Sunday, September 11, 2011

Euler poles and plate movement : Plate Tectonics' supporting pillars

( Blog for website at http://users.indigo.net.au/don )
(from the archives)



Fig.1. Manual construction.  Carey's caption reads, "Hemispherical table with the same radius as the globe behind, and spherically molded tracing foil for accurate comparison of continental shapes. The foil sheet on the upper left of the globe fits so accurately that it does not need sticking down, and North America shows through. On the table, two foil sheets have been joined to cover the whole arctic region." (Carey, 1989, Theories of the Earth and Universe, p.103).


The development of Plate Tectonics from sea-floor spreading was (and still is) all about the time (post-war funding generated by the politics of fear), place (the very few institutions who received it - and the correspondingly few 'key players' who had access to the data), - and spreading in the Atlantic (the cradle of it all :-: continental drift, sea-floor spreading, Plate Tectonics, and Earth expansion).

And so we begin this note with Sam Carey, the real father of Plate Tectonics, and his comment on Atlantic opening - though one could be pretty sure that is an attribution he would rather let pass to another. But history has it, (click the link and scroll down to comments by Moores, .. and Armstrong just below), so he doesn't have a choice.) Carey writes :-
" ..In 1929 appeared Sir Harold Jeffrey's prestigious book, The Earth - quite the most authoritative treatise ever on the physics of the earth, following the tradition of Osmund Fisher and Lord Kelvin. However, Jeffreys (1906 --) was completely opposed to Wegener's hypothesis, and in regard to the alleged fit of South America into the angle of Africa, he wrote: "On a moment's examination of the globe, this is seen to be really a misfit by almost 15 degrees. The coasts along the arms could not be brought within hundreds of kilometres of each other without distortion. The widths of the shallow margins of the oceans lend no support to the idea that the forms have been greatly altered by denudation and deposition.
From my many "moments" of accurate examination of this question that I had done, I knew this statement to be incorrect. I considered that the matter was rather trivial, that the true position would be generally realised, and that this criticism would fade away. But Jeffrey's prestige was so great that most workers accepted his pronouncement as final. Jeffreys repeated the statement in the second edition of his book in 1952, and to rub salt on the wound, Dr George Martin Lees (my former chief in the Anglo-Persian Oil Company), in his 1953 presidential address to the Geological Society of London, listed this as one of his three crucial reasons for rejecting the Wegener hypothesis. So I sent Lees my stereographic projections of two decades earlier [1933 - thirty years before 'Plate Tectonics' in 1960-1967 - d.f.] (Fig.11), proving that Jeffrey's statement was false. I added that "whether the continental drift hypothesis be true or false, this argument should never be used against it again." I asked Lees to arrange publication of this rebuttal, which he did.
When I went to England in the summer of 1960 as Tasmanian delegate to the third centenary of the Royal Society, Sir Edward Bullard invited me to lunch to discuss the Atlantic fit, which he then repeated with the aid of a computer. The Atlantic match has since been known as the "Bullard fit" and adopted generally. " (Carey, 1989, Theories, P.103.)

The "Bullard fit" of the Atlantic, usually figured so,

Fig.2. The Bullard fit. (Courtesy of On-line Encyclopedia Britannica.)

Many would say that anything better (finessing the dark blue /overlap parts) might be overkill, but Carey was prepared to address the point since many protested his derivative assertions.  Why I don'[t know. The figure is constructed of flat map cut-outs joined together, as you can tell from the skewed ("least squares") squares mirroring the projection. It's not a snap-shot of a globe.
[Addendum.  Scouring the web for an image from the original publication encounters a barage of paywalls.  Carey's first book (1976) shows the 'Bullard fit' to be the same as above but in black and white, from which it may be presumed that this is indeed the original. But to me this raises severe doubts about the efficacy of Bullard's 'least-squares' method of fit on a same-sized Earth, compared to Carey's on a half-sized Earth, which worked too (probably better - d.f. 2011-09-13)]  

Well, .. if geology was a romance, to be seen as either "philosophically satisfying or unsatisfying" when compared to the quantitative grit of the 'American Way' according to Oreskes, then the Atlantic was the elusively beguiling Queen, no matter from which perspective she was viewed.


