My most recent research project is looking at rain records for Sydney since 1980 to find correlations with planetary cycles. Most interestingly, over this 27 year period, the total rain on the dates ten days before each monthly Moon-Uranus conjunction is three standard deviations above average, and almost three standard deviations below average four days before each Moon-Uranus conjunction. This is a highly significant result which suggests a correlation between long term rain rhythms and planetary cycles. Similar but slightly weaker correlations exist between these rain records and the cycles of the moon with other planets. This result could easily be replicated against other long term daily rain records. I have planetary data since 1890, and would welcome the chance to examine other rain datasets. This is a purely astronomical question, looking at the strength of empirical rhythms to help quantify planetary effects.

I don't know. There's something almost obscene about rain being related to Moon-Uranus conjunctions.

Seriously, what are the units you're using to come up with your average and standard deviation?

Plus, Moon-Uranus conjunctions are not monthly in western calendar terms. They occur about every 27.5 to 29.5 days depending on whether you're using anomalistic months or synodic months.

Then there's the effect of the motion of Uranus in its orbit, which, except for some slight retrograde motion during opposition, contributes to making the aforementioned lunar months a bit longer.

Finally, what parameters are you using to identify a significant increase in rainfall? In Sydney the rainfall pattern is so even it's hard to see any trend month to month let alone day to day.

Remember, when there's a lot of noise in the data, apparent patterns detected in there can quite easily be mistaken for signals. Such things can result in snipe hunts as well as quests for snarks.

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My method for obtaining this result was as follows.

1. On request from the Australian Bureau of Meteorology (www.bom.gov.au) I obtained a data file for daily rain records at Observatory Hill near the Sydney Harbour Bridge from 1 January 1980 to 22 May 2007, 10003 days. I put this in an excel spreadsheet (column A).
2. In excel, I have a digital planetary ephemeris which enables easy creation of lists of planetary angles seen from earth over any period, including with sun and moon. In this spreadsheet each point of the zodiac cycle has a defined number from 1 to 13 with 1 the northern vernal equinox (Sun March 21), 4 the northern summer solstice, 7 the fall equinox and 10 the winter solstice, etc. I combined these two spreadsheets, and then, for each pair, eg Moon (B) and Uranus (C), extracted the rain records data for each day of the roughly 29 day monthly cycle. (Uranus orbit of 84 years is so slow that it barely moves each month).
3. A column (D = B - C) gives the difference between the positions of Moon and Uranus on each day. Minus six is opposition, zero is conjunction and plus six is opposition. For the sun-moon cycle, full moon is indicated by plus or minus six, half moon is plus or minus three, and new moon is zero. Difference numbers outside the -6 to 6 band are corrected by adding or subtracting 12.
4. Next step makes 29 columns in the spreadsheet dividing the numbers between -6 and 6 into even amounts, with increment 12/29 = ~0.41. The formula used in these columns is =AND($H3>=I$1,$H3<=I$2), where $H3 is the Moon Uranus difference (eg -5.8), I$1 is the lower bound (eg -6) and I$2 is the upper bound for that day (eg -5.59 for the first day after opposition). This formula returns TRUE for hits and FALSE for misses.
5. Next step is a further 29 columns with the formula =IF(I3=TRUE,$E3,0), where $E3 is the rain recorded in millimeters on that day and I3 is the result from step 4. This converts TRUE to the actual rain record in millimeters, and FALSE to zero The totals of each of these columns are the cumulated millimetres of rain for each day of the Moon-Uranus cycle in the 27 year period. Results are as follows for each day beginning from the opposition: 986.50; 1070.20; 1172.20; 1172.60; 1787.00; 1215.20; 1130.40; 1121.60; 1407.00; 971.90; 561.80; 1089.00; 892.60; 1137.80; 1281.20; 1122.80; 1081.00; 1257.00; 1130.90; 1363.00; 1082.60; 1164.90; 940.40; 1020.20; 1454.80; 1117.00; 1115.70; 1280.60; 1004.80
6. These 29 results have average of 1142.5 and standard deviation of 210.1283. Result 5 (1787mm ten days before conjunction) is most anomalous, 3.07 standard deviations above average. This result contains the rainiest single day, 6 August 1986, when 327.6 mm were recorded, but this single result accounts for less than half of the difference from the average. The other spike is result 11 (561.8mm). Five of the 29 results are more than one standard deviation from average.
7. All the obtained results showing the most anomalous results comparing planet-moon cycles against rain levels with the same data and method were as follows:
Test: Moon Planet Rain Cycle for Sydney 1980-2007 Minimum Result Maximum Result Ratio Max/Min Difference
Uranus-Moon Rain mm 561.80 1787.00 3.2 1225.20
Venus-Moon Rain mm 819.60 1663.20 2.0 843.60
Jupiter-Moon Rain mm 712.60 1508.60 2.1 796.00
Sun-Moon Rain mm 850.00 1620.80 1.9 770.80
Neptune-Moon Rain mm 729.20 1450.80 2.0 721.60
Saturn-Moon Rain mm 790.60 1386.80 1.8 596.20
Mars-Moon Rain mm 915.00 1401.20 1.5 486.20
Uranus Standard Deviations from average -2.76 3.07 5.83
Venus Standard Deviations from average -1.74 2.81 4.55
Neptune Standard Deviations from average -2.37 1.77 4.14
Sun Standard Deviations from average -1.46 2.39 3.84
Saturn Standard Deviations from average -2.13 1.48 3.62
Jupiter Standard Deviations from average -1.89 1.61 3.50
Mars Standard Deviations from average -1.59 1.81 3.40
8. Other results from this dataset involve counting the number of days of rain, light rain (<10mm) and heavy rain (>10mm) for each lunar-planetary combination and analyzing binomial distributions.

