Analysis, Appendix 1

8. Dialog on analysis questions, Jiri and Roger

Statistics

Jiri:

My next question deals with REGs auto-correlation properties; it's motivated by my reviewing a theoretical minimum of Markov chains this morning; then I realized that the two free parameters in the 2 x 2 transition matrix may change independently, and that there is no reason to assume that, shifting base probability by a delta, these two parameters change hand-in-hand. I know (and verified in your report just now) that you tested the auto-correlation of the bitstrings produced by your REG in the calibration procedure; but was there any study looking for changes in autocorrelation function under intention or field influence?

Roger:

I haven't done this thoroughly, but have looked at the possibility this and other transition-oriented analyses might be sensitive. I didn't see much. Meanwhile Atmanspacher and Scheingraber have applied a Scaling Index Analysis to the REG data from FAMMI, and there appears to be an impressive, statistically significant patterning in some of the datasets. This is one analysis I want to have in the EGG suite, even though I don't at present know now to implement it in such a complex dataset. On the other hand, in principle, we could simply make each new trace into yet another dimension or two, and look for the patterns. It takes lots of the trials (equivalent to Z-scores) — on the order of 5 to 10 thousand. But we can have that.

If I understand the whole story right, we're speaking all the time about changes of base probabilities from the theory-fixed 1/2, and corresponding significances assessed by Z's or Chi^2's. But yesterday, when I tried again to re-formulate my views concerning meaning of entropy in the REGG project, I realized that this is just part of emerging signs of order.

Yes, if I understand you correctly. It seems to me that the structures that are really of interest will be very complex. What we are trying to do is find a way of transmitting or receiving signals — signs of life. In this case, anything will do, but it will make sense for us to look for a very strong and simple channel, somewhat along the lines of rhythmic pulsing, or flashing red/green lights, or a siren, but through a medium that is like a dense fog or a film that covers our partner and stills her voice to a level where it is hard to whether it is whispers we hear, or only our willful imagination.

[4] If p = 1/2 + delta_p, then the deviation of entropy Delta H(p) from its maximum log 2 is -2 delta^2. From this simple result one can easily derived that corresponding Chi^2 is equal to -2N Delta H(p), so the proposals to express the deviations by Chi-squares or by entropy change are, in fact, equivalent. If the summation epoch (N) were equal at all sites, it would be something like an instrumental constant and we needn't care about the difference.

We will have equal summation epoch (N) for the standard analyses I have been able to think about. There may be some situation that requires something else, but I think this equal-N design is the right foundation.

The only problem with entropy change or Chi-squares is, of course, their ignoring the direction of the change; whether p attains .49 or .51, Chi-square is the same. But you obviously never treated this as a problem, and I'm now of the same opinion, as it's completely arbitrary what is called 0 or 1 if this convention is not translated to a visible (or audible :) change to be reflected by an operator's mind.

This is a fine question, and it may be possible to ask it in a formal, answerable way in the Project. We will be keeping the raw data as bitsums or signed Z's (I am still favoring bitsums) so we will be able to ask the question. Since we started from the lab experiments where intention was operationalized in terms of signed deviations, when we went to the field and dispensed with intention we lost the orientation or meaning of the sign. In practice, I have been able to see only faint indications that the direction of anomalous deviations in the FieldREG situation has a meaning. Just enough indication to keep the question very much alive.