|Exegesis Volume 4 Issue #29
Exegesis Digest Mon, 26 Apr 1999
Date: Fri, 16 Apr 1999 01:52:11 +1200
From: Susan Archer
Subject: Re: Exegesis Digest V4 #28
I am leaping in here, probably unwisely but here goes. I'm an astrologer living in New Zealand and a member of the Panplanet list to which Andre belongs. It was Andre who suggested I join this list which I am enjoying enormously. I share Andre's strong interest in the astrology/science interface and agree that astrologers need to do a lot more work to understand and explain how astrology works. This may or may not be in the terms of science but it's not a bad intellectual framework to start with. Re: testing. Is it too simple just to take one astrological event, eg Uranus crossing each of the angles of a natal chart, apply it to a large number of accurately timed births and make a specific statement about what is likely to happen and when? Working with several indicators at once it's too easy to fudge results: "Oh well, of course timing was going to be fuzzy with Neptune at a critical degree and Mercury retrograde!" It's much harder to fudge when you're working with just one factor. Progressed Sun crossing the Ascendant and MC, and Pluto transiting conjunct the Sun are other events we could use. Astrologers will disagree mightily about the selection of events - and everything else - but the ones I've mentioned are high-impact, low-frequency occurences that are clear-cut in time and hard to miss. And I'm assuming that Andre would work out protocols, controls and double-blind whatsits to make sure it's all properly done! Testing is the heart of the matter, isn't it? If we can prove & repeatedly demonstrate that astrology really does work, then our speculation about the astrological mechanism becomes a serious investigation. Synchronicity has been my favoured runner but I don't rule out some as-yet-undiscovered cause-and-effect mechanism. Or something else altogether - like a god. That's because I'm not entirely sure the Big Bang wasn't the splitting of a single atom in some other super-cosmos. But that's a another story! I'm sorry this post doesn't match the intellectual rigour of other contributions but I just had to wade in with my current thoughts. Look forward to more good stuff from William, Andre and co. Kind regards, Susan Archer
Date: Tue, 20 Apr 1999 08:48:23 +0930
From: Ian Thurnwald
Subject: Re: Exegesis Digest V4 #24
Hello Mr Tallman and others,
I have been following this list for some time. I wrote this respose about two weeks ago but never posted it. On the one hand I find the ideas expressed here of intellectual interest, on the other hand my experience tells me that astrology works on some 'other' level. To be quite frank I don't hold much hope that anyone will prove an astrological mechanism to the satisfaction of the hard sciences anytime in my lifetime. Nonetheless, I do have some basic ideas that others might want to run with, and, as the discussion seems to be grinding to a halt I thought it was time to throw some more suggestions into the ring. However, my original response rambles around a bit and my style is rather imprecise so I think I'd better summarise the main points here.
My position on "the search for the astrological meachanism" is:
1. To convince scientists that astrology has validity one must show that the geocentric model of planetary motion upon which it is founded has a measurable effect on human behaviour. Since retrograde motion is a fundamental feature of this model this is an obvious place to start.
2. The easiest and cheapest way to objectively analyse any astrological effect, like retrograde motion, is to find and utilise already extant data sets which apply to that specific astrological effect.
3. My suggestion is that retrograde Mercury periods could be studied in relation to road accident statistics.
In reference to "the search for the astrological mechanism." Mr Tallman said
> >It is not enough to show that a thing may or may not work. It is the why
> >and how of a thing that is convincing, and that is true for astrology as
> >well. Until we can link the astrological effect to measurable phenomena,
> >science and the world at large will continue to refuse us any kind of
> >legitimacy. < snip >
Well, I think we have to start somewhere and propose a few hypotheses about fundamental astrological principles which are open to being tested empirically. As I understand the methods of the social sciences it is a valid technique to utilise statistical, or quantitative, data to support an qualitative analysis, no? And I would suggest that the most convenient (and cheapest) way to do this is to think of ways to employ already extant data sets which might apply to the astrological effect we wish to test. (A recently released book has done this for Sun signs utilising the databases of insurance companies and so forth - those of you into statistical analysis can check his methods and delve into the raw data included: "The Astrology File: scientific proof of the link between star signs and human behaviour" by Gunter Sachs, Orion Books.)
