Part 67- Ma’at 02 Shows no Changes (Contrary to OSIRIS Findings)


UPDATE 12th April 2017

The lead author of the paper in question, Jean-Baptiste Vincent, responded to my email notifying him of this blog post. I’ve pasted it below. I’d refrained from doing so before now because it mentioned new discoveries that were as-yet unpublished but as of the date of this update two recent papers appear to have covered them. The original blog post begins after “///END”.

Dear Andrew,

I finally found some time to read your blog post and think about your criticism of the claims we made in the paper I published last year. As mentioned before, I strongly recommend that you publish your work in a scientific journal. MNRAS (Monthly Notices of the Royal Astronomical Society) is planning a new Rosetta special issue, with a submission deadline of 31 March 2017. I think you should submit a paper there.
Now regarding blog post #67. I would like to first clear some misunderstanding. 

The images you mention (Ma’at pit #2), are published in far lower resolution than the raw data we used for the analysis, and the conversion to jpg often introduces artifacts. Therefore, you should consider all these images as qualitative data only, and refer to the raw data for quantitative measurements. The raw images are publicly available on the ESA server (, with a resolution of 50 cm/px. This is the typical resolution at which we studied the comet morphology.

The ellipses overlayed on the images are not intended to mark precisely the edge of the “flow”, but rather show the region of interest where we have identified changes. It is done in this way as to not force our interpretation on the reader. It’s up to you to look at the region of interest and see for yourself whether you are convinced that the flow pattern has changed, or not.

The “after” image has been rotated in the paper, as to appear with roughly the same viewing angle as the “before” image, even though it was acquired from a very different direction due to orbital constraints (we needed to keep Rosetta in the terminator plane). After rotation,the azimuth of both images is comparable, but the elevation is still different, and this introduces a perspective distortion, which must be considered when comparing the images.

Because of the change of seasons, and different local time, the solar illumination is completely different in both images, by almost 180 degrees ! This is unfortunate, but there is nothing we could do to prevent it.

Therefore, as you noted in your post, both changes in perspective and illumination may fool us into seeing changes when there are none. I must admit that there was a heated debate in our team regarding this specific pair of images. Still today not everyone is convinced that the flow has changed, although the majority of our team members supports this interpretation, which is why we published it in this way. 

And there is an other complication: we have observed in nearby areas that a significant amount of dust has moved around (a couple of meters of dust thickness removed over 100m surface, and deposited elsewhere). This large scale resurfacing is changing the local albedo of the surface and complicates even more the interpretation.

I stand by my arguments that granular flows occur on the comet, and can repeat on a short time scale. We have multiple evidence for this and have recently submitted new papers with showing avalanches on >100m scale. The areas we mention in these papers were poorly observed by the NavCam, and the OSIRIS data is not yet public, which is why you may not have seen it already.

But how to really be certain about the changes I mention in the paper? I think the best way to get rid of most uncertainties is to work in full 3D by projecting both images on the shape model and then measure precisely the edges of the features of interest. Simply comparing features from one image to the next is not sufficient because of all the problems discussed above.

Such comparison was was not possible at the time of writing this paper. Today, we have performed a 3D “before and after” in a few specific areas of the comet, and hope to apply it to Ma’at in the coming months. 

It is also interesting to note that the crash site of Rosetta was selected especially because it would give us the chance to acquire higher resolution images of the pit and flows, with illumination conditions and viewing angle closer to what we had in September 2014. This new data set should also help us understand better if we are right with our original interpretation.
I’ll be happy to send you an update when we have progressed on this topic.

With best regards,


[End of email]

Here is the hi res version of the post-perihelion photo (Zoom plus original).



The pair of photos in the header is showing the pit known as Ma’at 02, located on the head lobe at Ma’at and near the head rim. It’s also called Deir El-Medina. It will be referred to here as Ma’at 02 or just 02 where it’s clear. That’s in keeping with Parts 62-65 where it’s called 02 so as to keep focussed on its middling position between the pits Ma’at 01 and Ma’at 03. This will become increasingly important as we see the significance of the fact that 01, 02 and 03 each sit on their own delaminated layers. That will be dealt with in another part soon. 

The header pair is from the paper, J.B. Vincent et al. 2015 entitled, “Are fractured cliffs the source of cometary dust jets? Insights from OSIRIS/Rosetta at 67P”. They constitute one set of before/after observations in figure 8 of that paper, which is in section 4.3.2 “Granular flows” on page 6. There are four photos in figure 8 showing two pairs of before/after observations. The full figure is reproduced below. 

Photo 2- J.B. Vincent et al 2015 figure 8 (hereinafter referred to as figure 8). 


The lower pair of photos will be dealt with in a future post. These two before/after pairs are the only two examples cited in Vincent et al. 2015 that claim visible evidence for changes in the supposed granular flow structures. We shall be focussing in detail on the upper pair, Ma’at 02, in this post. As you can see, the before photo is dated September 2014 and the after photo is dated March 2015. The caption claims that there are visible changes between the two photos. It says:

“Top panel: flows from Ma’at regions between two of the active pits have changed; their outline is different and they seem to have expanded laterally.”

This post will show that their outline isn’t different and that they haven’t expanded laterally. Therefore, the so-called flows in the the before/after pair haven’t changed, or at least, haven’t changed in any discernible way.

The claim of changes between the two photos was already called into question by Marco Parigi on his blog:

In his post, Marco reproduces the figure 8 photo and says, “Little effort is made to connect the dots for the reader to try to work out for themselves exactly what is happening and why.”

This post, Part 67, uses 34 photos, meticulously annotated in close-up, in order to define the same detailed features in the two figure 8 photos and does so at the 5- to 15-metre scale. This analysis is at a scale that’s an order of magnitude more detailed than the 130-metre ellipse placed over the entire flow in figure 8, without any further guidance. 

Since there was no discernible change at Ma’at 02 between the two photos, it follows that evidence for ongoing changes, less still erosion, at Ma’at 02 is not forthcoming. The reason this is important is that if the pits are virtually dormant it says something about their morphological evolution: that they perhaps had a more active period in the past but that their current very low activity is insufficient to produce any discernible changes over one perihelion passage. 

Alternatively, it’s possible that their current low level of activity is indicative of past activity and the pits were therefore formed over many thousands of years. This second scenario might be at odds with the assumed 13,000-year inner solar system dynamical history for 67P. Lack of erosion evidence also has implications for the heterogeneity of 67P: if a few pits are capable of being self-excavated slowly over a long period rather than by some other means, there must be pockets of volatiles stashed under the surface. 

