The earths axial tilt - presenting evidence for it being much larger 4000 years ago

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posted on Jul, 28 2010 @ 12:14 AM


This thread contains significant quantities of science and mathematics.
Thinking will also be required.

Not many of you, I'm sure, will have heard of a gentleman called George F. Dodwell. I certainly hadn't until just a few weeks ago when I unintentionally stumbled across some unpublished work of his dating back to the mid '30s that immediately piqued my curiousity and eventually became the subject of this thread. But before I delve further into the matter, let me give you a brief resume of Dodwell's career in an attempt to deflect any later criticisms that Dodwell was eccentric or delved into pseudo-science. In reality, Dodwell was to become one of the leading scientific minds in Australia during the early decades of the 20th century and commanded the highest of respect from his peers.

George Dodwell was born in Britain in 1879 but eventually moved to (my home state of) South Australia, where he obtained his Batchelor of Arts degree in mathematics (yes, it was considered an 'art' back then) at Adelaide University. He became a Fellow of the Royal Astronomical Society and later was appointed to the staff of the Adelaide Observatory. In 1909, Dodwell succeeded Sir Charles Todd and was appointed Government Astronomer for South Australia. He held this position until his retirement in 1952.

During his tenure at the Adelaide Observatory, many subsequent highly regarded and influential achievements were credited to Dodwell. The Observatory became the site of the 1st wireless installation in Australia for 'distant signalling'. This installation was instrumental when the occasion arose to fix the bounadary between the states of South Australia and Western Australia. Dodwell himself proposed that this be determined by wireless signals heard by Greenwich as well as the field stations at Deakin and Argyle Downs simultaneously. This boundary fixing process by wireless signals became an international project when radio time signals were transmitted from Bordeaux and Lyon in France, and Annapolis in America. This international project linked the Greenwich, Paris, Washington and Adelaide Observatories from April to July 1921 and was the very first time that the world had been measured from one side to the other by the combined use of wireless telegraphy and astronomical observations. This became a world "1st" for both Adelaide and George Dodwell.

In 1922, Dodwell led a combined party with Sir Kerr Grant of Adelaide University in one of the 1st attempts to test Einstein's theory of the effect of gravitation on light by observing and photographing the total solar eclipse from Cordillo Downs in South Australia. Later that year, he was appointed by the Commonwealth of Australia to be its representative at the International Astronomical conference in Rome.

As well as the above achievements, additional world recognition was achieved by the Adelaide Observatory under Dodwell's leadership as a result of the work carried out and completed of a magnetic survey of South Australia. This survey also resulted in Dodwell carrying out studies relating to latitude variations in conjunction with La Plata Observatory in Argentina, the International Latitude Congress and the International Astronomical Association.

With the above out of the way, we now come to the subject of this thread of mine; namely that through his studies of latitude variations, Dodwell began to investigate what is commonly referred to in astronomy as the 'Obliquity of the Ecliptic' or as its more popularly referred to, as 'the tilt of the earth's axis'.
He commenced this work in 1934, a year after his uncle, Sir Frank Dyson (K.B.E; F.R.S) had retired as Astronomer Royal in England. Dodwell had obtained a copy (published in 1933) of an ancient manuscript by a medieval Belgian astronomer called Godefroid Wendelin, which contained many observation of the tilt of the earths axis. The entire data set seemed to indicate that the earths axis, rather than being relatively stable as traditionally accepted, in fact may have undergone some type of 'event' approximately 4,000 years ago that had significantly altered it's axial tilt and from which it had only recently (in the 1800's) recovered from.
As a result of his additional research, Dodwell in 1935 sent a preliminary paper to the Royal Astronomical Society. However, rather than investigating Dodwell's hypothesis, the Society referees instead suggested a further study of potential errors in observation that may possibly explain this apparent anomaly in the data set.

It should also be stated that Dodwell was not alone in his belief that the earth's axial tilt is variable. In 1740, the astronomer Cassini discussed 16 observations of the earth's axial tilt over a span of nearly 2000 years. He considered the hypothesis that the amount of tilt changes linearly with time. After observing the data, Cassini claimed that the observed values were simply to great to be due to measurement errors.

