Abstract

It is suggested in this paper that random number generators will give non-random data when the data are used to determine whether or not to follow a course of action that is designed to make a significant impact on the outside world. This view can be reconciled with a physical theory proposed by Marshall nearly forty years ago, the Theory of Resonance. Marshall suggested that in the right circumstances quantum-scale events will take place spontaneously within complex structures (such as organisms or brains) which will make their internal logical patterns more similar to each other. It is here suggested that resonance can also influence (quantum-scale) events outside of brains, organisms etc. Coin-tossing experiments where a head resulted in an action which the experimenter felt (for subjective reasons) would significantly change the world, apparently support this view.

Introduction

Many investigators have aimed to show that it is possible to influence the toss of a coin, the throw of a dice or the click of a Geiger counter using the power of the mind alone (e.g., Rhine [1943], Schmidt [1976]). Some experiments were designed and executed so as to make fraud or misinterpretation of the data impossible, yet they produced results which are highly unlikely to have been due to chance alone (e.g. Schmidt [1993]). Events which science has predicted should be random have not always been random.

Nevertheless, after decades of effort, the results remain inconsistent - it is not yet possible to "strengthen the statistically weak effects so that they can be demonstrated on demand" (Schmidt [1996]). Inconsistent results can be ignored by mainstream science, and they have limited value since the phenomena cannot easily be investigated in more detail in follow-up experiments. As a result, most investigators of psychokinesis and other "paranormal phenomena" have concentrated simply on proving beyond all reasonable doubt that these phenomena exist (Utts [1995]). Good evidence has been collected (by the US government (e.g. Puthoff [1996]) and others) that they do exist. Utts and Josephson suggest [1995] that one of the greatest challenges facing science today is to invent a theoretical framework to explain these data. Unfortunately, there are very few ideas as to how to begin this task.

Rather than repeating psychokinesis or telepathy experiments with new variations in the design, I have therefore tried to use a different approach, and at the same time to explain the lack of consistent results in previous investigations.

If a coin is tossed many times it is expected that about 50% of the tosses will be heads. This is true when the tosses are simply recorded as part of a counting experiment. However, there is no compelling reason to believe that it will still be the case if other events are made conditional on the result (heads I do something, tails I do something else). This situation has apparently never been systematically investigated.

Thus, a simple view of the idea behind this project is that when events that are expected to be random are used to determine which of many courses of action are followed, the supposedly random events will not be random.

Marshall’s Theory of Resonance

The project also set out to investigate one interpretation of the ideas of Marshall [1960], who set out to explain telepathy, but invented a new physical theory with wide applications. Sheldrake [1981(i)] apparently invented the same theory independently, which he has extensively investigated. Marshall stated his hypothesis of resonance as follows:

"Any two structures exert an influence on each other which tends to make them more alike. The strength of this influence increases with the product of their complexities, and decreases with the difference between their patterns."

Marshall is suggesting that there are undiscovered laws of physics which become strong only when one is dealing with very complex structures, and that these influences tend to make patterns repeat themselves. Marshall calls these effects "eidopoic influences" (they are equivalent to Sheldrake’s "morphogenetic fields"). The structures that he has in mind include organisms, brains, and even complex computing machines providing they have a significant random element in their behavior. Marshall suggests that much of the information required for the development of an organism may be transmitted by eidopoic influences, which have been generated by previous generations of the same species. Similarly, resonance of a brain with a past state of itself leads to memory, and resonance of a brain with another brain (which contains a similar pattern that subsequently becomes even more similar) leads to telepathy.

Sheldrake [1981(i)] suggested that the forms of simpler structures can also be controlled by resonance. His examples included the folding of proteins and the forms of crystals.

