Approved For Release 2000/08/07 : CIA-RDP96-00787ROO0700090011-6 Four-State Eloctronic Random Nuiiber Generator This study provided an opportunity to determine whether the re- mote sensin.- capability could be extendod to the perception of the internal state of a piece of electronic equipment. For this purpose, an automated experiment designed around a four-state electronic random number generator was initiated. The solid-state machine has no moving parts and provides no sensory cue to the user as to its target genera- tion. In order to determine unambiguously whether a result was meaning- ful, the following strategy was used. First, the randomness of the machine was verified by over 10,000 pre-experiment trials (details given below). Second, the subjects interacted with the machine to generate the data Third, for any subject whose score was significant, the statistics of the machine during the successful experiment were tabulated to insure that the machine had not departed from randomness in the period in which a significant result was obtained. Fourth, a subject -eneratiii-- a good score was asked to repeat the entire experi- mant after a one-month lag period. Finally, the entire data analysis was carried'out by an independent statistics group at SRI. The machine configuration provides as a target one of four art slides chosen randomly (p = 1/4) by an electronic random generator. The generator does not indicate its choice until the subject indicates his choice to the machine by pressing a button (see Figure 11). (The Approved For Release 2000/08/07 : CIA-RDP96-00787ROO0700090011-6 Approved For Release 2000/08/07 CIA-RDP96-00787ROO0700090011-6 FIGURE 11 Four-state electronic random number generator used in this experiment. An incorrcct ciioice of target is indicated. Two of the five "encouragement lights" at the top of the machine are illuminated. The printer to the right of the machine records data on fan-fold pap-~r tape. Approved For Release 2000/08/07 : CIA-RDP96-00787ROO0700090011-6 I,ye elea~e IA-RDP~~-qp -6 ~,b?,OQO/08/07 :;q _T,~MO00700090011 nc~,ForfR Appc~o 0 a. al s -atos. z squarc-wave ias ur s e intern, oscillator sends PL11SCS to an electronic "scalo-of -four" counter which passes through each of its four states 250,000 tidies per second. The state of the counter is determined bythe length of time the oscillator has run, that is, the time between subject choices.) As soon as the subject indicates his choice, the target slide is illuminated to provide visual and auditory (bQll if correct) feedback as to the correctness or in"correctness of his choice. Until that time, both subject and experimenter remain ignorant of the machine's choice, so the experiment is of the double-blind type. Five legends at the top of the machine face are illuminated one at a time with increasing correct choices (6, 8, 10, ...) to provide additional reinforcement. The machine choice, subject choice, cumulative trial number, and cumulative hit number are recorded automatically on a printer. Following trial number 25, the machine must be reset manually by depressing a RESET button. A methodological feature of the machine is that the choice of a target is not forced. That is, a subject may press a PASS button when he wishes not to guess, in which case the machine indicates what its choice was. -The machine thus scores neither a hit nor a trial and then goes on to make its next selection. Thus, thesubject does not have to guess at targets when he does not feel that he has an idea as to which to choose. Approved For Release 2000/08/07 : CIA-RDP96-00787ROO0700090011-6 Approved For Release 2000/08/07: CIA-RDP96.rOO787ROO0700090011-6 Under the null hypothesis of random binomial choices with probability 1/4 and no learning, the probability of observing :~:k successes in n trials is approximated by the probability of a normal distribution Value, n _ .1 /-311/16 4 2 Pre-Experiment Randomness Tests The design objective was to build a four-state machine, with each state