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1 weak direct sum
Математика: слабая прямая сумма -
2 weak direct sum
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3 sum
1) сумма; итог || суммировать, складывать; подводить итог3) резюмировать•sum over sum — мат. сумма вдоль подпространства
sum taken over — сумма, взятая по…
to sum up — резюмировать, суммировать
to sum with respect to — суммировать по...
- free sum- rank sum- regression sum of squares- risk sum- row sum- sum of squares for contrasts- unit sum -
4 head
hed
1. noun1) (the top part of the human body, containing the eyes, mouth, brain etc; the same part of an animal's body: The stone hit him on the head; He scratched his head in amazement.) cabeza2) (a person's mind: An idea came into my head last night.) cabeza, mente3) (the height or length of a head: The horse won by a head.) cabeza4) (the chief or most important person (of an organization, country etc): Kings and presidents are heads of state; (also adjective) a head waiter; the head office.) cabeza, jefe5) (anything that is like a head in shape or position: the head of a pin; The boy knocked the heads off the flowers.) cabeza6) (the place where a river, lake etc begins: the head of the Nile.) fuente, nacimiento7) (the top, or the top part, of anything: Write your address at the head of the paper; the head of the table.) cabecera, principio8) (the front part: He walked at the head of the procession.) a la cabeza de, al frente de9) (a particular ability or tolerance: He has no head for heights; She has a good head for figures.) madera; cabeza10) (a headmaster or headmistress: You'd better ask the Head.) director; directora11) ((for) one person: This dinner costs $10 a head.) por cabeza12) (a headland: Beachy Head.) cabo, punta13) (the foam on the top of a glass of beer etc.) espuma
2. verb1) (to go at the front of or at the top of (something): The procession was headed by the band; Whose name headed the list?) encabezar2) (to be in charge of; to be the leader of: He heads a team of scientists investigating cancer.) encabezar, estar al frente de, dirigir3) ((often with for) to (cause to) move in a certain direction: The explorers headed south; The boys headed for home; You're heading for disaster!) dirigirse a, encaminarse hacia, ir rumbo a4) (to put or write something at the beginning of: His report was headed `Ways of Preventing Industrial Accidents'.) titular5) ((in football) to hit the ball with the head: He headed the ball into the goal.) cabecear, rematar con la cabeza•- - headed- header
- heading
- heads
- headache
- headband
- head-dress
- headfirst
- headgear
- headlamp
- headland
- headlight
- headline
- headlines
- headlong
- head louse
- headmaster
- head-on
- headphones
- headquarters
- headrest
- headscarf
- headsquare
- headstone
- headstrong
- headwind
- above someone's head
- go to someone's head
- head off
- head over heels
- heads or tails?
- keep one's head
- lose one's head
- make head or tail of
- make headway
- off one's head
head1 n1. cabezamind your head! ¡cuidado con la cabeza!2. cabecera3. jefe / directorhead2 vb1. encabezar / ir a la cabeza2. cabecear / dar de cabezato head for... dirigirse a... / ir camino de...I'm heading for home me dirijo a casa / voy camino de casatr[hed]2 (on tape recorder, video) cabezal nombre masculino3 (of bed, table) cabecera4 (of page) principio5 (on beer) espuma6 (cape) cabo, punta7 (of school, company) director,-ra8 (cattle) res nombre femenino■ four hundred head of cattle cuatrocientas reses, cuatrocientas cabezas de ganado9 (coin) cara10 (of cabbage, lettuce) cogollo; (of cauliflower) pella1 principal, jefe1 (company, list etc) encabezar2 (ball) rematar de cabeza, dar un cabezazo a, cabecear\SMALLIDIOMATIC EXPRESSION/SMALLfrom head to toe / from head to foot de pies a cabezaheads or tails? ¿cara o cruz?off the top of one's head sin pensárselo, así de entradaon your own head be it! ¡allá te las compongas!per head por barba, por cabeza■ it cost us £12 per head nos costó doce libras por barbato be head over heels in love with somebody estar locamente enamorado,-a de alguiento be off one's head estar chiflado,-ato bite somebody's head off familiar echar una bronca a alguiento do something standing on one's head hacer algo con los ojos vendadosto have a good head for figures tener facilidad para los númerosto have a