It should not be thought that this means that DNA, proteins and other biochemicals are not necessary to life or mental processes. Sheldrake used the analogy of a television [1981(ii)] - the transistors, capacitors and coils inside it are necessary to give a picture. This, however, does not mean that the pattern of dots on the screen is generated by those parts alone. As we know, the pattern is controlled by a signal that is transmitted to the TV. Similarly, biochemical machinery may be needed to transduce a biological signal that is transmitted by resonance. (The analogy would be even closer if each TV transmitted as well as received the signal.)

People are often confused by these ideas, assuming that because resonance causes structures to become more similar to each other, structures will therefore never change. This need not be the case - the individual parts of many systems are attracted to each other, but the average can nevertheless drift. For example, people may dress like each other because they are influenced by fashion. Fashions change, however, so such people frequently change their dress.

One may ask how we could be unaware of such an important influence. We may, in fact, experience resonance in our everyday lives without being aware of it. Common experiences which seem to be innate, such as feelings of awe when entering a cathedral, sadness when we hear music in a minor key, or the excitement of a small boy when he first sees a steam train, may be due to resonance rather than experience or genetic make-up. (I am not suggesting that the existence these experiences is evidence for resonance; only that the world is very like it would be if resonance existed.)

I shall make two assumptions, neither of which are made by either Marshall or Sheldrake:

1. I shall assume that the quantum events which give rise to resonance can take place outside the structure that is resonating (e.g. in the world outside a brain which remembers).

2. I shall assume that the structures in question need not be physically compact, and I will therefore consider entities which are made up from many dispersed structures which interact with each other.

To understand the first assumption, think what happens according to the Theory of Resonance when someone remembers something. Both Marshall and Sheldrake suggest that a pattern (possibly of electrical reverberation) in the brain will often lead to another, similar pattern, which in turn may lead to others, forming a sequence. These patterns correspond to memories which are associated with each other. For example, let us say that I hear a loud bang, then see a crashed car. The next time that I hear a loud bang (which sets up a pattern in my brain which is similar to that of the first bang) I may remember the crashed car.

According to Marshall, when I hear the bang for the second time, quantum-scale events in the brain occur in just the right places to convert the first pattern (corresponding to the bang) to the second (corresponding to the crashed car). For example, fluctuations in salt concentration near some of the millions of neurons that are in marginal states could cause them to fire in the appropriate configuration to generate the image of the crashed car. (Marshall reminds us [1960] that the voltage required to make a particular neuron fire varies according to a definite statistical law - the sensitivity of a neuron typically varies by about 8%. He estimates that at any moment there are around 10⁷ marginally stimulated cortical neurons in the brain.) Note that the events which cause the image (pattern) to be repeated are assumed to take place within the brain.

Now consider the situation where several people share a set of eidopoic influences, this time corresponding to a belief (I assume that beliefs, like images, must correspond to a pattern or patterns in the brain.) Let us say that they all believe that an electric light bulb uses more electricity when it is switched rapidly on and off than when it is left on. This belief is in fact false.

Now suppose these people are my friends, and I decide to write a letter to them, explaining that this belief about light bulbs is false. However, I decide to toss a coin to decide whether or not to post the letters. If the patterns corresponding to my friends' belief is to be repeated in their brains in future, my toss must dictate that I do not post the letters. Thus an event (tossing the coin) which took place outside these structures (brains) could determine the patterns that appear within them, and this event could be subject to an eidopoic influence. Experimental evidence presented in this paper apparently shows that such effects do indeed exist. Obviously, there are a great many other ways of changing how people see the world and very many other random events could determine whether or not these changes take place.

Assumption 2 can also shed light on whether resonance events must take place within the resonating structure, as follows.

Marshall states that the human brain is "the most complicated structure in the universe" (leaving aside the possibility of extraterrestrial life presumably). It may not be. An assembly of human brains (and possibly inanimate objects such as computers) may be the most complex structure.

