Approximating the Fine Structure Constant

The fine structure constant is described as one of the most fundamental physical constants. I don’t pretend to understand anything about it apart from its value, which is close to 1/137. We’ve only been using it for around 100 years.

So the fact that the Khafre pyramid uses 137 as a size multiplier (base is 3 x 137, height is 2 x 137) is annoying, especially since the Khufu pyramid references the speed of light in metres per second, twice. The ancient Egyptians are not supposed to know those things.

Since the fine structure constant itself is a messy decimal number (0.0072973525693…) it is usually referenced via its inverse, as 1/137, which provides a reasonable approximation.

However there have been attempts to find a better approximation, and Scott Onstott has a page with some approximations. Which naturally was a challenge I could not resist….

So I saw that one of the better ones was based on 137²+π²…. and since the royal cubit is π/6, and I have lots of approximations for that, it was simply a matter of finding the right one that produced a better result. That turned out to be based on the plastic number… so without further fanfare, here we are:

$\frac{1}{\alpha} \approx \sqrt{{137^{2} + (\frac{\rho^{9}}{4}})^{2}}$

The WolframAlpha version of the formula is √(137² + ((plastic number^9)/4)²), which produces

137.0359992970725102075551820936909082242952278384186387671

We can check the percentage accuracy as well:

100/137.0359992970725102075551820936909082242952278384186387671 / (fine structure constant)

The Secret is as Simple as e

I updated my paper on the alignment of the pyramids again, and included some new diagrams. The most important of which is this stunning bit of simplicity. As a reminder. ⦦e means “360/e”, which is 132.437°. The pure elegance of this may be disruptive to existing theories about the alignment of the pyramids. You read it here first 🙂  (Always wanted to say that.)

How the pyramids are aligned, based on e

You can see the paper itself for the accuracy table. Two are accurate to less than 0.1° and the other is below 0.3°.

408, 199 and 159

A follow-up to the 437 post, this time applying the same methodology to Khafre and the other two pyramids.

If you have seen my papers then you will know that Khafre is often connected to the number 3. This same idea pops up here.

So …. Khafre has a base length of 411 ₢. 411 – 3 is 408.

If we had a square with side 408, then the diagonal would be 408√2, or 576.999.

If we divide 1000 by that (a process which effectively takes the inverse, and fixes the location of the decimal point), then we get

1000/576.999 = 1.733104858, which is a close approximation of √3 … it differs by 0.0010540… Accuracy is of course limited by having to start with whole-cubit dimensions.

I have tried the same approach with the other two pyramids, as follows. SInce we are using smaller dimensions to start with, accuracy does suffer a bit:

437

While playing around with the calculator, looking at relationships between the numbers at Giza, I took another look at the diagonal of the great pyramid.

The great pyramid has a base of 440 ₢. This means the diagonal is 440√2, which is 622.25 ₢. This is about 4 ₢ more than 1000/φ, which is 618 ₢. The error percentage is about 0.6%, which is annoyingly close.

So I got to wondering what base size would produce a diagonal more or less exactly 1000/φ.

The answer turns out to be 437, which is 3 ₢ less the existing size.

437√2 = 618.011 which is as close as you are going to get using whole-cubit dimensions.

But the oddness does not stop there.

Public nuisances

One of the downsides of running a public web site is the junk mail you get. It has long been standard practice to have a feedback form for users to contact you. This was not a problem in the beginning, but it wasn’t long before the lowlife on the net started to abuse the facility to send spam.

Season 1 Final

For the first Douglas Modern chess final, I decided on a 10-game match between the two contenders, with time control set at 30 minutes plus 15 seconds per move. I was worried that, sans opening books, they would simply play the same games over and over, but it turns out that they’re smarter than that.

There were more draws this round, given that the engines were as equal in strength as I could get, without the neural network ones. I have not succeeded in getting those (eg Lc0, AllieStein, Stoofvlees, etc) to work yet.

Of the ten games, Stockfish won half (as both black and white) and drew the rest. So we declare Stockfish the official champion.

