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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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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