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I have moved the first part of the opening post back to its previous location. Hope that is okay.

Are you suggesting that the combined gravity of a Lunar-Uranus conjunction is causing abnormal weather patterns? Per Mr. Plait, Uranus's tidal influence on the Earth averages a mere 0.0000003% of the amount the moon has.

Did you first formulate a hypothesis, then test it against the data? Or, as the description of your methods suggests, did you trawl through a bunch of weather data and a bunch of ephemerides, and see what popped out?

So, what is special about Sydney Harbor Bridge? If it were more apt to rain every time 10 days before the Moon-Uranus conjunction, why would the rain just be centered on Sydney Harbor Bridge? Is this pattern world-wide? I ask that last one, since it really seems like it should be. Can you make predictions based on this observation? Finally, what is the statistical probability that this is just chance? Ya know, sometimes patterns just appear even when the data is truly random.

Uranus doesn't move very quickly in the sky, but the Moon obviously does. Have you checked to see whether what you're really looking at is the Moon being above a certain point on Earth relative to the Sydney area? Because at least over short timescales, that's more likely to have a bigger effect than Uranus.

(and why just Uranus? If it really did have an effect, wouldn't you expect Mars and Jupiter and Saturn to have an even bigger one because they're closer (and in two cases much more massive)?)

Mr Plait’s comments on relative gravity are correct, but this does not prove zero planetary effect. As noted at Science and Astrology , little Pluto, by dint of nothing more than gravity, has moved 100 million teralitres (km3) of earth water since the dawn of time, assuming that all the water of earth is moved each day by the moon’s gravity. If we assume just the top four metres of earth ocean is moved each day by the moon, Pluto gravity has moved 100,000 teralitres of our ocean. Over time this is a big effect. Uranus has a tidal effect on earth about 80,000 times bigger than Pluto, so by this calculation Uranus has moved eight billion teralitres of our ocean by tidal effect, six times the total ocean volume.

The issue here, in thinking through a conceptual reason for the observed statistical anomalies in lunar/planetary rain cycles, is that these tiny effects are permanent, in earth terms, and so present a rhythm which has been amplified and entrained by constant repetition over the fifty billion times the moon has orbited earth, within the constant presence of the rest of our solar system.