Dodwell continued his research and had almost readied it for publication at the time of his death in 1963. At that point it sank into obscurity and It was only recently that his family and descendents gave permission for his hypothesis, data and conclusions to be summarized and published online.

As I mentioned in my opening, his hypothesis of an earth that had a significantly greater axial tilt than observed today and the fact that there apparently was hard scientific evidence to back this claim up, interested me sufficiently for me to decide to re-analyze his data and conclusions and see if it still stands up to scrutiny even after almost 50 years after his death,
This I did and found that indeed, his hypothesis still stands and has sufficient data to substantiate the inferred conclusion that at a certain point back in time, the earth had demonstrated a significantly greater axial tilt due to some past 'event' and from which it had been recovering from during the last 4,000 years.

And now I'm using this thread to take those of you who are interested through the analysis and conclusions and will try my hardest to present them in an easy to understand manner.

Ok, lets start with a quick refresher of the ecliptic and axial tilt.

In the following image, the plane within which the earth orbits the sun is also referred to as the ecliptic.
As the earth orbits the sun, it is inclined at an angle (axial tilt) of approximately 23.5 degrees with respect to the orbital plane or ecliptic. It is this very inclination which is responsible for the existence of seasons.

Most people are aware of the earths axial tilt but mistakenly believe it to be a fixed and unchanging value of approximately 23.5 degrees. This however is not so as it was shown by the American astronomer J. N. Stockwell, in 1873, that the earths axial tilt is not constant but varies in a regular cycle over thousands of years between approximately 22 and 24 degrees maximum. At the present time, we are heading in the direction of minimum tilt and will reach that point in approximately 13,000 years.

Continued next post ...

posted on Jul, 28 2010 @ 12:14 AM
Continued from previous post ...

Stockwell's calculations were fit into an empirical formula and published by Simon Newcomb.

The value of T in the above formula represents the number of centuries from 1900 A.D. with positive (+) values for centuries AFTER 1900 A.D. and negative (-) values for centuries BEFORE 1900 A.D.

For example, to calculate earth's expected axial tilt in 1500 A.D, a T value of -4 (i.e. 1500 - 1900 = -4) would be used.

Newcomb's formula for the calculation of axial tilt values (past and future) had been accepted for many years as the international standard and was the one used by Dodwell in his original calculations.

However, an improved version of the formula was derived by L.J. Lieske in 1976 with a base year of 2000 A.D. (Newcomb's Formula used 1900 A.D)

Note that in my re-examination of Dodwell's data, I replaced his use of the Newcomb Formula with that of Lieske's in the hope of achieving an improvement in axial tilt calculations for previous eras.

Now I'll present a table containing 71 data points used in the analysis.

Data table:

Column 1 represents the source of the axial tilt measurement.
Column 2 represents the year that the measurement was taken.
Column 3 represents the OBSERVED axial tilt measurement in standard degree, minute and second format.
Column 4 represents the EXPECTED axial tilt measurement for that year derived from the Lieske Formula.
Column 5 represents the difference (in minutes and seconds) between the observed axial tilt and the Lieske Formula values.

Please note that the reason for the inclusion of the Stonehenge and Amun-Ra sources (highlighted in green) will be explained later.

A cursory examination of column 5 will show that looking backwards in time from 1976 towards the mid 1600's, the difference between the observed and calculated axial tilt values are fairly minimal and fall within the expected range of deviation. However, from the mid 1600's and looking backwards once again, we can see a sudden and progressive difference becoming very evident and a definitive divergence taking place between what the Lieske Formula tells us that the earths axial tilt SHOULD have been during those time periods; and what was actually observed and recorded by astronomers of those periods.
So, we have somewhat of a mystery on our hands ... either the actual observed axial tilt values as we head further back in time are in error ... or the internationally accepted Lieske Formula is in error.

Before we continue with the analysis, I'm sure that by now, some of you may be wondering just HOW does one go about measuring the amount that the earth's axis is tilted by ... and especially how were ancient astronomers able to measure it more than 3000 years ago ? Surely it must take sophisticated devices and advanced mathematics to work out how much the earth is tilted ?
To answer these questions, I'll try and provide a brief explanation.

