadened to state that physical la" rather than matter and energy is primary, i&e&, e+erythingcan e e=plained and understood in terms o% physical la"& 'his is called scientism, or scienti%icmaterialism&

    4% course, this immediately egs the

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    A maor prolem o% materialist philosophy is ho" to e=plain consciousness& Materialists canhardly deny the e=istence o% consciousness ecause it is a uni+ersal e=perience&'he generally accepted materialist e=planation is that consciousness is an epiphenomenon, oran emergent %eature, o% matter& .t de+elops "hen material oects reach a certain le+el o%comple=ity, that o% li+ing organisms, or at least o% certain types o% them& o"e+er, ecause it istotally dependent on matter %or its e=istence, it cannot a%%ect or in%luence matter& .t can only e

    a"are o% it& Matter is still primary&

    A related prolem is ho" to determine the le+el o% comple=ity at "hich consciousness ispresent& .% mammals are conscious, are irds Are insects What aout amoeas andacteria .% the aility to reproduce is the only criterion, "hat aout sel%@reproducing proteinmolecules, li8e prions (the in%ectious agent in Emad co"E disease) .% comple=ity is the onlycriterion %or consciousness, "hat aout inanimate oects .% they are included, at "hat le+el o%comple=ity .% they are e=cluded, "hy are they e=cluded Materialists ha+e no ans"ers tothese

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    near@human eha+iors& .% animals are included, do "e e=clude any o% them What aout plantsand microes What aout protein molecules and other inanimate oects Cartesian dualismhas no satis%actory ans"ers to these

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    something %rom "hich all things arise and to "hich they all return& e "as struc8 y the %actthat the "orld presents us "ith a series o% opposites, o% "hich the most primary are hot andcold, "et and dry& e thought o% these opposites as eing Eseparated outE %rom a sustance"hich "as originally undi%%erentiated&

    $lato (ree8 philosopher, c& -B 9C @ c& 3-B 9C) is o%ten considered the %irst idealist

    philosopher, chie%ly ecause o% his metaphysical doctrine o% !orms& $lato considered theuni+ersal .dea or !orm, sometimes called an archetypeO%or e=ample, redness or goodnessOto e more real than a particular e=pression o% the %ormOa red oect or a good deed&

    According to $lato, the "orld o% changing e=perience is unreal, and the .dea or !ormO"hichdoes not change and "hich can e 8no"n only y reasonOconstitutes true reality& $lato didnot recogniFe mystical e=perience as a route to true reality, only reason&

    .dealism "as %irst e=pounded y $lato in his ca+e allegory in The Republic(c& 30 9C) (see,e&g&, Julia Annas,An Introduction to Platos Republic, 1#B1, p& /)& 'he ca+e is a metaphor%or the mind& $risoners are in an underground ca+e "ith a %ire ehind them, ound so they cansee only the shado"s on the "all in %ront o% them, cast y puppets manipulated ehind them&

    'hey thin8 that this is all there is to see6 i% released %rom their onds and %orced to turn aroundto the %ire and the puppets, they ecome e"ildered and are happier le%t in their original state&'hey are e+en angry "ith anyone "ho tries to tell them ho" piti%ul their position is& 4nly a %e"can ear to realiFe that the shado"s are only shado"s cast y the puppets6 and they egin the

    ourney o% lieration that leads past the %ire and right out o% the ca+e into the real "orld& At %irstthey are daFFled there, and can ear to see real oects only in re%lection and indirectly, utthen they can loo8 at them directly in the light o% the sun, and can e+en loo8 at the sun itsel%&

    'his allegory is related to idealism in the %ollo"ing "ay& 'he ca+e is the mind& 'he shado"s o%the puppets that the prisoners are "atching represent their ta8ing o+er, in unre%lecti+e %ashion,

    the second@hand opinions and elie%s that are gi+en to them y parents, society, and religion&'he puppets themsel+es represent the mechanical, unreasoning minds o% the prisoners& 'helight o% the %ire "ithin the ca+e pro+ides only partial, distorted illumination %rom the imprisonedintellects& ieration egins "hen the %e" "ho turn around get up and go out o% the ca+e&4utside o% the ca+e, the real oects (the !orms) are those in the transcendental realm& .norder to see them, the light o% the sun, "hich represents pure reason, is necessary& A similarallegory using today5s symols "ould replace the ca+e "ith a mo+ie theater, the shado"s "iththe pictures on the screen, the puppets "ith the %ilm, and the %ire "ith the proector light& 'hesun is outside, and "e must lea+e the theater to see its light ("e must lea+e the mind)&

    1B

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    'he ne=t maor idealist philosopher "as $lotinus (0-G/ P *0 AD), "ho is generally regardedas the %ounder o% 2eoplatonism& e "as one o% the most in%luential philosophers in anti

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    .s there more than one consciousness .% so, "hat de%ines a consciousness

    .% there is more than one consciousness, ho" do di%%erent consciousnesses communicate

    Solipsism is a %orm o% idealistic philosophy that states that nothing e=ists that you yoursel% arenot oser+ing& 4n the other hand, nonsolipsisticidealistic philosophystates that nothing e=istsunless it is eing oser+ed y any conscious oser+er& 9ecause these are idealistic

    philosophies, there is no oecti+e reality in either o% them& A %la" in oth o% these +ie"s is theassumption that the oser+er itsel% is an oecti+e entity (see Section 1&1)& 9ut i% there is nooecti+e reality, neither can there e an oecti+e oser+er&

    !or our purposes in this section, "e shall consider a +ersion o% idealism, called monisticidealism, "hich states that Consciousness and only Consciousness is %undamental andprimary& +erything, including all matter and e+ery mind, e=ists "ithin Consciousness& !romthis point o% +ie", matter is an emergent %eature, or epiphenomenon, o% Consciousness, ratherthan the re+erse as in materialism& 'here are perple=ing parado=es in

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    "hat "e shall call a teaching& 'he purpose o% a teaching is to help a student to 8no" a reality,"hether it is phenomenal or noumenal& Since the emphasis is on 8no"ing rather than on logic,a teaching may use "hate+er concepts and techni

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    common usage& 9eginning in Chapter #, "e shall e more precise and shall start re%erring toConsciousness (capitaliFed) as All@'[email protected]& 'his includes 2oumenon (the >nmani%est) andphenomenon (the mani%est)& When "e spea8 o% our e=perience, "e shall o%ten re%er to2oumenon as A"areness, and to phenomenon as mind& 'hen the "ord mind "ill mean onlythe e=perience o% the mental, sensory, and perceptual %unctioning o% the indi+idual organism,not to any 8ind o% physical oect such as the rain& 'he comination o% ody and mind "e

    shall re%er to as the ody@mind organism& A%ter Chapter #, "e shall not use consciousness(uncapitaliFed) unless "e are %ollo"ing the usage o% other "riters&