head for heights no padecer vértigoto keep one's head above water mantenerse a floteto keep one's head mantener la calmato laugh one's head off reírse a carcajadastwo heads are better than one cuatro ojos ven más que doshead teacher director,-rahead start ventajahead office oficina centralhead ['hɛd] vt1) lead: encabezar2) direct: dirigirhead vi: dirigirsehead adjmain: principalthe head office: la oficina central, la sedehead n1) : cabeza ffrom head to foot: de pies a cabeza2) mind: mente f, cabeza f3) tip, top: cabeza f (de un clavo, un martillo, etc.), cabecera f (de una mesa o un río), punta f (de una flecha), flor m (de un repollo, etc.), encabezamiento m (de una carta, etc.), espuma f (de cerveza)4) director, leader: director m, -tora f; jefe m, -fa f; cabeza f (de una familia)5) : cara f (de una moneda)heads or tails: cara o cruz6) : cabeza f500 head of cattle: 500 cabezas de ganado$10 a head: $10 por cabeza7)to come to a head : llegar a un punto críticoadj.• primero, -a adj.• principal adj.n.• cabecera s.f.• cabeza s.f.• cabezuela s.f.• director s.m.• dirigente s.m.• encabezamiento s.m.• mayor s.m.• mollera s.f.• principal s.m.• testa s.f.expr.• atajar v.• cortarle el paso expr.v.• cabecear v.• descabezar v.• dirigir v.• encabezar v.• mandar v.hed
I
1) ( Anat) cabeza fto stand on one's head — pararse de cabeza (AmL), hacer* el pino (Esp)
from head to foot o toe — de pies a cabeza, de arriba (a) abajo
he's a head taller than his brother — le lleva or le saca la cabeza a su hermano
head over heels: she tripped and went head over heels down the steps tropezó y cayó rodando escaleras abajo; to be head over heels in love estar* locamente or perdidamente enamorado; heads up! (AmE colloq) ojo! (fam), cuidado!; on your/his (own) head be it la responsabilidad es tuya/suya; to bang one's head against a (brick) wall darse* (con) la cabeza contra la pared; to be able to do something standing on one's head poder* hacer algo con los ojos cerrados; to bite o snap somebody's head off echarle una bronca a alguien (fam); to bury one's head in the sand hacer* como el avestruz; to get one's head down (colloq) ( work hard) ponerse* a trabajar en serio; ( settle for sleep) (BrE) irse* a dormir; to go over somebody's head ( bypassing hierarchy) pasar por encima de alguien; ( exceeding comprehension): his lecture went straight over my head no entendí nada de su conferencia; to go to somebody's head subírsele a la cabeza a alguien; to have a big o swelled o (BrE) swollen head ser* un creído; he's getting a swelled o (BrE) swollen head se le están subiendo los humos a la cabeza; to have one's head in the clouds tener* la cabeza llena de pájaros; to hold one's head up o high o up high ir* con la cabeza bien alta; to keep one's head above water mantenerse* a flote; to keep one's head down ( avoid attention) mantenerse* al margen; ( work hard) no levantar la cabeza; (lit: keep head lowered) no levantar la cabeza; to knock something on the head (colloq) dar* al traste con algo; to laugh one's head off reírse* a mandíbula batiente, desternillarse de (la) risa; to scream/shout one's head off gritar a voz en cuello; to make head or tail o (AmE also) heads or tails of something entender* algo; I can't make head or tail of it para mí esto no tiene ni pies ni cabeza; to rear one's ugly head: racism/fascism reared its ugly head again volvió a aparecer el fantasma del racismo/fascismo; to stand/be head and shoulders above somebody ( be superior) darle* cien vueltas a alguien, estar* muy por encima de alguien; to stand o turn something on its head darle* la vuelta a algo, poner* algo patas arriba (fam), dar* vuelta algo (CS); to turn somebody's head: the sort of good looks that turn heads el tipo de belleza que llama la atención or que hace que la gente se vuelva a mirar; (before n) head injury — lesión f en la cabeza
2) (mind, brain) cabeza fI said the first thing that came into my head — dije lo primero que se me ocurrió or que me vino a la cabeza
he needs his head examined — está or anda mal de la cabeza
she has a good head for business/figures — tiene cabeza para los negocios/los números
use your head! — usa la cabeza!, piensa un poco!
if we put our heads together, we'll be able to think of something — si lo pensamos juntos, algo se nos ocurrirá
it never entered my head that... — ni se me pasó por la cabeza or jamás pensé que...