equally likely to occur on each trial, independent of tho past sequence of states. If the machine meets this objective, it should not be possible to devise a rule for future play that significantly differs from chance. A simple example of such a rule- would be to select the machine state observed in the preceding trial; if this strategy were to produce scores significantly above chance (25 percent hits), we would reject the hypothesis of randomness of the machine under test. Before experimentation machines purchased from Aquarius Electronics, Albion, California, were extensively tested for randomness. Data were analyzed on a CDC-6400 computer, and the machine finally selected for use met established criteria for randomness. In dev6lopin- randomness tests, we are 0 _guided in part by a knowledge of the machine lo--ic. V,11-ion one of the four choice keys or the pass key is depressed, the current machine state is displayed; then a brief time after release of the key, a now machine state is established (but not sho,A.,n to the subjec-0 by sampling I.-ho instantaneous state of a high- Approved For Release 2000/08/07: CIA-RDP96-00787ROO0700090011-6 Approved For Release 2000/08/07 : CIA-RDP96-00787ROO0700090011-6 speed four-state electronic counter. For the machine to be random, the times of dwell of the counter in each of the four states must be precisely equal; otherwise, the distribution of outcomes will be biased, The first randomness test is thus based on tallying the nunA)er of occurrences of each of the four states. This test should detect a stable bias, yet may miss a drifting bias. To test for this second possibility we also tally the distribution of outcomes in each group of 100 trials,. then compute a likelihood ratio test statistic.(sec- below) for each group. Under the null hypothesis of equal likelihood of the four states, these statistic values are distributed approxi- mately as chi-square with three degrees of freedom and their sum for m groups distributed approximately as chi-square with three m degrees of freedom. This test,may also detect stable bias, but is not as powerful for this purpose as the first test. Variable bias of still a shorter period, if substantial, can be tested for by tallying the frequency with which the previous machine state is repeated; an overall repeat ratio ("all") significantly above 0.25 is indicative of such bias. If for any reason the machine were to fail to sample the counter to establish a new state, th-3 previous machine state would be repeated. To test for this possibility, we tally the number of repeats following the depression of each key. A repeat ratio significantly greater than 0.25 should be considered a danger signal. Approved For Release 2000/08/07 : CIA-RDP96-00787ROO0700090011-6 Approved For Release 2000108107 : CIA-RDP96-00787ROO0700090011-6 We also tally the initial machine states followin_- reset and the transitions between states. In each case, the number of occurrences of each of the four possible outcomes should be approximately equal. When repeats are deleted from the sequence of trials ("nondiagonal transi- tions"), the four states should also be approximately equal in frequency. In testin.- the null hypothesis of four equally likely outcomas of a trial, a likelihood ratio test is used. The statistic -2 n tn la~4\ ~n under the null hypothesis is distributed approximately as chi-square with three degrees of freedom, with rejection for large values of this statistic.