The Eureka Effect

by Nicholas Kollerstrom

Abstract

Are there optimal times when inspiration strikes? Does the cosmos help scientists to gain their Eureka breakthroughs? It is here argued that a collection of such famous dates can be used to test and in fact validate the working of celestial aspects. In particular a hypothesis originally formulated by John Addey concerning the odd-number harmonics 5 and 7 was of central importance. A second part concerns dates when great inventions first began to work, which is a more material and practical thing, and here different harmonics were found to be relevant. An excess of septile aspects has been found to replicate though several different groups.

Introduction

Astrology concerns the moment of birth, and if it is to be applied to or tested on mundane events then one should examine moments of first-beginning or genesis-moments, when something new appears in the world. The progress of modern science offers the ideal opportunity to do this, because it is through the new ideas created by scientists that our modern world has come into being. Only in the history of science do we find absolutely new things coming into existence. The 'Eureka' experience has been well described in Arthur Koestler's book The Act of Creation:

The eureka act proper, the moment of truth experienced by the creative individual, is paralleled on the collective plane by the emergence, out of the scattered fragments, of a new synthesis

It is that 'new synthesis' which here concerns us. Koestler added, "I shall occasionally refer to discovery in its psychological aspect as the Eureka process or Eureka act" (in his chapter 'The Moment of Discovery.')1

That moment was, Koestler explained, an experience of 'bisociation' when two previously unconnected frameworks or 'matrices of logic' came together. I as a science historian decided to look at these moments, to see whether there was any particular celestial signature which they carried. I had been impressed by John Addey's book Harmonics in Astrology, and this gave an indication as to what one might try looking at:

...yet the charts of creative people often seem devoid of anything really noteworthy unless the fifth and seventh series of aspects are considered.2

I collaborated with Mike O'Neill in this project, whereby I would find the moments and he would score the quintile and septile aspects in them. Although the Addey quote had alluded to natal charts, we were here applying it to event charts.

One does not need to understand what it was that dawned upon the scientist, or only in a very general way, to collect these eureka-moments. We are here concerned with the inner experience of the scientist at these great moments, because they tend to get access to what Koestler in his Act of Creation called the 'self-transcending emotions' and these have a key importance for locating the eureka experience in historical time. English-language biographies exist for most of our E-scientists, and they often have a central chapter about the breakthrough experience. As Koestler has described, there will often be a great deal of stress and even despair sometimes which builds up in the individual before that moment arrives.

I believe our first indication that septiles might be important came from analysing a moment when Kepler described a great revelation he had in Graz while lecturing on maths to a nearly empty classroom on 19 July 1595. "It will never be possible for me to describe in words the enjoyment which I have drawn from his discovery..." Kepler wrote. That sense of exultation is a key feature of eureka-moments. We consulted people about the chart for this moment but there seemed nothing special about it, until Mike O'Neill noticed three septile aspects in the sky. Were these the key?

Another 'creative' moment I was then looking at, happened when a sample of plutonium was first created at the Berkeley cyclotron in California by Glenn Seaborg. This dated and timed event had a strong quintile presence. It was not to be sure a Eureka moment but yet suggested that quintile aspects might be important for mentally-creative events.

A first presentation of results was given at the 1987 Astrology Research conference in London3 featuring a list of 18 Eureka moments, showing a significant excess of quintile and septile aspects. We used the orbs suggested by John Addey: he recommended dividing twelve degrees by the 'harmonic number,' thus for quintile aspects one divides by five, to give 2°24' and for septile aspects one has 1°43.' The chance-expected frequencies we estimated as 2.2 and 2.4 per chart respectively, for these orbs, aspects between planets and excluding the lunar nodes.