The games in general were longer, some hit the 50 move rule, and there were those annoying shuffle endings as well. Anyway, here’s the numbers and the games.

Engine               Win     Draw    Lose
stockfish 111119 64  5 [3/2] 5 [2/3] 0 [0/0]
xiphos-0.6-linux-sse 0 [0/0] 5 [3/2] 5 [2/3]

Conventional scoring:

stockfish 111119 64  : 7.5
xiphos-0.6-linux-sse : 2.5

Games: 10; Draws: 5, DrawPercentage: 50 %
Whitewins: 3; Blackwins: 2, Draws: 5

Cute Chess scoring:

Score of stockfish 111119 64 vs xiphos-0.6-linux-sse: 5 - 0 - 5 [0.750]
Elo difference: 190.8 +/- 162.0, LOS: 98.7 %, DrawRatio: 50.0 %

10 of 10 games finished.

Points

stockfish 111119 64  : 374 : 74.8 %
xiphos-0.6-linux-sse : 124 : 24.8 %

Here are the games themselves. The “Mate of the Match” award goes to the 4th game.

I’m going to take a break from this now, though may post results on Github or write a paper, depending on how things go with work. Must finish the Giza papers.

Season 1 Semi finals

This was a double-round-robin between the top three CPU engines.

Engine               Win     Draw    Lose
xiphos-0.6-linux-sse 1 [0/1] 6 [4/2] 1 [0/1]
Ethereal 20191110    0 [0/0] 3 [1/2] 5 [3/2]
stockfish 111119 64  5 [3/2] 3 [1/2] 0 [0/0]

Conventional scoring:

stockfish 111119 64  : 6.5
xiphos-0.6-linux-sse : 4
Ethereal 20191110    : 1.5

Games: 12; Draws: 6, DrawPercentage: 50 %
Whitewins: 3; Blackwins: 3, Draws: 6

Cute Chess scoring:

Rank Name                          Elo     +/-   Games   Score   Draws
1 stockfish 111119 64           255     286       8   81.3%   37.5%
2 xiphos-0.6-linux-sse            0     125       8   50.0%   75.0%
3 Ethereal 20191110            -255     286       8   18.8%   37.5%

12 of 12 games finished.

Points

stockfish 111119 64  : 324 : 81 %
xiphos-0.6-linux-sse : 200 : 50 %
Ethereal 20191110    : 76  : 19 %

So Ethereal 20191110 drops out, and the other two go through to the final, which will be the longer game format.

Here are the games themselves. The “Mate of the Match” award go to the Ethereal 20191110 vs xiphos-0.6-linux-sse game (second one below).

Season 1 Round 4 Heat 1

This was supposed to be a double-round but I had to restart it because I selected the wrong version of Ethereal. And on the restart, forgot to make it a double round. Curiously, when I stopped it, Stockfish had a less-than-perfect score. So on the one hand, it had some losses or draws, and on the other hand, at least the engines are not simply playing the same game over and over. I will check the end boards when all is done and look for duplicates. So far there have not been any.

Anyway, here’s the results.

Engine               Win     Draw    Lose
Ethereal 20191110    1 [1/0] 3 [1/2] 2 [1/1]
stockfish 111119 64  6 [3/3] 0 [0/0] 0 [0/0]
Defenchess_2.2       0 [0/0] 2 [2/0] 4 [1/3]
xiphos-0.6-linux-sse 1 [1/0] 3 [1/2] 2 [1/1]

Conventional scoring:

stockfish 111119 64  : 6
Ethereal 20191110    : 2.5
xiphos-0.6-linux-sse : 2.5
Defenchess_2.2       : 1

Games: 12; Draws: 4, DrawPercentage: 33.33 %
Whitewins: 5; Blackwins: 3, Draws: 4

Cute Chess scoring:

Rank Name                          Elo     +/-   Games   Score   Draws
1 stockfish 111119 64           inf     nan       6  100.0%    0.0%
2 xiphos-0.6-linux-sse          -58     226       6   41.7%   50.0%
3 Ethereal 20191110             -58     226       6   41.7%   50.0%
4 Defenchess_2.2               -280     nan       6   16.7%   33.3%

12 of 12 games finished.