Personally I think it is a mistake to look at anything to do with natal astrology if one's aim is to convince the scientific community of the validity of astrology. My position is that astrology somehow measures, but only partially, the impact of the 'galactic weather' on the Earth. As such, I believe astrology has a more measurable effect at the mass level than at the level of the small group or the individual. To restate the obvious, astrology is founded on a geocentric model of planetary motion and what we now know to be only the 'apparent' irregular motion of the planets 'around' the Earth is basic to this model. After all, the Babylonians were concerned about predicting the motion of the Gods/planets in the sky not just because they followed a regular course against the backdrop of fixed stars, but because their Gods/planets exhibited anomalies in their motion; because they periodically slowed down, stopped and went backwards! (see Lee Lehman's account of this in chapter 2 of "Classical astrology for Modern Living").
The traditional astrological view is that retrograde planetary periods and planetary stations have powerful and/or malefic effects on the Earth itself and on the way people feel and act, but always in keeping with the symbolic meaning attributed to the planet concerned. For instance, Mercury stations and retrograde periods are said to coincide with glitches and breakdowns in communications and transportation both personal and commercial. The implication is that these glitches and breakdowns are usually caused by human error or oversight. Anecdotal evidence suggests that this is so, and when one takes notice of these periods there seem to be spectacular real world accidents one can point to which fit the bill.(For example, during this period of Mercury retrograde we have seen a couple of mass transit accidents caused by vehicles (trucks) transporting commercial goods: the Mont Blanc Tunnel accident of March 24 caused by a truck transporting margarine and flour catching fire; and the Amtrak passanger train crash near Chicago on March 15 allegedly caused by a truck hauling steel attempting to run the rail crossing.)
However, this is not the way to study if this effect applies, because accidents occur throughout the year and one could probably find similar accidents which reflect these Mercury ruled themes during Mercury direct periods too. I suggest a way to test if this effect applies generally is to utilise road accident statistics. Most cities where car use is prevalent keep such statistics. Given the astrological notion of the retrograde Mercury effect one would expect that minor accidents (i.e., those caused by bad judgement or simple distraction like rear-end collisions) will peak during retrograde Mercury periods.
Of course, in and of itself correlating gigabytes of crash data against retrograde periods would be a fairly boring, if relatively straightforward, exercise. But, should such a study show that this Mercury effect operates, a benefit for astrologers would be to settle the issue of when the retrograde effect comes into play and when it ends.
I have no ideas about how one would go about verifying retrograde Venus and Mars effects but I suspect a more qualitative (hence, more complicated and expensive) methodology would need to be employed, perhaps involving focus groups and questionnaires and the like.
As to the outer planets, my own observations of recent Pluto stations seem to suggest that these are significant and that the signs themselves colour their impact. It would be difficult to get any hard 'evidence' for this but a first step may be literature searches of current affairs at the time of the stations followed by analysis of the results to see what sort of themes predominate. Then again, with Pluto we'd very soon run out of accurate historical data to utilise. (Solar eclipses might also be studied in this way. The research benefit here is that information would only need to be gathered for the geographical regions where the eclipse was visible.)