The same procedure was then repeated for the natal charts of Eureka scientists. These had to have Rodden grade 'A' birth data, and to have been alluded to in Isaac Asimov's Biographical Encyclopaedia of Science and Technology (1975); those were our criteria for inclusion. But also one does really need a biography written about such scientists to ascertain whether or not they had anything resembling a Eureka-moment - these events are subject to considerable mythologising. Thereby we generated a group of eminent scientists of known birth-data, which could be divided into two groups, namely those who had experienced a eureka moment for their theory, and those who had arrived at their views by a more gradual process.

Having done this, we were startled to note that a fairly similar excess of quintile and septile aspects turned up in the natal group, as had been seen in the Eureka moment. The non- eureka group of eminent scientists of known birth-data had a deficit of these two aspects. Members of the non-Eureka group were in no way less eminent than those of the eureka group.

Many of the E-moments are untimed, which does generate the problem with the small orbs here used that their lunar positions are blurred, and some of the lunar aspects scored are doubtful.

Publication

In 1996 Mike O'Neil and I co-authored The Eureka Effect, citing a list of 21 E-moments, ranging from 1672 when Tycho Brahe first spotted a new star in the sky (a supernova) to 1953 when Crick and Watson discovered the structure of the DNA helix one Saturday morning. Experts such as Theodore Landscheidt checked through our list and generally felt that all our moments were valid, although doubt was expressed over one of the moments, when Pluto was discovered in 1930 by Clyde Tombaugh. This was, one person advised us, a moment of 'no special intellectual insight.' Our procedure was, that once we had decided to accept a moment and score it we were then unwilling to change anything, i.e. we didn't 'allow' ourself to subtract moments. At last I felt that my degree in history and philosophy of science had been of some use.

After the 1618 moment of illumination when Kepler discovered his 3rd law of planetary motion, he exclaimed: "Nothing holds me back, I give myself up to sacred frenzy." In contrast with that classic Eureka-moment, his earlier 1595 moment in Graz to which we have alluded was (rightly or wrongly) not included. Because, what then came to him concerned a funny geometrical arrangement to account for the distances between the heavenly spheres, that no-one after him ever took seriously: i.e., there is a general agreement that what came to him there was not 'science', whereas the later discovery of his 3rd law was. Thus we appeal to a consensus. I may not believe in Darwin's theory of evolution by natural selection; however there was a eureka experience when that insight, true or not, came to him (as described by his biographer Howard Gruber) and so it is included. There is agreement, amongst science historians, that that insight is part of 'science.'

I suggest that any qualified science historian asked to produce a list of dateable Eureka moments, eminent enough to have been written up, would necessarily come up with much the same list as has here been presented: accepting a Koestler-definition of the moments, which I think excludes technological innovations. For example, the book Eureka by Edward de Bono4 is just a history of technological innovation, such events being a lot easier to find - but they are not what we are here looking at.

Here is the list as earlier published but with two extra E-moments added: Edison getting his idea for the electric light and Hubble getting his theory of galaxies. No doubt this list is not final, and more will be found.

There was overall a fifty percent excess of the septile aspects, in this group of 23 Eureka-moments, as compared to our best-estimate control group. A somewhat smaller twenty percent of quintiles appeared, in both cases using the 'Addey orbs'. Adding together the excess of quintile and septile aspects gave a chi-squared value of 14.5, and that is significant at 0.00014 or 1 in 7000.

Two New Moments

Two new E-moments included, not included in the 1996 book The Eureka Effect, may here be outlined. The first, concerning Edison's electric light, was described in a book published in 1989:

Eureka moments and instantaneous insights are part of the lore of invention and discovery ... On 8 September 1878, Edison experienced a eureka moment when he discussed with the inventor and industrialist William Wallace the flawed incandescent lamp system of Wallace's collaborator ... After reflection, Edison found these and related insights of his own so promising that he telegraphed an associate, "Have struck a bonanza in electric light.."5

This E-moment is to be contrasted with what we will call invention-moments, when inventions were first made to work: Edison's electric light first reliably glowed a year later on 23 October, 1879. It's rare to have both an E- and I- moment in the life of one individual; Michael Faraday is the only other such case, at any rate for 'found' i.e. datable moment.