    =ercise: Whene+er you can thin8 o% it, as8, EWhat is it that does not change no matter "hat .am doing or "hat is happening 'hen loo8 and see& 'he purpose o% the

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    oser+ational astronomyE, the E%ather o% modern physicsE, and the E%ather o% modernscienceE& .n his 13 oo8, "ialogue#oncerning the T$o #hie% &orld S'stems, heargued %or the Copernican model o% the solar system against the traditional $tolemaicsystem& e "as con+icted o% heresy %or this y the Catholic Church in 133&

    -& Halidation o% the results o% e=perimental measurements y "idespread

    communication and pulication so that other scientists are ale to +eri%y themindependently& Although scientists throughout history ha+e communicated andpulished their results, the %irst scientist to articulate the need %or pulishing the detailso% his e=perimental methods so that other scientists could repeat his measurements"as nglish chemist oert 9oyle (1* @ 1#1), "ho "as strongly in%luenced y the+ie"s o% 9acon&

    /& .ntuiting and %ormulating the mathematical la"s that descrie the e=ternal, oecti+ereality& 'he most uni+ersal la"s are those o% physics, the most %undamentalscience& nglish natural philosopher .saac 2e"ton (1- @ 1**) "as the %irst scientistto %ormulate la"s that "ere considered to apply uni+ersally to all physical systems&

    'he last %our o% these components (three o% them y nglishmen) "ere all de+eloped in theremar8aly rie% period %rom 10 to 1B*&

    2*2* ?e+ton@s la+s and determinism

    .n order to understand

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    to e=plain the la"s o% erman astronomer and mathematician Johannes Qepler (1/*1 @ 130),"hich descrie the planetary orits, made use o% the %amous %ree@%all e=periments %rom theleaning to"er o% $isa y .talian scientist alileo alilei (1/- @ 1-), and in+ented thecalculus in order to gi+e a proper mathematical %rame"or8 to the la"s o% motion that hedisco+ered& 2e"ton considered himsel% to e a natural philosopher, ut contemporary custom"ould accord him the title o% physicist& .ndeed, he, proaly more than any other scientist,

    estalished physics as a separate scienti%ic discipline ecause o% his attempts to e=press hisconclusions in terms o% uni+ersal physical la"s& e is thought y some to ha+e een thegreatest scientist that has e+er li+ed& .n 1B* at the age o% -- he pulished his Philosophiaeaturalis Principia (athematica )(athematical Principles o% atural Philosoph'*in "hich heset %orth his la"s o% motion and gra+itation&

    is three la"s o% motion can e "ritten as %ollo"s:

    1& A ody mo+es "ith constant +elocity (speed and direction) unless there is anonFero net %orce acting on it& (A ody at rest has a constant Fero +elocity, thusthe net %orce acting on it must e Fero&)

    & 'he rate o% change o% the +elocity (change in speed or direction, called theacceleration) o% a ody is proportional to the %orce on the ody&

    3& .% one ody e=erts a %orce on another ody, the second ody e=erts an e

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    all motions, %rom those o% the planets and stars to those o% the molecules in a gas& 'hisuni+ersal success led to the "idespread elie% in the principle o% determinism, "hich says that,i% the state o% a system o% oects (e+en as all@encompassing as the uni+erse) is 8no"nprecisely at any gi+en time, such as no", the state o% the system at any time in the %uture canin principle e predicted precisely& !or comple= systems, the actual mathematics might e toocomplicated, ut that did not a%%ect the principle& >ltimately, this principle "as thought to apply

    to li+ing eings as "ell as to inanimate oects& Such a deterministic "orld "as thought to ecompletely mechanical, "ithout room %or %ree "ill, indeed "ithout room %or e+en a smallde+iation %rom its ultimate destiny& .% there "as a od in this "orld, his role "as limited entirelyto setting the "hole thing into motion at the eginning&

    .ntrinsic to the principle o% determinism "as the assumption that the state o% a system o%oects could e precisely descried at all times& 'his meant, %or e=ample, that the position and+elocity o% each oect could e speci%ied e=actly, "ithout any uncertainty& Without suche=actitude, prediction o% %uture positions and +elocities "ould e impossile& A%ter many, manye=periments it seemed clear that only the ine+itale imprecision in measuring instrumentslimited the accuracy o% a +elocity or position measurement, and noody douted that

    accuracies could impro+e "ithout limit as measurement techni

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    'he second la" o% thermodynamics can e stated in se+eral "ays& 'he %irst statement o% it,made y udol% Clausius in 1B/0, is that heat can %lo" spontaneously %rom a hot to a coldoect ut it cannot spontaneously pass %rom a cold to a hot oect& 'he second statement o%the second la" "as made later y Scottish physicist William 'homson Qel+in (1B- @ 1#0*)and erman physicist Ma= $lanc8 (1B/B @ 1#-*): eat energy cannot e completely

    trans%ormed into mechanical energy, ut mechanical energy can e completely trans%ormedinto heat energy&

    7uestion: What are some e+eryday e=amples o% the second la" o%thermodynamics

    'he third statement o% the second la" depends on a ne" concept, that o% entropy& .n order todiscuss entropy, "e %irst discuss the numer o% distinguishale arrangements o% a system, %rom"hich the concept o% entropy is deri+ed& Some readers may "ish to s8ip this discussion and godirectly to the de%inition o% entropy that is gi+en a%ter"ards&

    =ample T1: .magine a o= di+ided into t"o compartments, each o% "hich can hold only one all& $ut aall into one o% the compartments& Clearly, the numer o% "ays that you can do this is t"o@@the all can eput into either compartment& (Mathematically, this is the numer o% cominations o% t"o oects ta8en oneat a time6 this is gi+en y the inomial coe%%icient)&=ample T: .% there are three compartments, the numer o% "ays you can put a all in is three (thenumer o% cominations o% three oects ta8en one at a time)&

    =ample T3: .% there are %our compartments, the numer o% "ays you can put a all in is %our (the numero% cominations o% %our oects ta8en one at a time)&

    =ample T-: 2o" put t"o identical alls into a o= "ith t"o compartments& 'he numer o% "ays you cando this is only one (the numer o% cominations o% t"o oects ta8en t"o at a time) ecause i% the alls

    are interchanged, there is no distinguishale di%%erence in the arrangements&

    =ample T/: 2o" put t"o identical alls into a o= "ith three compartments& 'he numer o% "ays youcan do this can e counted in the %ollo"ing "ay:

    a) 'he %irst all in compartment T1, the second in either o% the other t"o& 'his adds up to t"o&) 'he %irst all in compartment T, the second in either T1 or T3& 9ut the %irst arrangement isidentical to the %irst arrangement o% a), so "e don?t count it& 'he second arrangement is ne", so"e count it& .% no" the %irst all is no" put into T3, the second can e put into either T1 or T, utthese are not ne", so "e don?t count them&