Of course, this blog has its own explanation for all the pits, which is laid out comprehensively in Parts 62 to 64 as well as informing Parts 32, 41, 52 and an upcoming part. It’s beyond the scope of this post to bring that hypothesis to bear on the lack of ongoing erosion at Ma’at 02, or at least, to do so in any substantive way. However, the upcoming part will deal with this and there’s also a very brief overview in the ‘stretch explanation for the flows’ sub-heading further down. 

Links to Parts 52 and 62 to 64 are at the bottom of this post. 


Firstly, the aim of this post is certainly not an attempt to disprove the J.B. Vincent et al. theory that granular material may once have flowed down gravitational slopes, here or anywhere else on 67P, at some time in the past. Nor is it tasked with disproving that cliffs may have collapsed due to sublimation-induced erosion in the past (they almost certainly have to some small extent). This cliff-collapsing is cited in Vincent et al. 2015 as a precursor to granular material no longer being supported near the cliff edge. It’s claimed that the granular material therefore flows towards and over the edge as a result of the support being removed. 

Furthermore it’s acknowledged here that cliff collapse and granular flow may be ongoing processes but happening at a very slow rate. Indeed, I may have found one such collapse at Aswan but I’m waiting for better photos. If it’s borne out, it will be the sixth separate discovery of changes over the 2-year mission discovered by Marco and me (three each). All these changes show shifted material; none proves erosion in the sense of mass-wasting. This is entirely consistent with stretch theory. 

What this post does aim to do is lay out an analysis that shows there are no discernible changes between the before and after photos of Ma’at 02 in figure 8. There may have been changes which are not discernible but the apparent changes cited in the caption to figure 8 are due to the confounding effects of 1) a different viewing angle and 2) different lighting throwing different structures into more or less relief. 


The flows are referred to as “so-called flows” above, despite the theoretical possibility that these features might have experienced granular flow. The modifiers are added because this post (and the subsequent one on the second photo pair) will show that figure 8 does not offer evidence that they have flowed either during perihelion 2015 or at any time in the past. Therefore, nothing of any substance can be said about these features actually being flows. Only speculative deduction based on their flow-like form can be made. Since they may be flows and look like flows, it would be reasonable to include the modifiers but it’s not reasonable to state as fact that they definitely are granular flows. However, now that this distinction has been made very clear here, they will be sometimes be referred to as flows for brevity from now. That’s because that’s what they are commonly known as and it’s unwieldy to keep saying “so-called flow”. 

It seems ‘flows’ and ‘flow’ are used interchangeably for Ma’at 02 and that’s continued here. It conveys the idea that there are several separate flow-like features within the entire area that’s itself deemed to be a flow. 


It would be appropriate to give this explanation at this point because it would seem strange to be exhibiting manifest scepticism for the theory that these might be ongoing granular flows without explaining why they’re thought not to be. It’s true that they’re tentatively entertained here as possibly being flows that might even have flowed recently. But stretch theory points to them being a one-off drawing out of surface material during stretch. That does admit the possibility of some small amounts of more recent, vestigial flow due to light, ongoing erosion, which would be solar-radiation induced. 

The photographic evidence for stretch being the cause of the flows and any ongoing flow being negligible to non-existent will be presented in the post mentioned as being published soon.


Header reproduced

The three confounding issues regarding the comparison of the Ma’at 02 pair in figure 8 are explained briefly below before being laid out in detail under separate headings further down. 

1- the viewing angle of the before photo is about 100° displaced from the viewing angle of the after photo. This has the effect of enhancing the apparent area of certain gentle slopes in the crumpled terrain of the flow when viewed from one direction and diminishing them when viewing from the other direction. 

2- the shadowing is noticeably different between the two photos with a lighting azimuth change of around 130° relative to the local comet surface. This has the effect of enlarging or diminishing the apparent size of (presumably) otherwise unchanged features. It also results in a substantial area of the actual pit being illuminated so brilliantly that it appears not to be in the pit but on the rim. This affects 3, below. 

3- the ellipses placed over the flow that’s claimed to exhibit changes aren’t placed over the same area. The illusion in 2 has led to a misidentification of the pit rim in the after photo. This means the ellipse in the after photo has been shunted further over into the pit so as to incorporate this fake rim in the same manner as the true rim was incorporated into the ellipse in the ‘before’ photo. This has in turn led to a misidentification of the fiduciary features around the outer perimeter of the flow because the opposite side of the ellipse has been shunted over by a commensurate amount. The result is that the entire ellipse in the after photo is shunted a few tens of metres over in a direction that is towards the centre of the pit. 

Copyright ESA/Rosetta/NAVCAM – CC BY-SA IGO 3.0/A.COOPER

Photo 3- (taken from Part 66). The red view on the right is the ‘before’ photo viewing angle in Vincent et al., Figure 8. The yellow view is the ‘after’ photo’s viewing angle. The circa 100° change in viewing angle means that, in the ‘after’ photo, we’re viewing Ma’at 02 from the other side and from an ‘upside-down’ position. It should be noted that the right hand, red view is, confusingly, related to the left hand ‘before’ photo of Ma’at 02 in figure 8. And the left hand yellow view corresponds to the right hand ‘after’ photo in figure 8. 

The left hand ‘before’ version in figure 8 is what one might call the classic view, taken from above the head lobe. The right hand ‘after’ version is clearly from a different angle. One might at first think that the camera has been shunted towards the top of the frame with respect to the ‘before’ version. This is indeed the case but it’s been shunted so far that it’s gone right past the vertical point over the pit and on to a similar angle on the other side. 

So we’re looking at the pit from a completely different angle in the ‘after’ photo. Both views are around 40° from the local horizontal across the pit top. This was calculated from the fact that the pit is near-circular and the apparent length/width ratio is 0.6 or thereabouts in both photos. Sin-1 of 0.6 is 38° so let’s round it to 40° because it looks around 45° or just under. So the viewpoint has been rotated by around 180°- (40° + 40°) = 100° through a plane that arcs almost over the centre of pit to the other side. 

Since it ends up on the opposite side, the two views are in almost opposite directions, about 150° to each other when looking vertically down from above and into the pit. The 150° would therefore be the azimuth change which is rather like seeing the two viewing directions as two angled clock hands against the surface without being able to see that they also slope up towards us at around 40°, that is, sloping up in the vertical plane above the pit. 