The second new eureka-moment, concerning galactic structure, perhaps struck Edwin Hubble as he was walking down Mount Palomar in dawn's early light. He had spent a night up alone in the big new telescope, whose huge reflecting mirror had taken five years to grind. While looking at the Andromeda nebula, he finally understood that it was a galaxy in its own right. An article about this moment, about the night, was entitled The Night the Universe Changed Forever6 and fortunately it gave both the time and date of this E- moment:

Hubble was forced to conclude that the Andromeda nebula was ...at least 300,000 parsecs from earth - the equivalent of a million light years, or more than triple the diameter of Shapley's entire universe [Hubble's mentor, Howard Shapley, had proposed that everything known was contained within the Milky Way]. It was a "eureka" moment. Andromeda's spiral arm was bejewelled by a Cepheid variable. The giant nebula was a sister to the Milky Way, composed of stars by the millions! Hubble crossed out the letter "N" for nova he had previously inscribed on the plate and printed "VAR!" for variable directly beneath it. And though the plate had been taken the previous night, he dated it "6-Oct 1923" to commemorate the moment when his mental tumblers had fallen into place.8

Both of these E-moment descriptions were published after our initial publication and have here been added on.

YearDateTimeScientist Eureka MomentQ,S

1572Nov 21 OS18hTycho BraheHven, DenmarkSupernova3,2

1610Jan 717hGalileo GalileiPaduaDiscovery of Jupiter's moons4,2

1618May 1513hJohannes KeplerPrague3rd Law1,47

1807Oct 614hHumphrey DavyLondonPotassium1,4

1831Aug 2914hMichael FaradayLondonElectromagnetism3,4

1838Sept 2814hCharles DarwinLondonNatural Selection4,5

1846Sept 2323.20Johann GalleBerlinDiscovery of Neptune3,5

1869Mar 114hDimitri MendeleevSt PetersburgPeriodic table0,5

1878Sept 814hThomas EdisonNew JerseyElectric light4,3

1895Mar 2310hWilliam RamsayUCL LondonHelium7,2

1895Nov 818hWilliam RöentgenMunichX-rays2,5

1896Mar 114hHenri BecquerelParisRadioactivity1,2

1915Nov 1813hAlbert EinsteinBaselTheory of Relativity4,3

1921Mar2802hOtto LoewiGraz, AustriaNerve transmission2,3

1923Oct 607hEdwin HubbleMt Wilson, CAGalaxies3,3

1925June 813hWerner HeisenbergGottingenQuantum mechanics4,2

1928Sept 319h50Alexander FlemingLondonPenicillin4,6

1930Feb 1823hClyde TombaughFlagstaff, AZDiscovery of Pluto3,1

1933Sept 1213hLeo SzilardLondonChain reaction3,4

1934Oct 2212hEnrico FermiRomeSlow neutrons0,1

1938Dec 2409hLise MeitnerGoteborg, SwedenAtomic fission1,4

1951April 2612h30Charles TownesWashington DCLaser beams3,7

1953Feb 2810hJames WatsonCambridgeDNA helix1,4

Total quintiles and septiles:Q: 61, S: 84

Chance-expected totals:Q: 50.4, S: 55.4

Percent Excess:Q: 21%, S: 52%

These 23 Eureka-moments can also be of interest as anniversary dates, to stimulate creativity, and as such I had them published in the now-defunct British journal Inventor's World.9

A book published in 2001, The Eureka Effect by D Perkins, had quite a few of the E- moments here designated, plus lot of other such E-moments that are undateable and so not here included. In common with our list, is that the last E-moment given was that of the discovery of the DNA helix structure by James Watson in 1953. This suggests that the absence of any more E-moments in the six decades since then may not be merely some oversight by the present author. Maybe science is more institutionalised today, moved more by big business, and the lone scientist's proverbial eureka cry may now be history?