    'hus, the total numer o% distinguishale arrangements %or t"o identical alls in three compartments isthree (the numer o% cominations o% three oects ta8en t"o at a time)&

    =ample T: 2o" put t"o identical alls into a o= "ith %our compartments& We count the numer o%possile "ays as %ollo"s:

    a) 'he %irst all in T1, the second in T, T3, or T-& 'his adds up to three&) 'he %irst all in T, the second in T1, T3, or T-& 'he %irst is the same as the %irst arrangement o%a), so there are t"o ne" distinguishale arrangements&c) 'he %irst all in T3, the second in T1, T, or T-& 4nly the last arrangement is ne", so there isone additional distinguishale arrangement&

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    d) 'he %irst all in T-, the second in T1, T, or T3& ach o% these arrangements is identical to a),), or c), so these are not ne"&

    'hus, the total numer o% distinguishale arrangements %or t"o identical alls in %our compartments is si=(the numer o% cominations o% %our oects ta8en t"o at a time)&

    =ample T*: 2o" put t"o alls into only the %irst three o% %our compartments& 'his is identical to =ample

    T/ e=cept that no" there are t"o alls in %our compartments instead o% t"o alls in three compartments&'he numer o% distinguishale arrangements is no" three as long as "e 8no" that the alls are in the %irstthree compartments& 'his e=ample sho"s that the numer o% distinguishale arrangements depends notonly on the numer o% alls and compartments, ut also on ho" the alls are distriuted in thecompartments&

    'he methods o% proaility allo" us to calculate the numer o% distinguishale arrangements in anynumer o% compartments "hether the alls are identical or not, and %or any gi+en distriution o% alls& !ora gi+en numer o% compartments and %or identical alls, the numer o% distinguishale arrangements issmallest (e

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    'he second la" is ased on our oser+ations o% the direction in time o% natural processes& Wesay that this direction depends on the uni+erse proceeding in time %rom a state o% lo"erentropy to a state o% higher entropy ut, in classical physics, the increasing direction o% entropyis identical to the %or"ard direction o% time& We cannot distinguish one %rom the other& .t istautological to say that entropy increases "ith time ecause the increase o% entropy cannot e

    distinguished %rom the %or"ard direction o% time& o"e+er, in

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    estalished to e=tract lo" entropy %rom others and to de%end o"n lo" entropy sources& Clothing andhousing reduces the di%%usion o% lo" entropy&

    Se=ual selection is the struggle et"een the indi+iduals o% one se=, generally the males, to communicatetheir attracti+eness to the other se= in order to %orm a partnership %or reproduction& uman eings, as "ellas other se=ually reproducing species, are the success%ul descendants o% the earliest se=uallyreproducing species aout a illion years ago& !or the system o% communication to e success%ul indi%%erent 8inds o% en+ironments o+er such a long time, the mode o% communication has to e simple,stale and uni+ersal& Since the entropy la", "hich states that closed systems tend to"ards states o%higher entropy, is the most uni+ersal la" o% the nature, it is natural that the display o% lo" entropy le+else+ol+es as the uni+ersal signal o% attracti+eness in the process o% se=ual selection&

    As oth natural selection and se=ual selection %a+or lo" entropy state, the pursuit o% lo" entropy ecomesthe main moti+e o% human mind and animal mind& .ndeed the lo" entropy state is the main "ay o%ad+ertisement %or most se=ually reproducing species& arge ody siFe, color%ul and highly comple=%eather patterns "ith large amount o% in%ormation content and e=otic structures are all di%%erentrepresentations o% lo" entropy states& Since a lo" proaility e+ent corresponds to a state o% lo" entropy,a no+el %eature is o%ten attracti+e in the competition %or reproduction& .t has een generally recogniFed thatse=ual selection is the main dri+e o% di+ersity&9esides communication "ith memers o% the opposite se=, social animals need to communicate theirattracti+eness and po"er in order to in%luence the eha+ior o% others& !or the same reason as in se=ualselection, the most general signal is display o% lo" entropy& Among all social species, human eings ha+ede+eloped the most comple= social structure& 'he creation o% distinct art "or8s, the demonstration o%athletic pro"ess, the accumulation o% "ealth, and conspicuous consumption @ all o% "hich representdi%%erent %orms o% lo" entropy @ are the maor methods o% ad+ertising one5s attracti+eness&

    As the social groups ecome larger and the di+ision o% laor ecomes %iner, people ecome less %amiliar"ith each other in their daily interactions, "hich ma8e it more di%%icult %or people to udge the aility o%others& 'he need %or people to ad+ertise their attracti+eness through e=ternal accumulation o% lo" entropyalso ecomes stronger& $eople usually signal their capaility y uying more e=pensi+e houses, cars,clothes, going to more e=pensi+e restaurants and attending more e=clusi+e schools& 'he great e%%ortshuman eings put into non@%ood acti+ities re%lect the high cost o% communication in a large and comple=society& istorical e+idences sho" that the transaction costs ha+e een increasing o+er time&

    'he Etransaction costsE that Chen spea8s aout mean that the struggle to achie+e and sustainlocaliFed lo" entropy states leads to higher entropy in the uni+erse as a "hole&

    7uestion: .n your o"n li%e, ho" do you e=perience the struggle to achie+e and sustain lo"entropy states What are the transaction costs o% this struggle, i&e&, in "hat "ay does yourstruggle increase the o+erall entropy o% the "orld o" success%ul ha+e you een in youre%%orts to achie+e and maintain lo" entropy states o" sustainale are such states

    An e=tremely important property o% 2e"ton5s la"s is that they are time re+ersal in+ariant& Whatthis oscure@sounding term means is that, i% the direction o% time is re+ersed, the directions o%motion o% all particles are also re+ersed, and this re+ersed motion is completely allo"ed y

    2e"ton5s la"s& .n other "ords, the motion in re+ersed time is ust as +alid as the motion in%or"ard time, and nature hersel% does not distinguish et"een the t"o& A simple e=ample o%this is the time@re+ersed motion o% a thro"n aseall, "hich %ollo"s a paraolic traectory ineither the %or"ard or the re+ersed direction& Without seeing the act o% thro"ing, and "ithout airresistance, "e "ould not e ale to distinguish the %or"ard paraola %rom the re+ersedparaola& Another "ay to state it is that a mo+ie o% a thro"n aseall seems ust as +alid to usi% it is run in the re+erse direction as in the %or"ard direction& 'ime re+ersal in+ariance is alsoapparent in the seemingly random motion o% the molecules in a gas& .% "e could see theirmotion in a mo+ie and then re+erse it, "e could not distinguish et"een the %or"ard motion