Surprisingly, the simple answer is that essentially all it takes is nothing more than a long wooden pole (or "gnomon" as it's normally referred to) and some very simple geometry. It is one of the first scientific instruments ever made, originating with the Chaldean astronomers of Babylon and then soon spreading to the ancient Greek, Chinese, Indian, Arab and Egyptian civilizations. All of them were perfectly capable of making the necessary observations and arriving at accurate answers. Indeed, this ancient method was the precursor to the simple sun-dial and has been in continuous use over the millennia.

Essentially, all that needed to be done was to ensure that an area of ground was prepared so that it was perfectly flat and the pole to be placed absolutely vertically in that flat area of ground. There were many simple ways that both of these preparations could have been easily accomplished even thousands of years ago.
Once the pole has been fixed in place, all that was then required was to wait until the day of either the summer or winter solstice and measure the length of the shadow cast by the pole at local noon on those particular days. Knowing the length of both the shadow and the pole, extremely simple geometry would provide the angle of the sun in the sky.

The following diagram should help illustrate just how simple and easy it is to determine and measure the angle of the earths axial tilt.

By measuring the angle formed by the corresponding summer and winter solstice shadows (in this case 47 degrees), then dividing that angle in half, will give the angle of the earths axial tilt of approximately 23.5 degrees. Naturally it goes without saying that the more accurate the measurement of the summer and winter solstice shadows cast by the pole, then the more accurate the resultant value of the tilt.

It needs to be emphasized MOST strongly that using the above procedure, it would have been EASILY within the capabilities (both technical and mathematical) of ALL of the ancient civilizations to arrive at extremely accurate measurements of the earths axial tilt. Saying that because measurements were made many thousands of years ago that they therefore could not possibly be accurate is doing a great disservice to the astronomers of those ancient times. Just take a look at the incredibly accurate measurements that would have been necessary in the construction of the Egyptian pyramids and monuments thousands of years ago to show quite clearly that people of those times were more than capable of measuring with extreme accuracy something as simple as the angle of a shadow cast on the ground by a wooden pole.

It should be mentioned at this point that even though the above method of determining the earths axial tilt is, in practice, simple and straightforward - that there are still potential sources of measurement errors that could impact the accuracy of the final value.
As an example, except for the last few hundred years, the concept of solar parallax and atmospheric refraction were unknown to the ancient astronomers and therefore were NOT factored into their observations and calculations when determining the sun's ACTUAL altitude and not just the OBSERVED altitude in the sky. Both solar parallax and atmospheric refraction cause light rays traveling through the atmosphere to bend slightly and therefore causing the altitude of the sun (to an observer) to appear slightly higher than it actually is, and so this had the effect of introducing slight errors into their calculations.

A simple example is that when we observe the sun just touching the horizon and about to set, in actual fact the sun has already set below the horizon but because of the effects of atmospheric refraction, we "see" the image of the sun as if it was still just above the horizon.

Dodwell was well aware of these (and other) potential sources of error in ancient observations and therefore ensured that all observed values of earths axial tilt had been corrected for parallax and atmospheric refraction. It is these corrected values that appear in column 3 of the data table shown earlier.

Continued next post ...

posted on Jul, 28 2010 @ 12:15 AM
Continued from previous post ...

Ok, from the preceding, hopefully I've managed to give a reasonably clear explanation of the concept of the earths axial tilt and how astronomers over the millennia have been able to quite easily determine that tilt value for their particular time period; whether a few hundred years ago or a few thousand years ago.

Now we'll move along and finally get to the heart of this thread and analyze the data and determine if there really is any justification to the hypothesis that the earth's axial tilt has indeed changed significantly over the last 4,000 odd years ... a hypothesis that flies in the face of conventionally accepted astronomical belief that the earth's axial tilt is secularly stable and only varies within a very limited upper and lower boundary range, and cannot possibly change to the large extent that the data being examined seems to imply that it has.

