Patrick D. Shaw Stewart

Running Title: Using random numbers to control events

May 12, 1999

Keywords

Random events, random numbers, theory of resonance, coin tossing, coin flipping, probability, psychokinesis, paranormal research

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Abstract (revised Jan 2000)
Data is presented which suggests that random number generators can give non-random results.  This occurs when each result is used to determine whether a course of action is followed that is likely to make a significant impact on the outside world. Coin-flipping experiments were performed where a head resulted in letters being posted to UK politicians, whereas no action was taken for a tail. The results suggest that non-random data was generated (there were many runs) and also suggest that there may be a bias towards conservative outcomes which reduce change in the world as a whole.

Introduction
The mathematics of random numbers is, of course, well-established. Its predictions have often been tested using real random numbers. It is therefore generally assumed that random numbers can be used to design experiments, surveys etc., and that random number generators will continue to generate random numbers when this is done. However, this assumption may never previously have been investigated experimentally. This study sought to remedy this omission and it provides experimental data which suggests that a (supposedly) random number generator gives numbers that are not random when those numbers are used to determine the course of events in the outside world.

The data in this report were generated by flipping coins. Paranormal researchers generally use automated random number generators rather than dice for three main reasons: firstly, they may hope that the automated generators will be especially susceptible to psychokineses (eg. [1]). Secondly, the researchers may be seeking to prove to skeptical colleagues that the phenomena that they are investigating are real, and therefore choose methods where results are difficult to fake (e.g. [2]). Thirdly, researchers may need to reduce the labor of experiments (e.g. [3]). Coin flipping is sometimes criticized as a method of generating random numbers. It is hard to see why. In practice, if a regular coin is rapidly spun in the normal way, it is almost impossible to bias the result, particularly if the number of spins is widely varied. If the number of spins varies by about 4 turns, the greatest bias that could result is about 0.4% (assuming that the number of turns is approximately normally distributed). This maximum potential bias decreases rapidly as the variation in the number of turns of the coin increases. An untrained coin flipper, such as the experimenter, varies the height of flipping by at least an inch, which corresponds to a variation in the number of turns of about 8. This gives a maximum bias of one part in 10⁷, many orders of magnitude below the effects that are reported. In the context of a preliminary study, therefore, using a coin is not inappropriate.

Of course it is possible that the experimenter may have practiced and learnt how to bias the flipping. However, it would be far easier simply to invent favorable results if the object was to cheat. Since this project is intended to be a preliminary study, no attempt is made to eliminate the possibility of dishonesty by the experimenter. Further and more sophisticated studies will be needed to prove conclusively that the effects reported are genuine and reproducible.

Methods
A coin-flipping experiment was designed, where each flip determined whether or not a course of action was followed. A tail was always taken to mean "do nothing", whereas a head meant that a letter was written to a member 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 current Labour 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.

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 letters 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/vatprop.htm . The letters appear to have had a significant effect. Twelve MPs wrote back and seven said that they found the idea interesting or very interesting.

In all experiments ordinary UK coins were used. The coin was always flipped by balancing it on the bent fore-finger and flicking it with the thumb. No attempt was ever made to interfere with, bias or control the coin in any way. The height of flipping varied from roughly 100 mm to 600 mm, and the number of spins was estimated to vary between about 40 revolutions and 200. The coin was generally not turned over between flips, i.e. the face which landed uppermost was generally kept on the top for the next flip. Very occasionally the coin was dropped, in which case the face which was up after it landed on the ground was used.

Great efforts were made to complete the experiment exactly as planned. This was accomplished. No changes were made to the design or procedure of the experiment after the first coin had been flipped.

Results
Table 1 shows the results. The sequence obviously has many runs, so the sequence of table 2 was generated from it as follows. The letters H and t (head and tail) were replaced with the letters s and D (same and different) according to this rule: if the letter is the same as the previous letter replace it with an s, if it is different replace it with a D. The count of the characters s and D is a measure of any bias towards runs. If the sequence of table 1 is random, that of table 2 will be random too.

The experiment described was one of a series. Thirteen similar (but more trivial) exploratory experiments were also carried out, giving a total of 1067 flips. Three other experiments gave similar trends to those described here. For simplicity, only the experiment giving the most significant results is described here. The complete data, together with analysis, can be found at http://www.douglas.co.uk/patrick/coins.htm .

