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Snakeboy
02-23-2014, 08:02 PM
There are some interesting loops in pi digits, thought I'd toss this out there for funsies :D

Excuse my novice notation, haha, Richard, if you have a more elegant way to write this out, please do

Following the rule that : the string becomes the position which becomes the string ( I'll use " Sn " for string number and " Pn " for position number, I started with the numbers 0 through 9, and located the number 0, the position of the number ( after the decimal ) becomes the next string to locate ( Sn → Pn → Sn )

The process is easy, you start with the number and find it's position in pi digits, the position of the number becomes the next string to search for.

For 0, 2 through 7, and 9, the series converge on each other fairly quick, 1 is a self-locating digit in pi ( a rarity in itself )

However, at 8 something neat happens:

As the series Sn → Pn → Pn progresses for 8, at the 12th step, you come to 3332, and progressing the series, it loops back on itself to 3332 after 11 steps.

The string 3332 occurs at position 48033, following the rule, it comes back to 3332, ( → ∞ )

I have not been able to find where and when the numbers actually loop back to themselves, if they do at all, However for the number 8 it seems impossible, following that rule of Sn → Pn → Sn :O

-----------------

There are some other loops, here's one:

The number 169, located at the 40th place, following Sn → Pn → Pn , loops back to 196 after 21 steps in the series

So, if you like:

1. Find when and where the numbers 0 - 7, and 9 loop on themselves in pi digits following the rule defined above, or, state why they cannot. ( I so far have not found them to loop )

2. There are two numbers we cannot do this with, 1 and 8

Explain why it's impossible with the number 8

3. Find a proof of whether or not there are an infinite amount of looping numbers in pi﻿

Here are the numbers 0 through 9, following the rule:

0 )→ 32 → 15 → 3 → 9 → 5 → 4 → 2 → 6 → 7 → 13...

1 )→ 1 → ∞

2 )→ 6 → 7 → 13 → ...

3 )→ 9 → 5 → 4 → 2 → 6 → 7 → 13...

4 )→ 2 → 6 → 7 → 13...

5 )→ 4 → 2 → 6 → 7 → 13...

6 )→ 7 → 13 → ...

7 )→ 13 → ...

8 )→ 11 → 94 → 58 → 10 → 49 → 57 → 404 → 1272 → 8699 → 3292 → 3332 → 48033 → 90311 → 7573 → 1959 → 985 → 2154 → 5276 → 33991 → 18316 → 32928 → 3332 → ∞

9 )→ 5 → 4 → 2 → 6 → 7 → 13...

--------

8 of the series converge at 13
8 of the series converge at 7
7 of the series converge at 6
4 of the series converge on 5
4 of the series converge on 4
6 of the series converge on 2

For 0 and 2 -9 , the series grow fast and and the strings show no signs of shrinking back towards their starting values

---------

Have fun, and if you can simplify the notation or find any more looping numbers, please add them

Cheers :yo:

Richard Amiel McGough
02-23-2014, 10:29 PM
There are some interesting loops in pi digits, thought I'd toss this out there for funsies :D

Excuse my novice notation, haha, Richard, if you have a more elegant way to write this out, please do

Following the rule that : the string becomes the position which becomes the string ( I'll use " Sn " for string number and " Pn " for position number, I started with the numbers 0 through 9, and located the number 0, the position of the number ( after the decimal ) becomes the next string to locate ( Sn → Pn → Sn )

The process is easy, you start with the number and find it's position in pi digits, the position of the number becomes the next string to search for.

For 0, 2 through 7, and 9, the series converge on each other fairly quick, 1 is a self-locating digit in pi ( a rarity in itself )

However, at 8 something neat happens:

As the series Sn → Pn → Pn progresses for 8, at the 12th step, you come to 3332, and progressing the series, it loops back on itself to 3332 after 11 steps.