First of all, lets examine the axial tilt data as physically observed by various sources (from column 3 of data table) over the millennia and place it in graph form.

Graph 1:

Immediately we can see that without much effort, ALL the data points appear to fit exceedingly well on to a simple curve, indicating that there is an inherent mathematical relationship in effect. If such a relationship did not exist, we would expect the data points to be displaying much more of a random nature.

Now we will examine the axial tilt data points as generated by the Lieske Formula (from column 4 of data table) and attempt to place them on to a graph. Again, we find that all the data points appear to have a mathematical relationship but one that is more linear in nature.

Graph 2:

For comparison purposes, I'll now overlay the previous 2 graphs.

Graph 3:

We can see very clearly that working backwards from a future projected date of 2200 A.D., that the computed and observed values are virtually identical as far back in time as the mid 1600's. But then as we move further back in time, we again clearly can see that the observed and computed axial tilt values began to diverge rapidly ... the Lieske computed values follow a linear path whereas the physically observed values follow a curved path.

From the above combined graph, it should be immediately apparent that rather than adhering to the Lieske Formula computed axial tilt values over the last 4,000 years, that instead some other unknown factor has come into play that has resulted in the earth's actual axial tilt values diverging more and more significantly from the Lieske predicted values the further back in time we look.

Also by looking at the curved 'observed data' graph, the downward falling graph appears to be heading asymptotically towards and converging on the date of approximately 2345 B.C. This seems to be indicating that whatever 'event' was the cause of the disparity between the 'expected' and 'observed' axial tilt values, that this 'event' occurred around this date of 2345 B.C. and that ever since that remote date, the earth's excessive axial tilt values have been slowly recovering from that event and gradually falling back into line with the expected Lieske tilt values. This recovery appears to have been completed somewhere around the mid 1600's A.D. and from that point on, observational and computed values are back in synchronization.

We can also use the differences (from column 5 of data table) between the observed and Lieske values to observe this unknown 'effect'.

Without going into unnecessary and complicating details (but will if requested), it can be shown that column 5 data actually displays an inherent mathematical logarithmic sine component. Furthermore, this component can be easily displayed in graph form as displayed below.

The actual logarithmic sine equation derived from the column 5 data and used to generate this graph is:

Graph 4:

As with the previous graphs, it can be readily seen that the left hand side of the log sine graph also converges asymptotically upwards towards the date of 2345 BC, once more confirming the presence of an unknown 'event' around that time that significantly increased the earth's 'expected' Lieske calculated axial tilt value of 23 degrees 57 minutes to the larger value of 26 degrees 57 minutes ... an unexpected increase of approximately 3 degrees in axial tilt.

As well as the observations that were physically carried out over the millennia by astronomers, Dodwell also decided to look into 3 of prehistories greatest constructions that have been shown to be undeniably linked to some form of solar (sun) worship by the civilizations that constructed them. These constructions were the Solar Temple of Amun-Ra at Karnak (Egypt); Stonehenge (Britain) and the Solar Temple at Tiahuanaco (Peru). Unfortunately Dodwell only managed to complete detailed research into Amun-Ra and Stonehenge before his death.

Even so, he was able to show quite conclusively that the principal alignment axis of both constructions were deliberately aligned at the time of construction with the solar solstices - and based on this, was able to accurately determine the associated axial tilts and therefore the construction time for each one.
Both the construction dates and corresponding axial tilts for those dates fit almost perfectly on to Graphs 1,3 and 4 and add further validity to the hypothesis that the earths axial tilt has undergone significant change over the millennia. I have also labeled these 2 constructions on Graph 4.

Ok, so here we are at the end of my re-analysis of Dodwell's data and my conclusion is that there is indeed something extremely unusual in the pattern of axial tilt values that have accumulated over the millennia by many observers. Not all of these observed values can be put down to errors of one kind or another. The actual technique of obtaining the earth's axial tilt value has been shown previously in this thread to be a remarkably simple process and well within the capabilities of virtually every major ancient civilization dating back to almost Babylonian times. Each of these civilizations had more than sufficient mathematical knowledge to be able to obtain very accurate values so it would be extremely difficult to explain the majority of these obtained values as being due to shoddy or inaccurate observational methods.