Having said that, a eureka-cry did appear in newspaper headlines around the world on 24 June, 1993. On the previous morning, Andrew Wiles at Cambridge had solved 'Fermat's Last Theorem', which had remained unsolved for 363 years.10 Our Eureka study had adopted the limitation of not including purely mathematical E-moments, as I did not feel competent to hunt for them. That moment had a Q+S score of {3,3}. That's the most recent claim for an E-moment of which I'm aware.

All of the dated E-moments here listed are by scientists sufficiently eminent, in that they have been described in a biography. It is normal for a scientific biography to have a chapter about the moment of breakthrough and insight and when it happened. One needs to be on guard against a tendency to mythologise the eureka experience, eg the story of Isaac Newton and the falling apple, but such mythic E-moments can never have a date.

Summarising, the above list was created and scored for celestial aspects using three basic references, which in retrospect appear as having been quite sound. Arthur Koestler's book The Act of Creation described the idea of a Eureka-experience, greatly helping us in looking for them; in addition it gave quite a lot of very helpful examples with some dates; the Isaac Asimov reference also gave helpful dates and reliably pointed out biographies which had E- moments, having sections on a thousand or so scientists and inventors; and John Addey's Harmonics in Astrology described the theory of harmonics here used, suggested orbs to use, and recommended the quintile and septile aspects.

The Natal Group

After we published in 1996 the list of eureka and 'non-eureka' scientists, I was a decade or so later able to rummage through my (UCL) college library for non-eureka biographies. This had not been a primary focus initially, and I was able to locate quite a few more of these, increasing the size of that group from 12 to 20. This group will grow continually as astrologers gradually improve their data-archives, and as more biographies of scientists are published. Here is the presently-final group of eminent scientists11 of reliably-known birth time, making a simple binary division into Eureka and non-eureka biographies:

Table 2: Eureka and Non-Eureka eminent Scientists of known birthtime with quintile and septile scores {Q,S}

Eureka Types Non-Eureka Types

Tycho Brahe3.7Nicolas Copernicus1,1

Galileo Galili2,4Andreus Vesalius1,1

Johannes Kepler5,3Robert Hooke2,1

Humphrey Davy2,6John Flamsteed2,1

Louis Pasteur4,0Edmond Halley0,2

Wilheim Röentgen1,3Antoine Lavoisier4,2

Thomas Edison0,6Johann Bode1,1

Alexandre-Edmond Becquerel3,2David Brewster4,4

Nicola Tesla2,3Urbain Le Verrier1,1

Albert Einstein4,3Thomas Huxley3,0

Werner Heisenberg0,2William Crookes3,2

Alexander Fleming5,2Marie Curie1,1

Louis de Broglie4,3Otto Hahn2,2

Enrico Fermi2,3Pierre Joliot-Curie1,0

Charles Townes2,3Linus Pauling1,0

James Watson4,6Emilio Segrè1,0

Hans Bethe1,3

Glenn Seaborg2,3

Paul Ehrlich3,0

Carl Sagan1,3

Total Quintiles, Septiles:43.56Total Quintiles, Septiles:38.29

Expected (n = 16):335.0,38.2Expected (n = 20):43.8,47.8

Excess23%, 46%Excess-13%, -39%

Also, Alexander Bell {3, 2} and G. Marconi {2, 1}.

Once again we see a large excess of quintiles and septiles, this time in the natal group of Eureka-scientists; but very surprisingly, an equal and opposite deficit of these aspects in the non-Eureka group.

The increase in size of the non-E natal group had not in any way decreased its huge septile deficit, which remained at around forty percent. We are astonished to see the group of Eureka-scientists here scoring 240% more septiles than the non-eureka group. That is the largest effect discovered in this investigation. No-one predicted it so we are not at liberty to assign a probability-value.