I was taught at school that it is helpful to think of a bee-hive not as a collection of organisms (the bees), but as a single organism (the hive) which spreads its tentacles in the form of worker bees into the nearby flowers. The hive may have "holistic" properties which cannot be predicted from the properties of bees. Equally, the French Resistance during World War II was made up from many highly dispersed individuals, but it was capable of coordinated action like a single person or physically compact organization. I shall call such assemblies of dispersed but connected structures "superstructures". The eidopoic influence of superstructures may be large enough to measure in simple experiments.

It seems likely that this interpretation of Marshall's ideas is reasonable. Consider the following thought experiment: suppose that an operation is carried out on, let us say, two snails, so that their brains are pushed together, with, say, a piece of cling film between them. Whether or not we accept the Theory of Resonance, it seems unlikely that the assemblage created would have any special properties. However, if we take away the cling film, unusual effects become a possibility. Intuitively, it seems likely that it is the interactions (in this case electrical and chemical) between the two structures which are important, not their physical proximity. The boundaries of a "structure" in Marshall’s sense are probably determined by function and causal linkage rather than by shape or the materials of construction. I am suggesting that whenever predetermined (or at least highly probable) interactions exist between structures, they may start to take on special characteristics which belong to a single larger combined structure.

Examples of superstructures might be human communities, professions (e.g. the community of doctors), companies, sports teams, and governments. I am not suggesting that they have well-defined boundaries. Rather that such superstructures are continually being formed and dissolved, but that while they exist they may transmit and pick up (from similar superstructures that existed in the past) strong eidopoic influences. Resonance may act at many levels at once - e.g. the individual human level at the same time as the group level.

If we assume that human superstructures can also include inanimate objects that interact with the humans, then it follows that the eidopoic influences can act on objects outside the brain, i.e. that assumption 1 above is correct. This is because the coin can become part of a superstructure.

To illustrate with an example, consider a business enterprise: this comprises its employees, but also its record-keeping systems including computers. The computers are designed to have very little random behavior, but randomness cannot be completely eliminated. The computers could therefore be subject to eidopoic influences. For example, one of the computers could develop a problem with its hard disk at a moment when the company was about to launch a life-changing product, delaying or preventing the launch. (In my experience this kind of thing happens very often. Another name for this aspect of the Theory of Resonance might be Murphy’s Law.)

Group influences on experiments

There are very many people who believe that the Theory of Resonance is wrong or at least far-fetched, and one could regard these people as a superstructure. The theory itself therefore predicts that a strong eidopoic influence will prevent experiments designed to demonstrate the existence of eidopoic influences from being successful. The beliefs and expectations of orthodoxy may thus have a powerful effect. (However, orthodoxy has other strong beliefs and expectations, and an experiment that took advantage of these may have a chance of success - see below.)

The tendency for nature to behave so that people's ideas and fundamental beliefs will be conserved may explain why previous experiments designed to test the hypothesis of resonance have either failed or given equivocal results. On the one hand, resonance with earlier structures may truly give rise to the eidopoic influence which the experiment seeks to measure. On the other hand, resonance of people's beliefs and behavior with other, earlier, beliefs and behavior may give rise to an opposing eidopoic influence, which cancels out the influence being measured. This may explain why Sheldrake's attempts to prove the resonance theory (e.g. [1985], appendix) have given results which are, he claims, statistically significant, but they are not sufficiently significant to be generally accepted as conclusive.

The same applies to paranormal research in general - maybe it often fails because consistent success would have a revolutionary effect in the world of beliefs. (Or maybe it often succeeds because consistent failure would have a revolutionary effect in the world of paranormal research - experimental data is needed here.) If this analysis is correct, it seems likely that the trend being measured by the experiments would be reduced enough to allow mainstream science to ignore it, but not enough to cause the investigators to completely abandon their research. This seems to be exactly what happens.

Indeed, an "uncertainty principle" seems to apply to paranormal events: the more reliable and influential the observers are, the less likely the events are to appear.