This is as far as Dodwell got prior to his death .... and so the mystery remains.

However, I personally believe that Dodwell may not have had the opportunity to delve deeper into the repercussions of his hypothesis. The following are my additional personal observations based on what I have learned during my re-evaluation of Dodwell's data

Effect of an additional 3 degree axial tilt
If around the period 2345 B.C. the earth's axial tilt was indeed 3 degrees greater than predicted by the Lieske Formula, which may not sound like much, we still should consider the probable flow-on effects that such an additional axial tilt would have on global weather patterns.

Continued next post ...

posted on Jul, 28 2010 @ 12:15 AM
Continued from previous post ...

Our seasons are a direct consequence resulting from the axial tilt of our planet. Therefore it stands to reason that any increase in the amount of tilt will result in seasons that have correspondingly greater extremes in temperature maxima and minima. Summers will tend to become warmer and winters will tend to become cooler. This increased seasonal temperature differential will eventually find its way into the atmosphere resulting in corresponding instability and pressure differentials and possibly generating storms of increasing severity and magnitude.
The seasonal temperature differential will also cause increased swings in average ocean temperatures which could potentially affect ocean salinity levels and current flows which in turn could then affect land based temperatures ... which then could further impact ocean temperatures ... which could then further affect land temperatures .... and a cycle is born.

Now 3 degrees on the earth's surface is the approximate equivalent to a distance of 333 kilometers. This is based on the fact that 1 minute of arc on the earth's surface is equal to 1 nautical mile, therefore 3 degrees converts to 180 minutes of arc which is the equivalent of 180 nautical miles. Finally, 180 nautical miles converts to 333 kilometers.

Imagine the current Arctic environment moving 333 kms further south and the current Antarctic environment moving 333 kms further to the north ... this is what a 3 degree additional axial tilt would be equivalent to. Now imagine the additional warming that would then occur each northern summer resulting in Arctic ice melting at an accelerated rate because of the additional 3 degree tilt. On the other hand, during the northern winter there would be additional cooling and greater ice formation. Therefore the overall ice levels in the northern hemisphere (and correspondingly in the southern hemisphere) would rise and fall at increased rates compared to those at the present time resulting in greater quantities of fresh water entering (in summer) the oceans and leaving (in winter) the oceans and again potentially affecting ocean salinity and overall stability.

Dodwell also apparently assumed that the data when graphed showed that the ends of the graphs essentially flattened out in the vicinity of 2345 B.C. and 1850 A.D. and continued indefinitely in an asymptote fashion in these two locations. This was a very reasonable assumption to make as the ends of the graphs do indeed appear to be asymptotic in nature ... and Dodwell didn't seem to consider investigating any further back in time past the 2345 B.C. date.

However, I found that this assumption was only viable at the original scales used in producing these graphs. Whilst recalculating the logarithmic sine graph (Graph 4), it occurred to me that a graph with a sine component is inherently a 'repetitive' type of graph. But Graph 4 appeared to show no such repetitive quality. At least not at the scale that Dodwell and I were using.
But the moment that I started to 'zoom out', I could see signs of repetitiveness appearing and the more I 'zoomed out', the greater the detail of repetitiveness.

Perhaps this series of images will help make it clearer.

This is a less-detailed version of the log sine graph shown at Graph 4. As can be seen at the scale used, there appear to be 2 asymptotes present i.e. where the upwards moving graph moves towards tihe y-axis and the horizontally moving graph moves towards the x-axis.

Now I'll 'zoom out' by increasing the number of time periods displayed on the x-axis.

We now see that what was assumed to be an asymptotic region along the time axis (x-axis) is actually no such thing. In fact, somewhere around the year 3000 A.D., the axial tilt begins to once again increase and diverge away substantially from the predicted values of the Lieske Formula and that just after 6345 A.D., the axial tilt reaches a maximum value.

So by extending the time line, we begin to see that contrary to Dodwell's hypothesis that this was a "one time" event where some unknown event altered the earth's axial tilt substantially away from predicted values, we are instead beginning to see that this process may in fact be a recurring and cyclical one.

