Computer Tests Shed Light on the Chance of Getting Historical ESP Lab Results

A classic work in the field of parapsychology was the 1940 book Extra-Sensory Perception After Sixty Years by J. G. Pratt and Joseph B. Rhine (a professor of psychology), along with Smith, Stuart and Greenwood. The book summarized sixty years of experimental research into extrasensory perception (ESP). Since the book is readily available online (at this URL), and is one of the chief pieces of evidence in support of ESP, no one who has not read this book has any business dismissing the evidence for ESP; but almost all who do that have failed to read this book.

The book is almost as good a book as you could ever hope for in terms of supplying laboratory evidence for ESP. But the book has one shortcoming, in that the evidence results are presented not quite as clearly as they could be. The main evidence is reported in tables with columns marked “Dev.” and “C.R.” Someone unfamiliar with statistics reading these tables may not be able to understand how dramatic the results were as evidence. Sometimes the results list a standard deviation in a column marked S.D., but most non-scientists cannot tell the difference between a standard deviation of 2 and a standard deviation of 30 (the first is weak evidence, and the latter is very strong evidence).

In the year 2018 there is a way to show how dramatic the results in this book are. The method is to run computer simulations that perform random guessing. For example, let us consider a result reported in the Extra-Sensory Perception After Sixty Years book. It is the result presented in Table 11, that in 1939 Pratt and Woodruff did 60,000 trials in which the deviation above the chance result was 489. Using a computer program I wrote, I can run 100,000 simulated runs that each involve 60,000 guesses, and I can see whether in any of these runs there is a chance result as impressive as Pratt and Woodruff got.

Below is a table comparing the Pratt and Woodruff result with the computer simulations I ran using a program I wrote (the text of which is at the end of this post).

Experimenter(s)	Pratt and Woodruff
Year	1939
Source	Extra-Sensory Perception After Sixty Years, Table 11 (URL). See also this URL.
Number of Trials	60000
Special test conditions	“Two experimenters, independent recording, sensory cues excluded, official record sheets, triple checked.” Opaque screens used between subject and experimenter.
Probability of random guess being correct	1 in 5
Number of correct guesses better than the number expected by chance	489
Number of computer runs, each consisting of 60,000 trials guessing a number between 1 and 5	100000
Maximum number of correct guesses better than the number expected by chance, in any of these runs	426
Average guess in these trials	2.999984948333333
Number of runs matching or beating the human experimental result	0
Program arguments (use code below to reproduce)	100000 60000 5

So in my computer experiments there were 100,000 runs that each consisted of 60,000 trials (the same number as in the historical ESP experiment described above). In the run that was most successful out of the 100,000, there were 426 more correct guesses than would occur on average by chance. But this best random result out of 100,000 was much less impressive than the actual experimental tests involving human subjects guessing, for in those actual tests involving humans there were 489 more correct guesses than we would expect by chance.

You can reproduce this result by compiling the code at the bottom of this post in a Java compiler, and using “100000 60000 5” as the program arguments.

In row 4 of Table 5 of the book we have data that corresponds to the top rows of the table below. The data is for ESP experiments in which the probability of guessing correctly was 1 in 5. The experiments were done between 1934 and 1939, by a variety of experimenters including Rhine.

Experimenter(s)	Rhine and others
Year	1934 to 1939
Source	Extra-Sensory Perception After Sixty Years, Table 5, Row 4 (URL)
Number of Trials	2757854
Probability of random guess being correct	1 in 5
Number of correct guesses better than the number expected by chance	52720
Number of computer runs, each consisting of 2757854 trials guessing a number between 1 and 5	10000
Maximum number of correct guesses better than the number expected by chance, in any of these runs	2113
Average guess in these trials	2.999995953592902
Number of runs matching or beating the human experimental result	0
Program arguments (use code below to reproduce)	10000 2757854 5

So in my computer experiments there were 10,000 runs that each consisted of 2,757,854 random trials (the same number in the historical ESP tests mentioned above). In the run that was most successful out of the 10,000, there were 2113 more correct guesses than would occur on average by chance. But this best random result out of 10,000 was very much less impressive than the actual experimental tests involving human subjects guessing, for in those actual tests involving humans there were 52,720 more correct guesses than we would expect by chance.

You can reproduce this result by compiling the code at the bottom of this post in a Java compiler, and using “10000 2757854 5” as the program arguments, although when I did this using the NetBeans Java compiler, it took 23 minutes for the program to finish.

