I came up with this in an Aha Moment, actually while lying in bed, as I was contemplating whether two 3×3 squares of a sudoku could be identical. The answer came quickly to me when I thought that if these squares were diagonally juxtaposed, they would be compatible if their elements were translated diagonally by one, along the same diagonal, of course, and these new ( identical ) squares were added to form a 2X2 sudoku.

Then, in a flash, I saw that this operation would allow THREE identical squares along a diagonal, with the diagonal translation performed twice, and with a third time producing the original square. That was it.

So the scheme is :

A B C
C A B
B C A

where A, B, and C are the 3×3 grids :

1 2 3   9 7 8   6 5 4
4 5 6   2 3 1   8 9 7
7 8 9   5 6 4   3 1 2

and the solution grid is:

1 2 3   9 7 8   6 5 4
4 5 6   2 3 1   8 9 7
7 8 9   5 6 4   3 1 2

6 5 4   1 2 3   9 7 8
8 9 7   4 5 6   2 3 1
3 1 2   7 8 9   5 6 4

9 7 8   6 5 4   1 2 3
2 3 1   8 9 7   4 5 6
5 6 4   3 1 2   7 8 9

So that’s the long and short of it, but it remains to specify the automorphism. Indeed, this whole question was perplexing to me, as I hadn’t been thinking in those terms.

Well, in the first place, we may specify the cyclic permutations of the “stacks” and “layers” ( i.e the columns and rows of the 3×3 squares ) .

Each of these, in our case, may be replicated, or reversed, by a permutation of the digits.

But also due to our particular configuration, these permutations may be replicated by permutations among the columns and rows within the stacks and layers.

So, at this point, I can only wonder how this particular case fits into the enumeration specified in the Wikipedia article.

So, it’s a mind bender, of this I feel sure.

We may also note that, as specified above, the downward rotation by one, among the layers, followed by, or “times”, the leftward rotation by one, among the stacks, “equals unity”, i.e. does not change the layout.

This is a consequence of the triplication of the three unique squares, and not usually to be found among other automorphisms.

… all presented for your consideration!

There is an extant video, from a traffic camera, I believe, that shows the moment of the onset of the the FIU bridge collapse of March 15, 2018.

I found a video showing the video on a screen with some people watching, and it is in a loop, which makes it easier to examine. It shows not only the moment, but the location of the onset, consistently with reports that the collapse “began at one end.”

Here is a two-frame gif from the video, showing the moments just before and after the onset:

I think this view is quite revealing, as it shows that the collapse was initiated by a break in the roof, meaning that it was bearing a critical load, or in crude terms, “It was the only thing holding up the bridge.”

This all makes sense from a simple point of view, considering the departure of the installation procedure from the initial design.

Here is a photograph of the bridge just before the installation, when it was being maneuvered into place. It is a very clear view, and answers many questions I had about the initial design … i.e. Had it been altered or even abandoned?

A comparison with an available diagram of the “cable-stay” design shows that all the design elements on the span itself are in place, and the installation allows for  the addition of the tower, and a second shorter span, as shown in the design:

A careful comparison of these shows that the configuration of the struts between the deck and the roof matches up very well, within the limits allowed by the images, of course.

Also, note the very prominent attachment points along the center of the roof. These “points” of attachment are very large and complex in appearance. I read that these attachment elements are not cables, per se, but “pipes”, but as per the design, they would have functioned as cables, that is, provided support under tension.

Compression vs. Tension

Here is a simple schematic analysis of an idealized truss, showing that in this configuration, the top and end pieces are under compression, and the bottom deck is under tension:

The red arrows show the forces on the nodes ( red dots ) due to the struts and deck, as per the requirement that the sum of the forces at each node must be zero.

So, the strut along the top is pushing outwards, and by reaction, it must be under compression. Conversely for the deck.

This logic applies exactly to the FIU bridge, and to me it accounts very well for the chain of events.

Well, I don’t mean to get into a particular analysis. I’ll just say that in my mind, “The Emperor has no clothes.”

After endless wanderings around the area of the announced drill site, it appears that they’re finally doing the deed, according to this sol 170 Navcam image, which shows the drill in position. That “telephone dial” is the opposite end of the drill axis, so the business end is at the surface. This is the first image I’ve seen showing this deployment.

This image taken a few minutes later shows the drill in another position, although it doesn’t seem to have been used yet. Subsequent sol 171 images show the drill being moved around some more, but again, no appearance of actual drilling:

Ok, big step here. I’ll be posting on  personal investigations and projects concerning science, math, and other subjects. Right now I’m hot on the Curiosity image gallery, so more on that soon.