My hypothesis is that these tiny planetary gravitational effects are like a weak net cast over the earth, to which each point on earth aligns each diurnal rotation. Furthermore, during alignments (eg Moon –Jupiter) these weak nets reinforce each other, like musical notes in harmony. The nets cast by the Moon and each planet reinforce each other positively at conjunction and opposition, and negatively at square, as shown in full and neap tides caused by gravitational reinforcement of moon and sun (diagram at http://en.wikipedia.org/wiki/Tide).

My hypothesis is that lunar-planetary cycles produce non-random effects on rain amounts. Testing this requires a data trawl, but the amount of data I have presented is not enough for proof. I do not have a hypothesis as to whether Uranus might have a bigger effect than other planets such as Jupiter, but am just looking at the data to see. My aim was to define a method able to test objective planetary effects. This is very easy to validate by replacing the Sydney data with data from any other official weather station.

May I say, the heliocentric hypothesis emerged from Copernicus’ observation of the inelegance of epicycles. He subsequently went in search of data to justify the heliocentric view, with only limited initial success due to his assumption of circular rather than elliptical planetary motion. Similarly, I believe this rain effect is elegant, in line with the gravity net hypothesis summarized above, and am in search of data to prove it.

The only thing special about the Sydney Harbour Bridge, for this purpose, is that Australia’s oldest weather observatory is next to it at Observatory Hill, and that happens to be my data source. My hypothesis implies that this pattern is world-wide, but may emerge differently within the lunar cycles due to interaction with global weather. For southern countries, the pulsing effect of Antarctic fronts could well mean that New Zealand or Chile would experience rain peaks at different points in the cycles.

A prediction just from this observation is that in 2007 Sydney will get three times as much total rain on 23/7, 19/8, 16/9, 13/10, 9/11 and 6/12 combined as on 29/7, 26/8, 22/9, 19/10, 15/11 and 13/12. I do not know if my dataset is big enough to justify this prediction. This will help show if the data is random. The probability of a result greater than 3 standard deviations above average is extremely low. I will check the binomial distribution.

Over the 27 years of the study, Uranus moved 114 degrees, almost one third of an orbit. My method looked at relative positions of moon and each planet, not position of moon above earth. I did expect Jupiter to have a bigger effect, and as my table in the second post (with apologies for loss of formatting) shows, the order of scale of planetary effects, in terms of the difference between peak and trough average rain over the monthly cycle for the study, was

Standard Deviations from average
Planet Driest Rainiest Range
Uranus -2.76 3.07 5.83
Venus -1.74 2.81 4.55
Neptune -2.37 1.77 4.14
Sun -1.46 2.39 3.84
Saturn -2.13 1.48 3.62
Jupiter -1.89 1.61 3.50
Mars -1.59 1.81 3.40
(Pluto and Mercury not yet tested)


What this means is that for example, the rainiest day of the Venus-Moon cycle was 2.81 standard deviations above average, while the driest day was 1.74 standard deviations below average, a range of 4.55 standard deviations.

Robert, thanks for the reply. I've read your description of your methods a little more carefully, and have a few more comments.

1. Your hypothesis is very vague. "If I look at rainfall data and a lot of lunar/planetary cycles, something will look non-random". In which direction, when and why?

2. If your hypothesis is driven by gravitational/tidal effects, why Uranus? With such a short run of rainfall data, if there's any effect, the Moon should overwhelmingly dominate, with the Sun a distant second, and anything else being utterly negligible.

3. If there's some sort of tidal interaction between the Moon and Uranus, shouldn't we expect to see peaks/troughs on or around days 1 and 15? Instead you see days 5 and 11.