to get something into somebody's head — meterle* algo en la cabeza a alguien
to be off one's head — (colloq) estar* chiflado (fam), estar* or andar* mal de la cabeza
to be out of one's head — (sl) ( on drugs) estar* flipado or volado or (Col) volando or (Méx) hasta atrás (arg); ( drunk) estar* como una cuba (fam)
to be soft o weak in the head — estar* mal de la cabeza
to get one's head (a)round something: I can't get my head (a)round this new system no me entra este nuevo sistema; to have one's head screwed on (right o the right way) (colloq) tener* la cabeza bien puesta or sentada; to keep/lose one's head mantener*/perder* la calma; two heads are better than one — cuatro ojos ven más que dos
3)a) ( of celery) cabeza f; (of nail, tack, pin) cabeza f; (of spear, arrow) punta f; ( of hammer) cabeza f, cotillo m; ( of pimple) punta f, cabeza f; ( on beer) espuma f; ( of river) cabecera fb) (top end - of bed, table) cabecera f; (- of page, letter) encabezamiento m; (- of procession, line) cabeza f4)a) ( chief) director, -tora m,fhead of state/government — jefe, -fa m,f de Estado/de Gobierno
the head of the household — el/la cabeza de familia; (before n)
head buyer — jefe, -fa m,f de compras
head girl/boy — (BrE Educ) alumno elegido para representar al alumnado de un colegio
head waiter — maître m, capitán m de meseros (Méx)
b) ( head teacher) (esp BrE) director, -tora m,f (de colegio)5)a) ( person)$15 per head — 15 dólares por cabeza or persona
6) ( crisis)to come to a head — hacer* crisis, llegar* a un punto crítico
7)a) ( magnetic device) (Audio, Comput) cabeza f, cabezal mb) ( of drill) cabezal mc) ( cylinder head) culata f8) ( Geog) cabo m
II
1.
1)a) \<\<march/procession\>\> encabezar*, ir* a la cabeza de; \<\<list\>\> encabezar*b) \<\<revolt\>\> acaudillar, ser* el cabecilla de; \<\<team\>\> capitanear; \<\<expedition/department\>\> dirigir*, estar* al frente de2) ( direct) (+ adv compl) \<\<vehicle/ship\>\> dirigir*which way are you headed? — ¿hacia or para dónde vas?
3) ( in soccer) \<\<ball\>\> cabecear4) \<\<page/chapter\>\> encabezar*
2.
viwhere are you heading? — ¿hacia or para dónde vas?
it's time we were heading back — ya va siendo hora de que volvamos or regresemos
Phrasal Verbs:- head for- head off- head up[hed]1. N1) (=part of body) cabeza f•
the horse won by a (short) head — el caballo ganó por una cabeza (escasa)•
he went head first into the ditch/wall — se cayó de cabeza en la zanja/se dio de cabeza contra la paredthe government is ploughing head first into another crisis — el gobierno avanza irremediablemente hacia otra crisis
•
to give a horse its head — soltar las riendas a un caballoto give sb his/her head — dar rienda suelta a algn
•
wine goes to my head — el vino se me sube a la cabeza•
to keep one's head down — (lit) no levantar la cabeza; (=work hard) trabajar de lo lindo; (=avoid being noticed) intentar pasar desapercibido•
to nod one's head — decir que sí or asentir con la cabeza•
to shake one's head — decir que no or negar con la cabeza•
he stands head and shoulders above the rest — (lit) les saca más de una cabeza a los demás; (fig) los demás no le llegan a la suela del zapato•
to stand on one's head — hacer el pino•
she is a head taller than her sister — le saca una cabeza a su hermana•
he turned his head and looked back at her — volvió la cabeza y la miró- have one's head up one's arse or ass- bite sb's head off- put or lay one's head on the block- get one's head downto go over sb's head —
- hold one's head up highwith head held high — con la frente bien alta or erguida
- laugh one's head off- stand or turn sth on its head- want sb's head on a plate- turn one's head the other way- bury or hide or stick one's head in the sand- scream/shout one's head offI can't make head nor or or tail of what he's saying — no entiendo nada de lo que dice
- turn heads- keep one's head above wateracid 3., cloud 1., hang 1., 1), knock, price 1., 1), rear, swell 3., 1), top I, 1., 11)2) (=intellect, mind) cabeza fuse your head! — ¡usa la cabeza!
it's gone right out of my head — se me ha ido de la cabeza, se me ha olvidado
•
it was above their heads — no lo entendían•
it's better to come to it with a clear head in the morning — es mejor hacerlo por la mañana con la cabeza despejada•
it never entered my head — ni se me pasó por la cabeza siquiera•
to have a head for business/figures — ser bueno para los negocios/con los números•
to do a sum in one's head — hacer un cálculo mental•
he has got it into his head that... — se le ha metido en la cabeza que...I wish he would get it into his thick head that... — ya me gustaría que le entrara en ese cabezón que tiene que...
who put that (idea) into your head? — ¿quién te ha metido eso en la cabeza?
•
I can't get that tune out of my head — no puedo quitarme esa música de la cabeza•
it was over their heads — no lo entendían•
I'm sure if we put our heads together we can work something out — estoy seguro de que si intercambiamos ideas encontraremos una solución•
to take it into one's head to do sth, he took it into his head to go to Australia — se le metió en la cabeza ir a Australia•
don't worry your head about it — no te preocupes, no le des muchas vueltas- keep one's head- lose one's head- be/go off one's headyou must be off your head! — ¡estás como una cabra!