Analysis
Clearly the sequence possesses several unusual features. For example, it contains a sequence of 28 flips with only two heads (note that extra tails were predicted at the start of all experiments). If one were to flip a coin 28 times the chance of getting 2 or fewer heads would be 1 in 341,956. This observation alone shows that the sequence is highly unlikely to be random. Secondly, two of the three political parties gave sequences that were depleted of heads as predicted (the likelihoods are 0.183 % for the Liberal Democrats' sequence and 4.8 % for Labour). Thirdly, the sequences for the same two parties were also enriched in runs (the likelihoods, calculated from the s/D counts listed above, are 0.0085% i.e. 1 in 11,800 for the Liberal Democrats and 6.31% for Labour). Since the set of 14 experiments involved 1067 coin flips, the probability of encountering the results for the Liberal Democrats would be around 1 in 11,800/1067*44 i.e. 1 in 490.

Discussion
At the beginning of the project it was anticipated that there would be fewer heads than tails, and that the size of this effect would depend on the degree to which the actions taken on flipping a head would produce new situations in the world. Since the concept of a "new situation" was not clearly defined, a variety of procedures were tried in the hope that some of them would show a strong effect. It is therefore to be expected that some of the experiments would give much more positive results than the others. This should not necessarily be taken as contradictory evidence - it might simply show that conditions were not right to give rise to the effect in some cases. For example the results of the experiment described might suggest that the Liberal Democrat and Labour politicians were influenced by the letter while the Conservatives were not.

These experiments were inspired by the ideas of Ninian Marshall [4] (later restated and extensively investigated by Rupert Sheldrake [5]) who suggested that there is a conservative principle in nature which causes patterns in a complex system to reappear in complex but similar systems. This "theory of resonance" proposes that quantum-scale events take place within random systems, thus tending to prevent rapid change. A consequence of one interpretation of this theory of resonance is that coincidence will tend to propagate old ideas at the expense of new ones, since ideas presumably arise from patterns in our brains. Therefore the effect which is postulated might act to prevent its own scientific discovery. This might explain why experiments that were designed to prove Marshall's theory have generally yielded results which were unconvincing to skeptics (e.g. see the appendix to [6]): since these ideas would cause a major intellectual upheaval if good evidence were to be found for them, one might (according to the theory) expect that such evidence will not be forthcoming. This project investigated a possible way around this difficulty in obtaining evidence - it was arranged that failure to prove the theory resulted in even greater change elsewhere.

The reason why runs of tails tended to occur is not clear. (In several of the earlier experiments long runs of both tails and heads appeared, with the heads generally appearing at the end of an experiment.) A somewhat speculative explanation based on a trend towards conservative outcomes runs as follows: at the start of the experiment the coin is influenced in the direction of tails because this gives a more conservative outcome (fewer letters are sent to politicians). After a while a preponderance of tails builds up in the sequence. This means that further tails have the disruptive (unconservative) effect of proving the existence of a new physical principle. Therefore the number of tails is reduced. This is consistent with the positioning of the long runs of tails, which generally appeared in the first half of the experiment.

At this point it is impossible to state precisely what is meant by a "conservative" outcome or a "new situation" etc., or to quantify these parameters. For the time being, however, these experimental systems can be treated as black boxes, i.e. we do not need to analyze them. In any event, further tests need to be performed to see if the trends seen are general and reproducible. For example, it is possible that coins behave differently to other random number generators in this respect.

Conclusions
Experiments were carried out where a coin was used to determine whether or not actions (which were designed to have a significant impact on the world) were taken. In this situation, the coin gave markedly non-random results. As predicted, there was a bias towards the outcome (tail) which resulted in no action being taken. There was also a much stronger trend towards runs (of tails). The probability of the runs being the product of pure coincidence was estimated to be around 1 in 490.

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.

[1] Beloff, J. and Evans, L. (1961). A radioactivity test of psychokinesis. Journal of the Society for Psychical Research 41, pp. 41-46

[2] Schmidt, H. (1993). Observation of a psychokinetic effect under highly controlled conditions. Journal of Parapsychology 57, pp. 351-372.

[3] Schmidt, H. (1972). PK tests with a high-speed random number generator. Journal of Parapsychology 36, pp. 105-118.

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

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

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