4. Estimating statistical significance by counting standard deviations from the mean is a very shaky approach for these data. Rainfall data have a very asymmetric distribution, with almost all the readings being near zero, and a scattering of days of very heavy rainfall far out on the right-hand-side of the graph. Hitting a couple of these on the same day of the cycle would give a very high reading purely by chance. I'd try a bootstrap approach, taking a long series of random samples of the data and seeing where your results lie in this empirical distribution. A cheaper and dirtier approach would be to take logs of the rainfall values and look at their distributions, although you'd need to fix the days of zero rainfall (try subtracting 1 from the log of the lowest non-zero reading). This would reduce the influence of the outliers, although you'd still have a very skewed distribution.

5. If you're claiming the effect to be planet-wide, it should be easy to get hold of other rainfall series for validation (assuming you have an effect in the Sydney data, and I'm not convinced you do). If there's nothing else in Australia, there should be plenty of cities in other continents with long runs of rainfall records.

6. I commend you for your generally rational approach to this issue, but please note that you automatically lose 25 credibility points for comparing yourself to Copernicus. I should warn you that if you go on to compare yourself to Galileo or Einstein, you drop off the credibility board altogether.

No, it isn't.

If the distribution is normal, about 99.5% of the observations would fall within +/- 3 SD of the mean.

You've got daily data for 24 years? About 8700 days? And the best evidence you have is just slightly over 3 standard deviations?

Get thee to an introductory statistics course.

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He's aggregating the ~8700 data points into 29 totals, so he's not looking directly at the individual values. I'm more concerned about his assumption of normal distribution - rainfall data are emphatically not normally distributed, and the totals are going to be highly sensitive to a handful of outliers. (In other words, a couple of good downpours might account for most of the total for a given aggregate).

I agree entirely with your last paragraph, though.

My purpose in presenting this data here is to validate the method, ensure I am explaining it clearly, and explore wider scientific ramifications. I greatly appreciate your assistance, including those questions which show my exposition was not understood.

The binomial function shows the probability of a randomly selected group of days receiving a specific amount of rain. I have checked the binomial distribution using excel with the following results.

Total Rainfall in Period (10003 days): 33132 millimetres
Average rain in random 345 days (1/29 or ~3.5% of total): 1142.5 mm

Probability (assuming random distribution) that a random group of 345 days will have
>1142.5mm: 50%
>1150mm: 40%
>1185mm: 10%
>1246mm: 0.1%
>1407mm: 2.2 x ten to the minus 15
>1787mm: ~0%

1787mm of rain fell on the 345 days when the moon was ten days before its Uranus conjunction. This result is way off the binomial scale, which gives results up to 1407mm. Even despite the non-random distribution of rainfall it proves the result is highly significant.

For reference, there were 23 days with more than 100mm rain. The top seven days had a total of 1515mm, of which only the first (326.7mm) and sixth (163.8mm) were in the anomalous Moon-Uranus ten day group. Next highest in this group was the 26th rainiest day (93.6mm) followed by the 50th rainiest (69mm). (Just for interest, I am not sure how to calculate the probability that the six rainiest days will be in a random group of 345 days).

The Sun-Moon cycle may well be more anomalous than the Uranus finding. Over the study period of 27 years, at the first quarter of the moon, a total of 1541mm fell on day 6 and 1620mm fell on day 7, having two days in a row with more than a foot (399mm & 478mm) above the average rain of 1142mm. These Sun-Moon results are separate from the Uranus effect.

No it doesn't. You don't have binomial data. Rainfall amounts for individual days may well be exponentially distributed (I'm guessing - I'm not a meteorologist), in which case the sums and/or averages will have a gamma distribution.

Your data is misleading. Gravity affects everything everywhere, so you can't say "Uranus has moved X amount of water since the dawn of time" because technically it affects all the water all of the time. But what you're not realizing is that Uranus has .0000003% the effect the moon does. You would need THREE HUNDRED MILLION planets the size and location of Uranus to have the same effect the moon does. This is infitesimally small. Not enough to do anything.

I'm sure a stadiumfull of people would have a larger net gravitational pull on nearby water than Uranus does, and stadiums don't flood just because a game is on.

