242) Monte Carlo validations of two protocols


Ludwik Kowalski (7/20/05)
Department of Mathematical Sciences
Montclair State University, Upper Montclair, NJ, 07043

Be aware that his unit is the continuation of what was described in units #240 and #241.

1) After posting units #240 and #241, I wrote to Bass: “I want you to know that the two last units on the my CF website are based on your 2002 paper. Your comments will be appreciated, especially about how the three essential parameters should be defined in my description of the protocol. You will see that I suspect typing errors in the pdf file (your paper). In the immediate reply Robert wrote: ” . . Moreover, it seems to me that you have entirely ‘missed the point.’. . . In the version [of the presented to ICCF10, the formulae are concise and elegant. For all I know they may already have been published in some standard book, but the expert, (who is a ‘household name’ in the field of Statistics) who told me that my derivation was ‘correct’ did not give me any literature reference. Therefore I shall stick with my own ‘de novo derivation from first principles’ as explained sufficiently adequately in the Abstract to be verifiable by anyone who knows undergraduate calculus. To suggest that these rigorously derived formulae are ‘unreliable’ is ludicrous.”

In a message received today Bob stated that all three parameters (P1, P2 and P3; see unit #241) were used correctly in my Monte Carlo code. My suspicion of typing errors, in P1 and P2, was not justified; my assumption that the summation symbol was omitted turned out to be correct. I will return to the issue of reliability later in this message. Before addressing that issue let me show another quote, also from the immediate Bob’s reply.

“Ludwik, Thanks for pointing out what you have posted in your items #240 & #241 regarding my presentation to ICCF10 in August 2003. You once told me that you can post documents in MSWord or ".doc" format; therefore I would much prefer that you post the attached ICCF10 Abstract, which is a great improvement by Mike McKubre over my original 2001-published version (in that numerous constraints have been relaxed without detriment to the main idea). . . . Also I would appreciate it if you would refer to this protocol as the ‘Bockris/Bass/McKubre Protocol’ or the ‘Bockris-Bass-McKubre Protocol’ because the main idea is something I learned from publications of John Bockris. Moreover, it seems to me that you have entirely ‘missed the point.’ . . . “

2) Following the suggestion I am going to display the description of the BBM protocol in the appendix, at the end of this unit. You will see that it is quite different from the first protocol (described in units #240 and #241 and downloadable from the library at <www.lenr-canr.org>). For that reason I prefer to address the issue of validity of each protocol separately. I will try to do this a little later. Let me point out that the adjective actually used was “tentatively unreliable;” not simply “unreliable.” Instead of trying to validate the protocol mathematically I decided to explore it numerically. What is wrong with this? A Monte Carlo simulation, if done correctly, is also a powerful tool of validation. Here is an illustration. Suppose a claim is made that by following an X protocol a person would be a casino winner, in a long run. To check this protocol one may decide to play many games and see what happens at the end. But that might be very expensive. Instead of following this approach one can play virtual computer games and see what happens at the end. Presence of a hidden error in the derivation of the protocol could be revealed by playing virtual games. But a reliable Monte Carlo code, like a reliable derivation, must be based on realistic assumptions.

The main issue, in this particular situation, has to do with my code, not with the idea of using the Monte Method of validation. What is wrong with my code? What am I missing? I am going to discuss this privately with Robert. Expect to see my conclusion in several days...

3) Appended on 7/22/05:
Messages from Bass are interesting and useful. Our discussion is in progress; I will probably write my conclusions it in two or three days. Meanwhile let me make another general observation. According to what Robert wrote (see above), a layman is expected to “reject any doubt.” Any doubt about what? That person, I suppose, knows the meaning of the term proportional; s/he should have no doubt that the term is used correctly when doubling, and quadrupling the duration also doubles and quadruples the amount of helium produced. But here are two questions that a critical thinker might really have:

a) Why should the stated values of A0, A1, A2, A3 ad A4 be taken for granted?
b) How can I be sure (after taking stated facts for granted) that helium was produced in nuclear reactions taking place in cathodes?

The purpose of statistical protocols, as far as I know, is not to answer that kind of questions. Such protocols are designed to deal with random experimental errors. For example, is a relation inferred from experimental data real or apparent (caused by randomness)? Robert’s protocol, in step 9, mentions the confidence level of 95%. What does the concept “level of confidence” mean? Statisticians deal with samples but their pronouncements refer to populations from which samples are taken. Levels of confidence tell us how reliable such pronouncements are. Samples of larger sizes usually correspond to more reliable inferences than samples of smaller sizes.

The important point is that statistical protocols are used to validate statements about populations, not about samples. In the situation described by Robert samples (experimental values of A0, A1, A2, A3 and A4) are taken for granted. His protocol can then be used to validate the claim of proportionality. Is the amount of helium really proportional to the duration of electrolysis (under specified conditions) or is the inferred proportionality apparent? After all, other kinds of relations, such as quadratic, cubic or exponential, are also possible. In that context a statistical protocol could be useful. But questions (a) and (b) above are not statistical. I do not think that a statistical protocol would help me to answer them. To decide about (a) I would ask about work of other scientists; do they also observe similar facts? To decide about (b) I would ask about other indicators of nuclear processes, for example, about excess heat, or about tritium. Experimental data are usually easier to accept when they are consistent with confirmed theories. But, according to scientific methodology, theories should be justified by experimental data, not the other way around.

