AI can’t do sums, Part 1: Olmo-7b-instruct.

I have been testing assorted so-called Artificial Intelligence Large Language models on their ability to do a relatively simple calculation. I ask, “Calculate πφ/e where φ is the golden ratio.”

You can paste “π*φ/e” into Google’s search box  (it needs the * to indicate multiplication and not Greek text), and it will tell you the answer, 1.87000613369.

Wolfram Alpha does it more precisely, as shown:

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Stockfish still the champ

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 as well as the rankings at and selected the following engines to compete:

Stockfish 15
SlowChess 2.83

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

The Great Pyramid is not 4th Dynasty

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.

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The Douglas Triangle

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)

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Zep Tepi Mathematics 101

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

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