Machine Self-Reference and Consciousness John Case Depa rtment of Computer and Info rmation Sciences 103 Smith Hall Universit y of Dela w a re New a rk, DE 19716 USA Email: case@cis.udel.edu http://www.cis.udel.edu/ � case 1
First Problem Can machines tak e their entire inter- nal mechanism into account as data? Can they have \complete self- kno wledge" and use it in their decisions and computations? W e need to mak e sure there is not some inherent pa rado x in this. 2
1. CAN MACHINES CONTAIN A COMPLETE MODEL ________ OF THEMSELVES? M MODEL OF M MODEL OF MODEL OF M . . . INFINITE REGRESS! M INF. HENCE, M NOT A MACHINE. THEREFORE, M CANNOT CONTAIN A MODEL OF ITSELF! _________ 3
So | 2. Can machines create a mo del of themselves | exter- nal to themselves? YES! | b y: a. Self-Replication o r b. Mirro rs. W e're gonna do it with mirro rs! | No smok e, just mirro rs. 4
3 + 4 = ? 172 x 123 The rob ot has a transpa rent front so its internal mechanism is visible. It faces a mirro r and a writing b oa rd, the latter fo r \calculations." It is sho wn having copied already a p o rtion of its internal mechanism, co r- rected fo r mirro r reversal, onto the b oa rd. It will cop y the rest. Then it can do anything p reassigned and algo rithmic with its b oa rd data consisting of: its complete (lo w-level) self-mo del and any other data. The ab ove essentially depicts Kleene's Strong Recursion Theo rem (1936) from Computabilit y Theo ry (see [Cas94,RC94]). 5
Levels of Self-Mo delling? The complete wiring diagram of a ma- chine p rovides a lo w-level self-mo del. Other, higher-level kinds of self- mo deling a re of interest, e.g., general descriptions of b ehavio ral p rop ensi- ties . A nice in human example (p rovided b y a machine) is: I compute a strictly increasing mathematical function . A human example is: I'm grump y , up on a rising, 85% of the time . F o r machines, which w e lik ely a re [Jac90,Cas99 ], such higher-level self- � kno wledge ma y b e p roved from some p o w erful, co rrect mathematical theo ry p rovided the theo ry has access to the complete lo w-level self-mo del . Hence, the complete, lo w-level self- mo del is mo re basic. � The exp ected b ehavio rs in a discrete, quantum mechanical w o rld a re computable! 6
Human Thought W e tak e the p oint of view that human thought inherently involves (attenuated) sensing in any one of the senso ry mo dalities. E.g., a. V o cal tract \kinesthetic" [W at70] and/o r audito ry sensing fo r inner sp eech. b. There is imp o rtant sha ring of b rain ma- chinery b et w een vision and p ro duction and manipulation of mental images . Many in- genious exp eriments sho w that the same unusual p erceptual e�ects o ccur with b oth real images and imagined ones [FS77,Fin80,She78,Kos83,CRS94]. In the follo wing w e will exploit fo r exp osition the visual mo dalit y since it admits of pic- to rially , metapho rically rep resenting the other mo dalities. Generally the only asp ects of our inner cog- nitive mechanism and structure w e humans can kno w b y conscious thought a re b y such means as: detecting our o wn inner sp eech, our o wn viseral concomitants of emotions, our o wn mental images, . . . . 7
The Rob ot Revisited Sensors Robot . ... Mechanism Internal Images Mirror/Board No w, mak e the mirro r/b oa rd tunable , e.g., as to its degree of \silvering," the degree to which it lets light through vs. re�ects it. 8
The Rob ot Mo di�ed A ttach, then, the tunable mirro r/b oa rd to the transpa rent and senso ry front of the rob ot to obtain the new rob ot: NewRobot Int. Images External Images Tunable Mirror/Board The new rob ot controls ho w much it lo oks at externally generated data and ho w much it lo oks at internally gener- ated data, e.g, images of its o wn mech- anism. The attached , tunable mirro r/b oa rd is no w pa rt of the new rob ot. 9