Photo 4- the azimuth change. Red and yellow are at about 150° to each other when looked down on from above Ma’at 02. This isn’t quite directly above but high enough to show the azimuth change. 
Copyright ESA/Rosetta/NAVCAM – CC BY-SA IGO 3.0

This upside-down illusion was dealt with in more detail in Part 66. That part used two very similar photos of Ma’at 02, taken from almost the same two angles as the ‘before’ and ‘after’ photos in figure 8. One was the Ma’at 02 mosaic, taken by Rosetta on its final trajectory to its controlled crash-landing. This was stitched together by Rosetta blog commenter, Gerald. The other photo used was a classic NAVCAM view. Part 66 was primarily for context for people trying to make out the viewing angle for the stitched mosaic and alerting them to the fact that there was something of an illusion at play. It was pure coincidence that Part 66 uses two Ma’at 02 photos that are almost identical views to the Vincent et al. 2015 figure 8 pair, so Part 66 acts as a perfect primer to this part. It’s worth reading that part for an extra grounding although you can still follow this part fairly well without it. Neither photo 3 nor photo 4 above is from the pair used in Part 66 to illustrate the illusion. They’re old photos showing sideways and above views simply to demonstrate the 100° angle difference for the Part 66 pair and, by coincidence, for the figure 8 pair in this part. 

Returning to the figure 8 pair, the orientation of the ‘after’ photo has been kept the same way up in the frame i.e. no rotation has been allowed. This would be eminently practical for small movements in viewpoint but with a hike of 100° right over the pit, it means that the view is essentially upside-down. It could be argued that there’s no upside-down in space but this pair of photos is being presented to humans for comparison and humans have a built-in difficulty in recognising things that are upside-down or when they themselves have to turn upside-down to keep the subject the ‘right’ way up. This is what we are being asked to do before we start comparing the two views.

And of course, strictly speaking, on 67P there is an upside-down because there is some gravity. It’s probably around 2.5e-4 m/sec^2 at Ma’at 02. So, in photo 3, the lady’s hanging-down hair really would hang down if she were standing on a tower at the required viewing point. It would just take about a minute or a bit less for her hair to succumb to the weak gravity. 

Now, let’s say for argument’s sake that we were already used to looking at Ma’at 02 from this angle because we had all been schooled in viewing the whole duck-shaped comet in upside-down mode. That would be fine as far as it goes. But then the left hand photo of the pair would be unfamiliar instead. That’s our usual, familiar view and it would be deemed to be upside-down. Because we’re human and don’t like comparing things upside-down we object and try to flip them round (rotate them 180°). Part 66 goes into more detail on this. The only problem with rotating the ‘after’ version is that the two versions then face in opposite directions when put side by side for comparison. But at least that way we can start to discern the fact that we’re now viewing the pit from the other side, which has significant implications for the apparent changes described in the figure 8 caption. 

Photos 5 and 6- the figure 8 pair with the ‘after’ version (March 2015) rotated 180°.  
Photo 7- another photo with roughly the same viewing angle as the rotated ‘after’ version. This is photo 4 without the annotations. It gives more context of the surroundings showing that we are indeed now on the other side of the pit. Ma’at 02 is dotted blue
Copyright ESA/Rosetta/NAVCAM – CC BY-SA IGO 3.0

Photos 8 and 9- these are the same as photos 5 and 6 but they’re festooned with fiduciary points that match across between the two. 

By toggling, you can start to see you’re looking at the pit from a completely different direction in the two photos. The biggest giveaway is the two red dips at the back of the pit in the ‘after’ (rotated) version. They can be seen in full 3D sloping down into the pit. In the ‘before’ photo, all you can see is the profile of the top rims and can’t see anything of the majestic troughs sloping down into the pit below the rim. The same goes for the pink dip. In the ‘after’ version, we’re looking directly at the back wall of the pit. In the ‘before’ version, we can’t even see the back wall of the pit because the viewpoint is way back behind that back wall. And of course, the reverse situation applies with the other side of the pit and this contributes to one of the errors explained below (the inclusion of the rugged terrace and cutting off the end of the flow).

Consequences of the two different viewing angles:

The flow in question undulates as it progresses away from the viewer in both versions of the figure 8 pair. It’s now easier to see this using photo 5 with the ‘after’ version rotated 180°. Any slope that was angled towards the viewer in the ‘before’ photo (September 2014) is liable to be somewhat foreshortened in the ‘after’ photo (March 2015) and vice versa. In fact, there’s one quite severe slope that runs across the field of view from left to right in both photos. Its left hand end in the ‘before’ photo is its right hand end in the ‘after’ photo and vice versa. The fact it runs across the field of view means that it’s very noticeable as a long, wide slope in the ‘before’ photo and much narrower (but the same length) in the ‘after’ photo. It’s angled very much towards us in the before photo so it’s somewhere near to square-on to the viewer. In the after photo it’s angled very much away from us. That’s what makes it look narrower. 

Photos 10 and 11- the sloping ridge that gets foreshortened. Outlined in white. 


Photo 12- shadowing of the sloping ridge proving the slope is quite marked. Just the two ends of the ridge are dotted white. This is Gerald’s stitch of the 30th September 2016 landing trajectory photo. It will be presented again below for another reason.

If the viewer doesn’t know about the angling of this slope they don’t realise that the entire flow is foreshortened along its length in the ‘after’ photo with respect to the ‘before’ photo despite the actual flow being unchanged. Without that knowledge, it’s reasonable to think that the flow has changed shape between the two photos. More importantly, if the flow as a whole has been foreshortened along its length in the ‘after’ photo due to the foreshortened ridge, it means by definition that the length-to-width ratio has been reduced which is another way of saying that the flow now appears wider. This is what the figure 8 caption says: “they seem to have expanded laterally”. We shall see below that there are two other factors that contribute far more to the lateral expansion illusion, but this foreshortening of the length due to the 100° difference in viewing angle also makes its own contribution, exacerbating the illusion still further. 

The foreshortened slope shown above is the most obvious one in the flow but there are several other less dramatic slopes. Combining them makes for a flow that appears to change shape and texture before our eyes over 6 months when in fact it hasn’t changed in any discernible way at all. If you laid tin foil on a table and crumpled it to a similar degree as the flow, it too would appear to change shape and texture if you viewed it from either side of the table. 


