Computer Model of a "Sense of Humour". II. Realization in Neural Networks

Computer Mo del of a ”Sense of Humour”. I I. Realization in Neural Net w orks I. M. Suslo v P .N.Leb edev Ph ysic al Institute, 119334 Mosco w, USSR 1 Abstract The computer realization of a ”se nse of h umour” requires the creation of an algorithm for solving the ”linguistic proble m”, i.e. the problem of rec- ognizing a con tin uous se quence of polyseman tic images. Suc h an algorithm can b e realized in the Hopfie ld mo del of a neural net w ork, if it is suitably mo dified . In [1] we analysed the general algorithm of information processing and sho w ed that on fulfillmen t of the natural requireme n ts imp osed by its biological purp ose suc h an algorithm will p oss ess a ”sense of h umour”. The presen t pap e r prop oses a p ossible realization of the algorithm in a system of formal neurons. Description of the mo del F ollow ing Hopfield [2] we shall consid er that the s tate of the i -th neuron is des crib ed b y the v ariable V i assuming t w o v alues: V i = 1 (excited state) and V i = 0 (state of rest). The link of the neuron i with the neuron j is determined b y the parameter T ij . The state of the syste m c hanges with time t according to the algorithm: V i ( t + δ t ) = 1 2 + 1 2 sign    X j T ij V j ( t ) − U i    , (1) where U i is the excitation threshold o f the i -th neuron a n d the nu m b er i is c hosen randomly . The prop osed mo del of the nerv ous system is a mo dification o f the trila y er p e rceptrone [3] adapted for w ork in real time. It con tains the follo wing ele men ts (Fig. 1). 1 Present address: P .L.K apitza Institute for Physical Pro b lems, 11933 7 Mo sco w, Russia E-mail: suslov@k apitza .ras.ru 1 The ass o ciative mem ory ( A – layer) represe n ts the neural netw ork whic h for simplicit y w e consider as described by the Hopfield mo del: the neurons of the A – la y er are link ed with eac h other with T ij = T j i , U i = 0. Within the A – lay er evolution according to (1) leads from the arbitrary initial state { V i } to one of the lo cal minima of energy E = − X ij T ij V i V j , (2) whic h are iden tified with the images written in t he memory { V s ij } , s = 1 , 2 , . . . , p . The recorded images determine the matrix of the links T ij [2]: T ij = p X s =1 µ s (2 V s i − 1) (2 V s j − 1) , i 6 = j ( µ s > 0) , T ii = 0 (3) The se nsory system ( S – layer) receiv es signals from the outside w orld (for example, from the retina of the ey e). The sensory neurons are not linke d b et w een themselv es, but eac h S – neuron is b ound to one of the memory neurons: the links S → A are p ositiv e (exciting) and the bac k links A → S are negativ e (inhibiting) (Fig. 1). The r e acting system ( R – layer) consis ts of a set of neurons eac h of whic h corresp onds to one of the images r ecorded in the memory: to the s -th neuron of the R – lay er con ve rge the p ositiv e (exc iting) links from those neurons i of the memory for whic h V s i = 1 (w e shall refer the last neurons as a carrier of the image { V s i } ). The bac k negativ e (inhibiting) links run from the R – ne urons to the memory neurons; the R – neu rons are not link ed b etw een themselv es (F ig. 1 ). The thresholds U i for the R – neurons ar e a djusted in suc h a manner that the excitation of the s - th neuron of the R – la y er o ccurs only when the configuration of the A – neurons is sufficien tly close to the image { V s i } . W e consider that the image is realized b y the biological individual only when there is excitation of t he corresp onding R – ne uron, i.e. the R – lay er represen ts the consciousnes s of the individual. The c entr e co ordinates the w ork of the syste m b y acting according to the built-in pro- gram: it exercises control o v er the macroscopic parameters of the system. The concrete functions of the cen tre consist in the follo wing. (1) The cen tre has links with a small part of the memory neurons ev enly distributed in the A – la y er whic h allo ws it to register (a) the presence of excited neurons in a certain p ortion of the memory and (b) the stationarit y or nonstationarit y of this p o rtion. (2) The centre pro duces lo cal c hanges of ”temp erature” in the A – lay er. Since the temp erature of the neural net work is determined by the no ise lev el in it (whic h can b e tak en into accoun t by in tro ducing the random force f i ( t ) in to the braces ( 1 )) then the regulatable noise source should b e at the