Zener cards used in ESP experiments

I can only wonder how many runs I would have to do in excess of 10,000 to get a random result as good as the result produced by actual human guessers. Given the very large gap between the 2113 number reported above and the 52,720 number given above, I think I would have to let the computer run for so long that it produced millions or billions or trillions of runs. I would probably die before the computer simulated result reached an excess above chance as great as 52,720.

For the next comparison I will use a test Rhine made with Hubert Pearce, who produced astonishing results under ESP tests. I will only cite only the results produced under the strict condition of an opaque screen between the subject (Pearce) and the experimenter.

Experimenter(s)	Rhine
Year	1937
Source	http://www.sacred-texts.com/psi/esp/esp14.htm (URL)
Number of Trials	600
Special test conditions	Screen between experimenter and subject
Probability of random guess being correct	1 in 5
Number of correct guesses better than the number expected by chance	95
Number of computer runs, each consisting of 600 trials guessing a number between 1 and 5	1000000
Maximum number of correct guesses better than the number expected by chance, in any of these runs	50
Average guess in these trials	3.0000910866666666
Number of runs matching or beating the human experimental result	0
Program arguments (use code below to reproduce)	1000000 600 5

So in my computer experiments there were 1,000,000 runs that each consisted of 600 random trials (the same number in the historical ESP experiment mentioned above). In the run that was most successful out of the one million runs, there were 50 more correct guesses than would occur on average by chance. But this best random result out of these million runs was much less impressive than the actual experimental tests involving a human subject guessing, for in those actual tests there were 95 more correct guesses than we would expect by chance.

ESP research didn't stop in the 1930's. There have been many ESP experiments in more recent decades. Some of the more successful have been tests using the ganzfeld sensory deprivation technique. In 2010 Storm and Tressoldi did a meta-analysis of ganzfeld ESP experiments, in a paper published in a scientific journal. The analysis summarized the results of 63 studies in which there were four possible answers. The studies involved 4442 trials and 1326 hits (correct answers), which was an accuracy rate of 29.9%, much higher than the 25% rate expected by chance. The table below compares this result with the result obtained in a computer test.

Experimenter(s)	Various
Year	1992 – 2008
Source	“Meta-Analysis of Free-Response Studies, 1992–2008: Assessing the Noise Reduction Model in Parapsychology” by Lance Storm, Patrizio Tressoldi and Lorenzo Di Risio http://deanradin.com/evidence/Storm2010MetaFreeResp.pdf Page 475
Number of Trials	4442
Special test conditions	Sensory deprivation of subjects
Probability of random guess being correct	1 in 4
Number of correct guesses better than the number expected by chance	215
Number of computer runs, each consisting of 4442 trials guessing a number between 1 and 4	100000
Maximum number of correct guesses better than the number expected by chance, in any of these runs	134
Average guess in these trials	2.5000297208464657
Number of runs matching or beating the human experimental result	0
Program arguments (use code below to reproduce)	100000 4442 4

So in my computer experiments there were 100,000 runs that each consisted of 4442 random trials (the number in the set of ESP experiments discussed above). In the run that was most successful out of the 4442, there were 134 more correct guesses than would occur on average by chance. But this best random result out of 100,000 was much less impressive than the actual experimental tests involving human subjects guessing, for in those actual tests involving humans there were 215 more correct guesses than we would expect by chance.

You can reproduce this result by compiling the code at the bottom of this post in a Java compiler, and using “100000 4442 4” as the program arguments.

These computer simulations help show that the experimental evidence for extrasensory perception (ESP) is overwhelming. In not one of the more than 1,200,000 simulations did the computer guessing produce a result anywhere near as high as was obtained using human subjects. Three of the four experimental results involved special precautions that should have excluded any reasonable possibility of cheating. In the book Extra-Sensory Perception After Sixty Years the authors address and debunk all of the common objections made against laboratory research into ESP.

Very many scientists reject the evidence for ESP, even though the evidence for ESP is vastly stronger than the evidence for some of the things that scientists believe in. Here is an example. Scientists tell us in a matter-of-fact manner that the Higgs Boson exists. But the wikipedia.org article on the Higgs Boson tells us that it was established with experimental evidence that had a standard deviation of merely 5.9 sigma, which corresponds to a probability of about 1 in 588 million of occurring by chance. That's an experimental result not nearly as strong as the Rhine result mentioned above. 

