Part 1 gave us the largest answer, Vicuna gives us the smallest. As a reminder, the correct answer is:
The first time I tested Vicuna, it said the following.
AI can’t do sums, Part 2: Vicuna-13b
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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:
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 https://www.tcec-chess.com/ as well as the rankings at https://ccrl.chessdom.com/ccrl/4040/ and selected the following engines to compete:
Bezerk
Stockfish 15
Ethereal
SlowChess 2.83
Koivisto_8.9
RubiChess
PeSTO
rofChade
Seer
arasanx-64
zahak
Igel
velvet-v3.3.0
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
Khufu’s Coffer is not 4th Dynasty
If the perspective looks odd, stand further away.
The 4th dynasty did not know π, φ, e, or ρ.
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.
How?
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.
The six pyramids and planets at Giza
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)
Astronomy 101 Final Exam
Time: 3 hours
Total marks: 200
Show all calculations. You may use a calculator and drawing equipment.
1a. Is Pluto a planet? [1]
1b. Justify your answer. [9]
Continue reading
Curious Local Government Elections Results Map
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.
Witzengerg:
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