Yes, in order for data to be binomial, it has to have only two mutually exclusive outcomes for each trial. Like heads or tails, true or false. Not a rainfall measurement.

And the outcomes have to be independent, daily rainfall is not, since weather systems can last for more than one day.

And the process has to be stationary, with the probability of success constant from trial to trial. So, no shifts in climate.

Strike three.

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You can see from these latest criticisms that my mention of Copernicus was more about learning from his error in assuming circular motion of planets than any claim to genius on my part! The issue remains that an average random 345 days in the study period has 1142mm of rain, but when these dates are sorted into moon-planet cycles the groups show surprisingly large spikes, as much as 600mm above or below average. When the data is aggregated in this way this variance is large. And, the point which the helpful comments on my method did not address, two big data spikes occur on adjacent days of the moon-sun cycle, at the first quarter. On the face of it this result looks much bigger than could arise from chance. I have studied some statistics, but not enough to know how to determine the probability that these results are from chance alone. The binomial method is obviously wrong in assessing outliers, but I would have thought it gave a good indicator of probability of results closer to the mean, certainly enough to show that these results are highly significant.

And regarding the small effect of Uranus, my point was that the permanent rhythm of this weak force is likely to be amplified and entrained over the extremely long period in which it has been present. There are no stadiums full of people which have been orbiting the sun with mechanical constancy for nearly five billion years.

Hello Robert Tulip,

I would first suggest you listen to what JohnW and the others are saying, they know what they're talking about.

I would also caution against testing a specific hypothesis, out of a multitude of hypotheses you consider, for statistical significance. What you really want to do is conduct a joint test of all of the hypotheses you consider. If you test enough hypotheses individually (how is the rain one day before conjunction, two days before, three days before, and so on), it is virtually guaranteed that some of them (in a particular data sample) will be statistically significant, even if there is no true relationship. You need a joint test of all of your hypotheses.

I'm still concerned about what looks like post hoc reasoning. From what I can see the hypothesis was that there should be some pattern related to astronomical/astrological configurations. The data was then trawled to find any pattern. In order to even to begin to assess the statistical significance of this (even forgetting about the approriateness of the different probability distributions) you need to determine the total number of possible patterns that would have been accepted as implying a correlation, otherwise you are just self-selecting for significance, i.e. if there are enough "valid" patterns available, then the probability is high that one of those would turn up in the data at an apparently high significance.

Robert, one way to fix things is to use more data. For example you could have used half of your dataset to find your pattern/correlation, and then used the other half to test it. Having derived the hypothesis from the full dataset, the only thing to do is to get more data and test it on that instead.

Why??...why is it "likely to be amplified"?? Because it is "permanent"? What is the mechanism involved??

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I suspect that this is down to confusion about forced simple harmonic motion, and that he assumes that the amplitude of a driven oscillator will increase over time without limit, i.e. neglecting the limiting amplitude that is always present in a system with a non-zero damping force.

Thank you for bearing with me on this discussion. Following Aurora’s kind suggestion, I have looked again at reference material at http://en.wikipedia.org/wiki/Standar...stributed_data

The null hypothesis is that Moon-planet cycles have no effect on terrestrial rain. Aggregating the 27 years of data into 29 groups of 345 days, one group for each day of each monthly Moon planet cycle, should therefore produce a normal distribution. (The actual gamma distribution of rainfall should be normalised by this aggregation process). We are looking at 29 data groups, not 10,000. The confidence intervals under the central limit theorem show that on average, one group of 345 days in every 29 will be more than ~1.67 standard deviations (SD) from the mean. Similarly, the chance that one of the 29 groups is more than two SD above average is 29/44 = 2/3 = 66%, while the chance that one group is more than 3.07 SD above average (the biggest finding in the sample) is 29/795 = 1/27 = 3.65%. This means it would take 27 random samples of dates grouped according to this method to find one result of this size. Statisticians may be able to help me consider whether both tails of the distribution should be included here – I assume not. I tested 7 samples, and found a number of significant results.