Finally, to add additional credence to this cyclical possibility, I'll once again increase the time periods along the x-axis.

From what we can see, it appears that there's approximately a period of 16,000 years between maximum axial tilts.
This makes me wonder if there's some kind of relationship between the above and the many recurring cooling/warming periods that the earth has been proven to have undergone during geological past ages.

Ok, well that's about it and hopefully if you've stuck with me all the way to the end of this thread, that I haven't bored you. As I mentioned in my opening, I found Dodwell's hypothethis intriguing and well worth spending some time on and re-confirming his results. There's always the chance that he was way of the mark and all the above results were due to nothing more than pure coincidence ... but somehow I don't think so.


Ancient, mediaeval, and modern observations of the obliquity of the Ecliptic, measuring the inclination of the earth's axis, in ancient times and up to the present
by George F. Dodwell B.A., FRAS

by A.D. Wittmann
Universitats-Sternwarte, Gottingen, Germany

by Alexander Jones
University of Toronto

by Willy Hartner
Reprinted from Silver Jubilee Volume of the Zinbun-Kagaku-Kenkyusyo
Kyoto University, 1954

by Clark Glymour
Monist, Apr 2001 Vol 84 Issue 2, p284

posted on Jul, 28 2010 @ 12:24 AM
A magisterial post. Many thanks for your effort in presenting this material and taking the steps necessary to evaluate the hypothesis. This is flipping brilliant imho.

posted on Jul, 28 2010 @ 12:50 AM
Good thread, tauristercus.

Very well written and laid out.

From what we can see, it appears that there's approximately a period of 16,000 years between maximum axial tilts.
This makes me wonder if there's some kind of relationship between the above and the many recurring cooling/warming periods that the earth has been proven to have undergone during geological past ages.

As far as I'm aware, the major global cooling periods (Ice ages) are measured in millions of years, not on such a short (relatively speaking) time frame of 16,000 years.

Um and also, you one clickable link is from a creationist website.
Not that there's anything wrong with that, just found it...odd.

[edit on 28/7/10 by Chadwickus]

posted on Jul, 28 2010 @ 01:16 AM
Thank you for this post. From the way you are writing and seem to have a true interest in this I think you should investigate polar shift as well. From my recolection it is about 1 degree per million years. While you are talking about the axis tilt of the earth this talks about the physical axis location shifting (more along the ice age issue).

I am not sure about you educational level but one would assume that you are somewhat educated. I believe that if this is an area of interest for you that many universities would enjoy having a doctoral candidate with a desire to study this phenomenon. I would assume you could look into the relationship for both and possibly discover the reason behind cooling and heating periods that are evidenced by geologic formations throughout time. Just an idea.

wikipedia link for polar shift. Just watch out for the pseudo-science presentations for any of these hypothesis'.

posted on Jul, 28 2010 @ 01:31 AM
Atta boy tauristercus.

This is one of the best posts that I have read on ATS.
It was rather lengthy, but it was written in such a fashion that kept me engaged.

Excellent data and flawless composition!

[edit on 28-7-2010 by KillenfizzenHumboflorator]

posted on Jul, 28 2010 @ 01:35 AM
Yes, it is true.

The Earth's axis completes one full cycle of precession approximately every 26,000 years. At the same time, the elliptical orbit rotates, more slowly, leading to a 21,000-year cycle between the seasons and the orbit. In addition, the angle between Earth's rotational axis and the normal to the plane of its orbit moves from 22.1 degrees to 24.5 degrees and back again on a 41,000-year cycle; currently, this angle is 23.44 degrees and is decreasing.

[edit on 28-7-2010 by mbkennel]

posted on Jul, 28 2010 @ 01:41 AM
Absolutely fabulous post! I was unaware that changes to the obliquity of the ecleptic was not accepted. Perhaps we should overlay your data to the perihelion and epihelion orbit dates and see if the data matches up with the iceages? Would be exciting if they did!

posted on Jul, 28 2010 @ 01:52 AM

Originally posted by Chadwickus
Good thread, tauristercus.