Header photos reproduced for easy reference. The ‘after’ photo is rotated 180° (not numbered).


The azimuth angle of the sun to the local surface across Ma’at 02 swings by around 130° between the ‘before’ and ‘after’ photos. This makes the shadowing noticeably different between the two photos and it has the effect of enlarging or diminishing the apparent size of otherwise unchanged features. This exacerbates the foreshortened slope issue described above, which leads to the flow being slightly foreshortened along its length dimension in the ‘after’ photo. 

Moreover, the lighting angle change allows the flow’s outer perimeter to creep, so to speak. Its edge is sharply delineated by shadowing in the ‘before’ photo because there’s a fairly steep-sided trough running along behind the perimeter’s leading edge. This is thrown into shadow in that photo. However, this trough is rather whited-out in the ‘after’ photo. This makes the flow and the smooth, dusty area beyond it look to be roughly on the same level as if the trough that had been shadowed in September 2014 has been smoothed out into the dust of Ma’at by a few metres. It would have to be at least a few metres in order to smooth the sharp, steep perimeter slope of the trough into a shallow, blended slope. This blending is again, an illusion. The reason we can be sure of this is that photos from much later, including Gerald’s stitch* of the mosaic (September 30th 2016, 18 months later) show that the flow perimeter has apparently returned to its old September 2014 shape and position, i.e. contracting from the apparently spread-out, washed-out version of March 2016 and remembering its old shape. This is of course impossible so if September 2014 and September 2016 look the same it means the peregrinations of March 2015 never really happened and are a trick of the lighting. 

*To allay any fears that Gerald’s stitching process may have caused anomalous artefacts in the outer perimeter shown, we can see it along with the relevant unstitched mosaic component below it. This shows that no stitching was required in the actual flow area because the entire flow was caught within one mosaic frame. 

Photos 13 and 14- photo 13 is photo 12 reproduced: Gerald’s stitch of the 30th September 2016 mosaic component of Ma’at 02. Photo 14 is the relevant mosaic frame. Gerald’s stitch shows the flow looking essentially the same as it did in the Vincent et al ‘before’ photo that was dated September 2014, two years before.

In photo 13 (September 2016) the flow may be completely unchanged from two years before, in September 2014 or there may be some as-yet unidentified changes. But just like the Vincent et al ‘after’ photo, the viewing angle is on the wrong side of the pit for making subtle comparisons with the ‘before’ photo. However, the point being made here is that seeing as the view is on the same side as the ‘after’ photo (March 2015) it can be compared with that photo and it looks substantially different from it. This might suggest at first glance that change really was afoot but, on closer inspection, it’s different in such a way that makes it strikingly similar to the September 2014 ‘before’ photo. This suggests the flow never did change up to March 2015 (the ‘after’ photo) and that the changes in that photo are an illusion. 

The extent to which the 2016 mosaic frame is similar to the ‘before’ photo and different from the ‘after’ photo is entirely consistent with the illusions caused by the three points being presented here: viewing angle, lighting angle and ellipse placement. These three factors aren’t simply presented here as general confounding issues. Further below, we shall carve out the exact anomalous chunk from the ‘after’ photo that arises from the lighting illusion and also add in a section that arises from the foreshortening illusion. As a result, we shall end up with the true shape of the flow itself in the ‘after’ photo, which will turn out to be the same shape and size as depicted in the ‘before’ photo. 

The creep issue, related to the lighting angle change, also applies to other lumps and dips within the flow and its this creep that exacerbates the foreshortened slope issue, extending and retracting the periphery of each lump and dip. The outer flow perimeter just happens to be the most obvious example of this because it’s a continuous dip or trough, meandering along the perimeter and is set against the smooth, untouched dust of Ma’at. It’s easy for the lighting angle (from above the head lobe) to illuminate the trough in the ‘after’ photo and thus blend it into the smooth dust as if it has spread out. When lit from the other side, as in the ‘before’ photo and also the mosaic photo, the trough reappears markedly. It reappears either side of March 2015 (i.e. in September 2014 and September 2016) proving the blending illusion in the ‘after’ photo. Nothing has changed in any discernible way over the two-year mission. 

Photos 15 to 17- the outer perimeter of the flow is well-defined by the same lighting angle in both September 2014 and September 2016 but whited and smoothed out in March 2015. 

Copyright: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA. For photo 16 (Sept 2016) stitching credit: GERALD

In photos 15 and 16, the trough running along just inside the perimeter is in shadow. However, the perimeter is whited out in photo 17 (March 2015) due to lighting from circa 130° towards the opposite direction. This illuminates the trough, giving the impression that the flow perimeter has spread out further into the dust of Ma’at.  

The illusion of the blending of the perimeter into the Ma’at dust is greatly exacerbated by the misplacing of the white, dotted ellipse in the figure 8 ‘after’ photo. The ellipse perimeter ends up around 20 metres closer to this apparently blended perimeter line, thus giving the illusion that the already non-existent blending extent is 20 metres and not a few metres. This ellipse placement error is discussed in more detail under its own heading below. 

The circa 130° lighting angle change also results in a substantial area of the actual pit being illuminated so brilliantly that it appears not to be in the pit but on the rim. This is by far the greatest illusion between the ‘before’ and ‘after’ photos. From the figure 8 caption statement, “and they [the flows] seem to have expanded laterally”, it appears that this illusion has gone unnoticed. The authors have added the section that’s inside the pit in the ‘before’ photo to the rest of the flow in the ‘after’ photo. The section in the pit clearly isn’t part of the flow in the ‘before’ photo but again, because of white-out from much higher illumination, the lumps and dips in this area of the pit get smoothed together in the ‘after’ photo. In addition they’re apparently smoothed into the flow, increasing its width. But the smooth area of the flow actually starts on the true rim, about twenty metres above all these rugged bumps and dips. Their rugged nature betrays their true nature: they’re consolidated material sitting on a terrace, below the pit rim and therefore very much inside the pit. 

Photos 18 to 20- the rugged terrace perimeter is pale blue and the true pit rim is pale yellow. Other colours are fiduciary points: three light blue boulders, a fuchsia crack (not visible in the ‘before’ photo due to the 100° viewing angle change) and a dark blue ridge. These fiduciary points aren’t in photo 18 but are in its reproduced version in photo 25. 