To illustrate what I'm talking about, the past four Pluto stations in Sagittarius have all coincided with announcements of profoundly important scientific 'discoveries' and/or the actual time of such discoveries. The fact that some of these 'discoveries' have since been disputed in scientific circles is besides the point; it is the profundity of the ideas expressed and their potential to upset and extend the accepted body of knowledge which is important. For example, just last week (Mar 19) an Australian geologist announced her accidental finding that life forms many times smaller than the smallest known bacteria (dubbed "nanobes") appear to survive in a dormant state in rock drilled from deep beneath the bottom of the ocean - it seems the nanobes on the core samples revived and began to grow. This recalls and supports the widely debunked finding, announced by NASA on Aug 7 1997, that a 4.5 billion year old Martian meteorite (discovered in an Antarctic ice field some 13,000 years after it landed on Earth) contained formations resembling fossilised bacteria, only much smaller. The March 1998 Pluto station coincided with the first discovery of other planetary systems (at Mt Kea observatory, Hawaii on March 16 and at La Serona observatory, Chile on March 19, the discovery was announce on April 21 at washington D.C.). The August 1998 Pluto station, if my memory serves me, coincided with the announcement of the first successful "transporter" experiment involving photons of light dematerialising on one side of a lab bench and rematerialisng on the other. Profound Pluto in Sagittarius stuff, eh?
At the beginning of this discussion Mr Tallman posed the question of whether the 'astrological mechanism' is dependent on sentience. I suppose the logical implication of my very broad environmental view is that this matters little, or at least that it would be extemely difficult to show that the existence of the effect is somehow dependent on our recognition of the effect. Badly stated, I know, but this area of the discussion is, I'm afraid, beyond my ken.
Ian Thurnwald Astrology on the Web < http://www.astrologycom.com > PO Box 109 Rundle Mall Adelaide 5000 South Australia
Date: Thu, 15 Apr 1999 21:16:25 +1200
From: Janice & Dennis
As above, so below seems to encapsulate the premise of the astrological belief system. Vehicle for transmission of ancient wisdom, embodying consensual perception, cited by many for millennia; or a statement of faith, a mere superstition?
Let=92s analyse its implications: first, a heaven/earth polarity; secon= d, a pattern common to both; third, a synchronicity of signs above and effect= s below. To the generic observer these implications derive from both consciousness of unity (the world, cosmos, one=92s entire surroundings, pattern of the whole) and also from consciousness of duality (sky/earth, world/me, event/experience, coincidence). So when we experience an event= , the inner/outer simultaneity produces a psychological state structured in the most primal way by both the unitary and the dualistic capacities of o= ur psyche.
Empirical observation of the signs in the heavens corresponding with even= ts on earth proved sufficiently frequent and widespread to generate a paradigmatic consensual belief system in ancient times, of which we have mainly inherited Ptolemy=92s description. Presuming it was not the colle= ctive projection of delusions, and the weight of collective verification means = it is real, how to explain this correspondence? OK, a wee digression now, t= o provide some list context=85
Exegesis v4#19, Andre Donnell wrote =93my own interest in what William ha= s to say is that he appears - astonishing concept! - to be trying to motivate the undoubted talent and wisdom on this list toward a concerted effort to get closer to certain mysteries that we may collectively agree upon. That may mean, novelly, a changing of views for all of us, and a more than merely ration= al outcome: better than the shaking of bones at each other (mostly on other lists) which I have lost patience with.=94 Bill Tallman replied =93Yes, = I am actively soliciting the involvement of the members of this list. I have t= he notion that those who subscribe hereto are genuinely interested in these subjects, and so we have the basis, I think, to assume they have the wisd= om to recognize them as important. Yet, they remain silent! Why is this? Can anyone explain?=94 Yes, I can. That=92s how paradigms work. Ever notic= ed how keen industrial robots are to get a new, improved set of operating instructions? Does your computer leap up and bark joyfully at you when a new generation of Windows is launched? Astrologers are just as indoctrinated by their programming; like scientists, they hug their beli= ef system as if it were a security blanket. After a decade of waiting and minimal progress in the astrological community, I had to write a book to = cut this particular Gordian knot (The Astrologer and the Paradigm Shift, 1992= ). Bill also wrote =93I fancy my contribution as an attempt to establish the parameters of the foundation upon which we can endeavor to construct a workable general field theory of astrology.=94 Likewise me for my book, = and this contribution. End of digression.