There were two cases where we were not confidently able to place them in one or the other category, Graham Alexander Bell and Guglielmo Marconi. They both had eureka-ish experiences, of apparatus working. It took a couple years before we developed the follow-on concept of invention-moments, when great inventions first worked, and it became evident that these two were more properly described in a quite different category, as inventors.

So the basic effect, of an excess of quintile and septile aspects, more strongly a septile excess, has replicated though the two groups event and natal, and is in deficit in the non-Eureka natal group.

Comparing the 16 natal Eureka scientists here given in Table 2 with the 14 we published back in 1995, it is evident that the two new cases added both have low scores, namely Werner Heisenberg and Wilheim Röentgen: their Q+S scores were {0,2} and {1,3}. Could this have been some selective prejudice whereby we had earlier omitted these cases? Both E-moments appeared in our originally-published Eureka list. Whatever the reason, I'll take the blame. Their birth-data appear as reliable.

Wilheim Röentgen had a dire E-moment around midnight of 8th November1895 (with seven septiles in the sky) when he saw own hand as a skeleton:

The apparition was so awful that Wilheim Röentgen wondered if he had taken leave of his senses. He could hardly have been more surprised if he had looked into a mirror and no reflection had stared back. He let go of the metal that he had been holding and jumped, startled, by the noise, as it hit the floor.

It was approaching midnight on 8 November, 1895. Earlier that day, as the November dusk darkened the laboratory, he had noticed that whenever he made sparks in the tube, a fluorescent screen at the other end of the laboratory table glowed slightly. This was the signal that he had been looking for, the sign that invisible rays were being produced in the spark tube, crossing the room, and striking the screen, producing the faint glimmer...

After a late meal Röentgen returned to the laboratory. He moved the piece of lead near to the screen, watching its shadow sharpen, and it was then that he dropped it in surprise: he had seen the black shape of the metal held by the hand of a dead man. Pulling himself together he slowly opened his clenched fist and looked astonished once again at the dark skeletal pattern of the bones as his hand moved across the face of the screen. Still doubting what he saw he took out some photographic film for a permanent record. Röentgenhad made one of the most monumental discoveries in the history of science - X-rays... If any single moment marks the start of modern physics and science it is that Friday evening of 8 November in 1895.12

Heisenberg's E-moment was more serene, as he finally came to understand the 'magic matrices' of quantum mechanics:

"I was shocked to the core", recalled Werner Heisenberg, of the time when the principle of quantum mechanics dawned upon him, on 8th June 1925. "I had the feeling that I was seeing through the surfaces of atomic phenomena to their deep underlying basis, which had a remarkable inner beauty. So excited was I that I could not think of sleeping, but remained awake all night and watched the sunrise."13

This happened after he had retired under great mental stress to the tiny island of Heligoland in the North Sea.

Overtones

Figure 1: the family of heptagons

The 23 E-moment charts display overtones of the 7th harmonic, i.e. the 14, 21st etc. harmonics. Thus the 21st harmonic scores a fifty percent excess, just as large as the basic 7th harmonic. Such a claim does involve rather small-orb planetary aspects over centuries gone by. Re-computing these using the modern Jigsaw program (Astrolabe) suggests that modern programs are accurate enough to achieve this, but one would appreciate further corroboration. Such overtones validate the theory of harmonics as described by John Addey, in which they occur somewhat as in a musical note; as well as tending to establish the reality of the 'Eureka effect'. For comparison, regular heptagons and star-heptagons contain different members of this 'family' of aspects. The vertices of the star-heptagon are a 1/14th division of the circle, the basic angle of the 14th harmonic.

Chance-Expected Aspect Frequencies

Expected septile frequency is calculated as follows. The ten planets yield 45 planet-pairs three of which (Venus/Sun, Mercury/Sun and Venus/Mercury) are only ever able to form two septiles between them, because their angular separation remains too small. Only 42 of these pairs form all of the septiles, i.e. the six angular positions which score as a septile (mono, bi- and tri-) excluding the zero position of conjunction. Taking the 'Addey orb' of 12/7°, the likelihood of any one septile chiming is 2x12/(7x360): the factor of two here allows for both approaching and separating aspects. Therefore, the expected number of septiles for a moment in time at that orb is given by 24/(7x360) (42x6+2) = 2.42.