Points

stockfish 111119 64  : 300 : 100 %
Ethereal 20191110    : 124 : 41.33 %
xiphos-0.6-linux-sse : 124 : 41.33 %
Defenchess_2.2       :  48 : 16 %

So Defenchess_2.2 drops out, and the other three go through to the next round.
Here are the games themselves. The “Mate of the Match” award goes to  the Ethereal 20191110 vs stockfish 111119 64 match (first one below).

Season 1 Round 3 Heat 2

Another somewhat unexpected result … I was expecting critter to finish last.

Engine                 Win     Draw    Lose
critter-16a-64bit      2 [2/0] 0 [0/0] 4 [1/3]
xiphos-0.6-linux-sse   2 [1/1] 2 [2/0] 2 [0/2]
laser                  1 [1/0] 1 [0/1] 4 [2/2]
stockfish 111119 64    5 [3/2] 1 [0/1] 0 [0/0]

Games: 12; Draws: 2, DrawPercentage: 16.67
Whitewins: 7; Blackwins: 3, Draws: 2

Conventional scoring:

stockfish 111119 64  : 5.5
xiphos-0.6-linux-sse : 3
critter-16a-64bit    : 2
laser                : 1.5

Cute Chess scoring:

Rank Name                          Elo     +/-   Games   Score   Draws
1 stockfish 111119 64           417     nan       6   91.7%   16.7%
2 xiphos-0.6-linux-sse            0     271       6   50.0%   33.3%
3 critter-16a-64bit            -120     nan       6   33.3%    0.0%
4 laser                        -191     nan       6   25.0%   16.7%

12 of 12 games finished.

Points

stockfish 111119 64  : 274 : 91.33 %
xiphos-0.6-linux-sse : 148 : 49.33 %
critter-16a-64bit    : 96  : 32 %
laser                : 74  : 24.67 %

So critter-16a-64bit and laser drop out, and the other two go through to the final round robin.

The line-up for the final round robin will be:

Defenchess_2.2
Ethereal 20191110
stockfish 111119 64
xiphos-0.6-linux-sse

This may produce more draws than the previous rounds.

Here are the games themselves. The “Mate of the Match” award goes to the xiphos-0.6-linux-sse vs critter-16a-64bit game (second one below).

Season 1 Round 3 Heat 1

This result was the first one that surprised me … I was not expecting Defenchess to come out on top. In fact I thought it was going to be eliminated.

Engine            Win     Draw    Lose
Defenchess_2.2    3 [2/1] 2 [0/2] 1 [1/0]
andscacs          1 [1/0] 3 [2/1] 2 [0/2]
Ethereal 20191110 2 [0/2] 3 [2/1] 1 [1/0]
Fire_7.1_x64      1 [1/0] 2 [1/1] 3 [1/2]

Conventional scoring:

Defenchess_2.2    : 4
Ethereal 20191110 : 3.5
andscacs          : 2.5
Fire_7.1_x64      : 2

Games: 12; Draws: 5, DrawPercentage: 41.67 %
Whitewins: 4; Blackwins: 3, Draws: 5

Cute Chess scoring:

Rank Name              Elo +/- Games Score Draws
1 Defenchess_2.2    120 333 6     66.7% 33.3%
2 Ethereal 20191110  58 226 6     58.3% 50.0%
3 andscacs          -58 226 6     41.7% 50.0%
4 Fire_7.1_x64     -120 333 6     33.3% 33.3%

12 of 12 games finished.

Points:

Defenchess_2.2    : 200 : 66.67 %
Ethereal 20191110 : 178 : 59.33 %
andscacs          : 122 : 40.67 %
Fire_7.1_x64      :  98 : 32.67 %

So andscacs and  Fire_7.1_x64  drop out, and the other two go through to the next round.
Here are the games themselves. The “Mate of the Match” award goes to the andscacs vs Fire_7.1_x64 game (last one below).