Since the signs were perceived to be generated by the Sun, Moon & planets and much human experience results from cause & effect relations, we can understand why the original and most popular explanation was causal. Eve= n today there is residual merit in this view: various cascading mechanisms= of influence from the Sun and Moon and (marginally) planets have been discovered. See =93Cycles of Heaven=94 (GL Playfair & S Hill, 1978), the astronomer Dr Percy Seymour=92s =93Astrology: The Evidence of Science=94= (1988) and =93The Scientific Basis of Astrology=94, not to mention =93Supernatur= e=94, =93Lifetide=94 and various other of biologist Lyall Watson=92s wonderful = books. However physical processes are characterised by built-in time lags, so th= is mechanistic approach is really a red herring.
The key must be found in the moment of synchronicity. Perhaps this is th= e theme of Geoffrey Cornelius in =93The Moment of Astrology=94. Seeing it recommended a couple of times in the website archive, I went looking for = it, but it turns out to be unavailable in this country either commercially or via the national library interloan system, though it=92s only 5 years old= ! Any way I came across a nice piece of his (from which the following quote= is excerpted) at the TMA site (http://www.mountainastrologer.com/cornelius.html), his address to UAC =92= 98.
=93Perhaps Carl Jung can help us. He is probably the most important singl= e, intellectual influence for astrologers in the 20th century. Whatever you make of him, the bottom line is that if anyone has given a conception of astrology that is workable for the modern age - one we can fall back on a= nd use to justify ourselves at parties when we're arguing with hard-nosed rationalists - it is Jung. His discussion of astrology as synchronicity - "an a-causal connecting principle" is the key here. His discussion prefigures the question I have raised with you. Is astrology a divination practice (like Tarot cards or tea leaves), and, therefore, dependent on a= n act of imaginative creation rather than objective facts that are establis= hed in nature (tables and chairs; atoms and molecules)? If so, should it be considered subjective? In other words, are the understandings I get throu= gh astrology actually my own subjective creations?
Jung could have given a very pat explanation of astrology on these lines, i.e., any results occurring in astrology are due to the nonrational breakthrough of archetypes at certain moments - pure synchronicity. Howev= er, as his letter to the French astrologer Andre Barbault makes clear, althou= gh much that occurs in astrology can be classed as synchronicity, it would b= e misleading to approach all of its phenomena in this way. Our categories o= f causality, synchronicity, and symbol are only our mental categories of su= ch things; "nature is not so simple," says Jung. =93The way things actually = are defeats any conclusive attempt to catch Nature in our boxes and categorie= s.=94 [from Jung, Letters V2, 1975] I think you will see why I quote these vie= ws of Jung in support of my suggestion that as a realistic way of proceeding= we should allow a double conception of astrological reality, rather than try= ing to unify the whole thing and find a single perspective or "explanation" t= o cover all its phenomena. However, remember the thrust of my argument, whi= ch is that our practice of judgment from horoscopes, and the results we get when we make those judgments, constitutes divination, and involves a profound dimension of psychic creativity.=94 ( from =93Is Astrology Divi= nation and Does It Matter?=94, G Cornelius, 1998)
He later advocates some extensive reframing=85 =93A much more radical mov= e is needed: to recognize that the very structure of what we do in interpreti= ng horoscopes depends not upon the influence of the heavens upon the seed, n= or upon some objective "time-quality" stamped out by the heavens, not even b= y synchronistic co-occurrence in objective time. It depends on the signific= ant presentation of the symbol to consciousness. The moment doesn't determin= e significance for us - we assign significance to the moment.=94 An excell= ent article, in the fine English tradition of Dennis Elwell, Charles Harvey a= nd John Addey. Probably the most elegant defence of the Rorsach ink-blot approach to astrology that you=92ll ever get. I remain unconvinced by th= e thesis, even while being impressed by his advocacy.
The point at issue here is I think the same one Bill Tallman was getting = at when he asked if the astrological effect happens whether someone is in th= e event or moment to experience it, or not. I know that theory is governed= by aesthetic preference in the formative stages, so I am merely expressing m= ine when I assert that the effect is indeed inherent in any moment in which t= ime manifests on this planet=92s surface. I have a rationale, albeit specula= tive: I believe there exist archetypes of nature that generate and shape natura= l forms and processes. The good news is that these are readily amenable to consensual recognition. Kepler wrote how he used them to recognise planetary harmonics and discover the equations of the planetary orbits, a= nd the Nobel Prize-winning physicists Pauli and Heisenberg both wrote about this in support of their existence.