- be out of one's head- he's got his head screwed on- be soft or weak in the head- go soft in the head3) (=leader) [of firm] director(a) m / f; (esp Brit) [of school] director(a) m / fhead of French — el jefe/la jefa del departamento de francés
4) (=top part) [of hammer, pin, spot] cabeza f; [of arrow, spear] punta f; [of stick, cane] puño m; [of bed, page] cabecera f; [of stairs] parte f alta; (on beer) espuma f; [of river] cabecera f, nacimiento m; [of valley] final m; [of mountain pass] cima fat the head of — [+ organization] a la cabeza de; [+ train] en la parte delantera de
to sit at the head of the table — sentarse en la cabecera de la mesa, presidir la mesa
5) (Bot) [of flower] cabeza f, flor f; [of corn] mazorca f6) (Tech) (on tape-recorder) cabezal m, cabeza f magnética; [of cylinder] culata f; (Comput) cabeza freading/writing head — cabeza f de lectura/grabación
7) (=culmination)•
this will bring matters to a head — esto llevará las cosas a un punto crítico8) heads (on coin) cara fheads or tails? — ¿cara o cruz?, ¿águila o sol? (Mex)
9) (no pl) (=unit)£15 a or per head — 15 libras por cabeza or persona
10) (Naut) proa fhead to wind — con la proa a barlovento or de cara al viento
11) (Geog) cabo m12) (=pressure)head of steam — presión f de vapor
head of water — presión f de agua
13) (=height) [of water]there has to be a head of six feet between the tank and the bath — el tanque tiene que estar a una altura de dos metros con respecto al baño
14) (=title) titular m; (=subject heading) encabezamiento mthis comes under the head of... — esto viene en el apartado de...
2. VT1) (=be at front of) [+ procession, league, poll] encabezar, ir a la cabeza de; [+ list] encabezar2) (=be in charge of) [+ organization] dirigir; (Sport) [+ team] capitanear3) (=steer) [+ ship, car, plane] dirigir4) (Ftbl) [+ goal] cabecear5) [+ chapter] encabezar3.VIwhere are you heading or headed? — ¿hacia dónde vas?, ¿para dónde vas?
he hitched a ride on a truck heading or headed west — hizo autostop y lo recogió un camión que iba hacia el oeste
they were heading home/back to town — volvían a casa/a la ciudad
4.CPDhead boy N — (Brit) (Scol) ≈ delegado m de la escuela (alumno)
head buyer N — jefe(-a) m / f de compras
head case * N — (Brit) majara * mf, chiflado(-a) * m / f
head cheese N — (US) queso m de cerdo, cabeza f de jabalí (Sp), carne f en gelatina
head clerk N — encargado(-a) m / f
head coach N — (Sport) primer(a) entrenador(a) m / f
head count N — recuento m de personas
head gardener N — jefe(-a) m / f de jardineros
head girl N — (Brit) (Scol) ≈ delegada f de la escuela (alumna)
head height N — altura f de la cabeza
•
at head height — a la altura de la cabezahead injury N — herida f en la cabeza
head massage N — masaje m en la cabeza
•
to give sb a head massage — masajearle la cabeza a algn, darle un masaje en la cabeza a algnhead nurse N — enfermero(-a) m / f jefe
head office N — sede f central
head prefect N — (Brit) (Scol) ≈ delegado(-a) m / f de la escuela (alumno/alumna)
head restraint N — (Aut) apoyacabezas m inv, reposacabezas m inv
head start N — ventaja f
a good education gives your child a head start in life — una buena educación sitúa a su hijo en una posición aventajada en la vida
to have a head start (over or on sb) — (Sport, fig) tener ventaja (sobre algn)
he has a head start over other candidates — tiene ventaja sobre or les lleva ventaja a otros candidatos
head teacher N — director(a) m / f
head waiter N — maître m
head wound N — herida f en la cabeza
- head for- head off- head out- head up* * *[hed]
I
1) ( Anat) cabeza fto stand on one's head — pararse de cabeza (AmL), hacer* el pino (Esp)
from head to foot o toe — de pies a cabeza, de arriba (a) abajo
he's a head taller than his brother — le lleva or le saca la cabeza a su hermano