For empirically-generated septile expected frequencies: the eureka moments span 1572-1953, however the great flow of these moments has mainly extended over a century and a half, over the 19th and first half of the 20th century. Here are some randomly-generated expected frequencies using the Jigsaw program (sampling five or ten thousand):

Over 1572-1953, mean 2.40; 1800-1953, mean 2.43; 1820-1930, mean 2.39.

These suggest a close agreement between the theoretically-computed estimated value and those randomly generated by the Jigsaw program, with an uncertainty of less than 1%. Mike O'Neill and I took the value of 2.41 as the best expected frequency (and 2.19 for quintiles). Maybe in retrospect we should have noticed that the natal E-group, spanning a slightly earlier period from 1546-1928, gave on random sampling a slightly lower expected value of 2.39 septiles per chart.14

Concerning quintiles in the natal E-group, let's take two samples: 1546-1800 (n=5), 2.22; 1800-1928 (n=12) 2.19, which gives us more or less the same value: one could possibly prefer 2.20 rather than 2.19 per chart. There is no 'exact' right answer here.

I: When Inventions Worked

To collect these moments when inventions first worked, the main textbooks used were the Readers Digest Inventions That Changed the World and the Biographical Dictionary of Scientists/Engineers and Inventors.

This list of 36 I-moments is almost the same as published in Correlation two decades ago,15 except that the 'Heliospectroscope' which various persons inspecting the list were doubtful about has been removed, and replaced by 'gene therapy'. The latter was first performed at Bethesda hospital in Washington DC on 14 September 1990:

A new era in medicine dawned at Bethesda hospital in Washington D.C. when a four-year old girl was treated by a transfer of genetic material. She was severely immune-deficient from a rare hereditary disease, due to a missing gene, leaving her a helpless prey to diseases. The new invention was a virus cleverly stripped of its harmful capability and having a copy of the missing gene. This gene had earlier been cloned and so it was quite well-known. The virus was capable of entering a human cell and donating this gene to the human DNA. The idea had to pass stringent medical, legal and ethical review boards, because of its far-reaching implications. When permission had been granted, the paediatrician Ken Culver muttered, "Well, here goes" and performed the injection, at 12.52 p.m., September 14th (16.52 GMT). It lasted half an hour. Over the following months the girl's immune system slowly recovered, and she is now living a normal life.16

Often, inventions have no specific date when they first worked. Thus, the invention of the world-wide web by Sir Tim Berners-Lee at CERN laboratories, Geneva over the days before Christmas 1990 had no date; it was a gradual sequence. I corresponded with him, and he firmly explained, "They are frustrated when I tell them, there was no Eureka moment."17

As with the E-moments, these dates can surely be of value to any industrial firms wishing to stimulate an air of inventiveness by using these anniversaries. There is a great excess of British eureka and invention-moments, while the Table also shows that somewhere in the mid-19th century the genius of invention passed over to America.

Computing of expected frequencies is nowadays easy using a research program such as Jigsaw: one generates say ten thousand charts over the interval of Eureka dates and thereby derives the average score of an aspect for any given orb. Such mean values are stable and easily-obtainable for higher-frequency harmonics, e.g. septiles, owing to the small orbs involved; whereas for trines they are liable to vary more with the interval selected, because a single trine aspect between two outer planets may remain in place for decades. Thus any claim made for a trine excess in I-moments has to involve careful modelling of the time- distribution of the moments.

Figure 2: the excess of conjunction, opposition and trine aspects, to each of the planets, in the group of 36 Invention-moments, at 5 degree orb.