At this point it would be a good idea for readers who are still with me t= o look up influence in the dictionary. For those without one handy, here=92= s a summary: [(Latin) fluere, to flow] =93the power or virtue supposed to fl= ow from planets upon men and things: a spiritual influx: power of producin= g an effect, esp. unobtrusively=94. Here is evidence of the profound effec= t of the ancient causal doctrine on subsequent civilisation. Also worth notin= g is the spiritual component, the flow/flux factor, but most of all that wo= rd unobtrusively. Occult means hidden. So rather than imagine invisible ra= ys or forces, we can theorise a hidden factor in the moment of coincidence t= hat produces the perception of synchronicity. Something that is multi-facete= d: natural archetypes, manifesting in the flow of time.
Now perception results from interpretation via the brain/mind of signals from the eyes. To some degree we see what we expect (or want) to see, because our expectations are influenced by memory and our interpretations= by our understanding of ourselves and the world. The organic operation of t= he right brain integrates input with prior context so we can know what is happening. This process seems to include input from the personal subconscious and collective unconscious. =93My thesis, then, is as follo= ws: In addition to our immediate consciousness, which is of a thoroughly personal nature and which we believe to be the only empirical psyche (eve= n if we tack on the personal unconscious as an appendix), there exists a second psychic system of a collective, universal and impersonal nature wh= ich is identical in all individuals. This collective unconscious does not develop individually but is inherited. It consists of pre-existent forms= , the archetypes, which can only become conscious secondarily and which giv= e definite form to certain psychic contents.=94 (p60, =93The Portable Jung= =94) Jung=92s diffidence here about the personal unconscious, relegating it to appendage status, leaves me rather bemused.
We now need to consider any generic factors that structure our vision. F= or a start we normally reference things we see to a local horizon, so this forms a generic frame of reference. We see day follow night and other natural time cycles regularly repeating themselves in relation to both th= is and that other collective frame of reference, the zodiac. Our relations with others are constantly energised via interactions with them after the= y approach our vicinity on the plane formed in our mind by the apparently f= lat earth. Half the cosmos is hidden from us by our perception of this plane stretching to the circular horizon: we directly perceive one hemisphere above this plane. The other seems hidden by the Earth, but we learn to imagine it in our mind via a pattern reflection: as above, so below.
So, in our cognition of the moment, we integrate all awareness of our surroundings in context with our intent, expectations, memory, etc. Courtesy of Rudhyar, the horoscope has evolved to become a map, not just = of a moment, but of our generic experience of same. The sphere of the cosmo= s around us collapses into the circle of the zodiac, and the bisecting horizontal plane into a linear axis called the horizon. Anciently, astrologers divined the meaning of the event from the collapsed diagram, = but then they decided they could answer a question from the diagram of the moment it was posed. No longer an event chart, the yet-more abstracted horoscope lost its basis in reality and became fully oracular. So again = the crux: is there a real effect in the moment, which the horoscope maps or models? Or is it merely a divinatory artifice for the interpreter to project personal fantasies onto, in order to maximise the flow of money b= y telling the client what they want to hear? What=92s really going on? Gi= ven that there is no longer any prospect of societal support for planetary causation, can we provide a credible alternative?
We can, actually. Rudhyar=92s comprehensive description of the horoscope= as model of the psyche needs to be refined and integrated with the tradition= al view of the horoscope as map of the event. It should be noted that munda= ne horoscopes have survived from the time of Alexander=92s conquests, so we = must transcend the myopic Jungian focus on our inner selves. The archetypes m= ust be identified in their manifestation in nature to the extent that this proves possible, in order to validate both natal and mundane interpretive traditions. Rudhyar perhaps did not emphasise this enough. Jung, to his credit, did point out the origin of the number archetypes in nature. It = has been the lack of follow-through on this profound insight by all bar one o= f his followers that has retarded the formation of a multi-disciplinary consensus. Even Rudhyar seems not to have fully grasped or utilised the comprehensive explanatory power of the number archetypes.