It is this extension of Marshall's ideas that I sought to test, by seeing if the eidopoic influences of many humans (and possibly many plants) can affect a random number generator. It was anticipated at the start of the project that the departures from randomness in this type of experiment would be in the direction which gives the minimum of change in the world. Methods of changing the world a lot with reasonable time and effort were therefore sought, which could form the basis of experiments. Note that it was not necessary to analyze or quantify these changes to the world, any more than a herbalist needs to study the biochemistry of a pathogen to diagnose an illness or the molecular structures of the active principles in a herb in order to cure a disease.

Methods

A number of coin-tossing experiments were designed, where each toss decided whether or not a course of action was followed. A tail was always taken to mean "do nothing", whereas a head meant follow a predetermined course of action that was designed to change the world in some way.

In all experiments ordinary UK coins were used. The coin was always tossed by balancing it on the bent fore-finger and flicking it with the thumb so that the coin rotated 20 - 100 times. Very occasionally the coin was dropped, in which case the face which was up after it landed on the ground was used.

The above experiments did not seem to give statistically significant results - that is to say, the heads and tails seemed to arise at random. One possible reason for this lack of success is discussed below - the final size of each experiment was not determined before the experiment began. The results are summarized in table 1. These experiments are included mainly to avoid the accusation that only successful experiments have been reported, and they will not be discussed in detail. All experiments that were performed along these lines are included.

Successful experiments

Other experiments were performed which gave more interesting results. In the first set (Ex11.01 - Ex11.12), each coin toss determined whether a handful of poppies would be scattered from a train window, or on some bare soil in a public garden. Blue poppy seeds were bought from a health food shop, and were produced by the German company Rapunzel. The sites of scattering were chosen so that the poppies would have a good chance of growing, and would be seen by many people if they flowered. This experiment was divided into 12 experimental runs of between 11 and 42 tosses each. I shall call an experimental run a "section" in order to avoid confusion with runs of sequential heads or tails which are discussed below. After each section the number of heads and tails were counted.

All experiments that were carried out with poppy seeds have been included in this report.

Two small experiments were performed after Ex11. Ex12 involved down-loading images of paintings painted by the experimenter to a world-wide web site -http://www.douglas.co.uk/patrick . The paintings were arranged in order, starting with what the experimenter considered the best, and ending with the worst. A coin was tossed for each painting in turn. If it was a head, the picture was down-loaded (and therefore made available to the public). It a tail, no action was taken as usual.

Ex13 used a slightly different design from all the other experiments reported here. Rather than using many tosses to determine which of a set of possible actions were taken, here many tosses were used to determine whether a single action would take place. This action - posting a letter to a relative in the House of Lords of the UK parliament - was considered to have a large potential to change the world. The letter proposed that it would be a good idea to extend the U.K. Value Added Tax (VAT) so that it applies to interest payments. (The experimenter and his colleague, who wrote the proposal, genuinely believed that it would be a good idea.) The text of the proposal can be found at http://www.douglas.co.uk/patrick . The coin was tossed 40 times and it was stated before the experiment that if less than 12 heads occurred (i.e. the probability is below 1%), the letter would not be sent. In the event 27 heads were thrown, which is improbable (the probability is 1.92%), but in the opposite direction to that predicted! This experiment is included in this report partly to illustrate this alternative experimental design for use in future investigations. Since it used a different design it will be analyzed separately.

The final experiment, Ex14, involved writing letters to members of the British parliament. First three lists were compiled, each containing 44 names. These were (1) members of the Liberal Democrat Party, (2) "front-bench" members of the Opposition (i.e. Conservatives who would be in the government if the Conservative Party were to be elected) and (3) "back-bench" members of the ruling Labour Party (Labour members of parliament who are not members of the government). These groups were selected as being the most likely to be open to new ideas, since it was assumed that members of the government might be too busy to consider new ideas carefully.

It was also anticipated that there might be differences between the responses of these three groups, and that these differences might be reflected in the coin tosses.