Aspects in the I-moment group

There was a huge excess of trine aspects in the I-moment group and also a huge 60% excess of major Uranus aspects (conjunctions, oppositions and trines to 5° orb) in that data, 60 as compared to 36.7 expected. Comparing the different planetary frequencies (see figure), Uranus at the top of the list and Saturn at the bottom well expresses their traditionally understood differences at these moments of revolutionary innovation.

The trine excess in the group of invention-moments was a total surprise. Over the span of two centuries 1800-2000 when the inventions mainly occurred, the trine expected frequency hovered around 1.72 per chart, from which the net excess of trines appeared at 48%. In contrast a deficit of quintiles appeared. The septile excess was smaller than found for the Eureka moments, significant at only quite a low level (1 in 20). Maybe the deficit of quintiles indicates the traditional meaning of this aspect as pertaining to creative, mental activity - surely absent at these grand moments of achievement, which are times of perspiration rather than inspiration.

Figure 3: This shows the same aspects as before, conjunction, opposition and trine, within the same group, but only to Uranus, and scoring per 2degrees of orb.19 There is an excess of 100% within the first two degrees of orb.

Harmonic Theory

The Invention-moments showed a large excess of 14th-harmonic aspects, stronger than the 7th, around +34%, which is curious. The higher harmonic 14th includes all of the 7th harmonic positions, but at half the orb, so overtones of the primary harmonic are bound to show some excess, as they re-sample the same angular positions.

An excess of septiles has thus replicated through several sets of data, in a way that may tend to confirm the 'inspirational' character of this aspect. To quote US astrologer Delphine Jay, 'I like to refer to the septiles as the consciousness-expanding aspect.'20

No differential has ever appeared in these results, between quintiles and biquintiles, nor between mono- bi-, and tri- septiles, which again tents to validate the Pythagorean- numerical approach of Addey, whereby it is the number of the harmonic, eg the number seven, which here 'means' something, rather than the angle as such. Philosophers may wish to discuss for example why the number five should be in deficit at moments when inventions were made to work (-19%), whereas they appear in excess at more mentally- creative moments.

For moments of action, excitement and success, the massive excess of trines, nearly fifty percent (see Table) in the group of Invention-moments seems in accord with traditional views about this aspect. For example, the authors of Mundane Astrology state:

The number three is related to the idea of life, vitality and enjoyment, and hence to what motivates us and moves us to action.

Table 4 - The Excess of Aspects: Trines, Quintiles and Septiles

GroupTrinesQuintilesSeptiles14th H.

E-moments (n=23) 61/50.4 = 21%84/55.4 = 52%
Χ2 = 1486/62.3 = 38%
Χ2 = 9

E-scientists (n=16) 43/35.0 = 23%56/38.6 = 45%

Non-E scientist (n=20) 38/43.8 = -13%29/48.2 = -40%

I-moments (n=36)92/62 = 48%64/79 = -19%107/88 = 22%130/96 = 34%

But there is also the point made by harmonic theorist David Cochrane, that: "The higher harmonics describe more internal, less conspicuously evident traits in the outer world. Lower harmonics describe more externalised traits."21 If perchance that is valid, it would be appropriate to find trines present at these energetic moments, while septiles are stronger at the more inner moments of illumination or inspiration.

Analysis of these Eureka groups has established the basic idea of the working of celestial aspects, where the orbs used from Addey's suggestion were not far off optimal. We should after all expect that these seed- or genesis- moments which have affected the course of history, should express the world-harmony.

Testability of Theory

The discoveries here made suggest predictions, in terms of aspect-totals found within groups e.g. of musical or mathematical eureka-moments, or the corresponding natal groups. I assembled a group of 17 moments of mystical illumination,22 some having time-of-day information, and found that collectively they had an excess of quintile and septile aspects that was somewhat comparable. Surprisingly there was a larger excess of quintiles. These mystic moments displayed a deficit of the even-numbered 4th, 6th and 8th harmonic aspects between planets, which are as it were to do with firm structure, evidently not required at such moments. Again John Addey's way of viewing aspect-harmonics appears as validated by this approach.