Following Carey in 1933, and Bullard in 1965, the next to have a go now that the computer had demonstrated its formidable intellectual power was Jason Morgan, .. but just while we're talking about the Atlantic, the following figure, also of the "Bullard fit "from Dan McKenzie's account of his own role in the evolution of Plate Tectonics in relation to that of Jason Morgan, deserves a mention in view of the Bullard "fit" above.  Accent on theoretical (inductive /armwaving) coastline-fitting was shifting to take into account the Great Cross-Faults of the ocean floors which were becoming available, and which looked for all the world like tramlines of continental displacement.)  Crikey! This was something! Obviously what was needed was some theory to show that they were indeed 'tramlines' of movement ('rails' of convectional flow). So, think of one, measure them up, stick it in the box and see what comes out. The one that Jason Morgan came up with - rotation on Euler poles - is figured in Dan McKenzie's account : -


Fig.3 The Bullard fit again. This time three-dimensional, showing the latitudinal lines of displacement about a pole of rotation (an Euler pole), which is not the same thing as the North Pole - although in the case of the Atlantic and within the latitude of the 'fair go', it is close. McKenzie's caption reads : -
"..The fit between Africa and South America obtained by Teddy Bullard and his colleagues using Euler's Theorem (Bullard et al., 1965). The theorem states that any motion of a rigid plate on the surface of a rigid sphere corresponds to a rotation of the plate about some axis that passes through the center of the sphere. The problem on the Earth is that every point on its surface is on a moving plate, and no rigid sphere exists. So one plate must be chosen and taken to be fixed. Then the motion of any other plate with respect to this fixed plate corresponds to a rotation about an axis. In this figure Africa has been taken to be fixed, so South America moves. (a) shows the location of this axis, marked with an arrow, that Teddy and his colleagues found for the motion between Africa and South America. The circles are lines of latitude about this axis, just like the usual lines of latitude about the Earth's rotational axis. (b) shows the original position of the two continents before the South Atlantic opened., obtained by fitting the edges of the continents together. These edges are under the sea and are not the present coast lines. As the continents move, every point on the South American plate moves in a direction that is parallel to the latitude lines. This behavior is easily seen by comparing the positions of the latitude lines in the two pictures before and after opening. Their position on South America does not change. [Note that by 'plate', McKenzie means not just the continent of South America, but the ocean floor west of the spreading ridge as well, which is half way between the two continents."  [in Oreskes (2001), Plate Tectonics, an Insider's history of the Modern Theory of the Earth, P.174)

Considering the anathema that Earth expansion presents to Plate Tectonics it should not go unnoticed that North America and Europe are missing in the figure, and therefore that the sphere is effectively half the size it should be. The fit therefore is shown on a half-sized Earth, which is a construction supporting Earth expansion, not Plate Tectonics!  Just a nicety that should not go unremarked, .. particularly in view of McKenzie's comment that, "I remembered I had disliked the method he (Bullard) used to fit the continents together." (Oreskes, p.180.)

Well, .. they were all young then, . didn't have the mantle of gravitas that age and career usually bestows, so the figure could be excused for being a bit 'iffy' as regards support for Plate Tectonics (but very good for Earth expansion!), but it does show the point of small circle rotations. Whether or not those are real is another matter we might look at later - particularly in the case of equatorial dilations (rather than longitudinal ones like the Atlantic.)

After seeing a two-page note by Bill Menard (published in Science in January 1967), on the linear configuration of the Great Cross-Faults in the Central Pacific, Jason Morgan wrote a computer program that showed their configuration as small circles too.

Menard writes : -
Jason had already submitted his abstract for the April 1967 meeting, of the American Geophysical Union when he saw my paper. He was due to talk on "Convection in a Viscous Mantle and Trenches," but he immediately stopped his project and spent two months generating a computer program. I had learned about the properties of great circle charts as a naval officer, and so had he. What struck him about my illustrations, however, was not that the fracture zones were almost straight, but that they were not completely straight. It appeared that they followed the arcs of enormous small circles and that the radii of the arc increased from north to south. Like Teddy Bullard, he recalled Euler's theorem, and what he was programming was a means of determining an Euler pole from the geography of fracture zones. ( ...  )  So, as the geological world tried to accommodate to the shock of Vine's paper in December, Jason Morgan was already developing the quantitive theory of plate tectonics that would subsume the qualitative miracle of sea-floor spreading.   ( .... )  Jason Morgan's paper provided the foundation for all subsequent work on ancient plate tectonics and may have been the most important paper ever written in geology, and certainly in tectonics." (Menard, 1986, The Ocean of Truth, P.284.)
Fig.4 Menard's caption reads : "Morgan 's evidence that the old fracture zones that I had plotted (heavy lines) followed small circles (dashed lines) around a single Euler pole. (Menard, 1986, The Ocean of Truth', Fig.24c)
"Ultimtely it was not geology or physics, but a theorem proposed by the Swiss mathematician, Leonard Euler two centuries earlier, that provided the linchpin of plate tectonics." (Menard, Ibid., p.2)
"The most important paper ever written in geology"? Well, .. high praise indeed, to be sure! But it doesn't sound to me that a paper talking about a computer program and 'small circle fault traces' is saying very much at all about geology, other than that there is a sea floor with lines on it. Global geology involves rather more than a computer program to describe small circles, -- particularly when possibly they may 1. not be very small at all, and 2. separation by rotation is not the same thing as separation by convection.   Black boxes = "Garbage in, garbage out," if you don't consider the facts, particularly geological ones. And the main geological fact that was not being considered was that (according to Earth expansion here)  those 'small circles' were formed very close to the Pangaean equatorial zone (Synoptic simplicity, Fig.1) where small circles do very closely approximate great circles, and half of their extent is concealed in American override of the Pacific anyway. In such a situation it would be almost impossible to tell the difference, and a smaller Earth getting bigger would exacerbate the problem.