For each name on the lists, a coin was tossed. If a head appeared, a letter was sent to the M.P. (member of parliament). The same proposal that was used in Ex13 was sent to the MPs, together with a covering letter.

The first section of an experiment with poppies, and the identification of three trends in the data

On May 5, 1998, I carried out the first experiment involving scattering poppy seeds. Handfuls of seeds were scattered from the guard’s van of a train traveling from Maidstone in Kent to Victoria Station in London. Earlier in the year, the weeds at the edge of the track had been sprayed with weed killer. This provided an area where poppies could grow which would be highly visible to passengers, which might increase their enjoyment of the train ride. Every 90 seconds a coin was tossed and seed scattered for approximately one minute. The results of this section were as follows (see also tables 2 and 4 below):

T T T T T T T H T H H H H H H H H H T H T

Prior to this result, it was anticipated that the data would show the following trend, as discussed above:

1. There would be more tails than heads. Tails are a more conservative outcome than heads because no change is made to the world outside the experiment.

After completing this section, two more trends were identified, and written down soon after:

2. There would be more tails in the first half of a section than in the second half.

3. There would be runs of consecutive heads or tails.

Neither of the two new trends were anticipated. They were identified and discussed with colleagues simply because the data seemed to be highly non-random, and to depart from randomness on those ways.

There are probably many possible rationalizations of these trends. I shall record here my favorite. With regard to the greater proportion of tails in the first half than in the second half of a section, one can argue as follows: as an experiment progresses, a score accumulates. This score changes the situation because a successful experimental result overall (in terms of trend 1 above) might make big changes in the world by changing people's beliefs. If an experiment is at first successful, a point is therefore reached where an opposing eidopoic influence outweighs the influence being measured. The number of tails is now reduced - making the experiment less successful.

The simplest explanation of the runs is that they are a direct consequence of trends 1 and 2. If the first part of (a section of) an experiment is enriched in tails as suggested by these two trends, then the chances of runs of tails are increased. If the second part is enriched in heads as suggested by trend 2, then a run of heads becomes more probable.

(1) The first section of the experiment with poppies did not have more tails than heads, so did not follow trend 1. However, (2) in the first half of the run 80% of the throws were tails, while in the second half 80% of the throws were heads. (In this and all subsequent runs which had an odd number of throws, the middle throw was ignored when calculating trend 2.) (3) It had runs of 7 sequential tails and 9 sequential heads.

Results of further experiments with poppies and other systems

The results of all sections of the experiment that used poppies are shown in table 2. The heads and tails tossed have been laid out so as to make it easy to compare the number of heads in the first and second sections (this is needed in order to investigate trend 2).

Table 3 shows similar data for Ex12, Ex13 and Ex14, the experiments where paintings were down-loaded onto a web-site (http://www.douglas.co.uk/patrick) and letters were written to politicians.

Note that a run of 16 tails in a row occurred in Ex14.1. One would expect to find a run of this length on average only once in more than 32,000 tosses.

For each section, table 4 shows the total number of tosses, the number of heads (trend 1), the number of heads in the first half of each section (trends 1 and 2), and (heads in the first half plus tails in the second half) - a measure of trend 2. It also shows the probabilities of getting these or more extreme results for each experiment. The probabilities were calculated with a computer program, described below. As can be seen, the number of heads tended to be low as predicted. This tendency was more marked in the first part of each section, where trend 2 reinforced trend 1, giving probabilities of 0.038%, 8.98% and 0.46% (as shown in column 6). The probabilities of the trend 2 results (column 8) were also significant. Table 4 also shows any sequential runs of above 6 in a row (trend 3) and the mean run length (a measure of trend 3). In calculating the mean run length the sequences of individual sections and experiments were concatenated (otherwise the breaks introduced would tend to reduce the mean run length). One would expect the average run length to be (almost exactly) 2 for any significant number of tosses. From this the likelihood of obtaining this data can be calculated - see the next section.