head over heels: she tripped and went head over heels down the steps tropezó y cayó rodando escaleras abajo; to be head over heels in love estar* locamente or perdidamente enamorado; heads up! (AmE colloq) ojo! (fam), cuidado!; on your/his (own) head be it la responsabilidad es tuya/suya; to bang one's head against a (brick) wall darse* (con) la cabeza contra la pared; to be able to do something standing on one's head poder* hacer algo con los ojos cerrados; to bite o snap somebody's head off echarle una bronca a alguien (fam); to bury one's head in the sand hacer* como el avestruz; to get one's head down (colloq) ( work hard) ponerse* a trabajar en serio; ( settle for sleep) (BrE) irse* a dormir; to go over somebody's head ( bypassing hierarchy) pasar por encima de alguien; ( exceeding comprehension): his lecture went straight over my head no entendí nada de su conferencia; to go to somebody's head subírsele a la cabeza a alguien; to have a big o swelled o (BrE) swollen head ser* un creído; he's getting a swelled o (BrE) swollen head se le están subiendo los humos a la cabeza; to have one's head in the clouds tener* la cabeza llena de pájaros; to hold one's head up o high o up high ir* con la cabeza bien alta; to keep one's head above water mantenerse* a flote; to keep one's head down ( avoid attention) mantenerse* al margen; ( work hard) no levantar la cabeza; (lit: keep head lowered) no levantar la cabeza; to knock something on the head (colloq) dar* al traste con algo; to laugh one's head off reírse* a mandíbula batiente, desternillarse de (la) risa; to scream/shout one's head off gritar a voz en cuello; to make head or tail o (AmE also) heads or tails of something entender* algo; I can't make head or tail of it para mí esto no tiene ni pies ni cabeza; to rear one's ugly head: racism/fascism reared its ugly head again volvió a aparecer el fantasma del racismo/fascismo; to stand/be head and shoulders above somebody ( be superior) darle* cien vueltas a alguien, estar* muy por encima de alguien; to stand o turn something on its head darle* la vuelta a algo, poner* algo patas arriba (fam), dar* vuelta algo (CS); to turn somebody's head: the sort of good looks that turn heads el tipo de belleza que llama la atención or que hace que la gente se vuelva a mirar; (before n) head injury — lesión f en la cabeza
2) (mind, brain) cabeza fI said the first thing that came into my head — dije lo primero que se me ocurrió or que me vino a la cabeza
he needs his head examined — está or anda mal de la cabeza
she has a good head for business/figures — tiene cabeza para los negocios/los números
use your head! — usa la cabeza!, piensa un poco!
if we put our heads together, we'll be able to think of something — si lo pensamos juntos, algo se nos ocurrirá
it never entered my head that... — ni se me pasó por la cabeza or jamás pensé que...
to get something into somebody's head — meterle* algo en la cabeza a alguien
to be off one's head — (colloq) estar* chiflado (fam), estar* or andar* mal de la cabeza
to be out of one's head — (sl) ( on drugs) estar* flipado or volado or (Col) volando or (Méx) hasta atrás (arg); ( drunk) estar* como una cuba (fam)
to be soft o weak in the head — estar* mal de la cabeza
to get one's head (a)round something: I can't get my head (a)round this new system no me entra este nuevo sistema; to have one's head screwed on (right o the right way) (colloq) tener* la cabeza bien puesta or sentada; to keep/lose one's head mantener*/perder* la calma; two heads are better than one — cuatro ojos ven más que dos
3)a) ( of celery) cabeza f; (of nail, tack, pin) cabeza f; (of spear, arrow) punta f; ( of hammer) cabeza f, cotillo m; ( of pimple) punta f, cabeza f; ( on beer) espuma f; ( of river) cabecera fb) (top end - of bed, table) cabecera f; (- of page, letter) encabezamiento m; (- of procession, line) cabeza f4)a) ( chief) director, -tora m,fhead of state/government — jefe, -fa m,f de Estado/de Gobierno
the head of the household — el/la cabeza de familia; (before n)
head buyer — jefe, -fa m,f de compras
head girl/boy — (BrE Educ) alumno elegido para representar al alumnado de un colegio
head waiter — maître m, capitán m de meseros (Méx)
b) ( head teacher) (esp BrE) director, -tora m,f (de colegio)5)a) ( person)$15 per head — 15 dólares por cabeza or persona
6) ( crisis)to come to a head — hacer* crisis, llegar* a un punto crítico
7)a) ( magnetic device) (Audio, Comput) cabeza f, cabezal mb) ( of drill) cabezal mc) ( cylinder head) culata f8) ( Geog) cabo m
II
1.
1)a) \<\<march/procession\>\> encabezar*, ir* a la cabeza de; \<\<list\>\> encabezar*b) \<\<revolt\>\> acaudillar, ser* el cabecilla de; \<\<team\>\> capitanear; \<\<expedition/department\>\> dirigir*, estar* al frente de2) ( direct) (+ adv compl) \<\<vehicle/ship\>\> dirigir*which way are you headed? — ¿hacia or para dónde vas?