disposal o f the cen tre. (3) The cen tre pro duces lo cal switc hing on the ”magnetic field” in the A – la y er whic h correspo nds to the addition in energy (2) of the term X i h i V i (4) 2 Figure 1: Prop osed mo del of the nerv ous syste m is a mo dification of the three – la y er p erceptrone [3]: filled circles are neurons; solid lines a re constan tly acting links b et w een neurons; brok en lines are links switc hed on the command from the cen tre; the sym b ols + and − indicate the excitatory and inhibitory c haracter of the links; the S – la y er is the sensory system; the A – lay er is the asso ciative memory; the R – lay er is the reacting system or ”consciousness”. Roman nume rals mark: ( I ) information from the A – lay er, ( I I ) the con trol of the links, ( I I I ) the outer w orld, ( I V ) the motor cortex. Inset in the right upp er corner sho ws p ossible realization of the con trollable link. 3 (in (1) h i are added to the thresholds U j ). Switc hing on the field is achie v ed with the aid of a ”magnet” — group of neurons con trolled from the cen tre, eac h o f whic h is connected with a certain region of the A – la yer. (4) The cen tre carries o ut the con trol of the links sho wn in Fig. 1 by a brok en line. The simplest realization of the con trollable link AB is p ossible with the aid of the in termediate neuron C (see Fig. 1), the t hreshold of whic h is so a djusted that it is excited only in the sim ultaneous presence of the exciting signal from the neuron A and from the cen tre. In the presence of a signal from the cen tre the neuron A excites or inhibits the neuron B — the link is switc hed on, in the absence of a signal from the cen tre the neuron A cannot act up on the neuron B — the link is switc hed off. The command for switc hing on and off is giv en not to the individual links but sim ultaneously to thei r large groups. (5) The cen tre gives the command for the learning o f the plastic links. Recognition of a separate image Recognition of the images o ccurs with the links A → S and R → A switc hed on. In the initial state of the system all the neurons are not excited. Since the state of the A – lay er with V i ≡ 0 is unstable ( see (1) at U i = 0), so the presence o f the stabilizing magnetic field is necess ary . Let t he stim ulus ˜ B = B + δ B (i.e. the ” noisy” image B ) is presen ted to the sensory system; this induces excitation of some of the S – neurons (F ig . 2,a ). Then the centre switc hes out the magnetic field a nd excitation is transmitted to the A – neurons (Fig. 2,b) whic h, in turn, quenc h the sensory neurons (Fig. 2,c) (it is assumed that the links S → A and A → S are suffiic ien tly strong). Then in the A – la ye r there is free ev olution according to (1) whic h ends in relaxation to the stable state corresp onding to the image B (Fig. 2,d); the neuron resp o nsible for this image is excited in the R – la yer (Fig. 2,e). The bac k signal is send into the memory , quenc hing the exc ited neurons (Fig. 2,f ) and the image B is deleted from the ”consciousne ss” (Fig. 2,g): the system returns to the initial state and is ready for the p erception of a new image. Learning The links betw een the A – neurons are plastic and c hange according to the rule [2] δ T ij ∼ (2 V i − 1)(2 V j − 1) δ t ( i 6 = j ) , (5) if the neurons i and j sta y in the states V i and V j during the time δ t . If in the initial state T ij ≡ 0 then the presen tatio n to the system of p configurations { V s i } , s = 1 , 2 , ..., p leads to the matrix of links (3). Since T ij ma y ha v e an y sign, the neurons of the A – lay er 4 Figure 2: Seque n tial states of the system in the course of recognition of a separate image; op en circl es ( I ) a re exc ited neurons, dark circl es ( I I ) — not excited ones. F or clarity , only the links are sho wn along whic h excitation w as transmitted at the preceding momen t of time. 5 Figure 3: Learning o ccurs with the S → A and R → A links switc hed off. m ust hav e b oth exciting and inhibiting synapses (sp ecialization of the synapses is known [4, pp. 62 – 65] to ha v e in v a rian t c haracter). The links A → R in t he initial state ha v e a zero v alue and can be learned only in one, p ositiv e direction δ T ij = ( cδ t ( c > 0) for V 1 = V j = 1 0 (in other cases) , (6) i.e. hav e only exciting synapses. The remaining links ( R → A , S → A , A → S ) are not plastic and ha v e in b orn c haracter. The learning of the system is similar to the learning of