It is interesting to compare the number of letters sent to each of the political parties with the response in terms of the number of M.P.s who wrote back. This is shown in table 5. The Theory of Resonance suggests that the Liberal Democrats were most likely to make changes as a result of the letter, since they received the fewest letters (they had the fewest heads - 12 out of a possible 44 - with a probability of 0.18%). They were also by far the most responsive, since 50% (6 out of 12) of those who received letters wrote back. This correlation is not born out by the other two parties: the Labour Party also seemed to receive an improbably low number of letters (16 out of a possible 44, with a probability of 4.81%), but none of them wrote back. The Conservatives received the greatest number of letters (26 out of a possible 44) but 24% of them wrote back. (The Labour party may have discussed the letters and decided as a group not to respond.)

Ex13 is analyzed separately in table 6. Instead of an abnormally low number of heads there was an abnormally low number of tails (13 tails out of 40 tosses). The probability of this is 1.92%, but we must multiply by two because the trend is in the opposite direction to that predicted (see the discussion below). The data also showed a tendency towards runs of over 2.

Calculation of probabilities

The probabilities for trends 1 and 2 were calculated using a program for Windows 95 written by my colleague Peter Baldock, called Binomial_Distribution_Calculator.exe. This calculates the likelihood of getting a certain number of heads or fewer, in the chosen number of tosses. The program calculates the probability of getting 0 heads, then adds this to the probability of getting 1 head, continuing this process up to all heads. This information is tabulated by the program. The program is available at http://www.douglas.co.uk/patrick .

Table 7 is a summary of the results of the three main experiments, Ex11, Ex12 and Ex14. At the outset of the project it was predicted that there would be a low level of heads (trend 1). This trend was supported with a modest level of probability (1 in 152). The two new trends, described above, were supported with much greater certainty. These trends, identified after the first section of Ex12, predicted that the beginning of each section would show a preponderance of tails while the end of each section would show a preponderance of heads (trend 2), and that there would be runs of sequential heads or tails (trend 3).

Since neither of these trends were predicted at the start of the project it could be argued that if the opposite effects had been observed (i.e. heads at the start of a section with tails at the end, and many runs of one), some other rationalization would have been invented to show that the data supported the theory. Therefore we should calculate the probabilities of getting results as extreme as these in either direction. So the probabilities initially calculated should be multiplied by 2. On this basis, the chance of getting the number of heads that occurred in the first half of each section (predicted by both trend 1 and trend 2) would be 1 in 208,000, while the chance of getting the number of heads in the first part and tails in the second part would be 1 in 15,000.

It is very difficult to estimate directly the probability of getting the combination of different length runs (predicted by trend 3) that occurred. Taking only the most extreme result, the probability of getting a 16-run in this number of tosses is modestly impressive on its own (1 in 138). The average run length, 2.35, can, however, be used as a measure of trend 3. The expected run length for a significant number of tosses is almost exactly 2, with a standard deviation of 0.103 for 188 runs (this is calculated as the standard deviation for many experiments of one run each (Ö 2), divided by the square root of the number of runs, i.e. it is Ö 2 / Ö l88). The observed value is thus more than 3.6 standard deviations from its expected value. The likelihood of this or a more extreme result occurring by chance is 2 x 0.033%, or 1 in 1,500.

I will not attempt to combine these probabilities to come up with a figure for the "unexpectedness" of the data of the whole project. Clearly, the trends are not completely independent (e.g. high levels of trends 1 and 2 will tend to produce trend 3 as a by-product). However, when the three trends are considered together, it seems highly unlikely that the data are the result of pure coincidence.