    #

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    and the re+ersed motion (see http:GG"""&colorado&eduGphysicsGphetG"e@pagesGsimulations@ase&html$hysicsVeat and 'hermoVas $roperties)&

    o"e+er, i% "e consider the motion o% an oect containing many ordered particles (%ore=ample, "ith a recogniFale siFe, shape, position, +elocity, and orientation), "e encounter adi%%erent phenomenon& .t is easy to tell the di%%erence et"een the re+ersed and %or"ard

    motions o% a person, a horse, a gro"ing plant, a cup %alling %rom a tale and rea8ing, andmost other e=amples %rom e+eryday li%e& Another e=ample is the %ree e=pansion o% a gas thatinitially is con%ined to one side o% a o= y a memrane& .% the memrane is ro8en, the gasimmediately e=pands into the other side (initially assumed to e e+acuated), and "e can easilytell the time re+ersed motion %rom the %or"ard motion& .n all o% these cases, the motion at theindi+idual molecule le+el is time re+ersal in+ariant, ut it is clear that the gross motion o% themacroscopic oect is not&

    4ur

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    .n 1B*3, these disparate phenomena and theories "ere all pulled together into one eleganttheory y Scottish physicist James Cler8 Ma="ell (1B31 @ 1B*#)& Ma="ell5s %our e

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    'hese parameters are related y the %ollo"ing e

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    7uestion: i+e some e=amples o% "a+es "hose oser+ed +elocities depend on theoser+er +elocity&i+e some e=amples o% "a+es "hose oser+ed +elocities do not depend on the oser+er+elocity&

    2*9* 4elativity

    .mplicit in the preceding discussion o% classical physics "as the assumption that space andtime "ere the conte=ts in "hich all physical phenomena too8 place& >ntil 1#0/, physicistsassumed that space and time "ere asolute in the sense that no physical phenomena oroser+ations could a%%ect them, there%ore they "ere al"ays %i=ed and constant& 2e"tonthought this assumption "as necessary %or his la"s o% motion to e +alid and until 1#0/, nophysicist douted its +alidity&

    .n 1#0/, the erman@S"iss@American physicist Alert instein (1B*# @ 1#//) re+olutioniFedthese ideas o% time and space y pulishing his theory o% special relati+ity& (ESpecialE means

    that all motions are uni%orm, i&e&, "ith constant +elocity&) .n this theory, he aandoned theconcept o% the ether, and "ith it the concept o% the asolute motion o% an oect, realiFing thatonly relati+e motion et"een oects could e measured& >sing only the assumptions that theoser+ed +elocity o% light in %ree space is constant, and that the la"s o% motion are the same inall re%erence %rames mo+ing "ith constant +elocity, he sho"ed that neither length nor time isasolute& 'his means that oth length and time measurements depend on the relati+e+elocities o% the oser+er and the oser+ed&

    An oser+er standing on the ground measuring the length o% an airplane that is %lying y "illotain a minutely smaller +alue than that otained y an oser+er in the airplane& An oser+eron earth comparing a cloc8 on a spaceship "ith a cloc8 on earth "ill see that the spaceship

    cloc8 mo+es slo"er than the earth cloc8& (4% course, an oser+er on the spaceship sees theearth cloc8 mo+ing slo"er than his cloc8 'his is the %amous t"in parado=& .t is resol+ed yrealiFing that, "hen the spaceship returns to earth, the spaceship oser+er and cloc8 "ill ha+eaged less than the earth oser+er and cloc8& 'he di%%erence et"een the t"o oser+ers is thatthe spaceship has undergone deceleration in order to come to rest on earth& 'his deceleration,"hich is negati+e acceleration, is nonuni%orm motion6 there%ore special relati+ity does notapply&)

    !or an oect ha+ing a nonFero rest mass, the special theory produced the %amous relationshipet"een the total energy () o% the oect, "hich includes its 8inetic energy, and its mass (m):

    X mc

    "here c is the speed o% light in a +acuum& instein5s special theory has een con%irmed ythousands o% e=periments, oth direct and indirect&

    .n instein5s special theory o% relati+ity, e+en though space and time "ere no longer asolute,they "ere still uclidean& 'his meant that t"o straight lines in space@time (e&g&, in an =,y,F,tcoordinate system) "hich "ere parallel at one point al"ays remained parallel no matter "hatthe gra+itational %orces "ere&

    33

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    7uestion: Suppose there is an ether& o" "ould that a%%ect instein?s special theory o%relati+ity

    7uestion: Suppose the special theory o% relati+ity had een pro+en "rong& What "ould e thee%%ect on your li%e no"

    .n 1#1/, instein completed his greatest "or8, the general theory o% relati+ity& Whereas thespecial theory deals "ith oects in uni%orm relati+e motion, i&e&, mo+ing "ith constant speedalong straight lines relati+e to each other, the general theory deals "ith oects that areaccelerating "ith respect to each other, i&e&, mo+ing "ith changing speeds or on cur+edtraectories& =amples o% accelerating oects are an airplane ta8ing o%% or landing, a carincreasing or decreasing its speed, an ele+ator starting up or coming to a stop, a car goingaround a cur+e at constant speed, and the earth re+ol+ing around the sun or the moonre+ol+ing around the earth at constant speed&

    A particularly important e=ample o% acceleration is that o% an oect %ree@%alling in the earth5sgra+ity& A %ree@%alling oect is one that is acted upon only y the gra+itational %orce, "ithout air%riction or other %orces& All %ree@%alling oects at the same spot in the earth5s gra+itational %ield%all "ith the same acceleration, independent o% the mass or material o% the oect& A %ree@%allingoect, such as an astronaut in a spaceship, does not e=perience a gra+itational %orce (i&e&,heGshe e=periences "eightlessness), hence "e can say that the acceleration o% %ree@%allcancels out the gra+itational %orce& Another "ay to state this %act is that a gra+itational %orce ise

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    eneral relati+ity also predicts the e=istence o% lac8 holes, oects that are so massi+e ut sotiny that space around them cur+es into them& A light eam that gets close enough to a lac8hole "ill e ent into the lac8 hole and ne+er escape&

    A %undamental %eature o% general relati+ity is that it predicts that matter, energy, space, andtime depend on each other and e+ol+e together so that space and time are not independent

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    'here are po"er%ul theoretical reasons %or elie+ing that the cur+ature o% our space is neitherpositi+e nor negati+e ut is e=actly Fero& 'he cur+ature depends on the a+erage energydensity (the a+erage amount o% energy per cuic meter), the e=pansion rate o% the uni+erse,and the rate o% increase in the e=pansion rate& .n practice, it is too di%%icult to measure thecur+ature y measuring the cur+ature o% light eam traectories, ut it can e estimated i% thea+erage angular siFe o% the intensity spots in the cosmic micro"a+e ac8ground, the

    e=pansion rate o% the uni+erse, and the rate o% increase in the e=pansion rate are all 8no"n(http:GG"""&computer"ee8ly&comGArticlesG00#G0BG0BG3*#G'he@%ate@o%@the@cosmos@Dar8@energy@can@shape@the@uni+erse&htm)&