So what specifically do we need in the way of archetypes from nature, in order to =93save the appearances=94 of astrology? Most obviously, the pl= anetary archetypes, conceived as deriving from the orbits rather than the bodies = of the planets. The number archetypes, with descriptions of their primary effects in shaping the physical universe and human society. Then there a= re sphere and circle, line and plane, spiral and helix. It can readily be s= een that the numbers 3 and 4 structure space/time, there being 3 spatial dimensions and a time dimension. 4 cardinal directions, or 6 if you incl= ude up and down. 4 elements, or states of matter if you are a scientist. 3 gives us reproduction, the genesis of family and social relations of the child. Sex is 2, of course. The trinity also arises from duality in tim= e, when the past/future polarity is conceived in relation to now: past/present/future. It also arises in debate, when thesis and antithesi= s produce synthesis.
One cosmos, one Sun, one Earth, one head. 2 eyes, 2 ears, 2 brain hemispheres, 2 thumbs. The real bonus is when we realise the number archetypes 1 & 2 are all we really need to explain the synchronicity evok= ed by the saying `as above, so below=92, but this returns me full circle to = my first paragraph like the worm Ourobouros, so a good time to close=85
Regards to all,
Date: Fri, 09 Apr 1999 04:00:28 +1200
From: Andre Donnell
Subject: Re: Statistical truth, Castle Besiegement
On second thoughts, I decided to consider the castle besiegement research (CBR) now. My treatment is hurried, but I think generally correct. Unless there are exceptional objections, I do not intend to address this matter again unless definite progress beyond merely talking about CBR occurs.
Also, an advance apology. I had finished an earlier version of this post and was about to 'send' it when "the penny dropped" and I realised that Lehman had made a blunder!
Rather than re-write the two sections 'Use of the binomial distribution' and 'What about the significance levels', I have just inserted new commentary here and there. This may produce uneven transitions; and in the second section it is some time before I point out the error. It would have been clearer if I'd re-written the section - but I'd already expended close to six hours on this, which was five hours more than I could afford...
The statistical treatment ================= Unfortunately Lehman has erred in her statistical analysis. The blunder is unfortunate, but not necessarily fatal. I explain this below, in relation to the Ashes data.
Use of the binomial distribution ======================= Although the analogy of throwing a pair of double-sixes four out of six times was used, a better one is trying to correctly guess a series of coin flips. As Lehman and Brady state "we analysed the results using the Binomial Distribution, with an estimated probability of getting a correct answer being 50%" (Statistical Analysis section, p.17). This is just like a coin flip.
Lehman's approach appears to be that the outcome can only be right or wrong, and that this is therefore a 50/50 proposition. Although I accept this proposition in the rest of this analysis, I suspect it is only true retrospectively. Lehman divides the Ashes data into six categories: Aust draws; Eng draws; Aust (holder) wins; Eng (holder) wins; Aust (challenger) wins; Eng (challenger) wins. Thus, knowing that a particular game was a draw, the question is "does the CBR model also predict a draw?" - which one *might* treat as a 50/50 (head or tail) proposition. However, in predicting any *future* outcomes, the model (as Lehman and Brady point out themselves, near the beginning) has to accomodate three outcomes. In this case, the binomial expansions should perhaps be entered with a probability of 33%, rather than 50%. But Lehman does point out that the (Ashes) model is a two step process, so that (presumably) there is a 50/50 choice at each step.
Let's provisionally accept the Binomial (coin flipping) approach. Runs of correct guesses don't matter: only how many were predicted rightly out of a given number of games. Thus, one might have several wrong predictions in a row, and do badly in short runs in particular, but still come out doing well over all. In such a case, one has a model that does better than chance, and which a gambler (for example) would be very interested in using.