Restating the likelihoods of other Moon Planet findings listed at #13 which were above 2SD from mean, we have:

1. Uranus Rainiest Day SD = 3.07: Likelihood 3.65%
2. Uranus Driest Day SD = -2.76: Likelihood 18.8%
3. Venus Rainiest Day: SD = 2.81: Likelihood 15.7%
4. Neptune Driest Day: SD = -2.37: Likelihood 43%
5. Sun Rainiest Day SD = 2.39: Likelihood 41% (note this was adjacent to the second rainiest day with SD = 1.98)
6. Saturn Driest Day: SD = -2.13: Likelihood 58%

Correct me if I am wrong, but I would expect the products of these results would give combined probability: ie the likelihood of both the Uranus Rainest Day and Uranus Driest day occurring by chance would be 3.65% x 18.8% = 0.686%. Combining all six results above in this way give a result with likelihood of one in 9000. Significant.

I previously discussed the amplification issues in terms of the Lorenz observations of weather cycles in complex systems: see Science and Astrology
Science and Astrology (paras 10-15) and Science and Astrology

OK, Robert, I'll correct you.

You can't cherry-pick the results you like and disregard the others, and you certainly can't just multiply the probabilities together like that. Especially when they're drawn from the same raw data, so the same outliers are probably responsible for multiple "effects" - in other words, your probabilities are not independent. If you want to look at combined effects, you'll need to do a multivariate regression or at least an analysis of variance.

Your best result, assuming your assumption of normality is correct (and I'm sceptical - did you test this assumption?), and assuming all your numbers here are kosher, gives p=0.04 - we would expect one in 25 tests to be this significant, purely because of random variation. And that's with a one-tailed test - given the vagueness of your initial hypothsis, I think a two-tailed test would be preferable.

I think your best course of action from here would be to look into either some classes in probability and statistics, or at least get hold of a textbook and work through it. Wikipedia's statistics pages are pretty good (by Wikipedia standards), but they're no substitute for a systematic education in the subject.

Very patient, John W, your posts are great, I enjoyed them.

Thanks, John M.

John – I am not cherry-picking. Moon cycles with Sun, Venus, Saturn, Uranus and Neptune all returned results outside that produced by random numbers. I am not just using the probability of the most significant result in isolation, but am dividing it by 29 to recognize there are 29 samples, and then comparing this against other tests.

The results are independent. The two most significant results are different dates on the Moon-Uranus cycle, and these have no data points in common. The same applies for days 6 and 7 of the Sun-Moon cycle. Only four of the sixty rainiest days were on the significant Moon-Uranus -10 dates. These four dates only accounted for 1.97% (653mm) of total rain in the sample, proving that the same outliers are not actually responsible for multiple effects.

My multiplication of probabilities is valid. By comparison, if a result is seen in 10% of normally distributed samples, and one test produces two such results, this combined result has probability of 1%. In my test, I applied this method to assess the probability of both the Moon-Uranus peak (seen in 3.65% of random samples) and the Moon-Uranus trough (seen in 18.8% of random samples) to indicate a probability of 0.68% (~1/150) that both results would occur in one random sample.

I note that no one has asked to see my data. I assure you it is accurate, but of course looking at it would give credence to a new scientific theory which is against the mainstream.

There is no reason other than a planetary effect why this data would not be normally distributed.

For comparison, I replaced the planetary data with random numbers and over several runs as expected found all 29 results had Standard deviation less than 2. It would take 150 such random samples to see both the Moon-Uranus results observed in the Sydney rain data.

You are correct about gravity, but my aim with this crude example was to show that the miniscule planetary effect could over time aggregate to something big, even if the damping of tidal systems means such an effect would be barely detectable. If the statistical tidal variation on earth was found to change by ten nanometers in line with Uranus cycles my point would be supported, but measurement is not precise enough to detect this. Your statement “not enough to do anything” is based on faith, not evidence.