Very well written and laid out.

As far as I'm aware, the major global cooling periods (Ice ages) are measured in millions of years, not on such a short (relatively speaking) time frame of 16,000 years.

Thanks for the thumbs up, Chadwickus ... much appreciated !

I agree with you regarding the enormous time periods normally quoted between major global cooling periods but in my defense I was basically just tossing around a "what if" and "thinking out loud" on a possible link between the cycles and any significant global temp alterations.

Your comment got me to do a quick Google on the last significant (and recent) temp spike/drop and came up with

Around 12,800 years ago the northern hemisphere was hit by the Younger Dryas mini ice age, or "Big Freeze". It was triggered by the slowdown of the Gulf Stream, led to the decline of the Clovis culture in North America, and lasted around 1300 years.


Out of curiousity, I then extended the logsine graph backwards in time about 30,000 years to see if there was any potential correlation between the timing of the Younger Dryas and one of the past cycles.
We're particularly interested in that period for the start of the Younger Dryas of around 12, 800 years ago ... that would make it circa 10,800 B.C.

Here's the graph ...

I not sure if we can assign any significance to the fact that the Younger Dryas seems to correlate strongly with an obvious period where the axial tilt is at a maximum value in the cycle previous to our current cycle ... might be pure coincidence but is thought provoking nontheless.

posted on Jul, 28 2010 @ 02:22 AM
Thinking here...

A question.

What does the asymptotic variation of the y axis represent exactly? Being a logarithmic function, the actual value approaches infinity at the asymptotes. What is happening to the obliquity? How does the cycle repeat?

It seems to me that asymptotes and natural cycles would be natural enemies. If the curve goes asymptotic it does not return to its origin, it is a discontinuous curve. It seems that it indicates a problem with the theory of the existence of a cycle.

[edit on 7/28/2010 by Phage]

posted on Jul, 28 2010 @ 02:44 AM

Originally posted by Phage
A question.

What does the asymptotic variation of the y axis represent exactly? Being a logarithmic function, the actual value becomes infinite at the asymptotes. How does the cycle repeat?

It seems to me that asymptotes and natural cycles would be natural enemies. If the curve goes asymptotic it does not return to its origin, it is a discontinous curve. It seems that it indicates a problem.

Thats a good question indeed Phage, and one that occurred to me immediately I saw it the first time. Truthfully I don't have a ready answer to give you as that particular section of the graph does indeed appear to be discontinuous.

The y-axis in the logsine graph represents the difference between the observed axial tilt value (for any given time period) by astronomers over the millennia and the 'expected' axial tilt value (for the same time period) as computed by the internationally accepted Lieske Formula. Consequently the range of the y-axis, based on the supplied 'observed' and 'formula derived' axial tilt values, will range between 0 degrees (meaning full agreement) and approximately +3 degrees (meaning significant disagreement).
It needs to be stated that as far as I can tell, this 0 - 3 degree range is specific to the current operating cycle and there are indications (by looking at other past/future) cycles that the axial tilt could potentially range from 0 - 6 degrees.

Anyway, in an attempt to try and get some (any) kind of answer, I've experimented by increasing the y-axis range way past 6 degrees and have yet to see the vertically rising asymptotes at any point suddenly connect over or link to adjacent cycles. To the best of my observations, each cycle appears to be independent and stand-alone.

So, confusing ? certainly ... does this invalidate the base data or the hypothesis ? hard to say.

After all, if we stick to just the current 'cycle', it's obvious that there is some 'unknown factor' at work causing the significant divergence of the observed axial tilt values from the expected Lieske output. And it was this 'factor' that allowed the derivation of the logsine curve in the 1st place .. .and as is easily seen, the derived logsine curve 'works' because the resultant differences between the observed and calculated values fits the derived curve beautifully.

Anyway, didn't say I had all the answers ... did I ?

posted on Jul, 28 2010 @ 02:44 AM

off-topic post removed to prevent thread-drift


posted on Jul, 28 2010 @ 02:46 AM
reply to post by tauristercus

I'm no scientist but for some reason it may just reach a "tipping point" and reverse...