The string 3332 occurs at position 48033, following the rule, it comes back to 3332, ( → ∞ )

I have not been able to find where and when the numbers actually loop back to themselves, if they do at all, However for the number 8 it seems impossible, following that rule of Sn → Pn → Sn :O

-----------------

There are some other loops, here's one:

The number 169, located at the 40th place, following Sn → Pn → Pn , loops back to 196 after 21 steps in the series

So, if you like:

1. Find when and where the numbers 0 - 7, and 9 loop on themselves in pi digits following the rule defined above, or, state why they cannot. ( I so far have not found them to loop )

2. There are two numbers we cannot do this with, 1 and 8

Explain why it's impossible with the number 8

3. Find a proof of whether or not there are an infinite amount of looping numbers in pi﻿

Here are the numbers 0 through 9, following the rule:

0 )→ 32 → 15 → 3 → 9 → 5 → 4 → 2 → 6 → 7 → 13...

1 )→ 1 → ∞

2 )→ 6 → 7 → 13 → ...

3 )→ 9 → 5 → 4 → 2 → 6 → 7 → 13...

4 )→ 2 → 6 → 7 → 13...

5 )→ 4 → 2 → 6 → 7 → 13...

6 )→ 7 → 13 → ...

7 )→ 13 → ...

8 )→ 11 → 94 → 58 → 10 → 49 → 57 → 404 → 1272 → 8699 → 3292 → 3332 → 48033 → 90311 → 7573 → 1959 → 985 → 2154 → 5276 → 33991 → 18316 → 32928 → 3332 → ∞

9 )→ 5 → 4 → 2 → 6 → 7 → 13...

--------

8 of the series converge at 13
8 of the series converge at 7
7 of the series converge at 6
4 of the series converge on 5
4 of the series converge on 4
6 of the series converge on 2

For 0 and 2 -9 , the series grow fast and and the strings show no signs of shrinking back towards their starting values

---------

Have fun, and if you can simplify the notation or find any more looping numbers, please add them

Cheers :yo:
Hey there Snakeboy,

It's an interesting coincidence that you bring up loops in pi because I wrote a little program yesterday to confirm your previous observations about pi, and for fun I modified it to look for loops in the first million digits. But your comments do not seem entirely accurate. The numbers don't cycle or converge like you say they do. I have only found a few numbers that cycle even when looking in 200 million digits of pi. A good example of a cycle starts with 37:

37 => 46 => 19 => 37

And here is another cycle that begins with the number 40:

40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40

The number 8 does not cycle in the first 200 million digits of pi. I used this page (http://www.angio.net/pi/) to check the results that were larger than a million (which is all my little program could handle). Here is how it begins:

8 => 11 => 94 => 58 => 10 => 49 => 57 => 404 => 1272 => 8699 => 3292 => 3332 => 48033 => 90311 => 112817 => 1149731 => 24909936 => 1838500 => 5264650 => 29232231 => 76236585 => 64535680 => 49758988 => 191873638 => not found

The "not found" means that it the number 191873638 does not appear in the first 200 million digits of pi. It did not "converge" to anything. It did not cycle. The sequence could continue increasing forever for all we know.

I think you mistake is to use the word "converge." In mathematics, that word means that a sequence gets closer and closer to a single value. For example, consider the sequence defined by ratios of Fibonacci numbers:

R(n) = F(n)/F(n-1)

This sequence converges to the Golden Ratio: R(n) => Phi as n => infinity. It begins 1, 2, 1.5, 1.666..., 1.6, 1.625, etc.

Now I do understand what you are getting at when you say that they "converge" - what you mean is that two sequences beginning with different starting numbers merge and become the same sequence, whether or not the sequence diverges to infinity or loops. I don't find that particularly significant because the you were just looking at single digits, and they are first found near the beginning so their place numbers would be expected to be small, and hence coincide with small integers.

In any case, math is fun. Thanks for sharing your research.

Richard

Snakeboy
02-23-2014, 11:44 PM
Sweet, I figured you'd catch anything, it's good you caught that early, it seemed odd, lol.

Anyway, I'm up to 20 so far, 16 seems to go to 40 and loop back, and 19 seems to loop on 37

You ever see how the Fibonacci numbers can all be reduced down to the same 24 digit string ?

I thought that was pretty cool, read about it while trying to learn some series analysis.

Snakeboy
02-24-2014, 12:00 AM
aha, I just realized the search window on my pi search page seems to randomly count a space as a digit of some sort

I'll have to try your page

Snakeboy
02-24-2014, 11:09 AM
Well, this does seem interesting, excluding my hare-brained mistakes right off the bat :D

Is it safe to say that all numbers within a loop are themselves looping numbers ?