Much work went into identifying the pale yellow rim across the apparently featureless ‘after’ photo. This was done using the ‘before’ photo as a reference for finding fiduciary points along the rim line (those fiduciary points are not shown here). Also, these fiduciary points on the ‘before’ photo were cross-referenced with other Ma’at 02 photos for confirmation. Photos were annotated with the yellow rim fiduciary points including the ‘before’ and ‘after’ photos. The after photo does exhibit enough faint features to catch the rim line. These photos will be added in an appendix in due course for completeness. However, if you look hard enough at the originals (using the annotations only as an initial guide), you can see the rim on the after photo. It takes some time though. 

UPDATE (INLINE APPENDIX- 5th November 2016)

As promised above, here are the photos with the fiduciary points for the pale yellow rim line. They’re in the following order with an ‘A’ for Appendix. 

A1-‘before’ photo with different, coloured dots acting as fiduciary points sitting on specific features (shape vertices and lines) near the pale yellow rim and across the flow area. 

A2- before photo ‘original’ but this is actually a zoomed in crop of an earlier version which still has the other annotations but is missing the ones dotted near the rim and on the flow as in A1 above. 

A3- the ‘after’ photo with the same coloured fiduciary dots as A1, i.e. placed on the exactly the same features near the rim and on the flow. 

A4- the ‘after’ original in the same manner as A2 is presented for the ‘before’ photo. 

A5- Gerald’s stitch with the same fiduciary points.

A6- Gerald’s stitch (original).

Key for the fiduciary dots on all three photos follow.

Light grey, brown, beige and slate blue single dots denote tips of pointed sections on the outer flow perimeter. Brown is more elusive than the rest.

Yellow- this nestles at the tip of a triangular set-back at the top of the slope and at the back end of one of the ‘fat tip’ areas. See further down for the fat tips. 

Green- this sits at one end of a small, smooth, straight section. The section is a narrow rectangle and other end of this rectangle is the slate blue tip. The width of the rectangle separates the fat tip area (whose apex is the slate dot) from the slope. 

Two dark blue dots- these sit on the two tips of a a swallow-tail feature at the back end of the area that leads across to the beige-dotted tip. The after photo shows the whole length of this area, from blue pair to beige as being one distinguishable area due to the apparent sweeping direction of the flow between them. This is partially apparent in the other two photos as well. 

Terracotta- a single dot along the sweeping flow between the blue pair and beige. This denotes a dip. 

Curving slate blue line- this is an obvious majestic curve. 

Light mauve- adjoining the slate blue line, this is a zig zag line. 

Fuchsia outcrop- this is actually part of the original annotations. The pale yellow line shows it consistently sitting inside the pit on the correct side of the rim. However, without any annotations, the outcrop apparently jumps out of the pit in the ‘after’ photo and sits perched on the rim with two sides bordering the flow. In the ‘before’ photo, just the tip of the fuchsia outcrop can be seen and it’s clearly in the pit. In Gerald’s photo, more of it is visible because it’s the same viewpoint as the after photo. It certainly looks more in the pit than out. The tip is in the pit, as for the ‘before’ photo and the rest is forming the pit sidewall, i.e. it’s inside the rim. 

The crucial point here is that Gerald’s photo and the after photo are from the same viewpoint and yet the everything left of the pale yellow line in Gerald’s is in shadow beyond the rim. This is in complete contrast to the ‘after’ photo that apparently shows the same area to the left of the pale yellow line as being just an ordinary continuation of the flow. It appears to be at about the same level as the rest of the flow, continuing on to a rim that would be about a third of the way across Gerald’s pit. The obvious drop-away into the pit in this portion of the ‘before’ photo shows that this can’t possibly be part of the flow. It therefore corroborates Gerald’s shadowed area that suggests a sharp drop-away too. So it’s clear that the area to the left of the pale yellow line in the ‘after’ photo is in the pit, beyond the rim, and yet appears to be part of the flow above the rim. 

All the fiduciary points marked in A1, A3 and A5 are apparently much further from the pit rim in the ‘after’ photo even though they have been very carefully placed on the same features. The most obvious example is the pair of dark blue dots on the swallow tail. The swallow tail is definitely right on the pit rim. And yet it’s apparently marooned in the middle of the flow in the ‘after’ photo. This is further corroborated in photo 18. The blue dots aren’t marked but the swallow tail tips can be made out fairly easily. They’re at the 8th and 13th pale yellow dots from the bottom. According to the ‘after’ photo, these two dots should be right out in the middle of the flow. And yet they’re on the rim in photo 18 as well.

UPDATE 2 (same date)- I decided to annotate photo 18 with the swallow tail dots after all. It’s important because identifying the shape of the swallow tail precisely, allows us to clinch the argument for the tail being apparently in mid-flow in the ‘after’ photo but on the rim in the before photo.
Photos A7 to A10 are variations on photo 18. 
A7-shows two larger dark blue dots on the central areas of the two fins of the tail and two small blue dots at the fin tips. It also shows the beige pointed tip and the terracotta dip (whited out). 
A8- shows the same as A7 but with the perimeter of the shape that’s obvious in the ‘before’ and ‘after’ photos as an identifiable shape in the flow- almost like an embedded mini-flow. With a swallow tail and a beak, it doesn’t quite look bird-like but it is a characteristic shape that can also be discerned in the ‘before’ and ‘after’ photos. Notice the characteristic, curved dip between the two fins that is especially visible in the ‘before’ photo, sitting right on the rim and just visible in the ‘after’ photo. 
A9- photo 18 reproduced to allow a dot-free analysis of the swallow tail while still having the pale yellow rim for guidance. 
A10- the true original with no dots for a completely dot-free analysis of the swallow tail and rim. 
The upper fin in A7 to A10 stays resolutely on the rim in all photos. The lower fin in A7-A10 appears to drift from the rim and across the flow by a few metres when viewed in ‘before’, ‘after’ and Gerald’s stitch. This is probably due to the A7-A10 photo being very well-lit and the other photos being subject to the same shadow-drift or ‘creep’ anomaly as described further above. However, the drift is small and it’s just one part of the whole swallow tail, which as a whole, is on the rim in the ‘before’ photo and halfway across the flow in the ‘after’ flow. 

Photos A7 to A10
And finally for this update, the ‘after’ photo with the same shape in beige with original (A11 and A12). Fins are in the centre of the flow.