a chil d: a certain image B is presen ted t o it generating in the S – la ye r a certain configuration of excited neurons; then it is ask ed to ”memorize B ”, whic h excites one of the neurons of the R – lay er app oin ted to b e responsible for the image B . Learning o ccurs with the A → S and R → A links cut out (F ig. 3 ), so that the configuration of the S – neurons is pro jected in to the A – lay er and p ersists for a certain time: the links T ij in the A – lay er c hange according to (5) forming the matrix (3), while the links A → R c hange according to (6) ensuring the connection of the s -th neuron of the R – la y er with a carrier of the image { V s i } . In the resting state V i ≡ 0 the system sp ends a considerable time and the learning according to (5) should result in ”ferromagnetic” interact ion b et w een the neurons ( T ij > 0 for all i, j ) and the single state V i ≡ 1 b eing stable. Therefore, w e supp ose that there is 6 no learning in the state V i ≡ 0, and the learning command is given only on presen tation of the image. Short-range action of the links and lo calization of images In the usual Hopfield mo del [2] all the neurons are link ed with eac h other and the carriers of images { V s i } are spread out o v er the whole neural net. In reality the links T ij ha v e a finite ra dius of action ξ : in the h uman brain eac h neuron has ∼ 10 4 synapses , while a complete n um b er of neurons ∼ 10 11 [4, pp. 31– 3 3]. Exp erimen tal indications on lo calization of the images also exis t [3, pp. 64, 65]. W e shall consider that eac h image { V s i } is written in a certain r egion Ω s con taining man y neurons, but small as compared with the size of the whole neural net work; so that V s i = 0 for i not b elonging to Ω s (the carrier { V s i } is lo calized in Ω s ) and for i ∈ Ω s the magnitudes V s i with equal probabilit y assume the v alues 0 and 1. 2 Since recognition of the images in an y ev en t m ust b e preceded by tra nslational shift, rotation and change of the sc ale (whic h can b e ac hiev ed by a certain mo dification of the Hopfield mo del [5]) then the assumption on the lo calization of images do es not ha v e an y serious consequences . The command for switc hing off the magnetic field, c hange in t emp erature (see below ) and learning of plastic links is giv en only on presen tation of the image { V s i } and only for neurons of the region Ω s . T aking all this in to accoun t, we accept that the learning rule for the A – neurons instead of (5) has the form δ T ij ∼ D ij δ s i δ s j (2 V i − 1) (2 V j − 1) δ t ( i 6 = j ) (7) when the image { V s i } is prese n ted; here D ij = ( 1 , for r ij < ξ , i 6 = j 0 , in other cases , δ s i = ( 1 , for i ∈ Ω s 0 , for i / ∈ Ω s (8) and r ij is the distance b et w een the neurons i and j . The matrix o f the links after writing p images instead of (3) assumes the form T ij = D ij p X s =1 δ s i δ s j µ s (2 V s i − 1)(2 V s j − 1) , µ s > 0 . (9) T o demonstrate stabilit y of { V s i } let us compose t he combin ation [2] H s i = X j T ij V s j = X s ′ µ s ′ δ s ′ i (2 V s ′ i − 1) X j ∈ Ω ss ′ D ij V s j (2 V s ′ j − 1) , (10) 2 T o raise the stability of the sy stem r elative to the destruction of s o me of the neurons the reg ion Ω s can b e mu ltiply connected. 7 where Ω ss ′ is the in tersection of Ω s and Ω s ′ . By virtue of the randomness of V s i and the large n um ber of terms in the sum for j the latter is close to its mean: H s i = 1 2 µ s δ s i X j ∈ Ω s D ij (2 V s i − 1) (11) F or i ∈ Ω s the sum o v er j is p ositiv e a nd δ s i = 1 so that t he configuration of { V s i } is stable b y virtue of the algorithm (1); for i / ∈ Ω s the state V i = 0 is main tained b y the magnetic field. Because of the localization of the images it suffices for the s -th neuron of the R – la ye r to ha v e links only with the neurons of t he region Ω s of the A – la y er. Recognition of the am biguous image Ab o v e it w as assumed that the stim ulus presen ted, ˜ B = B + δ B , is close to image B con tained in the memory so that the initial state ˜ B alw a ys relaxes to the final state B , i.e. the in terpretation of the image ˜ B is clearcut. In terms of energy this means that the state ˜ B lies in a p oten tial well, whose minim um corresponds to the image B and ev olution o ccurs at zero temp erature. No w let us consider the recognition of an ambiguous image. W e ha v e in mind the mo delling of the follo wing situation: the w ord B is shown to