    RSide note: .n his initial papers, instein had constructed a model o% the uni+erse "ith Ferocur+ature that "as not e=panding at all& ater, in 1# ut also e%ore ule5s disco+ery,ussian physicist Ale8sandr !riedmann (1BBB @ 1#/) disco+ered solutions to the generalrelati+ity e

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    scientists per%orm are al"ays +ery speci%ic to a particular prolem in particular circumstances&Any attempt to comprehend the results o% many such e=periments on many similar topics"ould e %utile "ithout some 8ind o% uni%ying model that is presumed to represent some aspecto% the e=ternal, oecti+e reality a%%ecting those e=periments&

    !or e=ample, %orce %ields are theoretical models o% gra+itational or electromagnetic %orces, and

    cur+ed space@time is a model o% space@time that accounts %or the gra+itational %orce& 'here areother models that account %or the "ea8 and strong %orces that act on elementary particles& Andthere are models o% the nucleus, the atom, molecules, crystals, and gases& All o% these modelsare highly mathematical ecause mathematics is the uni+ersal language o% physics&

    When a model is %ound that accurately accounts %or e=perimental oser+ations, there is astrong tendency to thin8 o% the model itsel% as the e=ternal, oecti+e reality& 'hus, othphysicists and the general pulic routinely spea8 o% elementary particles, nuclei, atoms, andspace@time as eing real oects, rather than simply as mathematical models& We shall seelater that this tendency creates intractale prolems in trying to understand the true nature o%eality&

    7uestion: !rom your o"n e=perience alone, ans"er the

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    1& =ercise: Hie" the +ideo o% the ule telescope?s %irst 1/ years o% oser+ations athttp:GGimgsrc&hulesite&orgGhuGgalleryGdG+ideoGhm1/thanni+ersaryG%ormatsGhm1/thanni+ersary-0=-B0&mo+

    & 7uestions: What is the ule +ie"ing Stars ala=ies Space A mathematical conceptConsciousness 4ursel+es 2othing

    7uestions: !rom your o"n e=perience, and "ith a minimum o% concepts, e asspeci%ic and as accurate as possile in ans"ering the %ollo"ing

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    7uestion: According to the ao+e de%inition, is your ody a lac8 ody 2ote: 'he human odycan e seen in pitch dar8ness "ith thermal imaging goggles&

    Classical physics could not e=plain the spectra o% lac8 odies& .t predicted that the intensity(po"er emitted at a gi+en "a+elength) o% emitted light should increase rapidly "ith decreasing"a+elength "ithout limit (the Kultra+iolet catastropheL)& .n the %igure elo", the cur+e laeledKayleigh@Jeans la"L sho"s the classically e=pected eha+ior&

    o"e+er, the measured spectra actually sho"ed an intensity ma=imum at a particular"a+elength, "hile the intensity decreased at "a+elengths oth ao+e and elo" thema=imum& .n order to e=plain the spectra, in 1#00 the erman physicist Ma= $lanc8 (1B/B @1#-*) "as %orced to ma8e a desperate assumption %or "hich he had no physical e=planation&

    As "ith classical physics, he assumed the ody consisted o% +irating oscillators ("hich "ereactually collections o% atoms or molecules)& o"e+er, in contrast to classical physics, "hichassumed that each oscillator could asor an aritrary amount o% energy %rom the radiation oremit an aritrary amount o% energy to it, $lanc8 "as %orced to assume that each oscillatorcould recei+e or emit only discrete,

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    X h% ($lanc8?s %ormula)

    "here h ($lanc8?s constant) is an e=ceedingly small numer "hose +alue "e do not need here,and % is the %re

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    .n classical physics, the electromagnetic %ield connects charged particles to each other (seeSections &-, &)& .n

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    When classical physics "as applied to such a model o% the atom, it predicted that the electronscould not remain in stale orits aout the nucleus, ut "ould radiate a"ay all o% their energyand %all into the nucleus, much as an earth satellite %alls into the earth "hen it loses its 8ineticenergy due to atmospheric %riction& .n 1#13, a%ter Danish physicist 2iels 9ohr (1BB/ @ 1#)had learned o% these results, he constructed a model o% the atom that made use o% the

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    electron oriting a nucleus o% one proton& 'he theory e=plained many o% the properties o% theoser+ed line spectrum o% hydrogen, ut could not e=plain the ne=t more complicated atom,that o% helium, "hich has t"o electrons& 2e+ertheless, the theory contained the asic idea o%

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    .n physics, i% there is a "a+e, there must e an e

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    2. The +ave only tells us the probability of finding something if +e loo$ not +hat isthere if +e do not loo* Quantum theory is not a theory of obectively real matter,although 0orn thought the SchrBdinger +ave +as obectively real.*

    7uestions: Suppose you accepted the principle that reality is proailistic rather thandeterministic& o" "ould it a%%ect your notions o% %ree "ill o" "ould it a%%ect your sense o%

    control o+er your thoughts, %eelings, decisions, and actions o" "ould it a%%ect yourperceptions o% other people5s control o+er their thoughts, %eelings, decisions, and actions o""ould it a%%ect your udgments aout yoursel% and others

    'he %irst %eature +iolates the second %undamental assumption o% classical physics (see Section&), i&e&, that oth the position and +elocity o% an oect can e measured "ith no limits ontheir precision e=cept %or those o% the measuring instruments& 'he second %eature +iolates the%irst %undamental assumption o% classical physics, i&e&, that the oecti+e "orld e=istsindependently o% any oser+ations that are made on it&

    3*3* A striing eample of probability measurement

    $roailities can e measured using sophisticated instrumentation& A stri8ing e=ample issho"n in the %ollo"ing diagram, measured "ith a scanning tunneling microscope, o% theproailities o% the locations o% -B iron atoms circling the proailities o% the locations o% a seao% electrons(http:GGpicasa"e&google&comG.9MesearchAlmadenG.9MCelerates0ears4%Mo+ingAtomsT/3B//00#BB1/***B):

    -/

    http://picasaweb.google.com/IBMResearchAlmaden/IBMCelebrates20YearsOfMovingAtoms#5385522009881657778http://picasaweb.google.com/IBMResearchAlmaden/IBMCelebrates20YearsOfMovingAtoms#5385522009881657778http://picasaweb.google.com/IBMResearchAlmaden/IBMCelebrates20YearsOfMovingAtoms#5385522009881657778http://picasaweb.google.com/IBMResearchAlmaden/IBMCelebrates20YearsOfMovingAtoms#5385522009881657778
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    'he terms Eiron atomE and EelectronE are heuristic attempts to gi+e names to the locations&o"e+er, this diagram in no "ay pro+es that there are in reality such things as iron atoms andelectrons& 'here is no "ay to pro+e that (see Section 1&1), ut, y gi+ing them names, "e tendto e con+inced that the oects actually e=ist&