Photo 18 is another one of the last photos of Ma’at 02, taken during the landing phase and it’s a very good overhead shot. Photos 19 and 20 are our usual ‘before’ and ‘after’ photos and the originals for all three follow them. The area enclosed by the pale blue and pale yellow lines is the same in all three photos and is the rugged terrace area. It’s the same area even though it changes shape due to the very different perspectives. There’s also some shadowing of the area in the ‘before’ photo. In that photo, the light blue dots turn to a darker blue in the shadow to show it’s an estimated line. And there’s some obscuration of the rugged terrace by the rim in the ‘after’ photo. This area enclosed by the pale blue and pale yellow lines, the rugged terrace, has been added to the flow area, in error, in the ‘after’ photo, March 2015. 

The spurious addition of the rugged terrace to the flow greatly increases the apparent width of the flow in the ‘after’ photo when compared with the ‘before’ photo. This illusion certainly would lead us to believe that the flow had “expanded laterally” when in fact it remained unchanged. 

The additional area taken up by the rugged terrace is on the opposite side to the outer perimeter that appears to be blended by 20 metres due to the ellipse border being placed 20 metres closer to the perimeter than in the ‘before’ photo. This means apparent width has been added to both sides of the flow. So with the inclusion of the rugged terrace, the apparent extension of the width of the flow is even greater. 


Photos 21 to 23- the misplacing of the ellipse. Photo 21 shows the ‘after’ ellipse superimposed over the ‘before’ photo, showing the discrepancy. Photos 22 and 23 are the originals with their respective ellipses for comparison. 


Further below we shall see how the ellipse crosses the outer flow perimeter in a different place in the ‘after’ photo from its crossing point in the ‘before’ photo. However, the most important things to note in the meantime are:

a) the inclusion of the rugged terrace by shunting the ellipse over into the pit in the ‘after’ photo.

b) the noticeably narrower area of smooth dust enclosed between the outer flow perimeter and the ellipse perimeter in the ‘after’ photo. as compared with the wider area of smooth dust enclosed in the ‘before’ photo. You can use the terracotta dots as a guide so you know what it is you’re looking for but then it’s best to toggle between the two original white-dashed ellipses to see this different-size area of smooth dust outside the flow perimeter. The markedly narrower area in the ‘after’ photo is enclosed between the 9 o’clock point and (almost) the 12 o’clock point on the white ellipse.

Photos 24 and 25- photo 24 is photo 18 reproduced. It shows the rugged terrace from overhead. Photo 25 shows the crucial part of the ‘after’ photo ellipse projected onto photo 24. The original follows. No apology is made for the weird ellipse shape. It follows the fiduciary points impeccably and is thus shaped due to the fact that the ‘after’ photo ellipse was projected onto different topographical layers (pit rim and pit base) causing parallax, and projected from a substantially different direction. 


Pale yellow- the pit rim as depicted very obviously by shadowing and topography in the ‘before’ photo (see the fuller description further below). 

Pale blue (medium size)- the perimeter of the rugged terrace, which is low down in the pit. The official term in the OSIRIS papers for ‘rugged’ is ‘consolidated material’ which is considered as being rocky in appearance, presumably comparatively solid (consolidated) and without any dust covering. In other words, consolidated material is wholly different in nature from granular flow that has to comprise dust and grit by definition. 

Pale blue (small)- the very small pale blue dots denote the best assessment of the bottom of the slope that runs between terrace and rim. This slope is also rugged and is shown here to be part of the area that’s been added to the flow area in the ‘after’ photo. In that sense it should be considered as being part of the rugged terrace for our purposes: a rugged area that’s been mistaken for a smooth, flowing area. 

In photo 24, the true pit perimeter is dotted pale yellow. This is the same line for the rim as is strongly suggested in the Vincent et al. 2015 ‘before’ photo. In that photo, this line is the dividing line between the obvious flow-like features bordering the rim and the steeply sloping, rugged terrain that drops away into full or partial shadow. The difference in terrain type either side of the rim (flow versus rugged) is very obvious in both photo 24 photo and the ‘before’ photo. However, it’s not at all obvious in the ‘after’ photo where the rugged terrace, including the rugged slope, is included and is assumed to be part of the flow. 

The spurious addition of the rugged terrace in the ‘after’ photo means that the rim of the Ma’at 02 pit has been misidentified in that photo whilst it’s been correctly identified in the ‘before’ photo. This leads to the ellipse being shunted over by about 20 metres, possibly 30 metres, in the ‘after’ photo. It’s shunted right into the pit area in the belief that the perimeter of the ellipse is just about enclosing the pit rim and therefore the flow perimeter that starts at the rim. But the ellipse perimeter is in fact enclosing the rugged terrace that’s well inside the pit.

Since the ellipse gets shunted by 20 or so metres on the pit side, it also gets shunted by the same amount on the other side at the outer perimeter of the flow. Otherwise, the ellipse would get fattened into a circle and the shunting error would be noticed immediately. 

This shunting means that the point at which the ellipse crosses the outer perimeter of the flow is further along the perimeter in the ‘after’ photo than in the ‘before’ photo. This discrepancy is about 20 metres which is roughly commensurate with the rugged terrace width of around 30 metres. 

The ellipse doesn’t only cross the outer perimeter of the flow 20 metres too far along. It also gets placed about 20 metres closer to the unchanged flow perimeter. This means there’s a 20-metre-narrower area of unblemished dust between the flow perimeter and the ellipse than in the ‘before’ photo. This is done in error and for no good reason. The viewer can’t help but look at the flow perimeter being substantially closer to the ellipse perimeter in the ‘after’ photo and assume that it has crept towards the ellipse perimeter by that amount between September 2014 and March 2015. But the simple truth is that it’s the ellipse perimeter that has crept towards the unchanging flow perimeter by virtue of being misplaced. 

This apparent movement towards the ellipse perimeter is exacerbated by the blending illusion described above where white-out in the ‘after’ photo seems to smooth the trough along the perimeter further out into the dust. 

When trying to identify changes with a +\- error of 2 metres, a 20-metre ellipse placement error is an order of magnitude greater than the error bars. This is in addition to the mistaken inclusion of the rugged terrace. Including the circa 30-metre-wide rugged terrace in the flow adds up to 50% to the flow’s width (50% across its central width, 10-40% either side- see below). This completely skews its apparent shape, rendering the comparison of the ‘before’ and ‘after’ photos in figure 8 completely useless. This is of course unacceptable.