3) ( in soccer) \<\<ball\>\> cabecear4) \<\<page/chapter\>\> encabezar*
2.
viwhere are you heading? — ¿hacia or para dónde vas?
it's time we were heading back — ya va siendo hora de que volvamos or regresemos
Phrasal Verbs:- head for- head off- head up -
5 rule
1) правило, норма; норматив || устанавливать правила или нормы2) строит. прав'ило3) линейка || линовать, разлиновывать4) правление || управлять, руководить, командовать5) мат. закон6) графить, разграфлять•set closed under rule — множество, замкнутое относительно операции
- blind man's ruleto lay down the rule — формулировать [устанавливать] правило
- box rule- cut rule- em rule- slow-in- sum rule- three sigma rule -
6 Artificial Intelligence
In my opinion, none of [these programs] does even remote justice to the complexity of human mental processes. Unlike men, "artificially intelligent" programs tend to be single minded, undistractable, and unemotional. (Neisser, 1967, p. 9)Future progress in [artificial intelligence] will depend on the development of both practical and theoretical knowledge.... As regards theoretical knowledge, some have sought a unified theory of artificial intelligence. My view is that artificial intelligence is (or soon will be) an engineering discipline since its primary goal is to build things. (Nilsson, 1971, pp. vii-viii)Most workers in AI [artificial intelligence] research and in related fields confess to a pronounced feeling of disappointment in what has been achieved in the last 25 years. Workers entered the field around 1950, and even around 1960, with high hopes that are very far from being realized in 1972. In no part of the field have the discoveries made so far produced the major impact that was then promised.... In the meantime, claims and predictions regarding the potential results of AI research had been publicized which went even farther than the expectations of the majority of workers in the field, whose embarrassments have been added to by the lamentable failure of such inflated predictions....When able and respected scientists write in letters to the present author that AI, the major goal of computing science, represents "another step in the general process of evolution"; that possibilities in the 1980s include an all-purpose intelligence on a human-scale knowledge base; that awe-inspiring possibilities suggest themselves based on machine intelligence exceeding human intelligence by the year 2000 [one has the right to be skeptical]. (Lighthill, 1972, p. 17)4) Just as Astronomy Succeeded Astrology, the Discovery of Intellectual Processes in Machines Should Lead to a Science, EventuallyJust as astronomy succeeded astrology, following Kepler's discovery of planetary regularities, the discoveries of these many principles in empirical explorations on intellectual processes in machines should lead to a science, eventually. (Minsky & Papert, 1973, p. 11)5) Problems in Machine Intelligence Arise Because Things Obvious to Any Person Are Not Represented in the ProgramMany problems arise in experiments on machine intelligence because things obvious to any person are not represented in any program. One can pull with a string, but one cannot push with one.... Simple facts like these caused serious problems when Charniak attempted to extend Bobrow's "Student" program to more realistic applications, and they have not been faced up to until now. (Minsky & Papert, 1973, p. 77)What do we mean by [a symbolic] "description"? We do not mean to suggest that our descriptions must be made of strings of ordinary language words (although they might be). The simplest kind of description is a structure in which some features of a situation are represented by single ("primitive") symbols, and relations between those features are represented by other symbols-or by other features of the way the description is put together. (Minsky & Papert, 1973, p. 11)[AI is] the use of computer programs and programming techniques to cast light on the principles of intelligence in general and human thought in particular. (Boden, 1977, p. 5)The word you look for and hardly ever see in the early AI literature is the word knowledge. They didn't believe you have to know anything, you could always rework it all.... In fact 1967 is the turning point in my mind when there was enough feeling that the old ideas of general principles had to go.... I came up with an argument for what I called the primacy of expertise, and at the time I called the other guys the generalists. (Moses, quoted in McCorduck, 1979, pp. 228-229)9) Artificial Intelligence Is Psychology in a Particularly Pure and Abstract FormThe basic idea of cognitive science is that intelligent beings are semantic engines-in other words, automatic formal systems with interpretations under which they consistently make sense. We can now see why this includes psychology and artificial intelligence on a more or less equal footing: people and intelligent computers (if and when there are any) turn out to be merely different manifestations of the same underlying phenomenon. Moreover, with universal hardware, any semantic engine can in principle be formally imitated by a computer if only the right program can be found. And that will guarantee semantic imitation as well, since (given the appropriate formal behavior) the semantics is "taking care of itself" anyway. Thus we also see why, from this perspective, artificial intelligence can be regarded as psychology in a particularly pure and abstract form. The same fundamental structures are under investigation, but in AI, all the relevant parameters are under direct experimental control (in the programming), without any messy physiology or ethics to get in the way. (Haugeland, 1981b, p. 31)There are many different kinds of reasoning one might imagine:Formal reasoning involves the syntactic manipulation of data structures to deduce new ones following prespecified rules of inference. Mathematical logic is the archetypical formal representation. Procedural reasoning uses simulation to answer questions and solve problems. When we use a program to answer What is the sum of 3 and 4? it uses, or "runs," a procedural model of arithmetic. Reasoning by analogy seems to be a very natural mode of thought for humans but, so far, difficult to accomplish in AI programs. The idea is that when you ask the question Can robins