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Tuesday, July 29, 2008

Rendlesham Forest and The Utsuro Bune

A well recorded and little known event in the Western world would be the events of the Utsuro Bune. This is a myth dating from circa 1800 Japan. It states that a USO ( unidentified submerged object) washed up on the shore. The inhabitants of the village witnessed the object on the shore stating that is was spherical with strange writing on it. Out of the capsule came a woman dressed in fine clothing. She spoke a different language and was not able to communicate with the locals.
The Rendlesham forest story involves an American Air Force base in England. As I understand the story a UFO began shining a light beam ( as if to scan for something) across several portions of the base. The executive officer at the time a Lt. Colonel Halt led a team into the woods to chase after the craft. Apparently one of them got close enough to record symbols on the craft.
Image from the Utsuro Bune scroll
Writing seen on UFO at Rendelsham Forest
Here I would like to show the similarities between these two writings, despite the time difference of 200 years.It seems rather odd that there would be any similarties between these two. However, it can be seen that the commonality is the triangle with 2 circles. The differences being that the midpoints of the circles are lined up with the midpoints of the triangles in the Utsuro bune while in the Rendlesham the triangle is inscribed within a circle. The midpoints of the two circles seem to be in line with the centroid of the triangle.
I merely wish to present this curiosity and I have no intention of offering an explanation for it. Perhaps in the future there will be a greater connection.

Monday, July 28, 2008

Ancient Egyptian Binary Multiplication

I will be showing the method used by the Ancient Egyptians as seen in the Text - " A History of Mathematics" by Jeff Suzuki. This is an excellent text and should be read by those with a great interest or love of mathematics and or history.
To do this multiplication we can use Suzuki's Pseudo-Hieratic notation. This involves writing a number such as 23 as 20,3. Another example would be writing 156 as 100,50,6.
So I will use the example Suzuki gives in the text. Namely, that of multiplying 13 by 27 or in Pseudo-Hieratic as 10,3 by 20,7. This may be considered a form of binary arithmetic because of the doubling. This method is also known as the Method of doubling and halving.
I will first show a step and then explain what is happening.

Step 1.

Col. 1 Col. 2
1 20,7

2 50,4

4 100, 8

8 200, 10, 6

Pick one of the numbers in this case 20,7 (27). Now, write a separate 1 term in a column to the left. Now double the row.That makes 1 go to 2 and 20,7 go to 50,4 (27*2 = 54).Doubling again makes turns the 2 into a 4 and 50,4 into 100,8 (54*2=108). Doubling once more 4*2 = 8 and108*2 = 216.The doubling does not go on forever of course. We do this until with some combination of the factors present in column 1 can make up the other original multiplying term. In this case 1,4, and 8 make up 10,3 (i.e 1+4+8 = 13).

Step 2.
Col. 1 Col. 2
\1 20,7
2 50,4
\4 100,8
\8 200,10,6

In step 2 we simply highlight the rows where the single digits in column 1 add up to 13. So Row's 1,3 and 4 have single digits 1,4,and 8 which sum to 10,3 (i.e 13).

Step 3.

20,7 + 100,8 + 200,10,6 = 300,50,1. ( 27 + 108 + 216 = 351).

Now, in step 3 we are looking at the rows of interest pointed out in Step 2. From there we add the terms in Column 2.