* The computer program used in testing randomness includes a subroutine for computing the probability of a chi-square value as large or larger than that observed. In testing the null hypothesis that the probability of a.repeat is 0.25, the binomial probability of obtaining the observed number K or more repeats in N trials is computed. For K greater than 1000, a normal distribution approximation is computed, assuming the statistic K - 1/2 - 0.2 N 5) JF3 ~1 6 ( to be approximately normal with mean zero and standard deviation one. *Alexander Mood, Intro~luction to the Theory of Statistics (McGraw Hill, Now York, 1950). Approved For Release 2000108107 : CIA-RDP96-00787ROO0700090011-6 Approved For Release 2000/08/07 : CIA-RDP96-,00787ROO0700090011-6 The typical test pattern LISOd was six passes followed by 25 choices of one color, repeating this for each of t1ne four colors. In this way each of the five keys other than rosetwero given approximately equal use. Typically, 2000 to 6000 trials were made in each sitting. In the absence of any unusual results in the randomness tests, a minimum of 10,000 trials were made before using a machine with experimental subjects. With 10,000 trials, the expected fraction of repeats is 0.25 with a standard deviation of 3/200 = O.OD866. A computer listing of the results of randomness tests is included in Table 1. No signifiCant departures from randomness were.observed. Subject Data Data was collected from subjects S1 through S6. Each subject was asked to complete 100 25-trial runs (i.e., a total of 2500 trials each). The results are tabulated in Table 2. .(One subject, -S3, declined to complete the 2509-trial run, indicating a lack of rapport with the machine and, hence, a lack of motivation for the task.) For the six subjects, only one (S2) scored significantly above chance. For the 2500 trials'that subject averaged 29.36 hits/100 trials rather than the expected 25/100, a result whose a priori probability under the null -7 hypothesis is p = 3xlO His scores are plotted in Figure 12. Th:~ statistics of the machine- during the successful run of subject S2 were tabulated fol, the entire 3488 machine transitions (2500 choices, Approved For Release 2000/08/07 : CIA-RDP96-00787ROO0700090011-6 a~ o ca doparturo from random expectation durin- the SLICCOSSfUl run, and therefore, the significant result cannot be attributed to machine malfunction. At a later time, subject S2 was asked to repeat the entire exper- iniont, and lie was able to replicate successfully a high moan scoring rate (27.88/100 average over 2500 trials, a result whose a priori -4 probability under the null hypothosis is p = 4.8xlO We thus conclude from this part of the study that of the 'six sub- jects tested, one subject 02) gencrated a significant result replicable and not attributable to machine malfunction. Finally, the study taken as a whole (15,750 trials) was significant, yielding an average scoring rate 26.47 hits/100 trials, a result 5 whose a priori probability under the null hypothesis is p 1.lxlO The bit rate associated with the information channel can be cal- culated from R = H(x) - H(x y where II(x) is the uncertainty of the source m,?ssage containing symbols with a priori probability P 4 11 W P lo- P and 11 (x) is the conditional entropy based on the a posteriori pro- y babilities that a received symbol was actually transmitted 4 IIW P(i,j) log2 Pi i,j=l Approved For Release 2000108/07 : CIA-RDP96-00787ROO0700090011-6 Apprp%nq F?r,~elease 2000/08/07 - CIA-RDP96-00787ROO0700090011-6 'o s I t run, with P 1/4,,.P(k,k) 0.2936, and an avera-e of '30 seconds por choice, we have a Source uncertainty ii(x) 2 bits and a calculated bit rate C R ~:~ 0.007 bits/symbol or R/T ~~ 2x10-4 bits/sec. Approved For Release 2000/08/07 : CIA-RDP96-00787ROO0700090011-6 Approved For Release 2000/08/07 CIA-RDP96-00787ROO0700090011-6 Table 1 Initial states Transitions Y To G Fr B O~ R All states Nondiagonal transitions Diagonal transitions PRE-EXPERIMENT RAINDOMNLSS TESTS Buttons Number Binom. Yellow Blue Red of Chi-Sq.Prob. Green Trials 107 116 113 128 464 1.996 0.57 728 764- 765 790 3047 2.573 0.46 77-1 784 773 863 3197 6.745 0.08 776 796 810 773 3155 1.158' 0.76 787 852 803 805 3247 2.877 0.41 3175 3312 3264 3359 13110 5.667 b.is 2340 2412 2341 728 784 810 1 2426 1 9519 1 2.630 1 0.45 805 3127 5.414 1-0.15 Bionomial Prob. Diagonal transitions as a function of key press Key N-Trials Repeats allow2774 705 reen 2755 674 lue 2761 706 ad 2742 667 -iss 1614 375 11 12646 3127 0.2541 0.313 