But it did at the time serve to describe plate *movement*. That is, .. if you ignored the along-ridge spreading, manifested in the difference in lengths between the spreading ridges and their original breakout from continental margins, which implied it was not movement at all in the rightful meaning of the word, but *growth* in the opposite direction, which in turn (when both sides of the ridge were considered simultaneously) implied UP, .. and Earth expansion.

Next was Dan McKenzie, who showed from earthquake first motions around the Aleutian Trench that this Pacific plate with the Great Cross-Faults (transform faults) could also move bodily in a direction other than that indicated by those faults (/cross-faults /transform faults). (Fig.5).




















Fig.5. Pacific plate motion according to Dan McKenzie's analysis of earthquake first motions. The caption reads : -
".. This figure shows the motion of the Pacific plate, obtained from the motion on faults during earthquakes,. when the North American plate is fixed. The solid dots show the locations of a number of large earthquakes produced by the motion between these two plates. The arrows show the direction of motion between the two sides of the faults on which these earthquakes occur when the side of the fault that is part of the North American plate is taken to be fixed and the Pacific side is moving. The map is in a special projection, chosen so that the motion of the Pacific plate is everywhere parallel to the big arrow if the plate moved rigidly. (b) Contours of the depth of the ocean around Hawaii, using the same projection as (a). If the volcano that forms the Hawaiian Ridge is fixed to North America, the ridge should be parallel to the large arrow, which is approximately true. (Courtesy of Oreskes, 2001, P.179)
So, .. Morgan says the Pacific plate moves west according to the tramrails of transform faults, and McKenzie says the same plate moves north according to the first motions of earthquakes. Different spatial moves for both of them, but both in the same time frame. This difference is rationalised in Plate Tectonics, not by trying to understand the information in terms of a single data-set and finding a single solution (the scale problem again), but by considering the data sets as independent and trying to find a solution that will suit each independently. Puzzling at first, this apparent contradiction is rationalised by hypothesising that the reference frames for the two movements are different : the Pacific plate (moving west in respect of original continental separation) is also moving north with respect to the fixed American plate. So relatively speaking, one movement is a subset of the other (a solution reminiscent of the olden days of astronomy when inventing epicycles to the planets was what the demonstration of intellectual endeavour was all about, and which earned the pleasure of the Pope as a demo. of God's work.)


But NASA's time series satellite data shows America is not fixed but is moving in accord with overriding (as Earth expansion maintains). So if we reverse the movement frame and consider the Pacific plate to be fixed and the American plate that's moving, then it also reverses the hotspot story : a fixed Pacific plate means the hot-spot must move.  But this would disturb the convection story necessary for the whole concept of plates - so we can't go there.
















Fig.6 Synopsis of the data. (You need to right-click this one to see a bigger figure.) Red arrow (visible on the larger figure) shows plate movement according to Morgan, pink arrow shows movement according to McKenzie, big white arrow shows direction of *growth* (projected on to the present-sized Earth) according to Earth expansion, small white arrows (pointing south) shows overriding according to NASA's time-series data and also according to expansion, and the smallest arrows with the red flag (pointing north) shows movement according to the USGS plate movement (presumably after McKenzie).

So, .. complications. ... Jason Morgan writes the paper that "provided the foundation for all subsequent work on ancient plate tectonics and may have been the most important paper ever written in geology, and certainly in tectonics", .. and Dan McKenzie's paper is the one generally cited as "the first paper on Plate Tectonics", yet both are citing exactly opposite conclusions regarding plate movements - for the very same plate, .. for the very same time. For the hypothesised reconcilliation of this, Jason gets a gong from my fishing buddy, .. and Dan gets the credit for laying the foundation of plate movement over hotspots. This is the doublethink Orwell warns us about, otherwise known as the PMWS syndrome - the Principle of Multiple Working Stories - much beloved of 4-year-old children as a way of rationalising 'the terror' - of the adult occupation of their world.