4) Appended on 7/23/05:
A newspaper may refer to a confidence level while describing a gallup poll. Suppose that a random sample consists of 15,300 questioners collected from a very large population of potential voters. After using a protocol a statistician makes a prediction (an inference based on the sample) that the election will be won by X. The level of confidence, such as 95%, refers to a particular prediction about the entire population; it does not refer to the sample.

Suppose that 8307 of questioned voters said that they will vote for X. The statistician would probably assume that only a negligible error, if any, was made in extracting this number from the pile of returned 15,300 questioners. Numbers, like 15,300 and 8,307, are assumed to be exact. But the inference made from the sample might not be very reliable. In that respect the situation described by Robert is different. Each of the five numbers (five laboratory measurements: A0, A1, A2, A3 and A4) is always associated with random errors, such as 5% or 25%. The bar of error associated with a single laboratory measurement depends on the instrument used; it can be determined by a technician after performing measurements on many samples containing the same amount of helium. Systematic errors can be minimized, if not totally eliminated, through frequent calibrations of laboratory instruments. But random errors are always associated with results of single measurements. That seems to an important difference between samples of physicists and samples of sociologists.

Suppose the goal is to decide whether or not the true relation between the amounts of helium ( A_k) and durations of electrolysis (t_k) is linear. That is an inference and the concept of level of confidence is applicable. Results of five laboratory measurements of A_k, when plotted against durations, usually do not fall on a straight line. That is why bars of errors, associated with numbers, become important. The initial hypothesis is that the relation is linear. But then it is either accepted or rejected, acccording to known error bars. It is impossible to be 100% certain that the true relation is linear (or quadratic, cubic, etc.) when error bars are very large. Yes, I know that most readers are familiar with all this.

Before finishing these observations let me focus on another well known fact. Physicists make inferences about laws of nature. Such laws are either deterministic or probabilistic. The field of cold fusion has no laws; only working hypothesis, based on irreproducible data. Are these hypotheses deterministic or probabilistic? How can an error bar be associated with the result of a single irreproducible measurement? I do not know how to answer that question. But I can think about a similar situation in sociology. Suppose a survey is conducted to predict the result of an election. A social scientist uses a protocol and makes a statement that 57% (plus or minus 5%) people support X. The level of confidence of that inference, is said to be 95%. Then a scandalous revelation about X appears in the news and less than 1% of people actually vote for X on the election day.

Does this mean that the protocol was faulty? Not at all. The protocol is based on the assumption that the conditions influencing people to vote, one way or another, do not change significantly. Behavior of social groups becomes unpredictable when such conditions change frequently. Essential conditions on which successful observations of cold fusion phenomena, such as generation of helium, depend have not yet been recognized. Presumably these conditions change frequently without our ability to control them. That is how irreproducibility is usually interpreted by cold fusion researchers. In my opinion inferences (based on logically derived protocols, or on Mont Carlo codes, are useless when one is dealing with irreproducible data. Identifying essential conditions, and finding ways of controlling them, should be the number one priority of cold fusion researchers. Everything else, including attempts to commercialize “magic devices,” should wait till experimental data become reproducible. Yes, I know that everybody knows this.

5) Appended on 7/24:

I have no doubt that both Robert’s protocols were written under the assumption that experimental data are reproducible. That would certainly apply to generation of oxygen (rather than helium) during ordinary electrolysis of water. In one of my messages about the first protocol I wrote that the “much larger than” seems to be too vague to be associated with the single level of confidence. The reply is worth quoting.

Ludwik, Thanks for pointing out that there is some vagueness in the original 2002 Bockris-Bass-McKubre (BBM) Protocol <http://www.lenr-canr.org/acrobat/BassRWfivefrozen.pdf> as published in JNE by me alone, before Mike McKubre suggested the improvements in generality leading to our ICCF10 version [attached], which would benefit from clarification. I was tacitly assuming that any randomness in the errors is a Gaussian stochastic process. Also I should not have assumed that dA > 0 so I should have written |dA| instead of dA in the first test. In that case, if one accepts the approximate sample value of sigma as an "estimator" for the Standard Deviation sigma, then One Sigma gives a 68% Confidence Limit and Two Sigma gives a 95% Confidence Limit, and Three Sigma gives a 99.7% Confidence Limit, etc.So, my first test

|dA| << delta-A

        2*sigma  <  delta-A
 
and in order to claim that the confidence is much "greater" than 95% [as I said] one would HOPE that
 
        2*sigma  <<  delta-A  in the sense that 3.sigma/(delta-A)  <  1,  or
 
        sigma/delta-A   <  1/3  =  0.33

 
Test 1:
 
        (|dA|/delta-A) < 0.10   ==>   estimator of sigma is OK
 
Test 2:
 
