It’s been a while since I’ve posted any chess, and development in the engine world has continued apace, so it was time to see how they do with Douglas Modern Chess.
I consulted recent events at https://www.tcec-chess.com/ as well as the rankings at https://ccrl.chessdom.com/ccrl/4040/ and selected the following engines to compete:
Pesto was not one of the top engines, it’s new, from the rofChade team, so I thought I would include it. I did try to add LC0, Cute Chess loaded it, but they still won’t talk to each other so there is still something wrong with my installation.
Initial rounds were round-robin and run at short time controls (3 min + 5 seconds, slowly adding 1 minute for each succeeding round). Continue reading
If the perspective looks odd, stand further away.
The 4th dynasty did not know π, φ, e, or ρ.
So I published the most important archaeological paper of the century …. which provides evidence (academic weasel words for “proves”) that the Great Pyramid is not 4th Dynasty.
Simply, the so-called King’s Chamber has at least π, φ, e, and √2 all built into the block patterns on the walls. Since the 4th dynasty did not know π or φ, let alone e, they could not possibly have built it (unless you have a flock of black swans in your back yard).
The paper is at The Writing is on the Wall: The King’s Chamber Game with an addendum with all the diagrams at The King’s Chamber Game Diagrams.
Here’s π and φ combined into one diagram.
π and φ in the King’s Chamber
The first two rows have 31 blocks, the next two have 42 … 3142 … π.
I have uploaded a new paper that shows how the pyramid sizes at Giza are related to the planets.
You can read the paper on Zenodo or Academia.
Here’s a teaser image.
Giza with planet names.
As 2021 drew to a close, I uploaded a new paper about the Douglas Triangle, and its use at Giza. It provides the missing link between the base sizes of Khufu and Khafre,
The triangle looks like this:
The Douglas Triangle
The triangle has some interesting properties, which are discussed in the paper, available at Zenodo or Academia.
As usual, soon after, I realised a few more things, and now need to update it, but that may have knock-on effect on Zep Tepi Mathematics 101 (ZTM101), so I need to run some checks first.
I have not found a direct use of the triangle (as triangle) at Giza, but have now found the three side ratios. Consider: (click images for larger view)
Time: 3 hours
Total marks: 200
Show all calculations. You may use a calculator and drawing equipment.
1a. Is Pluto a planet? 
1b. Justify your answer. 
The official results map from the IEC is at best confusing and at worst, deliberately misleading.
Here is the overview map of the Western Cape. The circled areas are 100% complete, but the detailed view is very different to the overview. Starting top left, moving counter-clockwise.
A few weeks back I released another paper, entitled Zep Tepi Mathematics 101, which I thought was an appropriate title, but it looks like it was a bad choice and is not appealing to the target market.
The first part is actually a simple explanation of how the Giza site was laid out, using mostly √2, √3, and √5. No Orion required.
You can find the latest version at Zenodo (current version is 1.1.0), and also at Academia.
Here are some of the more important images discussed:
Six pyramids aligned, 55.5k BCE
There is an inscription carved into the rock near the actual entrance to the great pyramid. There seems to be only one decent photo available, but it is copyrighted, so you will have to accept my hand-drawn version instead:
Inscription at entrance to Khufu
Various people have offered their interpretation of what it means, usually based on a reading of Proto-Sanskrit or Proto-Libian or similar.
My own interpretation is much simpler. It’s basically what is arguably the most well-known mathematical formula in the world, taught to every primary school child.
How do we typically indicate “area” on a drawing? Usually by some form of shading or hatching, and indeed, Unicode includes some characters indicating exactly that, for example
Today, we use the Greek letter π to represent the ratio of a circle’s circumference to its diameter. A different culture would have used a different symbol … perhaps a symbol with a diameter and a circumference, like this?
Circle with diameter … ancient symbol for π?
Which leads to …
πr² = A
And thus the mystery is solved …
I haven’t post anything in a while… got caught up with keyboard layout optimisation again, but am now back detangling Giza.
My guides nudged me to stumble across this last night.
At first I was flabbergasted, I was stunned…
Kept thinking I could not be the first …
Meawhile I got the distinct impression my guides were doubled over with laughter …
Rechecked the calculation on Wolfram Alpha (full values, rounded values) but it’s right… Using the rounded values, the answer is 1618.0049443… or 1618 rounded.
Asked Google who else has seen this but could not find anything … if you know, please leave a comment …
So this is a somewhat cryptic image … those “skilled in the art” will immediately understand what it is about and what it means.
The dimensions of the rectangle are thanks to John Legon.