The Human Case? The rob ot's tunable mirro r/b oa rd is analogous to the human senso ry \sur- face." The latter is also tunable as to ho w much it attends to internal \im- ages" and ho w much it attends to ex- ternal. Ho w ever, w e humans can only \see" the pa rt of our internal cognitive struc- ture o riginally built from sense data and sent back to our senso ry surface to b e re-exp erienced as mo di�ed and, t yp- ically , attenuated, further sense data. This is not surp rising since w e lik ely evolved from sensing-only o rganisms. Of course, any further depth of human cognitive structure o r mechanism w e a re to lea rn ab out will dep end on such w onderful a rti�cial techniques as scien- ti�c exp eriments, e.g., directly in neu- rophysiology , indirectly from the hu- man genome p roject, . . . . 10
Lessons Of Machine Case? F rom Kleene's Recursion Theo rem (eventually) came our mo di�ed rob ot with attached, tunable mirro r/b oa rd. In applications of Kleene's Recursion Theo rem [Cas94,RC94] (within Com- putabilit y Theo ry) w e see that, while is it not needed to compute all that is computable, a. It p rovides very succinct p ro ofs and p rogram constructs. b. F rom a game-theo retic viewp oint, in some cases, a (machine) pla y er's self-kno wledge is an imp o rtant comp onent of its winning strategy . Quite p ossibly , then, our o wn, less complete, human version of self- re�ection evolved thanks to a p remium on compact (i.e., succinct) b rains and the need to win survival games. 11
Summa ry Kleene's Strong Recursion Theo rem p rovides fo r self-referential machines/p rograms . In e�ect , such a machine/p rogram externally p rojects onto a mirro r a complete, lo w level mo del of itself (i.e., wiring diagram, �o w cha rt, p rogram text, . . . ). W e analyzed this machine self-reference as an idealization of the self-mo deling comp onent of human consciousness. Human self-mo deling is rather p o o r (but vastly b etter than self-mo deling in other animals). Analyzed w as the manner in which the sepa ra- tion ab ove b et w een 1. the externally p rojected self-mo del and 2. the machine so-mo deled and doing this p rojection applies to the human case. The analog of the mirro r ab ove is the human senso ry \surface," tunable as to its degree of \silvering!" F rom applications of Kleene's Theo rem in Computabilit y Theo ry: complete machine self- mo deling aids with machine/p rogram suc- cinctness and with winning games . P erhaps the uses of consciousness a re simila r: need to have a compact b rain and to win survival games. 12
References [Cas94] J. Case. In�nita ry self-reference in lea rning the- o ry . Journal of Exp erimental and Theo retical Arti- Intelligence , 6:3{16, 1994. �cial [Cas99] J. Case. The p o w er of vacillation in language lea rning. Computing , 1999. T o SIAM Journal on app ea r. [CRS94] J. Case, D. Rajan, and A. Shende. Rep resent- ing the spatial/kinematic domain and lattice com- puters. Journal of Exp erimental and Theo retical Intelligence , 6:17{40, 1994. Arti�cial [Fin80] R. A. Fink e. Levels of equivalence in imagery and p erception. Review , 87:113{ Psychological 139, 1980. [FS77] R. A. Fink e and M. J. Schmidt. Orientation- sp eci�c colo r after-e�ects follo wing imagination. Journal of Exp erimental Psychology: Human P er- rmance , 3:599{606, 1977. ception and P erfo [Jac90] R. Jack endo�. Consciousness and the Compu- Mind . Bradfo rd Bo oks, 1990. tational [Kos83] S. Kosslyn. Ghosts in the Mind's Machine: Brain . Ha rva rd Creating and Using Images in the Univ. Press, Camb ridge, Massachusetts, 1983. [RC94] J. Ro y er and J. Case. Sub recursive Program- ming Systems: Complexit y and Succinctness . Re- sea rch monograph in Progress in Theo retical Com- Science . Birkh auser � Boston, 1994. puter [She78] R. N. Shepa rd. The mental image. American Psychologist , 33:123{137, 1978. [W at70] J. W atson. rism . W.W. No rton, 1970. Behavio 13
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