the p erson and it is ex plained to him that this w ord ma y assume sev eral meanings: in the memory of the p erson the images B + b 1 , B + b 2 , . . . are fixed where b 1 , b 2 , . . . are the elemen ts of the giv en explanation; if no w the word B is presen ted for recognition its in terpretation will b e a m biguous leading to one of the results B + b i . F or mo delling it suffices to assume that recognition b egins at the temp erature T exceeding the p otential barriers b etw een images B + b 1 , B + b 2 , . . . and then the temp erature decreases and the system relaxes to one of the lo cal minima corresp onding to the images B + b i . Hereafter, we shall consider that decrease of temp erature from the initial v alue T 0 o ccurs adiabatically so that the system with ov erwhelming probability relaxes to the deep est of the lo cal minima. Sim ultaneous recognition of seve ral images Supp ose that after presen tatio n of the stim ulus A the system relax to one of the images A 1 , A 2 , . . . and after presen tation of the stim ulus B to one of t he images B 1 , B 2 , . . . What will happ en, if the stim uli A and B are presen ted sim ultaneously? The pro cess of recognition b egins with switc hing out the magnetic field in the p o rtion of the A – la y er, where the image carrier is lo calized. Let presen tation of the images A and B requires switc hing out the field in the regions Ω A and Ω B of the asso ciativ e lay er. Let us assume for simplicit y that the regions Ω A and Ω B do not o v erlap (the qualitativ e 8 Figure 4: P oten tial relief for recognition of the images A a nd B separately ( contin uous curv e) and for sim ultaneous recognition (brok en line). picture p ersists in the general case); then V i = V A i + V B i where V A i and V B i differ from zero respectiv ely for the neurons i lying in the regions Ω A and Ω B . The energy (2) ass umes the form E { V A i + V B i } = − X ij T ij V A i V A j − X ij T ij V B i V B j − 2 X ij T ij V A i V B j (12) If the stim uli A and B are presen ted separately , then correspondingly V B i ≡ 0 or V A i ≡ 0, so that only the first or second term remains in the righ t part of (12). The third term in (12) show s that with the sim ultaneous presen tation of the st ym uli A and B , they exert on eac h other a n effect equiv alen t to the presence of a magnetic field. The result of suc h in teraction is particularly clear if the configurations A 1 , A 2 , . . . and respectiv ely B 1 , B 2 , . . . are almost degenerate. If the links T ij b et w een the regions Ω A and Ω B are absen t then the equilibrium states of the system hav e the form ( A s , B s ′ ) and are almost degenerate. Inclusion o f the we ak links T ij b et w een the regions Ω A and Ω B do es not change significan tly the equ ilibrium configurations, but c hanges the relative p osition on the energy sc ale. If on separate recognition o f the images A and B certain configurations (e.g. A 1 and B 2 in Fig. 4) are energetically adv an tageous, then on their sim ultaneous recognition other configurations ma y pro v e more adv an tageous (e.g. A 2 and B 1 ). I t may b e visually imagined that the in teraction c hange t he p otential relief where A and B relax (Fig. 4). As a result, the in terpretation of the p olyseman tic image pro v es to dep end on the con text. In the preceding pap er [1], the existe nce of an a lg o rithm w as p ostulated for the recog- 9 Figure 5: Recognition of a con tin uous sequenc e of imag es A 1 , A 2 , . . . : in the asso ciativ e la y er there is seque n tial excitation of the regions Ω 1 , Ω 2 , . . . , whic h lo oks fik e ”diffusion”. nition of N sim ultaneously presen ted p olyseman tic images; no w it is clear that suc h a n algorithm can b e naturally realized in the Hopfield mo del in the follo wing conditions: (a) recognition b egins at finite temp erature T 0 whic h then adiabaticatty diminishes; (b) the p oten tial barriers b et w een the meanings of the p olyseman tic image are less than T 0 ; (c) the p oten tial bariers betw een the differen t p o lyseman tic images are considerably greater than T 0 ; and (d) the in teraction b et w een the images is sufficie n tly w eak. Recognition of a con tin uous sequence of images Ab o v e w e assumed that all the images { V s i } ha v e lo calized carriers. Due to short- range nature of links T ij , the asso ciative ly-related images should hav e closely p ositioned or o v erlapping carriers, while the uncorrelated images hav e the