fly? the system might reason that "robins are like sparrows, and I know that sparrows can fly, so robins probably can fly."Generalization and abstraction are also natural reasoning process for humans that are difficult to pin down well enough to implement in a program. If one knows that Robins have wings, that Sparrows have wings, and that Blue jays have wings, eventually one will believe that All birds have wings. This capability may be at the core of most human learning, but it has not yet become a useful technique in AI.... Meta- level reasoning is demonstrated by the way one answers the question What is Paul Newman's telephone number? You might reason that "if I knew Paul Newman's number, I would know that I knew it, because it is a notable fact." This involves using "knowledge about what you know," in particular, about the extent of your knowledge and about the importance of certain facts. Recent research in psychology and AI indicates that meta-level reasoning may play a central role in human cognitive processing. (Barr & Feigenbaum, 1981, pp. 146-147)Suffice it to say that programs already exist that can do things-or, at the very least, appear to be beginning to do things-which ill-informed critics have asserted a priori to be impossible. Examples include: perceiving in a holistic as opposed to an atomistic way; using language creatively; translating sensibly from one language to another by way of a language-neutral semantic representation; planning acts in a broad and sketchy fashion, the details being decided only in execution; distinguishing between different species of emotional reaction according to the psychological context of the subject. (Boden, 1981, p. 33)Can the synthesis of Man and Machine ever be stable, or will the purely organic component become such a hindrance that it has to be discarded? If this eventually happens-and I have... good reasons for thinking that it must-we have nothing to regret and certainly nothing to fear. (Clarke, 1984, p. 243)The thesis of GOFAI... is not that the processes underlying intelligence can be described symbolically... but that they are symbolic. (Haugeland, 1985, p. 113)14) Artificial Intelligence Provides a Useful Approach to Psychological and Psychiatric Theory FormationIt is all very well formulating psychological and psychiatric theories verbally but, when using natural language (even technical jargon), it is difficult to recognise when a theory is complete; oversights are all too easily made, gaps too readily left. This is a point which is generally recognised to be true and it is for precisely this reason that the behavioural sciences attempt to follow the natural sciences in using "classical" mathematics as a more rigorous descriptive language. However, it is an unfortunate fact that, with a few notable exceptions, there has been a marked lack of success in this application. It is my belief that a different approach-a different mathematics-is needed, and that AI provides just this approach. (Hand, quoted in Hand, 1985, pp. 6-7)We might distinguish among four kinds of AI.Research of this kind involves building and programming computers to perform tasks which, to paraphrase Marvin Minsky, would require intelligence if they were done by us. Researchers in nonpsychological AI make no claims whatsoever about the psychological realism of their programs or the devices they build, that is, about whether or not computers perform tasks as humans do.Research here is guided by the view that the computer is a useful tool in the study of mind. In particular, we can write computer programs or build devices that simulate alleged psychological processes in humans and then test our predictions about how the alleged processes work. We can weave these programs and devices together with other programs and devices that simulate different alleged mental processes and thereby test the degree to which the AI system as a whole simulates human mentality. According to weak psychological AI, working with computer models is a way of refining and testing hypotheses about processes that are allegedly realized in human minds.... According to this view, our minds are computers and therefore can be duplicated by other computers. Sherry Turkle writes that the "real ambition is of mythic proportions, making a general purpose intelligence, a mind." (Turkle, 1984, p. 240) The authors of a major text announce that "the ultimate goal of AI research is to build a person or, more humbly, an animal." (Charniak & McDermott, 1985, p. 7)Research in this field, like strong psychological AI, takes seriously the functionalist view that mentality can be realized in many different types of physical devices. Suprapsychological AI, however, accuses strong psychological AI of being chauvinisticof being only interested in human intelligence! Suprapsychological AI claims to be interested in all the conceivable ways intelligence can be realized. (Flanagan, 1991, pp. 241-242)16) Determination of Relevance of Rules in Particular ContextsEven if the [rules] were stored in a context-free form the computer still couldn't use them. To do that the computer requires rules enabling it to draw on just those [ rules] which are relevant in each particular context. Determination of relevance will have to be based on further facts and rules, but the question will again arise as to which facts and rules are relevant for making each particular determination. One could always invoke further facts and rules to answer this question, but of course these must be only the relevant ones. And so it goes. It seems that AI workers will never be able to get started here unless they can settle the problem of relevance beforehand by cataloguing types of context and listing just those facts which are relevant in each. (Dreyfus & Dreyfus, 1986, p. 80)Perhaps the single most important idea to artificial intelligence is that there is no fundamental difference between form and content, that meaning can be captured in a set of symbols such as a semantic net. (G. Johnson, 1986, p. 250)Artificial intelligence is based on the assumption that the mind can be described as some kind of formal system manipulating symbols that stand for things in the world. Thus it doesn't matter what the brain is made of, or what it uses for tokens in the great game of thinking. Using an equivalent