Binomial distributions (individual terms) have unusual properties however: see next.
What about the significance levels? ========================= The longer the series of games, the less likely and hence the more "significant" a given proportion of correct guesses. For example, to make two correct calls from four coin tosses by chance the probability (p) is .375 (37.5%); to get 10 from 20 by chance, p drops to .176 or about 18%.
However, in a sense getting 10 out of 20 by chance is the most likely outcome. Getting 11 right ("predicting" - i.e. betting - more successfully) the likelihood is only 16%, and to do still better and get 12 out of 20 it drops to 12%.
BUT, the same applies to DOING WORSE:
p(9/20)=p(11/20)=16% (only 9 right same as 11 right)
p(8/20)=p(12/20)=12%. (only 8 right same as 12 right)
In a 50/50 game such as this, once the number of games reach 100 the highest p obtainable is .08 or 8%. This is the limit of my calculator, but I would guess that p < =.05 would occur at about 130-150 games. In other words, WHATEVER number of correct calls one makes, one will "meet" the p < .05 significance test!
There is a comparable situation in psychology: the larger the sample, the easier it is to get "significant" results from tiny effects. In simple correlations between one "cause" factor and one "effect" factor, a sample size of 200 produces a significant (p < =.05) result from a correlation of only r=.1366. Such a value is very low: it means that the "cause" factor explains less than 2% (r-squared) of the variation in the results. This is very difficult to detect, or for any psychologist to consider useful in practice, even though the result is "significant". (The result *may* still be theoretically meaningful however!).
Note also that the adoption of .05 many decades ago by R. A. Fisher is entirely arbitrary (as he acknowledged himself). In common psychological practice, results of p >.05 are deemed failure (the null hypothesis is retained), results of p < =.05 are "true". This is an absurdity based on pushing crisp (true/false) logic into the arena of chance, and it is one of which researchers are increasingly conscious.
To continue: if one does BETTER, or WORSE, than calling half the number of games right, one "beats" the p < .05 test sooner. One can see this in the 27 correct English draws called for 40 games, where using the binomial formula yields .010944152 on my calculator, which of course is exactly as Lehman reported (with fewer digits).
(Note: you can look up 'binomial distribution: individual terms' in any stat's book to see the formula I have used).
Thus, Lehman's comparison of her findings with the p < .05 significance test is specious; and I wish the point had been avoided.
NEW INSERT - THE BLUNDER ======================== HOWEVER, all the discussion above applies to the "binomial distribution: individual terms" (BIT). I know this because I was able to reproduce the probabilities presented by her from the 'individual terms' formula. You may also verify this by looking up BIT tables: for example my old school reference "Eton's Four-Figure Mathematical and Statistical Tables" lists .273 for correctly guessing 4 win/loss games from 8 played (lookup n=8, x=4, pr=.50).
Unfortunately, individual terms apply to getting EXACTLY a certain number of guesses right. This is what Lehman has presented, but it is surely not what she actually meant. It is like a gambler saying "I will predict EXACTLY 4 (or 10, or 16, etc) games out of 20". In that case, the BIT tells how likely this is. The MOST likely is that one would get half of them right (the 17.6% probability I quoted above), rather than 9 right or 11 right (16%).
What Lehman surely wants to claim is that the CBR can perform at the level shown consistently. That is, as a gambler she would like to say "my model will always do at *least* this well", i.e. BETTER THAN all the other models which get 1/20, 2/20, 3/20 etc. To do this, you need to SUM the individual terms better than and including the result obtained. What Lehman needed to do was use the CUMULATIVE BINOMIAL DISTRIBUTION (BIC). To give an example, the correct probability for getting at least 4 out of 8 is .637, not .2734 (quoted in the Super Bowl analysis).
Nevertheless, some of Lehman's statistics remain "impressive" - the 18/22 Super Bowl result (which incidentally was quoted as .1762 and is wrong even for the BIT) is probably around .005. The other individual breakouts with good figures will degrade under the BIC, but should still be good., in particular the 38/45 and 28/36. The 27/40 may not stand up so well.