carriers lo calized in the remote parts of the memory . Therefore, presen ta tion of a con tin uous sequenc e of stimu li A 1 , A 2 , . . . giv e rise to sequen tial excitation o f the regions Ω 1 , Ω 2 , . . . in t he asso ciativ e lay er, whic h lo oks like ”diffusion” (F ig. 5 ): the nearest in success ion images are correlated and their carriers form conglomerations , whereas to the remote images in sequence corresp ond carriers remote in space, as a result of w eak ening of the correlations. It g iv es the p ossibilit y to establish the corresp ondence of the time of app earance of the image with the p osition of its carrier in space, whic h greatly simplifies the w ork of the cen tre. After fixing the app earance of the excited neurons in a certain p ortion of the A – lay er, the cen tre raises the temperature of this p ortion to the v alue T 0 , and after the characte ristic time τ 0 b egins 10 its adiabatic decreasing. This stim ulates establishmen t of the steady state, the bringing of the corresp onding images in to the R – lay er and the zeroing of the corresp onded p ortion of the memory (Fig . 2,d–g). Thereb y , the tra jectory of the ”diffusion” mo v emen t (Fig. 5) is ”wip ed off” after a certain time so that at eac h momen t o nly its finite segmen t exists in the memory; recognition of a con tin uous sequence of images is thereb y reduced to the sim ultaneous recognition of a finite n um b er of images (see ab ov e). Time dela ys and h umorous effect Let at the momen t of time t = 0 the neurons are excited in a certain p ortion of memory (Fig. 2,b), at the momen t τ 0 the corresp onding image is brought in to consciousnes s (Fig. 2,e) and at the momen t τ 1 the portio n of memory under consid eration is zeroed (Fig. 2,f ). The dela y τ 0 correspo nds to the interv al AC a nd the dela y τ 1 to the in terv al AB in Fig. 2 of the pap er [1]; the latter is related to the fact that the p ossibilit y of rein terpreting the image p ersists un til the corresp onding p ortion of memory is n ullified. Ob viously , τ 1 ≥ τ 0 : t his result was deriv ed in [1] from requiremen ts of the optimal pro cessing of the algor ithm, but no w it holds due to the constructiv e features of the mo del. The dela y τ 0 is determined b y the rate of decreasing of temp erature (see ab ov e), while the dela y τ 1 b y the momen t of activ ation (fro m t he cen tre) of the R → A links. The optimal c hoice of the parameters τ 0 and τ 1 is determine d b y differen t principles : the parameter τ 0 correspo nds to the dela y from the momen t infor matio n is receiv ed b y the brain till its app earance in consciousnes s and is upw ardly limited by the v alue τ max [1], while the parameter τ 1 regulates the loading of memory 3 , i.e. the fraction of excited neurons in the A – la y er (Fig. 5). This fraction should not b e to o small for t he o p erativ e p ossibitities of the brain to b e used in full, and not to o large for in terference of the images arriving at differen t times not to appear. Let at the momen t t = 0 the image A en ters the memory; ev olution in the corresp onding p oten tial relief (Fig. 4, contin uous curv e) leads at the momen t t = τ 0 to stabilization of the memory neurons in the configuration A 1 and excitation of the corresp onding R – neuron. Let in the interv al b et w een τ 0 and τ 1 new image B en ters the memory and c hanges the p oten tial relief for A (Fig. 4, bro ken line). If the temp erature at this moment is sufficien t to ov ercome the bar rier, the system b egins to relax to the configuration A 2 (in fact, lea ving of the state A 1 is p ossible eve n at T = 0 since the minim um corresponding to A 1 ma y disappear). Suc h breaking of stationarit y in a certain memory region after exciting of the correspo nding R – neuron is conside red as a sign of the h umorous effect [1]. The image A 1 (or, in the general case, a v ersion consisting of sev eral images) is realized a s ”false” a nd should b e immediately deleted from consciousne ss; how ev er, it cannot b e done in the course of the usual routine (Fig. 2,e,g) b ecause of the need to obtain a new steady configuration A 2 . 3 Unlik e the gener al case [1], in the present mo del there is no spec ia l op er ative memory . 