set of tokens and rules, we can do thinking with a digital computer, just as we can play chess using cups, salt and pepper shakers, knives, forks, and spoons. Using the right software, one system (the mind) can be mapped into the other (the computer). (G. Johnson, 1986, p. 250)19) A Statement of the Primary and Secondary Purposes of Artificial IntelligenceThe primary goal of Artificial Intelligence is to make machines smarter.The secondary goals of Artificial Intelligence are to understand what intelligence is (the Nobel laureate purpose) and to make machines more useful (the entrepreneurial purpose). (Winston, 1987, p. 1)The theoretical ideas of older branches of engineering are captured in the language of mathematics. We contend that mathematical logic provides the basis for theory in AI. Although many computer scientists already count logic as fundamental to computer science in general, we put forward an even stronger form of the logic-is-important argument....AI deals mainly with the problem of representing and using declarative (as opposed to procedural) knowledge. Declarative knowledge is the kind that is expressed as sentences, and AI needs a language in which to state these sentences. Because the languages in which this knowledge usually is originally captured (natural languages such as English) are not suitable for computer representations, some other language with the appropriate properties must be used. It turns out, we think, that the appropriate properties include at least those that have been uppermost in the minds of logicians in their development of logical languages such as the predicate calculus. Thus, we think that any language for expressing knowledge in AI systems must be at least as expressive as the first-order predicate calculus. (Genesereth & Nilsson, 1987, p. viii)21) Perceptual Structures Can Be Represented as Lists of Elementary PropositionsIn artificial intelligence studies, perceptual structures are represented as assemblages of description lists, the elementary components of which are propositions asserting that certain relations hold among elements. (Chase & Simon, 1988, p. 490)Artificial intelligence (AI) is sometimes defined as the study of how to build and/or program computers to enable them to do the sorts of things that minds can do. Some of these things are commonly regarded as requiring intelligence: offering a medical diagnosis and/or prescription, giving legal or scientific advice, proving theorems in logic or mathematics. Others are not, because they can be done by all normal adults irrespective of educational background (and sometimes by non-human animals too), and typically involve no conscious control: seeing things in sunlight and shadows, finding a path through cluttered terrain, fitting pegs into holes, speaking one's own native tongue, and using one's common sense. Because it covers AI research dealing with both these classes of mental capacity, this definition is preferable to one describing AI as making computers do "things that would require intelligence if done by people." However, it presupposes that computers could do what minds can do, that they might really diagnose, advise, infer, and understand. One could avoid this problematic assumption (and also side-step questions about whether computers do things in the same way as we do) by defining AI instead as "the development of computers whose observable performance has features which in humans we would attribute to mental processes." This bland characterization would be acceptable to some AI workers, especially amongst those focusing on the production of technological tools for commercial purposes. But many others would favour a more controversial definition, seeing AI as the science of intelligence in general-or, more accurately, as the intellectual core of cognitive science. As such, its goal is to provide a systematic theory that can explain (and perhaps enable us to replicate) both the general categories of intentionality and the diverse psychological capacities grounded in them. (Boden, 1990b, pp. 1-2)Because the ability to store data somewhat corresponds to what we call memory in human beings, and because the ability to follow logical procedures somewhat corresponds to what we call reasoning in human beings, many members of the cult have concluded that what computers do somewhat corresponds to what we call thinking. It is no great difficulty to persuade the general public of that conclusion since computers process data very fast in small spaces well below the level of visibility; they do not look like other machines when they are at work. They seem to be running along as smoothly and silently as the brain does when it remembers and reasons and thinks. On the other hand, those who design and build computers know exactly how the machines are working down in the hidden depths of their semiconductors. Computers can be taken apart, scrutinized, and put back together. Their activities can be tracked, analyzed, measured, and thus clearly understood-which is far from possible with the brain. This gives rise to the tempting assumption on the part of the builders and designers that computers can tell us something about brains, indeed, that the computer can serve as a model of the mind, which then comes to be seen as some manner of information processing machine, and possibly not as good at the job as the machine. (Roszak, 1994, pp. xiv-xv)The inner workings of the human mind are far more intricate than the most complicated systems of modern technology. Researchers in the field of artificial intelligence have been attempting to develop programs that will enable computers to display intelligent behavior. Although this field has been an active one for more than thirty-five years and has had many notable successes, AI researchers still do not know how to create a program that matches human intelligence. No existing program can recall facts, solve problems, reason, learn, and process language with human facility. This lack of success has occurred not because computers are inferior to human brains but rather because we do not yet know in sufficient detail how intelligence is organized in the brain. (Anderson, 1995, p. 2)Historical dictionary of quotations in cognitive science > Artificial Intelligence
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