Discussion

The original rational of the poppy experiment was that the poppies would grow and influence people, mainly by giving people in trains or public parks the pleasure of seeing masses of bright red flowers. The poppies did grow in reasonable numbers, but they turned out to be an inconspicuous pale pink. It is therefore not likely that any effect on people is the reason for the non-random data generated by the coin. An alternative explanation is that the poppies were of a species or variety that had seldom or never been grown in England. Many new ecological and biochemical interactions will therefore be set up when they are planted here. For example, many species of invertebrates may have encountered these poppies for the first time when I planted them.

The data from these experiments can be explained in a variety of ways:

1. they could be the result of pure coincidence. Thus the data has no meaning and the hypothesis is not valid. This explanation can only be ruled out by designing successful new, similar, experiments, until the likelihood of the overall results occurring by chance becomes vanishingly small.

2. A second class of explanations states that the results are meaningful, but that they are not related to my hypothesis. Here the data is meaningful, but the theory is not valid. I cannot think of any better hypotheses to explain the data, but I invite readers to do so.

3. The third class of explanation is that the theory, or a variation of it, is correct, and that the results support it, i.e. the data is meaningful and the theory is valid.

An explanation of the data, which apparently belongs to class 2 above, is that the intense desire of the experimenter to get a positive result somehow influenced the coin to make positive data appear. However, this explanation could be compatible with the Theory of Resonance: my desires, like my beliefs, are part of my mental state, and are presumably caused by a physical pattern in my brain. Moreover, events which change my desires not only change the patterns in my brain, but they also change my behavior, so they change the set of probable future human situations.

A point that was overlooked in the early stages of the project was that it is essential to define in advance exactly how many throws (and therefore potential actions) will be performed in a set of experiments. Consider the situation where this is not done, but instead the experimenter decides to perform a pilot study by trying out a system with a short experimental run to see if it is going to give positive results. He might intend to perform further experiments with the same system if the pilot study gives positive results. In such a case, is it likely that the coin will give a preponderance of tails in the pilot study? I suggest that even if an eidopoic influence exists which tends to prevent the actions in question, the coin will probably give near random results. This will discourage the experimenter from performing further such actions in the course of doing a larger in-depth study.

If my interpretation is correct, it seems surprising that there were often long runs of heads or tails. The hypothesis suggests that nature "knows" everything about the current state of the world. It "knew", for example, that I had written down tend 3 above (that there will be runs) long before I tossed 16 tails in a row in the VAT letters experiment. It is therefore surprising, after a run of, say, 6 tails had built up, that the coin did not give at least one head so that the run was broken and trend 3 was not supported. The explanation may be that most of my readers will correctly assume that trend 1 was the main point of the project, and pay little attention to trends 2 and 3.

I would like to clarify the use of the word "knows" above. Clearly nature does not know anything in the normal sense since it is not using a brain to think about the problem. What I mean it that there is a statistical trend which has consequences that are the same as if an intelligence were to take the available facts and apply the Theory of Resonance. Scientists use a similar short-hand when they say that nature "abhors" a vacuum, or that a gene "wants" to be passed on to the next generation. In this sense of knowing, I suggest that nature knows everything about the current situation in the world, probably including our thoughts. It therefore knows what is likely to happen in the near future, but may not know what will happen later on. For example, nature probably does not know what the temperature in New York will be three months from now.

Marshall’s hypothesis, and this interpretation of it, can be criticized because the theory is difficult to prove conclusively, or to describe mathematically, as Marshall himself found. Some of the expressions that I have used, such as "changing the world" are at present inexact and unquantifiable. In these respects however the hypothesis seems similar to Darwin’s Theory of Evolution, before the discovery of molecular biology. In 1974 Karl Popper described the study of evolution as "a metaphysical research program" (as opposed to a scientific theory). The Theory of Evolution was enormously helpful in visualizing situations and suggesting experiments, and the Theory of Resonance may help in the same way. Like the current theory, it was difficult to design experiments which would disprove evolution, and only circumstantial evidence can be collected for both theories. Both deal with situations which are constantly changing. Apparently identical experiments cannot be expected to give identical results when they are carried out at different times - in the case of a resonance experiment the situation has changed because when the second experiment is performed another experiment has already been performed.