Recapping the figure 8 caption in Vincent et al. 2015, it says:

“Top panel: flows from Ma’at regions between two of the active pits have changed; their outline is different and they seem to have expanded laterally.”

The changes in the flow are stated as fact in the caption whereas the analysis in this post shows there are no discernible changes in the flow at all. 

The statement above should be withdrawn along with the photos and an erratum issued for this paper regarding the certainty of ongoing granular flow or indeed any granular flow, ongoing or historical, on the comet. 

We’re still left with the hypotheses that granular flow may well have happened in the past but that is all. 


Photos 26 to 28. This is a sequence of three annotations showing essentially the same two things: (1) the extent of the rugged terrace area that was added and (2) the circa 20-metre section of the outer flow perimeter that was cut off the end. This sequence of pairs is the original header without the ‘after’ photo flipped. This is so as to compare the flow shape more easily in the context in which it was originally intended to be appreciated in figure 8, along with its caption. 


Photo 26 shows the before/after pair with the flow shape perimeters dotted in red as the viewer can only be expected to perceive them, given the visual cues and the explanation in the figure 8 caption. 

Photo 27 has the ‘after’ photo showing the true perimeter of the flow without the rugged terrace included. The ‘before’ photo is unchanged because it never included the rugged terrace nor was it truncated along its outer perimeter. You can now see the extra chunk of the flow that was cut off due to the 20-metre error. It’s encroaching into the ‘before’ photo because it was cut right out of the ‘after’ photo. 

Photo 28 shows the rugged terrace area in pale blue just to show how much area had to be removed in order to show the correct area of the flow. The measurement across the pinched central dimension of the true flow area is the same as the widest part of the rugged terrace area. This means the flow area’s width was doubled, no less, across its central dimension. It’s no wonder the flow looks like a fat rectangle in the ‘after’ photo. Its true, pinched shape is hiding in plain sight within the whited-out area. 

The 20-metre cut-out is shown in pale green in photo 28 as well. 

It should be stressed that, as with the rim perimeter of the flow, the true outer perimeter isn’t guessed. It’s been meticulously researched using several photos and by matching fiduciary points between them. This was needed to understand exactly where the ellipse crosses the outer perimeter in the ‘before’ and ‘after’ photos. 


You may wonder how different points on the the outer flow perimeter could be misidentified, since certain wavy sections look fairly obviously the same in both photos. However, there are also two different sections that look uncannily similar in both photos. The manifold illusions described above have resulted in a particular fat, pointed area on the flow perimeter in the ‘after’ photo being mistaken for the next fat, pointed area along in the before photo. That next area is highly visible in the ‘before’ photo and is at the true end of the flow. It’s the fat point that should have been chosen in the ‘after’ photo but it’s hardly visible there for reasons laid out below. The incorrect fat point that was ultimately chosen is the first one along from the true end point. It was probably chosen because it was:

a) the first discernible point along the perimeter in the ‘after’ photo. This was due to white-out and foreshortening of the true, first point.

b) this second point is roughly the same shape in the ‘after’ photo as the first point in the ‘before’ photo. 

Photos 29 to 31- the five fat points along the outer perimeter of the flow. The dots in photo 29 are just outside the tips of the points. Photo 30 shows the notional fat bodies of the points. Photo 31 shows them named ‘a’ to ‘e’. It should be noted that the light grey dot is sitting just inside its fat body and on the inside of its point tip. That’s because the rounded point tip is off-frame. The rounded tip is very obvious in all the other photos so it’s easy to judge that it’s only just off-frame. 

Incidentally, this being another September 2016 landing trajectory photo, it was taken within about an hour of Gerald’s stitched mosaic. Again, you can see that the outer perimeter, as defined by the coloured dots, is remarkably similar to the September 2014 ‘before’ photo perimeter. There are white-out issues in places but you can just about see the same line. 

It was d in the ‘after’ photo that was mistaken for e in the ‘before’ photo. e is the true last point at the end of the flow. e’s point is pink but e has a white perimeter because it comprises the sloping ridge mentioned above that’s already dotted white. Yellow and green are fiduciary points for other photos that may get added later. 

Incidentally, there’s a triangle between c and d that exhibits slight flow-like appearance but it’s less marked than the fat points along the rest of the perimeter. It was left out from being annotated in all three photos because it’s confusing in that it’s more apparent in some photos than others. The main thing is that it is there in all three photos and doesn’t change in any discernible way. That is itself one small additional piece of evidence for the flow not expanding laterally as claimed. 

This mistaking of d for e along the perimeter was possibly an error that was forced by the exigencies of moving the ellipse further over into the pit which was itself an error. In other words, it’s an error that might not otherwise have been made. However, if you were ever going to mix up two of the points along the outer perimeter, it would be these two. This is because the misidentified point, d, sits right at the top of the well-defined slope described in (1). That’s the white-dotted slope that’s much-diminished in the ‘after’ photo due to foreshortening. The correct fat point, e, is at the end of the flow perimeter. It’s perfectly visible in the ‘before’ photo and, crucially, its fat area (next to its actual pointed tip) comprises the very slope in question, the foreshortened slope. So, when trying to identify point e in the ‘after’ photo, it’s not there or it’s so hidden by foreshortening that it’s not very easy to see at all. This is compounded by the different lighting angle that whites out the sloping ridge anyway (it’s directly facing the sun) and smudges any vestige of the ‘e’ point because the ‘e’ point itself comprises the sloping ridge. In fact, the e point was so elusive that it was cut right out of the ‘after’ photo.

Photos 32 to 34- photos 32 and 33 show the foreshortened white ridge in relation to the fat points numbered a to e. You can see how the ridge comprises e and also that e’s shape in the fig 8 ‘before’ photo looks similar in shape to d’s shape in the ‘after’ photo. Photo 34 is Gerald’s stitch again, showing a similar angle to the ‘after’ photo but from a bit lower down.

Gerald’s photo shows the e fat-point perimeter in white (i.e. the end of the foreshortened ridge). This is somewhat guessed but that upper, white portion is nevertheless fairly accurate because there’s a faint white streak beyond it, leading to a double-bumped, pointed outcrop beyond. Those fiduciary features are just about visible in the ‘before’ photo and are foreshortened in that photo due to the 100° viewing angle change. In the ‘before’ photo, the white streak is almost invisible to the right of the dotted ellipse (and may admittedly be an artefact of the ellipse-dotting). The double bump, however, definitely does have highly foreshortened terrain between it and the bottom of the sloping ridge. Since we’re looking into a U-shaped dip in both photos, the white ridge is fairly square-on in the before photo while the white streak and outcrop are foreshortened. And conversely, in the after photo, the white ridge is foreshortened while the streak and double bump are more square-on. This apparently mind-numbing detail will help us greatly in understanding the stretch theory explanation for the flows, coming out soon. 