Another book you can read online (at this URL) is the "Handbook of Tests in Parapsychology" by Betty Humphrey. We read on page 42 of that book that a Critical Ratio of 5.0 corresponds to a probability of  1 in 3,384,000.  The Pratt-Woodruff experiment described above is listed in the Extra-sensory Perception After 60 Years book (Table 11) as having such a Critical Ratio of 5.0 (4.99 to be precise).  The Humphrey book tells us that a Critical Ratio of 6 corresponds to a probability of 1 in 1,000,000,000. The Rhine set of 2757854 trials (discussed above) is listed in Table 5 of the Extra-sensory Perception After Sixty Years book as having an enormous Critical Ratio of 79.  If a Critical Ratio of 5 equals a probability of 1 in 3,384,000, and a Critical Ratio of 6 equals a probability of 1 in 1,000,000,000, you can get an idea of what a "never by chance in the history of the universe" probability would correspond to a a Critical Ratio of 79.  Such a result is vastly more impressive than the 5.9 sigma result cited for the Higgs Boson.  In the Riess ESP test discussed here, a test in which the subject and the experimenter were in separate buildings, a young woman achieved a phenomenal 73 percent accuracy rate (making 1850 guesses that should only have been 20 percent accurate by chance).  The Critical Ratio for that experiment was 53. 

Inexplicably, many a physicist believes in the Higgs Boson, but not in ESP, even though the experimental evidence is incomparably stronger for ESP. The evidence for ESP includes other experimental results even stronger than the ones mentioned here (see the table at the end of this post for examples), along with a vast amount of anecdotal evidence in which people sensed or had thoughts of things that had not been revealed by their senses.

Below is the simple Java code I used for these experiments. You can run these experiments (using the program arguments listed above) by compiling this code with a Java compiler (I used the Net Beans compiler). 

package randomnumbertrials;
import java.math.*;
import java.util.Random; 
/**
 *
 * @author Mark
 */
public class RandomNumberTrials {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
               
       if (args.length < 3)
       {
           System.out.println("Must supply 3 program arguments:");
           System.out.println("Number of runs, number of trials per run, max guess per trial");
           return;    
       }    
        long numberOfRuns = Long.parseLong(args[0]);
        long numberOfTrials = Long.parseLong(args[1]);
        int maxGuessPerTrial =  Integer.parseInt(args[2]);

        double averageResult = 0;
        long maxNumberOfSuccesses = 0;
        long totalTrials = 0;
        double resultTotal = 0;
        for (long i = 0; i < numberOfRuns; i++)
        {
           Random rand = new Random(); 
            int numberOfSuccesses = 0;
            for (long j  = 0; j < numberOfTrials; j++)
            {
           
                int randomInt = getRandomNumber(rand,  maxGuessPerTrial);
                int guess = getRandomNumber(rand,  maxGuessPerTrial);
                if (randomInt == guess)
                    numberOfSuccesses++;
                if (numberOfSuccesses > maxNumberOfSuccesses)
                    maxNumberOfSuccesses = numberOfSuccesses;
                totalTrials++;
                resultTotal += guess;
            }
            
        }
          System.out.println("Ran " + numberOfRuns + " each with " + numberOfTrials + " trials.");
          System.out.println("Highest number of successes: " + maxNumberOfSuccesses);
          double averageExpectedResult = numberOfTrials / maxGuessPerTrial;
          double deviation = maxNumberOfSuccesses - averageExpectedResult;
          System.out.println("Highest deviation above expected result: " + deviation);
           averageResult = resultTotal/totalTrials; 
            System.out.println("Average result =  " + averageResult);
    }
    static public int getRandomNumber( Random rand,  int highestNum)
    {
       int retVal = rand.nextInt(highestNum+1);
       while (retVal == 0)
        // This function returns a number between 0 and highestNum
          retVal =  rand.nextInt(highestNum+1);
       //System.out.println("Random number =  " + retVal);
       return retVal;
    }
 }

Postscript: I have had many personal experiences strongly suggestive of extrasensory perception. I'll give just one example, not at all the most impressive one. I once asked one of my daughters to fill in the statement "Why is there ___ rather than ___?" I was thinking of the classic philosophical question "Why is there something rather than nothing?" but also thought of the question, "Why is there war rather than peace?" My daughter answered, "Why is there fighting rather than peace?" I asked her to ask my wife the question over the phone, and my wife said that there was too much noise where she was, and she needed a peaceful place to think about it. She later answered, "Why is there so much death rather than life?" which is pretty much the same as "Why is there war rather than peace?" I then asked the question by email to my other daughter, and she answered, "Why is there war rather than peace?"  You can try this with your friends.