Conclusions

Marshall introduced a new physical theory in 1960 to explain phenomena including the development of complex organisms, telepathy, memory and perception. He called it the Theory of Resonance. A theory that is now much more well-known but is essentially the same (the theory of morphogenetic resonance) was applied in 1981 by Sheldrake to these and other phenomena such as crystallization and the folding of proteins. Sheldrake has since tried hard to test the theory experimentally [e.g. 1985] , but although the results were often suggestive, they were never accepted as conclusive.

The Theory of Resonance can be reinterpreted and extended by making two assumptions: (1) that quantum scale events both inside and outside a structure can give rise to resonance within the structure, and, (2) that when many structures interact with each other in predetermined ways they are equivalent to a single, larger, structure.

Taken together or singly, these assumptions provide a rationale of testing the theory by searching for eidopoic influences that act on events taking place outside complex structures. The assumptions also provide an explanation for the poor results obtained in other resonance experiments, and by paranormal research in general.

Data is presented here which tends to support the Theory of Resonance. In coin-tossing experiments the total number of heads was, as predicted, unusually low (total 195 heads in 442 tosses - having a probability of 1 in 132). Two other unexpected trends in the data made it look highly non-random: firstly, the first part of each section of the experiments tended to have more tails, the second more heads (trend 2). Only 176 out of 436 tosses disagreed with this trend - by chance this or a more extreme result would occur only once in 15,000 experiments. Secondly, the data contained a great many runs of sequential heads or tails (trend 3). The chance of these runs being the result of coincidence alone was one in 1,500. Both of these unexpected trends seem to be in agreement with the Theory of Resonance - they appear to be the result of distortions of the data set which tend to minimize trend 1.

Acknowledgements

I would like to express my heart-felt thanks to Peter Baldock for many hours of fruitful discussion, for guidance on analysis of the data, and for writing the computer program that I used to calculate the binomial probabilities. I would also like to thank Geordie Burnett-Stuart for an ingenious piece of lateral thinking and analysis that allowed me to calculate the probabilities of runs.

References

Marshall, N. [1960]: "ESP and Memory: a Physical Theory", The British Journal for the Philosophy of Science, 10, pp. 265-286.

Popper, K. [1974]: "Autobiography of Karl Popper" in The Philosophy of Karl Popper in The Library of Living Philosophers, ed. P.A. Schilpp, Open Court Publishing Co., Illinois.

Puthoff, H.E. [1996] "CIA-Initiated Remote Viewing Program at Stanford Research Institute", The Journal of Scientific Exploration, 10, p. 63.

Schmidt, H. [1976]: "PK Effect on Pre-Recorded Targets", The journal for the American Society for Psychical Research, 70, pp. 267-291.

Schmidt, H. [1993]: "Observation of a Psychokinetic Effect Under Highly Controlled Conditions", Journal of Parapsychology, 57, December.

Schmidt, H. [1996]: "Channeling Psi Effects", unpublished manuscript available at the Retropsychokinesis Project at http://bavard.fourmilab.ch/rpkp/schm-manu.html

Sheldrake, R. [1981(i)]: A New Science of Life: the Hypothesis of Formative Causation, London, Blond and Briggs.

Sheldrake, R. [1981(ii)]: "A new Science of Life", New Scientist, 11 June, pp. 766 - 768.

Sheldrake, R. [1985]: A New Science of Life: the Hypothesis of Formative Causation (A New Edition), Anthony Blond, London.

Utts, J. [1996]: "An Assessment of the Evidence for Psychic Functioning", The Journal of Scientific Exploration, 10, pp. 3-30.

Utts, J. and Josephson, B.D. [1996]: "The Paranormal: the Evidence and its implications for Consciousness", The Times Higher Education Supplement’s special section on Consciousness, April 5^th, p. (v).