Happens with other things,

posted on Jul, 28 2010 @ 02:50 AM
Great thread, and a fascinating read. I'm not quite sure I followed you when you leapt to the conclusion that this is a cyclical sort of thing. I think that the one-time major event is just as likely, could you clarify for me?

posted on Jul, 28 2010 @ 02:53 AM
reply to post by tauristercus

Anyway, in an attempt to try and get some (any) kind of answer, I've experimented by increasing the y-axis range way past 6 degrees and have yet to see the vertically rising asymptotes at any point suddenly connect over or link to adjacent cycles. To the best of my observations, each cycle appears to be independent and stand-alone.

Logarithmic trig functions do that.

posted on Jul, 28 2010 @ 03:19 AM

Originally posted by Loki
Great thread, and a fascinating read. I'm not quite sure I followed you when you leapt to the conclusion that this is a cyclical sort of thing. I think that the one-time major event is just as likely, could you clarify for me?

Thanks for that

It wasn't so much as a "leap" as an observation based on what happened to the "appearance" of the graph if there was an increase in dates (x-axis) and/or an increase in axial tilt (y-axis).

Initially the resultant logsine graph allowed the plotting of the 71 sets of data points incredibly well indicating that the equation used to create the logsine graph MUST be valid. Furthermore, based on the starting values used for the y-axis (0 to +3 degrees) and a date range for the x-axis (2345 B.C to 2145 A.D.), we had ourselves a beautifully functional graph that appeared to be asymptotic at either end.

It was only when I began to increase to date range on the x-axis that it became apparent that the part of the graph approaching the x-axis was not at all asymptotic to the x-axis but only APPEARED to be when based on a narrow date range.
But when the date range was increased significantly, you can see for yourself that the right side of the graph (almost parallel to the x-axis) begins to lift itself and go asymptotic in a vertical direction instead.
And then all of a sudden we see that there are similar cycles appearing for as far back in the past or as far forward into the future as you care to look.

My problem here is that I can't explain (at the moment) the significance of the multitude of cycles surrounding our current cycle and I'm not prepared to "throw" them away or ignore them either because the current cycle clearly handles the axial tilt data almost perfectly.

Anyway, why should our current cycle be granted a "special or favoured" position amongst ALL the cycles ? I can't justify taking such a stand.

posted on Jul, 28 2010 @ 03:27 AM
reply to post by Phage

Well we are able to completely rule out any issue with asymptotes due to the fact that a cubic polynomial has no asymptotes. This would be a continuous curve. The layout of the graphs displayed above look perfectly fine. The graph would get a little wavy around 8500 on the y axis but other than that it seems fairly logical.

posted on Jul, 28 2010 @ 03:52 AM
reply to post by tauristercus

Wow! Great thread!
I find many semi-connections with the work presented here and other alternate theories that I have read about in the past. At first the book, "Worlds in Collision", by Immanuel Velikovsky came to mind with his theory of a near collision with the planet Venus. I have done a bit of research on this idea and found quite a lot of evidence that seems to support Velikovsky's theory (or at least part of it).

Then you bring up the idea of this being a cyclical event rather than a one time deal. This reminds me of other theories I have read about. One pertains to precession of the equinoxes being caused by our Sun in a binary stellar orbit rather than from lunar/solar tidal effects. More on this can be found here, Binary Research Institute-
In my opinion this theory suggests a cycle that would cause a dramatic shift in the Earth's axial tilt due to a change in acceleration as the Sun drags Earth, and the other planets, around an elliptical stellar orbit. If this is the case then evidence could be found in the change of the axial tilt of the other planets in our solar system.

Another theory that comes to mind from reading your thread has to do with Yuga cycles pertaining to Earth's axial precession. Some call this the Great year and there are many documentaries about these theorized cycles and how they effect humanity. The key here, and what I find most intriguing, is the tie-in to astrology.

How can you be sure that this isn't a one time deal and is rather cyclical?
How accurate do you think your estimate of a 16,000 year cycle is?

I also notice the disconnect between the curves in your long timescale graph and wondered if this isn't half of a continuous wave.

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