    'he proaility measurements are represented y points so densely pac8ed that they appear

    to %orm sur%aces rather than indi+idual measurements& 'he Eiron atomsE are seen to e mostproaly located under the lue pea8s "hile the EelectronsE are seen to e more di%%uselylocated under the circular rings& 'hese are proaility measurements o% locations only, notactual locations&

    3*'* "ncertainty and complementarity

    As 9orn proposed,

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    uncertainty in +elocity is in the same direction as the uncertainty in position& .n the dra"ingao+e, the uncertainty in position is a +ertical uncertainty& 'his means that the uncertainty in+elocity is also a +ertical uncertainty& 'his is represented y the lines di+erging (y an uncertainamount) a%ter the electrons emerge %rom the hole (uncertain +ertical position) rather thanremaining parallel as they are on the le%t&

    i8e"ise, an e=periment designed to measure momentum "ith a certain accuracy "ill not eale to locate the position o% the particle "ith etter accuracy than the uncertainty relationshipallo"s&

    2otice that in the uncertainty relationship, i% the right side e

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    A "a+e o% less precisely determined momentum can e otained y superposing (see Section-&1) "a+es o% slightly di%%erent "a+elength (and there%ore slightly di%%erent momentum)together, as is sho"n in the second o% the t"o patterns ao+e& 'his results in a "a+e pac8et"ith a momentum spread [p (uncertainty [p), ut "hich is unched together into a region o%"idth [= (uncertainty [=) instead o% eing spread o+er all space&

    'he uncertainty relation is closely related to the complementarity principle, "hich "as %irstenunciated y 9ohr& 'his principle states that

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    does re

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    !igure 1

    When "e are dealing "ith "a+es, "e ha+e a di%%erent rule& 'he superposition principle is onethat is oeyed y all "a+es in material media pro+ided their amplitudes are not too great, andis rigorously oeyed y all electromagnetic "a+es and

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    Crest added to a crest gi+es a higher crest&

    Crest added to a trough gi+es cancellation&

    '"o "a+es added out o% phase gi+e an intermediate "a+e&

    A computer animation o% the superposition o% t"o "a+es is gi+en inhttp:GG"""&phy&ntnu&edu&t"Gntnua+aG+ie"topic&phptX3/&'he superposition principle leads to the phenomenon o% inter%erence& 'he superposition, orsum, o% t"o "a+es "ith the same "a+elength at a point in space "here oth "a+es ha+e eitherpositi+e or negati+e heights results in a summed "a+e "ith positi+e or negati+e height greaterthan that o% either one, as is sho"n elo"& 'his is called constructi+e inter%erence& .% theindi+idual heights ha+e opposite signs, the inter%erence is destructi+e, and the height o% thesummed "a+e is smaller than the largest height o% the t"o&

    /1

    http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=35http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=35
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    oo8ing do"n on a "ater "a+e& 'he right lines are crests, the dar8 ones are troughs&

    .nter%erence o% t"o "ater "a+es& Crests added to crests %orm higher crests& 'roughs added totroughs %orm deeper troughs&

    A computer simulation o% a t"o@slit inter%erence pattern using "ater "a+es is gi+en inhttp:GG"""&%alstad&comGrippleG, and using light "a+es in http:GG"""&"alter@

    %endt&deGph1-eGdouleslit&htmand in http:GG"""&colorado&eduGphysicsG000Ginde=&pl('ale o%ContentsVAtomic aVClassic '"o@Slit =periment)&

    An important measurale property o% classical "a+es is po"er, or intensity . (po"er per unitarea)& $o"er is proportional to the s

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    amplitude& A computer animation o% the comparison et"een particles and "a+es in a t"o slite=periment is sho"n athttp:GG"""&upscale&utoronto&caG$H9GarrisonGDouleSlitG!lashGDouleSlit&html&

    !or

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    in the ottom panel o% !igure 1, has the same shape as the intensity distriution o% the "ater"a+es sho"n in the middle panel ecause oth distriutions are deri+ed %rom the s

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    '*2* SchrBdinger@s cat parado

    'his thought e=periment "as originally created y Schr;dinger in an attempt to sho" thepossile asurdities i%

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    source& (See the animation o% the radioacti+e decay o% E9aloniumE athttp:GG"""&upscale&utoronto&caG$H9GarrisonG!lashG2uclearGDecayG2uclearDecay&html&)

    Since the "a+e%unction o% the nucleus is a solution to the Schr;dinger e

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    %inal "a+e%unction contains t"o terms, one descriing a detected particle, plus released gasand a dead cat6 and one descriing no detected particle, no released gas, and a li+e cat& 9othterms must e present i%

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    until the 1#B0s is the principle o% local causality, or locality %or short& 'his principle ("hichcomes %rom instein?s theory o% special relati+ity) states that no physical e%%ect can etransmitted "ith a +elocity %aster than light& Also implied, ut not al"ays stated, is the principlethat all physical e%%ects must decrease as the distance et"een the source o% the e%%ect and theoect a%%ected increases& .n practice, this principle prohiits not only all instantaneous action@at@a@distance, ut also any action@at@a@distance "hen the distances are so large that the

    longest@range 8no"n %orce that can transmit signals, the electromagnetic %orce, cannot %easilyproduce the e%%ect& .% the particles o% a system are assumed to e independent o% each othere=cept %or physical e%%ects that tra+el no %aster than the +elocity o% light, the system is said toe local& 'his means, e&g&, that i% a measurement is made on one particle, the other particlescannot e a%%ected e%ore a local signal %rom the %irst particle can reach them&

    .n addition to locality, the other strongly held principle "as the principle o% oecti+e reality (seeSection 1&1)& 'his principle states that there is a reality that e=ists "hether or not it is oser+ed&$rior to the disco+ery o%

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    !ollo"ing the $ paper, many physicists e=pended a great deal o% e%%ort in trying to de+isetheories that "ere complete, namely theories that assumed that parameters li8e position and+elocity are at all times de%inite e+en i% they are un8no"n, and "hich at the same time ga+eresults that agree "ith

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    'hese e=periments could not distinguish et"een a reality that is not strongly oecti+e ut islocal6 one that is nonlocal ut is strongly oecti+e6 and one that is neither strongly oecti+enor local& !urthermore, the measured +alue o% the %unction S "as al"ays in agreement "ith thepredictions o%

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    2o" "e must as8 "hether any class o% hidden +ariale theories, "hich are all designed to estrongly oecti+e, can e e=cluded y e=periment& (9ell?s theorem and the Aspect e=perimentssay only that hidden +ariale theories must e nonlocal& .t does not e=clude any class o%nonlocal hidden +ariales theory&) 'o help ans"er this

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    correlations et"een the patterns are discerned y the rain, and a three@dimensional image isseen&