11 Mec hanism of laugh ter The ”emergency” deletion of the false v ersion from the R – lay er is achie v ed b y activ ation of the links b et w een the R – lay er and the motor cortex (Fig. 1); excitation of the R – neurons is transmitted to t he motoneurons and pro duce the con traction o f certain m uscles, i.e. laugh ter. In fact we return to the old idea by G. Sp encer [6] that the humorous effect is accompa- nied b y release from the men tal pro cess of nerv ous energy whic h is directed at the m uscular reaction. This idea w as supp orted b y D arwin [7] and F reud [8] but was criticized by later in v estigators [9] in view o f the difficult y to introduce the concept o f ”nervous energy”. In fact, the definition of energy f or neural net w orks ma y b e g iv en only under condition T ij = T j i [2], whic h is not very realistic and do es not hold for the considered mo del as a whole; so the concept of ”nerv ous energy” should not b e tak en seriously . Nev ertheless , the qualitativ e picture agrees with Sp encer’s h ypothesis: it lo oks as if the energy of excitation is expelled from the R – neurons in to the motor cortex. The release of nerv ous energy in the presence of the hu morous effect w a s v alidated by Sp encer using the concept of ”descending incongruit y” — transition f rom a high to low st yle, i.e. from the state with rich asso ciations to the state with p o or asso ciations. Suc h an in terpretation of the hu morous effect is surely limited and cannot la y claim to univ ersalit y . In the propo sed sch eme the ”release of nerv ous energy” (in the conditional sense indicated ab ov e) is related with the need t o delete the false v ersion from consciousness , whic h requires ”zeroing” of a certain p ortion of the R – la y er (i.e. transition of the excited neurons to the nonexcited state). Since la ughter is in terpreted as an unconditioned reflex to the h umorous effect, the kno wn cases of ”ousting” o f laugh ter b y secondary emotions require an explanation. Laugh- ter may b e ousted b y the emotions of indignation (an indecen t anecdote is told to a puritan), fear (a bush suddenly turns ouf to b e a b ear), compass ion (a man in front of y ou slips on a w at er melon rind and badly hurts himself ), shame (y ou slipped on a w ater melon rind) and so on. Within the Sp encer hy p othesis [6] all these instances are explained b y the fact that the ”released nerv ous energy” is directed not to the motoneurons but to other parts of the nerv ous system and go es on the formation of a secondary emotion (the R – la y er is connected not to the motor cortex but to the lim bic system). The same ideas [8] are used to explain the kno wn fact that a jok e pro duces the greatest effect if it is told extremely laconically: laconicit y reduces the probabilit y of formation of secondary asso ciations liable to absorb the ”nerv ous energy”. Casting the excitation of the neurons into differen t p ortions o f the motor cortex, a man can regulate the lev el of the m uscular reaction: this can explain its dep endence on mo o d, the psyc hological setting, the presenc e of a laughing en viromen t [10] and so on. 12 Conclusion The realization of a sense of h umour requires a quite intric ately org anized syste m. W e w ould emphasize, ho w eve r, that this complex organization is entirely go v erned b y the task of treating a contin uous sequence of p olyseman tic images; the existence o f the h umorous effect is a secondary consequence . It is w ell-kno wn [4, pp. 219–2 41], that differen t parts of the brain ha v e their own sp ecialization; the prop o sed mo del ma y lay claim to b e a description of only the region of the brain where the linguistic functions are concen trated (so-called Bro ca and W ernic ke zones); other p ortions o f the brain ma y ha v e a differen t organization. The author is grateful to D . S. Cherna vskii for fruitful disc ussions. References [1] I. M. Suslo v, Biofizik a , 37, 318 (1992) [Bioph ysics 37, 242 (1992)]. [2] J. J. Hopfield, Pro c. Nat. Acad. Sci. USA, 79, 2554 (1982). [3] F. Rosen btat t, in The Principles of Neurodynamics. P erceptrones and the Theory of Brain Mec hanisms, Mir, Mosco w (1965). [4] The Brain (Ed. P . V. Simono v), Mir, Mosco w (1984). [5] V. S. Dotsenk o, J. Ph ys. A, 21, L783 (1988). [6] G. Sp encer, The Ph ysiology of Laugh ter, St. P etersbu rg (1881). [7] Ch. Darwin, Collected W orks, V ol. 5 , Chapter VlI I, USSR Academ y of Sciences, Mosco w (1953). [8] S. F reud, Wit and its Relation to the Unconsc ious, Moscow (1925). [9] D. E. Berlyne, in Psyc holo g y of Humor (Eds J. H. Goldstein and P . E. McGhee), Academic Press, New Y ork (1972). [10] H. Lev en tal, J. Comm unication, 26, 190 (1976). 13