Earth expansion dispenses with all of these stories, beginning by recognising that ocean floors cannot move the way Plate Tectonics says, in a direction of either Morgan or McKenzie, but must grow towards the ridges.  And therefore move up, ..as Menard was reaching for with his "moving ridge" as a way of rationalising the difference in length between the magnetic anomalies at the ridges and those further away.  Expansion explains overriding as gravitational correction attributed to the brittle outer crustal shell, not gravitational correction due to a sinking slab, and overriding (not subduction) is supported by the satellite time series data (which is more recent than the USGS arrows. (I can't paste a quick-fig convenient copy of that since it is 'interactive', but if you go to the site you'll see what I mean..)

So which is to be believed? .. and on what grounds? The PMWS-supporting-pillars of Plate Tectonics? ... Or the ("neither of us believed for a moment ")  unbelievable, .. the unthinkable, .. the un-IMAGINABLE  Earth expansion, that solves all of these multiple (and contradictory) movements at a stroke?

...........................

Plate Tectonics is slowly having to admit the support for expansion in the OVERRIDING shown in NASA's own time-series data (Fig.6) (and in the Flat Subduction of the circum-Pacific. But it's taking its TIME. You know why? Because it's not a geological issue, .. and never was.  The issue is the corner Plate Tectonics has painted itself into.

"Least noticed, but most important of all, a generation of conservative geologists had passed on.  As Max Planck wrote in his autobiography, "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." (Carey, op.cit., p.121)

Now that Carey himself has passed on we are left with the tribal 'volunteers' from the compost of the mentis, convinced by the fatherly gravitas of those who firstly couldn't get their minds properly around what Earth expansion was saying, secondly were afraid of the implications for funding if they did understand it aright, .. and thirdly were denied the powerful three dimensional manipulation of the data that is now casually available to schoolchildren, thanks to Google Earth.


Well, we began this post with Carey, .. meandered through the young-lad supporting pillars of Jason Morgan and Dan McKenzie (and my fishing buddy George). In view of where all this is heading we might let Menard have the last word in regard to attempts to rationalise the along-ridge spreading, in a meeting discussion : -
"The discussion was brief, but it offered Vine the occasion to refer to convection cells as "presumed" and "mythical." Certainly , the many problems related to convection that had been troubling the conference members would have been solved by eliminating convection entirely. " (Menard, The Ocean of Truth, p.276.)
"Along ridge spreading", ..not from the continental side of any initial split, but from the oceanic side of differences in length of magnetic anomalies between those at the ridges (bigger) and those away from the ridge (smaller). Menards' remark that "It certainly helps to think about these things (ridge-length difference) at leisure.." has now had its leisure lengthened to half a century with still no takers on the Plate Tectonics side. Nobody has done it, because to do so challenges both the fundament and the firmament of Plate Tectonics. Menard did suggest that it might be explained by the ridges themselves moving (sideways), but moving sideways only works for one side of the ridge at a time (and provided the implications for the other side are ignored). If it is considered for both sides at once, .. well, .. that means (again) .. the only way it can do that is if the ridge moves UP (which means expansion).

You can see the problem that would have posed for Menard, given the hatchet job they already did on Bruce Heezen, which was also (I think) why as he says, "There is no record in the published account of any discussion after this talk." No wonder. Lurking under the surface here is probably the reason why Carey never took up the offers either, of a position in the States despite being quite pally with Hess, ..
"Harry Hess, chairman of the Princeton geology school, and I cemented a warm friendship that deepened until his premature death." (Carey, 1988, Theories of the Earth and Universe, 1988, P.119.
.
..and why he thought Tasmania on the other side of the world was just fine to pursue the geo-*logical* questions, instead of those arising from geophysical PMWS syndrome. Those guys and the institutions that housed them would not have thought twice about doing a hatchet job on him too, given half a chance, had he threatened the Big Story. They would have found a way, as Armstrong did in time in response to Carey's book, Theories of the Earth and Universe; (Hollywood Cowboys post and scroll down to 'Armstrong' again). And as many others have done too, labelling Carey (politely) as 'misguided'). But it would have had to have been more forceful than just removing handles from office doors (Ewing on Heezen), or forbidding him to use certain data at conferences (Ewing on Heezen again ).

Between the lines (of "Truth"), .. the story is actually quite murky.

("From the ashes, ..a phoenix rises.")


[See also blog for Earth expansion at :-
http://earthexpansion.blogspot.com/ ]

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