    Magic ye images may e easier to see i% +ie"ed on paper rather than a computer screen& .%possile, print this image and %ollo" the instructions elo"& (ou don?t need to print in color&)old the center o% the printed image right up to 'our nose6.t should e lurry& !ocus as thoughyou are loo8ing throughthe image into the distance& Ver' slo$l'mo+e the image a"ay %romyour %ace until the t$o s5uaresao+e the image turn into three s5uares& .% you see %ours

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    assumption o% an oecti+e reality (Section 1&1), it cannot e +eri%ied& !urthermore, it leads tothe additional assumption that there is an oecti+e E.E that su%%ers&)

    8*1* 6hat are the characteristics of conscious mind7

    Mind is the conscious e=perience o% the %unctioning o% the rain and senses& 'his is to edistinguished %rom the %unctioning itsel%& Mind has three important aspects:

    a) 'he contents o% mind: Mental contents include thoughts, emotions, %eelings, dreams,and +isions& $erceptual contents include those that are internal to the ody as "ell asthose that are e=ternal& $erceptual contents that are internal include sensations o% pain,pressure, stretching, tension, mo+ement, proprioception, and interoception& Many o%these in+ol+e emotional components as "ell, such as %ear or pleasure& Analogs o% thesemental and perceptual contents are the shado"s on the "all in $lato5s ca+e allegory(see Section 1&-), or the images on the screen in a mo+ie theater&

    ) A special case o% the contents o% mind is the %ield o% mind& 'he %ield o% mind +aries%rom "ide to narro" depending on the degree o% %ocus, and can e directed to"ards anyoect& An analog is the %ield o% +ie" o% an optical system such as a telescope orcamera&

    c) Another special case that is normally assumed to e among the contents o% the mindis the suect o% mind& (We shall see in Chapters #and 11that there really is no suectin the mind&) .n oth $lato5s allegory and the mo+ie theater metaphor, the suects arethe oser+ers in the audience&

    'here are se+eral ordinary states o% conscious e=perience, the most common eing "a8ing,dreamless sleep, and dreaming& 'here are also altered states o% consciousness that can ee=perienced in meditation or under the in%luence o% mind@altering drugs& 4ther states are thosethat are e=perienced under hypnotic trance, sedation, or anesthesia& All o% the contents o% ourminds are essentially pri+ate since our thoughts, %eelings, emotions, and sensations, areentirely our o"n& !or e=ample, any sensation, such as Ered,E is an e=perience that "e 8no"intimately, ut it is impossile to con+ey that e=perience to anyody else& We assume thateach person has had a similar e=perience, ut "e can ne+er 8no" this to e true& Consciouse=perience may include the state in "hich there are no oects e=cept the suect andGor the%ield, and e+en the state in "hich there are no oects at all& Such states are achie+ale indeep meditation&

    7uestion: .% all o% our e=periences are essentially pri+ate, "hat does that imply aoutthe e=istence o% an e=ternal, oecti+e reality

    8*2* !traordinary abilities of the mind

    'here is a great deal o% e+idence@@some reliale, some not so reliale@@that the mind is muchmore than merely the central processor %or sensory in%ormation& We 8no" that sensoryprocesses are all local, i&e&, they depend on local transmission o% in%ormation& o"e+er,e=trasensory processes may e nonlocal, i&e&, they may depend on nonlocal correlations

    3

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    et"een t"o minds or et"een a mind and an e+ent that is remote, either spatially ortemporally (see Section -&3)& 2e+ertheless, "hether the e=trasensory processes are local ornonlocal, "e shall re%er to all o% them as nonlocal mind& Much more "ill e said aout this inChapters #, 1, and 1&ussell 'arg and Jane Qatra in their 1##B oo8, (iracles o% (ind, list a %e" o% the e=trasensoryailities that ha+e een demonstrated:

    'elepathy: Direct mental communication et"een one mind and another&

    emote +ie"ing: 4taining a mental image o% a remote target oect at "hich anaccomplice is located& 'his is di%%erent %rom telepathy ecause the image o%ten containsdetails not noticed y the accomplice&

    Clair+oyance: 4taining a mental image o% a remote target "ithout the aid o% anaccomplice&

    $recognition: 'here are se+eral types o% precognition& A prophecy is a dream or +ision

    o% a %uture e+ent "hen there is no possiility o% ta8ing any action that could change the%uture& =amples are recording a prophecy and re+ealing it only a%ter the e+ent hasoccurred, or prophesying in a +ague, nonspeci%ic "ay& '"o %amous prophesiers "ere2ostradamus (http:GGen&"i8ipedia&orgG"i8iG2ostradamusG) and dgar Cayce(http:GGen&"i8ipedia&orgG"i8iGdgarCayceG)& .% the precognition is speci%ic enough toallo" an action to e ta8en to a+ert a %uture e+ent, then it is called a %orecast,premonition, or presentiment (pre@sentiment)& =ample: a dream o% an airplane crashthat allo"s a person to a+oid that %light&

    Distant hypnosis: .nducing hypnosis o% a person at a distance&

    $sychic healing: A type o% remote +ie"ing and healing in "hich the healer acti+elytransposes intuiti+e impressions into thoughts and speci%ic healing actions in a patient?sody to remedy a percei+ed prolem&

    Spiritual healing: emote healing in "hich the healer is in a recepti+e, a"are,nonudgmental state "hich allo"s his or her consciousness to e used as a conduit %orhealing y nonlocal, uni+ersal mind&

    nergy healing: ealing in "hich the healer directs his or her attention to the patientand concentrates on replenishing or manipulating the patient5s +ital energy %lo"&=amples are rei8e, therapeutic touch, laying on o% hands, pranic healing, and 7iong&

    .ntuition: Direct, nonanalytical a"areness that can come %rom nonlocal mind, internalsuconscious processes, psychic sources such as mind@to@mind connections, or directclair+oyant perception o% the outside "orld&

    'he e=istence o% e=traordinary ailities attained through the practice o% yoga is "ell estalishedand documented in the literature o% yoga, "here they are called siddhis& 'he %ourth century 9C

    -

    http://en.wikipedia.org/wiki/Nostradamus/http://en.wikipedia.org/wiki/Edgar_Cayce/http://en.wikipedia.org/wiki/Nostradamus/http://en.wikipedia.org/wiki/Edgar_Cayce/
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    sage $atanali enumerated the %ollo"ing siddhis in his 7oga Sutras(as listed y 'arg andQatra):