0.2446 0.748 0.2557 0.250 0.2433 0.793 0.2323 0.953 0.2473 0.763 Randonuicss in groups of 100 trials: Chi-sq. = 299.61z~l D.F. 345 Prob. = 0.9628 Approved For Release 2000/08/07 CIA-RDP96-00787ROO0700090011-6 Approved For Release 2000/08/07 : CIA-RDP96-00787ROO0700090011-6 TABLE 2 FOUR-STATE ELECTRONIC R,,11NDOM NMIBER GEINEI~UITOR MEAN SCORE/100 TRIALS BINOMIAL SLTBJECT OVER 2500 TRIALS PROBABILITY S1 25.76 0.22 S2 29.36 3 x 10-7 S3 24.67 (750 trials) 0.60 S4 25.76 0422 S5 25.20 0.42 S6 25.40 0.33 S7 27.88 4.8 x 10-4 (replication) Ail trials 26.47 1.1 x 10 -5 (15750 trials) Approved For Release 2000/08/07 : CIA-RDP96-00787ROO0700090011-6 Approved For Release 2000108107 CIA-RDP96-00787ROO0700090011-61 TABLE 3 N1ID-E'X,PERIKENT RANDOMNESS TESTS BUTTONS Number of Binont. Yellow GreenBlue RedTrials chi-Scl.Prob. Initial States24 29 23 24 100 0.880 >0.80 Transitions 204 199 199 216818 0.944 >0.80 Y To G 192 223 222 207841 3.043 >0.30 F B 212 207 226 222867 1.064 >0.70 r o mr R 209 207 222 221859 0.860' >0.80 All States 841 865 892 8903488 1.988 >0.50 Nondiagonal Transitions 613 613 643 6452514 1.535 >0.50 Diagonal Transitions 204 223 226 221874 1.341 >0.70 Approved For Release 2000108107 : CIA-RDP96-00787ROO0700090011-6 Approved For Release 2000/08/07 CIA-RDP96-00787ROO0700090011-6 50 '10 ~A 41 30 0 0 1 jS' 20 ul) 0 q. Z cr \ P 10 0 10 20 30 RUN NU?,[BER - 100 Trials/111111 pc I- t r i, FIGURE 12 DATA SUMMARY FOR SUBJECT 2 Approved For Release 2000/08/07 : CIA-RDP96-00787ROO0700090011-6 I.IDIC . 111.1- . I I (D Q C) W Q Q Q Q Q Q 00 I- Q Q (6 (D CL 00 Q 04 42) 0 M 42) W L_ 0 LL V a) > 0 L_ CL CL Te L Doscript ion Scorinp, SI S2 S3 S4 I I S6 I I I S5 Halstead CategoryNonverbal test requiring abstraction of conceptual relation- 7 4 1 33 26 6 28 Test ships. Score: Total errors. Tactual PerformanceRequires placement of 10 geometrically shaped blocks in Test their correct locations on a formboard 16,4 11187.7 7.7 11.4 619 while blindfolded. Separate RT, LT, and bimanual trials. Score: Total time (min.). I Speech Perception,~,imination of non-word speech sounds. Di 4 2 S r, 0 2 5 3 Tes L c Total errors. . Seashore RhythmDiscrimination of nonverbal rhythrns. Score.27 25 28 29 26 29 Test Number correct. Finger TappingMeasure of finger oscillation rate for RT/LT RT/LTRT/LTRT/LTRT RT/LT Test 10-sec. period, both / U RT and LT hand trials. Score: No. taps/10 53/50 53/4948/4754/5347/4748/43 sec. Trail Making Requires connecting numbered circles in Test order from I to 25. 40 16 is 9 (Part A) Paper and pencil task. Score: Total times 1 30 27 (sec) Trail Making Requires connecting alphabetic and numbered Test circles by 56 50 5 0 5 5 54 53 (Part B) alternating 1-A-2-B, etc. Score: Total time (sec) Knox Cube TestMeasure of attention span and immediate visual memory. 13 14 3 6 1 1 17 17 I Score: Number correct. - Raven ProgressiveNonverbal intelligence test involving spatial39 5 4 matrices. 3 9 55 60 54 Matrices Score: Number correct. Verbal ConceptRequires abstraction of verbal conceptual relationships. 22 24 27 23 21 24 Attainment Score: Number correct. Test Total: Buschke MemoryRequires learning a 20-word list in a maximum Test of 12 trials with 1419-017/2018/2019/202012020/20 repetition of words omitted after each 1 trial. Score: Max. no. t words correctly remembered; List: no. wordsList- consistently remembered 8/20 14/2011/2016/2015/2016/20 rials)(7 trint') (8 t Grooved PegboardRequires insertion of 25 pegs in their RT/LT RT/LTRT/LTRT/LT. RT/LT Test holes in a pegboard. Both RT/LT RT and LT hand trials. Score: Total time 76/74 69/7058/6759/67 48/50 (sec). 1 Spatial RelatiRequires mental rotation and identification o of fitures - - 60 52 rotated in 2 dimensions. Score; no. correct ubtest of the - no. errors. P,'-IA n - __ GoctschaldL Requires tracing outline of simple figure Hidden hidden~ithin Figures Test lines of more complex figure. Score: Time Poor Avg. v.goodoutst.outst. and no correct. ~7 Q Q (D Q Q C) Q Q 00 P_ C) Q 1 CL 00 a a Q 04 a) W 0 LL > CL CL