My use of the term ‘amplified’ was not intended to mean ‘increase without limit’, but a way of saying that natural systems tend over time to harmonise with the presence of regular planetary rhythms built deep within the foundations of all terrestrial systems, just as DNA adapts to its niche. For weather, my study suggests that this effect produces underlying variance in rain amounts. I have previously argued that the cumulative adaptation of DNA should in principle reflect these subtle tiny constant factors, thereby ‘amplifying’ them in terrestrial systems.

The following points summarise material linked in my previous post.

http://www.physics.ubc.ca/~berciu/TE...YS349/alex.pdf explains that when pendulums or clocks are ‘coupled’ through contact with one wall, they fall into step or are entrained, through common vibration. The description of entrainment of firefly lights is also worth reading - showing that events can be linked in surprising ways. Another good example is that soldiers break step when marching over bridges, because the natural vibratory oscillation of the bridge might become entrained with the soldiers’ steps, and the bridge could become increasingly unstable and collapse.

http://ludix.com/moriarty/entrain.html comments “The moon and sun are the most pervasive entraining influences in our environment. The entire planet is under their sway. But you don’t need a cosmic mass to initiate entrainment. Even a very modest rhythmic impulse, given the right frequency and insistent repetition, is enough to coax any elastic system into significant oscillation. The destruction of the Tacoma Narrows bridge by a passing breeze is a compelling case in point.”

James Gleick’s Chaos – Making a New Science makes a number of general comments relevant to the matters discussed here. He defines chaos as “a science of the global nature of systems” (p5) in which “The power of self similarity … is a matter of looking at the whole” (p115). The climate models of Lorenz, which “saw order masquerading as randomness” (p22) precisely describes the way in which these planetary effects are postulated. Lorenz’s observation that sensitive dependence on initial conditions was "an inescapable consequence of the way small scales intertwined with large,” (p23) and a “quality [which] lurks everywhere” (p67) illustrates the mechanism of the sensitivity of planetary inter-relations.

Gleick discusses the cultural problems of scientific change, noting that “a revolution has an inter-disciplinary character … problems that obsess these theorists are not recognized as legitimate” (p37), “the rare scholars who are nomads by choice are essential to the intellectual welfare of the settled disciplines” (90), and “non-specialists find the new things” (132-3).

Part of the problem in recognizing complexity is that “graphic images are the key” (p38). I previously offered to share graphic images which illustrate my ideas, and remain eager to do so. These images of geocentric patterns of the planets help to illustrate Gleick’s observations that “disorderly behaviour of simple systems … generate complexity: richly organized patterns … with the fascination of living things” (p43), and “the chaos Lorenz discovered … was locally unpredictable, globally stable” (p48).

As Gleick comments “Chaos is ubiquitous, it is stable, it is structured … complicated systems could be understood in terms of easy discrete maps” (p76) and “Over and over again, the world displays a regular irregularity” (98).

The conceptual universality of fractals as the geometry of nature emerges in the comment that “fractal scaling [is] … universal in morphogenesis” (p110) ie that the origin of biological form is inherently fractal, with each natural entity reflecting the larger whole of its niche.

Gleick says “Strange attractors fed the revolution in chaos by giving numerical explorers a clear program … wherever nature seemed to be behaving randomly” (152). He observes that “Phase space portraits of physical systems exposed patterns of motion that were invisible otherwise” (135), and asks “What other changes … would prove to be phase transitions?” (127). These points make me wonder about the planets as attractors.

The objective of my study here is to show that apparently chaotic events on earth correlate with planetary patterns as tabulated in the ephemeris, such that these patterns provide predictive indicators. The null case (disproof) is that no planetary patterns provide predictive indicators for events on earth. There is a steady gradient of complexity of claimed planetary effects, from the obvious (tides) to the little known (rats increased activity when moon is below horizon) to the debated (Gauquelin statistical effects of planets at eastern horizon; Tarnas correlations between outer planetary aspects and cycles of human history).