The inscription on the Great Pyramid

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 …

Somewhat cryptic message

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.

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The silliness continues

I received another embarrassing email from this multi-talented Afrikaans lady who is both a sheriff and a lawyer, working at Adobe Inc (apparently).

Pathetic email

This one even includes the “you can trust us because we warn you about a scam” footnote.

Douglas Modern Chess, Season 2 Final

So I figured out the flaw in my scoring system. Because it uses the length of the game as part of the calculation, an engine that manages to get early draws (perhaps by threefold repetition) can game the system and get a higher score.

So I modified the system so that drawn games result in no score for either side. Also, computer chess often has arbitrated decisions to avoid tiresome endgames, which results in abnormally-shorter games, further complicating the concept of using game length as a determinant.

So the revised scoring for the semifinal was:

Raubfisch X41d3._sl         : 4.71
Stockfish 11                : 0.9
Zeus 4.1.7 M                : 0
Raubfisch_ME262_GTZ20d3._sl : -5.01

This does show a rather dramatic difference between the two Raubfisch variants, as well as between winner and second place. So I ran the final between the top two above, 10 games, time control 30 minutes plus 30 seconds a move.

The results were disappointing, of the 10 games, 9 were drawn, and those that I saw were rather boring, so I’m not going to post them. I will post the only one which had a result, and that was a mate as well. So Raubfisch X41d3._sl is crowned the winner with a score of 5.5 to 4.5 by conventional scoring.

My scoring was

Raubfisch X41d3._sl : 2.09
Stockfish 11        : -2.26

and the points system awarded

Engine                    Points  Percentage
Raubfisch X41d3._sl     : 274   : 54.8
Stockfish 11            : 224   : 44.8

The SuperFinals at TCEC usually have a lot more games, because most of them are drawn, which is very tedious.

Herewith the winning game. Stockfish was outplayed somewhere in the middle. The trapped bishop around move 48 led to disastrous loss of material.

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Elegance defined

Even though I’ve been staring at these numbers and relationships since 2018, I only tumbled onto this sequence this week. Those Egyptians loved mixing their units of length into irrationals.

The sequence is this, it’s a set of ratios:

F : ₢ :: 1 : é :: ℳ : φ² :: ₷ : π.

F = foot 0.3047 m (probable original length, not 0.3048 as declared now)
₢ = royal cubit 0.5236 m
1 = 1 metre
é = e – 1 = 1.71828…
ℳ = 1 + ₢ = 1.5236 ( == 5 feet)
φ² = golden ratio squared
₷ = six feet = metre + cubit + foot
π = pi.

Douglas Modern Chess, Season 2 Semifinal

Herewith the results of the semifinal, which was between Stockfish and three derivatives. I was actually expecting the the Raubfisch variants to come out on top, based on their performance in the heats, but it was not to be. Perhaps the longer time control affected things.

The results revealed a flaw in my own scoring system, which was supposed to prevent confusion about results, as shown below. First and fourth are mostly clear, but the 2nd and 3rd spots are more problematic. So I need to rethink my scoring before deciding who makes it into the finals.


Games: 12; Draws: 9, DrawPercentage: 75 %
Whitewins: 0; Blackwins: 3, Draws: 9

Longer time control, and stronger engines, means more draws. Curious that white was unable to win.

Conventional scoring:

Raubfisch X41d3._sl         : 4
Zeus 4.1.7 M                : 3
Stockfish 11                : 3
Raubfisch_ME262_GTZ20d3._sl : 2

Results table:

Engine                 Win     Draw    Lose
Raubfisch X41d3._sl    2 [0/2] 4 [3/1] 0 [0/0]
Stockfish 11           1 [0/1] 4 [2/2] 1 [1/0]
Zeus 4.1.7 M           0 [0/0] 6 [3/3] 0 [0/0]
Raubfisch_ME262_GTZ2   0 [0/0] 4 [1/3] 2 [2/0]

My scoring system which takes black/white and number of moves into account:

Zeus 4.1.7 M                : 14.82
Raubfisch X41d3._sl         : 11.61
Raubfisch_ME262_GTZ20d3._sl : 6.07
Stockfish 11                : 5.94

The problem with these scores is that an engine that failed to win, despite never losing, should not rank higher than an engine that did win (twice) as well as never losing. Hence I need to rethink.

My points-based scoring system, which takes black/white into account:

Engine                        Points  Percentage
Raubfisch X41d3._sl         : 202   : 67.33 %
Stockfish 11                : 152   : 50.67 %
Zeus 4.1.7 M                : 150   : 50 %
Raubfisch_ME262_GTZ20d3._sl : 102   : 34 %

These scores are better.

Cutechess scoring:

Rank Name                         Elo +/- Games Score Draws
1    Raubfisch X41d3._sl          120 162 6     66.7% 66.7%
2    Zeus 4.1.7 M                   0   0 6     50.0% 100.0%
3    Stockfish 11                   0 173 6     50.0% 66.7%
4    Raubfisch_ME262_GTZ20d3._sl -120 162 6     33.3% 66.7%

Cutechess also appears to rank Zeus above Stockfish, but it may just be sorting alphabetically based on score, without taking anything else into account.

So you can see the different scoring systems produce conflicting results, which I need to resolve before running the final.

Here are the games themselves. Time control was 20 minutes plus 20 seconds per move.

The only mate was between Raubfisch X41d3._sl and Zeus 4.1.7 M, the rest were decided by adjudication.

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