In terms of the refutability of the conclusions here presented, it would merely be necessary for someone to gather a group of famous Eureka moments using some other criteria, or of famous invention-moments, and demonstrate that the aspects here described were not present. If that could be done, it would show that the effects here described were a mere consequence of this author's idiosyncratic / biased mode of collecting the data.

Musical groups could be advised of times that had strong quintile and septile aspects (I and M.O. devised a Harmogram program that will show the strength of these aspects as a function of time) to see whether they felt that such times were good for creative work. Or, for the launch of a new invention which can be a risky and expensive business - say for example a new space-ship, one might wish to choose carefully a time of strong trine and septile aspects, and avoid basic Mars-Saturn aspects.

This study has definitively refuted the words of that most careful investigator Michel Gauquelin, that the effect of celestial aspects cannot be proved. The harmonic theory of john Addey is very much in tune with the theory of celestial aspects developed by Kepler in his 1618 Harmonices Mundi23 except that his is more arithmetic-numerical while Kepler's was more musical-geometric. Kepler concluded that the number seven could not be effective, because it was geometrically not constructible and moreover no pleasing musical harmonies could be made using it. This is the sole point on which we are here obliged to disagree with him.24

References:

1 Arthur Koestler The Act of Creation p.1989, Arkana, p.225, 107

2 John Addey Harmonics in Astrology 1976,p.123

3 See Appendix. NK and MO, "The Eureka Effect" The Astrological Journal 1988, 2, pp.90-136.

4 Edward de Bono Eureka: An Illustrated History of Inventions from the Wheel to the Computer 1979.

5 Hughes, T. American Genesis: A Century of Invention and Technological Enthusiasm 1870-1970, Viking 1989, p.75.

6 Gale Christiansen "The Night the Universe Changed Forever" The Griffith Observer June 1997,pp.4-10. I would not normally come across such a journal, but happened to be visiting Diana Rosenberg in New York and she had a copy of it.

7 For a full account, see the author's Eureka! The Celestial Pattern in Moments of Scientific Inspiration 2014.

8 Gale Christianson Edwin Hubble, Mariner of the Nebulae Bristol 1995, p.158.

9 NK "Eureka Moments - Anniversaries that Shaped History" Inventor's World Autumn 1998.

10 Barry Mazer Fermat's Last Theorem 2002,p.270-2.

11 Rightly or wrongly, our list excluded persons where doubt and controversy would arise as to whether or not they were 'scientists' ie Rene Descartes (philosopher) Leonardo da Vinci (artist) and Sigmund Freud (psychoanalyst), all of whom have reliable birth-data and are in the Asimov reference.

12 Frank Close Lucifer's Legacy: The Meaning of Asymmetry 2000, pp.77-79.

13 W. Heisenberg Der Teil und das Ganze Munich 1973,p.78 (reference kindly supplied by Theodore Lanscheidt)

14 I confirmed that the period 1928-1953 did have a higher septile expected value, of 2.52

15 N.K. and Mike O'Neill "Invention-Moments and Aspects to Uranus" Correlation Dec '92, pp.11-23.

16 N.Lemoine and D. Cooper Gene Therapy 1996, p.5.

17 Tim Berners-Lee Weaving the Web 1990

18 NK Eureka, The Celestial Pattern at Times of Historic Inspiration 2013, p.224

19 The horizontal line indicates chance-expected frequency: there are four angular positions for the three aspects, so likelihood of UR being in aspect with any one planet to 2° orb is 4x4/360; given nine planets that form aspects in 36 charts, 16x9x36/360=14.4 expected aspects, per 2° orb

20 D.Jay Practical Harmonics AFA, CA, 1983, p.7

21 D Cochrane Astrology in the 21st Century Florida 2002, p.94.

22 NK "Quintiles, Septiles, and Moments of Mystical Illumination" ISAR journal August 2011 (PDF available online here)