    Qno"ledge o% past and %uture6 understanding o% the sounds made y all creatures68no"ledge o% past li+es6 8no"ing "hat others are thin8ing6 prior 8no"ledge o% one5sdeath6 the attainment o% +arious 8inds o% strength6 perception o% the small, the

    concealed, and the distant6 8no"ledge o% other inhaited regions6 8no"ing aout thestars and their motions6 8no"ledge o% the interior o% the ody6 control o% hunger andthirst6 steadiness6 seeing the adepts in one5s o"n interior light6 intuition6 understandingo% the mind6 entering the odies o% others6 lightness and le+itation6 rightness6 control o%material elements6 control o% the senses6 per%ection o% the ody6 ni+ersity ha+e sho"n that operator intention alone can producesmall ut statistically signi%icant (p*=10 @/) e%%ects on the %unctioning o% +arious physicalde+ices operating randomly (http:GG"""&princeton&eduGUpear)&9ill 'iller and colleagues o% Stan%ord >ni+ersity (http:GGtiller%oundation&comGinde=&php) ha+edisco+ered that it is possile to ma8e a signi%icant change in the properties o% a materialsustance y consciously holding a clear intention to do so& !or e=ample, they ha+e een aleto change the acidGal8aline alance (p) in a +essel o% "ater either up or do"n, "ithout addingchemicals to the "ater, merely y creating an intention to do so& .n addition, they ha+e eenale to use a simple electronic de+ice to EstoreE a speci%ic intention "ithin its electric circuit&'his Kintention programmedL de+ice can e placed ne=t to a +essel o% "ater at any physical

    location to otain the same results they ha+e achie+ed in their la& .n this "ay, others ha+ereplicated these "ater p results at multiple locations around the "orld&R2ote: We shall see later that it is not surprising that the mind can directly a%%ect matter& .nChapter , "e shall see that, in one +ersion o% the Copenhagen interpretation o%

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    More e+idence o% nonlocal mind appears in the data o% 'he loal Consciousness $roect (seehttp:GGnoosphere&princeton&eduG), "hich has maintained many random e+ent generators ()scattered throughout the "orld since 1##B& 'hese s sumit their data automatically to aser+er in $rinceton, 2J %or archi+ing& 'he archi+ed data can then e searched %or e+idence o%nonrandom correlations et"een the s& Such correlations ha+e een %ound "hen a large%raction o% the "orld?s population is %ocused on some e=traordinary e+ent& !or e=ample, strong

    correlations et"een the s "ere %ound on Septemer 11, 001 eginning a %e" minutesa%ter the last attac8 and continuing %or se+eral hours a%ter"ards& 'he odds that thesecorrelations e=ceeded chance "ere aout 3/ to 1&

    !or our purposes, the main conclusion that "e "ish to glean %rom these ailities is that themind %unctions not only through the senses, ut also through e=trasensory processes& 'hismeans that large regions o% space, possily all space6 and large eras o% time, possily all time,past and %uture6 may e open to it&

    .n addition to the possiility o% healing remotely, the mind demonstraly can heal locally& $roo%is gi+en y the "idespread e=perience o% the placeo e%%ect& esearch has con%irmed that a

    %a8e treatment, made %rom an inacti+e sustance li8e sugar, distilled "ater, or saline solution,can ha+e a placeo e%%ect@@that is, the sham medication can sometimes impro+e a patient?scondition simply ecause the person has the e=pectation that it "ill e help%ul& !or a gi+enmedical condition, it is not unusual %or one@third o% patients to %eel etter in response totreatment "ith placeo (8"A #onsumer maga1ine,January@!eruary 000)& 'he placeoe%%ect has e+en een demonstrated in sham 8nee surgeries (e$ +ngland 9ournal o%(edicine, July 11, 00), and in sham rain surgeries on $ar8inson?s disease patients (atureeuroscience, May 00-)&

    'here are mi=ed data on the po"er o% prayer in physical healing& A recent "ell@designed study"as designed to determine the e%%ects o% intercessory prayer on coronary ypass patients(American eart 9ournal1/1,#3-@-, April 00)& .t %ound that there "as no ene%icial e%%ect o%intercessory prayer on the healing o% the patients, and, in %act, i% the patients 8ne" they "erethe suects o% such prayers, they su%%ered %rom more complications than did those "ho did not8no"& o"e+er, se+eral millenia o% e=perience attest that praying %or others is o% spiritualene%it to those "ho are praying i% not o% physical ene%it %or the persons prayed %or& 4ne can+ery easily demonstrate this %or onesel%& 4ne important %orm o% prayer %or others is the lo+ing@8indness meditation o% 9uddhism (see Section -&)&

    7uestion: a+e you e+er prayed %or anyody else5s healing Did you e=periencea healing in your o"n mind

    8*3* The unity of the human mind

    !rom this discussion, "e still cannot ans"er the

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    .n some respects, our mind appears to e a uni

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    'o re+eal the di%%iculties in this type o% measurement, suppose that my mind is directly sensiti+eto your mind "ithout my depending on any cues %rom your eha+ior or your physical reactions&We might thin8 that such might e the case in certain 8inds o% telepathic e+ents& 2o", %ore=ample, could "e determine "hether my e=perience o% KredL is the same as yours

    'he ans"er is no ecause my e=perience o% red is still inescapaly in my mind, ne+er in

    yours& 'hus, a telepathic techni

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    could e done y means o% mechanical operations on mechanical components& A human couldta8e the same input statements (in a readale, ut not understandale, %orm) and y merely%ollo"ing instructions (the algorithm) per%orm all o% the mechanical operations "ithout anyunderstanding o% the meaning o% the input@output statements or the algorithm& (!or e=ample, ahuman can sol+e a ig@sa" puFFle y %itting the pieces together, ut might not e unale tounderstand the resulting picture&) 'hus the computer need not understand either&

    .% consciousness "ere really a %unction o% comple=ity, then an e=tremely comple= computermight e conscious& 9ut "hat "ould e the %unction o% consciousness in a computer thatoperates algorithmically, i&e&, y %ollo"ing a prescried procedure

    .n 1#30, Austrian@American mathematician Qurt ;del (1#0 @ 1#*B) sho"ed that, in any%initely descriale, logical system (one that can e descried y a %inite numer o%statements), that is sel%@consistent and that contains the rules o% arithmetic, there are truestatements that are not theorems o% the logical system& is proo% sho"s that these truestatements can e seen to e true e+en though they are not theorems&

    9e%ore "e discuss this theorem, "e %irst de%ine "hat "e mean y a logical system& Consider thestatements

    a> and >c

    "here a, , and c are integers& We assume that oth statements are true, i&e&, that they are the a=ioms&'hen "e must conclude that

    a>c

    'his is a theorem that must e true i% the a=ioms are true& 'his is an e=ample o% the simplest possilea=iomatic logical system& .t consists o% a set o% a=ioms, "hich are accepted ut are not pro+ed, and theset o% all o% the theorems that %ollo" %rom the a=ioms&

    ;del5s theorem sho"s that no logical system can produce all o% the true statements that arepossile& .n other "ords, there are some true statements that cannot e pro+ed "ithin anylogical system& A conclusion one might dra" %rom this theorem is that consciousness can learntruths that a computer %ollo"ing the rules o% logic can ne+er disco+er& 'his might mean that adeterministic computer can ne+er model consciousness, or no deterministic computer can econscious no matter ho" comple= it is& !urthermore, it might mean