One might say that the features either side of this wrongly chosen point (which is point d at the top of the slope) should have shown up the error. However, the white-out and creep issues described above for the ‘after’ photo cause the fat area of the d point in that photo to mimic the shape of the e point area in the ‘before’ photo. The e area (sloping area) is perfectly visible in the before photo but now all but disappeared in the after photo, with its tip actually disappeared, off frame. If you hunt for it without knowing it’s disappeared you are liable to pick this same-shaped d area that’s actually the next area along, starting at the top of the slope. 

Just to complicate matters further, the somewhat larger, flat area that’s visible on the other side of this wrongly chosen d area in the ‘after’ photo, does apparently match between the two photos and is apparently correct. How can this be if the correct area (area e) is between the two? Again, it’s because area e has all but disappeared due to the foreshortening and white-out effects. This allows the area at the top of the slope to appear to join seamlessly to the larger area at the bottom of the slope. But the large area at the bottom of the slope has area e between it and area d at the top of the slope. 

The ‘after’ photo ellipse therefore cuts the outer flow perimeter off at the second-to-last fat point tip (the tip of area d), which is about 20% of the way along the perimeter length from e, thus shortening the flow’s outer perimeter length dimension by 20%. But since the ellipse is supposed to be showing the same area (because it crosses what is thought to be the same place as in the ‘before’ photo, point e), we’re led to believe that the outer perimeter length presented within both ellipses is the same. But the the flow perimeter in the ‘after’ photo is missing 20% of its length while masquerading as the full-length flow. This might seem automatically to result in an apparent 20% apparent extension in width by virtue of the law of proportionality. This is without even the addition of the rugged terrace. It’s probably more like 10% owing to the vicissitudes of the 100° difference in viewing angle.

Once this notional 10% is factored in, we still have the fact that the ellipse perimeter is 20 metres closer to the flow perimeter in the ‘after’ photo leading us to believe that it’s the flow perimeter that has crept towards a stationary ellipse by 20 metres. But the flow perimeter has stayed rock solid within the bounds of discernibility. 

The 10% is a length-to-width proportionality illusion. The 20-metre creep towards the ellipse is a translational shunt illusion. The foreshortened length due to the foreshortened slope is a also a length-to-width illusion. The rugged terrace is an actual inclusion of a real area, widening the flow even more. All four illusions work together to widen the flow substantially between September 2014 and March 2015. But in reality it remained unchanged. 

And indeed, it appears to have remained the same right up to the very last photo taken of Ma’at 02 in September 2016. 

This is notwithstanding further scrutiny of all the available photos on a much finer scale (at the same level of resolution as was conducted in this post) but using photos with similar viewing angles and lighting. I haven’t had the time to do this because of having a backlog of posts on other areas of the comet.  


This post has studied the ‘before’ and ‘after’ photos in the upper pair in figure 8 of Vincent et al. 2015. By analysing them at the 5- to 15-metre scale, it has been found that there were no discernible changes to the so-called flows between September 2014 and March 2015. This is in direct contradiction to the figure 8 caption which states:  

“Top panel: flows from Ma’at regions between two of the active pits have changed; their outline is different and they seem to have expanded laterally.”

It would be appropriate here to make a comment about the scale at which OSIRIS appear to be analysing the comet and the scale at which Marco Parigi and I are analysing it. Although OSIRIS have a shape model that’s accurate to the 5-metre scale, the photos in the OSIRIS papers are rarely analysed or annotated at a scale of less than 50 to 100 metres. In contrast, Marco and I consistently analyse the comet at the 5- to 15-metre scale, zooming right out to the 100m scale or more for context, then zooming back in to the 5- to 15-metre scale again for continuing the analysis on the adjacent area. This is reflected in our blog posts and our photo annotations. 

It would have been impossible to find the fiduciary points necessary to ascertain no change in the Vincent et al 2015 photo pair without employing this method and doing so using multiple photos from different angles (including many not actually reproduced in this post). This necessitated 34 annotated photos and 6000 words. This is because the flow area was scrutinised at the ~10 x 10 metre scale, meaning the flow was potentially divided into about 100 small areas instead of one big area (i.e. what was enclosed by the ellipse in figure 8). Around 20 of these smaller areas were shown via annotation and at least as many more were ascertained for orientation purposes but not used in the post. 

It’s therefore impossible to describe the shear intricacy of the Ma’at 02 pit in 23 words and two photos as figure 8 attempted to do. 

This assiduous approach to our analysis is why the four corrections I’ve made to OSIRIS papers to date (including this post) aren’t serendipitous finds. It’s borne of a rigorous analysis of almost the entire northern hemisphere down to the 5- to 15-metre scale. The same goes for Marco’s recent correction of the El Maarry et al. 2016 OSIRIS paper regarding the placing of the Anuket/Sobek border and notifying them of a cliff collapse. I made two further corrections in that paper (counting together as one of the four corrections mentioned above). All these corrections in El Maarry et al. 2016 were kindly acknowledged and corrected. One of the other two corrections I made for other OSIRIS papers was also acknowledged and corrected. 

I’m therefore loath to criticise sharply because Marco and I want to continue to be of help. However, it has to be said that, until the comet is scrutinised assiduously at the 5- to 15-metre scale, its morphological evolution won’t be understood. Analysing at this scale doesn’t furnish us with the last 5% of understanding; it furnishes the first 95%. It’s why this, the stretch blog, and Marco’s blog are currently well-advanced in understanding the evolutionary morphology of 67P. There are many additional discoveries of sub-mechanisms that drive morphological change and that have followed on naturally from what is now a nuanced understanding of the main stretch mechanism. A number of these sub-mechanisms are already documented in the previous 66 parts. Several more are still to come, along with dozens of parts showing examples of how these sub-mechanisms dramatically reshaped specific features. 


Part 52

Part 62 (click through to Parts 63 and 64)



Copyright ESA/Rosetta/NAVCAM – CC BY-SA IGO 3.0

To view a copy of this licence please visit:

All dotted annotations by A. Cooper. 




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