        (sigma/delta-A)  <  1.00   [68.3% Confidence]
 
        (sigma/delta-A)  <  0.50   [95.4% Confidence]
 
        (sigma/delta-A)  <  0.33   [99.7% Confidence]

a) So much about the first protocol; I would be happy to check the validity of the BBM protocol (with another Monte Carlo code) after learning more about how to turn the inequality shown in the last line of the appendix into confidence levels of specific inferences.

b) Personally I would not rely on a protocol to convince a layman that a relation is linear; I would simply plot A,sub>k versus t_k. But that is only a matter of pedagogy and taste.

c) A relation, by the way, does not have to be linear; a positively exponential relation, for example, would likely to be more desirable, from practical point of view.

d) As you probably know, from the 2004 document at:

http://powermarketers.netcontentinc.net/newsreader.asp?ppa=8knpq_ZknqphiqYUok%22EN%26bfej%5B!

a Canadian company, iESi, made a difficult-to-accept claim: "The new clean energy plant will enable Norwood Foundry to generate six times (12 MW) more electricity than it consumes (2 MW) at its foundry located in Nisku, Alberta, Canada." Please write to me what you know about the present status of that plant, and about the origin of excess energy. I would be happy to post a unit containing what you write, unless I see a clear indication that the message is confidential.

Generalized Cold Fusion Demonstration Protocol

Robert W. Bass, Michael C. H. McKubre

==================
Greek mathematical symbols were changed (by Ludwik Kowalski) when the good-looking MSWORD document was turned into the web page. This was necessary to compensate for his limited familiarity with html tags. Saving the original document as a webpage produced a monster that was hard to edit. That monster displayed different symbols (in the same equations) when viewed in different browsers.

Lower case sigma was replaced by SIG
Capital sigma (summation) was replaced by SUM
Lower case delta was replaced by DEL (also note that DELE stands for deltaE)
Lower case alpha was replaced by ALP
Lower case beta was replaced by BET
Lower case gamma was replaced by GAM

Multiplications are indicated by asterisks. In the inequality (LEFT << RIGHT), in the last line, the LEFT is simply either SIG or dE, depending which is larger. That what the max is for. The RIGHT, in the same inequality, is the product of DELE by the smallest value in the {Ck} set. That what the min is for.
================================================

This is a generalization of the protocol proposed by Bass [1], which is more realistically flexible in several respects. An arbitrary number N <= 3 of similarly prepared samples is allowed, and neither the voltage nor the current is required to be constant. However, the previous protocol may be recovered as a special case when N = 5.

Let N >= 3 denote the number of similarly prepared samples. Let the suffix k denote any particular sample, k = 0, 1, 2, ... , (N -1), where the suffix k = 0 is reserved for the case of a control blank. Let { Ck }, k = 0, 1, 2, . . . , (N -1), denote the hypothesized causal inputs, where, as in Bass & Gleeson [2], each Ck may be e.g. the result of continuous monitoring of the input electrical power [product of instantaneous voltage & current] and its numerical integration over the complete duration of the preparation of the kth sample to give the total amount Ck ( 0 of electrical work done on the sample, or the total energy input. By definition, C0 = 0. Similarly, let {Ek }, k = 0, 1, 2,. . ., (N -1), denote the measured effect outputs. Three possibilities for the output effects { Ek }are:

(1) Ek = amount of excess enthalpy;
(2) Ek = amount of Helium-4;
(3) Ek = amount of Helium-3.

Now define the estimator of variance SIG² by the sum over all k of

SIG² = [1/(N-2)] * ( { (Ek - dE - Ck *(E)2 } )

where dE denotes mean effect-bias error, and where (E denotes mean effect-increment factor. Next, again summing over all k, define

ALP = SUM { Ek },

BET = SUM { (Ek *Ck.) },

GAM = SUM { Ck },

DEL = SUM { ( Ck )² },

and verify by setting to zero the gradient of SIG with respect to the vector [ dE, DELE ]^T that a necessary & sufficient condition for sample standard deviation SIG to be minimized is that

dE = ( DEL*AL - GAM*BET ) / DENOM

DELE = (N*BET - GAM*ALP ) / DENOM

where DENOM stands for the N*DEL - GAM²

The confidence in cause/effect correlation is great if

max( SIG, |dE|) << |DELE|*min {Ck}.

Dr. Robert W. Bass, BAE SYSTEMS, 44414 Pecan Court, California, MD 20619
robert.w.bass@baesystems.com

Ergerences:
[1] Robert W. Bass, "5 Frozen Needles CF Protocol," Journal of New Energy, vol. 6, no. 2 (Fall, 2001), pp. 30-32. Also available online at: http://www.lenr-canr.org/acrobat/BassRWfivefrozen.pdf
[2] Robert W. Bass and Wm. Stan Gleeson, "Theoretical and Experimental Results Regarding LENR/CF," Trans. of the American Nuclear Society, vol. 83 (Winter, 2000), pp. 355-56; and: http://www.padrak.com/ine/BASS_7.html