However, it would be better to apply the BIC to the overall Ashes result of 67.5%, which on the face of it does sound impressive. Without a computer or calculator program (simple to write, but I don't have the time), this can be a lengthy process, and so I have not attempted to correct Lehman's breakout figures or compute the overall probability. I invite someone else on the list to do so.
All is not lost ========== Although I say the "These distributions...are impressive" claim is founded on faulty reasoning (the wrong application of the Binomial distribution), Brady and Lehman have nevertheless come out - overall - on the right side of the ledger. There is a general trend for the CBR model to predict better, not worse, than 50%. In fact, they achieved 67.5% for the Ashes and better for the Super Bowl, which on the surface sounds like pretty good utility. It is THIS figure which is ultimately important, rather than specious comparisons with the p < .05 decision rule.
Problems with the development of the model ================================ In general I was pleased that most of the model was a fairly direct application of Bonatti's procedure.
However, the following points disturbed me:
(1) As they pointed out, VALUES had to be determined for each rule. These had to be derived empirically. Unfortunately, they do not make clear what data was used to derive these values. If the *entire* Ashes sample was used, then OF COURSE the model will produce good results WITH THAT SAMPLE. This is called the development sample in psychometrics, and it cannot be used to validate itself.
If only PART of the Ashes data was used as the DS, this is not a problem - but otherwise this is a serious weakness for the 67% claim until support is obtained from independent test samples.
(2) A non-astrological term ("Home country advantage") was introduced. I would rather this had not been done, as it makes the model at least partially non-astrological (there were no astrological reasons to do this), and it means the RESULTS are not pure demonstrations of astrology. The model has been biased to get it right, perhaps gaining 2% or so.
Conclusions ========= I consider the development sample issue as crucial; the use of the BIT rather than the BIC was a blunder; and the subsequent comparison with p < .05 was flawed in consequence, and probably unnecessary anyway given the arbitrary nature of the .05 level.
However, if the model *as presented* (without adjusting the present values) stands up to testing on other samples and reliably achieves maybe 55-60%, I believe something promising will have been demonstrated.
Incidentally, it is quite likely that a dedicated follower of the particular sport could predict as well or better. It is not necessary that the CBR achieve this: only that the CBR on PURELY ASTROLOGICAL GROUNDS demonstrate a consistently better than chance (if you like, better than a totally unknowledgeable sports bettor) ability to get it right.
Truth and Probability =============== In closing, I make the general observation that despite the capricious nature of depending on probability to formulate conclusions, it *is* nevertheless part of real life (everytime we take a chance or decide "that's probably (not) going to happen to me today"). In the scientific view, truth is always tentative. I believe it is John Wheeler (the physicist) who has speculated that there may BE no general laws governing the universe: that all our present laws are merely the accidental values pertaining to our present span of observation.
Nevertheless, in general research practice, if one develops a technique which "beats chance" on a number of occasions, there are two possibilities. It may have been a spurious finding, quickly refuted by further testing. (It is possible, actually, that chance has capriciously acted to make a valid technique look random, but that's another story). However, if the technique or finding continues to hold up, one is has either (A) found something "valid", or (B) is the beneficiary of a very long run of good luck.
To this point, there is no way to tell A and B apart. However, the usual procedure at this point is to look at the THEORETICAL implications of the finding. Here, theory should be understood as increasing our comprehension of possible links between different parts of our experience. If, using this procedure, (non-trivial., i.e. "unlikely") things are able to be said about those other parts of our experience - AND THEY TURN OUT TO BE SO - the finding is then considered to have both GAINED validity from, and CONTRIBUTED validity to, those other things. It is ultimately possible of course that all these things are just having lucky runs TOGETHER - but so long as they continue to serve reliably in our experience, that is neither here nor there.
In general, we consider we have found something "valid", and so I say again that theory-building, as well as technique-validation, is a matter that crucially demands our attention.
End of Exegesis Digest Volume 4 Issue 29
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