Like the 40 to 40 loop you gave as an example.

Snakeboy
02-24-2014, 02:18 PM
So I went through the first 50 numbers, double checked everything, so I hope this is correct :D

16, 19, 23, 37, 39, 40, 43, 45, 46 will all end up in a loop

Something neat, I thought, :

19*37 are factors of the triangular figurate number 703

Number 19 will loop and have 46, 37, and 19 in the series of the loop

19 numbers down the line:

Number 37 loops on itself with 46, 19 and 37 in the series in the loop

Further down the number line is number 46, which loops on itself with 19, 37 and 46 in the loop

---------

Numbers 16, 23, 39, 40, 43 all have the same loop as well, consisting of 20 numbers, in the series of the loop.

1, 14, 21, 45 all loop back to the first self-referencing digit in pi, 1

Richard Amiel McGough
02-24-2014, 09:32 PM
Well, this does seem interesting, excluding my hare-brained mistakes right off the bat :D

Is it safe to say that all numbers within a loop are themselves looping numbers ?

Like the 40 to 40 loop you gave as an example.
Yes, any number that is part of or leads to a loop could be called a "looping" numbers. The other numbers would be divergent because they lead to a sequence that ultimately goes to infinity. I doubt there is any way to prove that any numbers ultimately diverge, since that would probably require knowing all the digits of pi. And it seems unlikely that even most numbers loop because the density of the digits smaller than "place number n" keeps getting thinner.

To understand this, consider how many distinct 2 digit numbers we could fit in the first hundred digits of pi:

x1 (i.e 11, 21, 31, etc.)
x2 (i.e. 12, 22, 32, etc.)
x3 (i.e. 13, 23, 33, etc.)

The problem is that we are concatenating them and we only have a string of 100 digits to work with.

x0: 102030405060708090
x1: 11213141516171819
x2: 12232425262728292
x3: etc.

As you can see, each line requires about 18 digits to cover all the possibilities. But there are ten lines. So that means we need about 180 digits, but we only have 100, so about 45% of the two digit starting numbers won't be found in the first hundred digits, in which case the position number will be larger than the starting number and the sequence will diverge. So I predict that cycles will be pretty rare in the digits of pi, or any sequence of random numbers. With a little work this could be written as a formal theorem.

Richard Amiel McGough
02-24-2014, 09:52 PM
So I went through the first 50 numbers, double checked everything, so I hope this is correct :D

16, 19, 23, 37, 39, 40, 43, 45, 46 will all end up in a loop

Something neat, I thought, :

19*37 are factors of the triangular figurate number 703

Number 19 will loop and have 46, 37, and 19 in the series of the loop

19 numbers down the line:

Number 37 loops on itself with 46, 19 and 37 in the series in the loop

Further down the number line is number 46, which loops on itself with 19, 37 and 46 in the loop

---------

Numbers 16, 23, 39, 40, 43 all have the same loop as well, consisting of 20 numbers, in the series of the loop.

1, 14, 21, 45 all loop back to the first self-referencing digit in pi, 1
So you are doing this all by hand, putting the numbers in one at a time? You should learn a little javascript programming. It does all the work for you. Here are all the looping numbers less than a thousand found in the first million digits of pi. (There may be more if we used a larger set of pi digits.) It took about ten minutes to write, and 5 seconds to run.

----------------
Start: 1
1
----------------
Start: 14
1
1
----------------
Start: 16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 19
37
46
19
----------------
Start: 21
93
14
1
1
----------------
Start: 23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 37
46
19
37
----------------
Start: 39
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 45
60
127
297
737
299
2643
21
93
14
1
1
----------------
Start: 46
19
37
46
----------------
Start: 60
127
297
737
299
2643
21
93
14
1
1
----------------
Start: 61
219
716
39
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
70
----------------
Start: 71
39
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 73
299
2643
21
93
14
1
1
----------------
Start: 93
14
1
1
----------------
Start: 96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
70
96
----------------
Start: 115
921
422
1839
9323
14
1
1
----------------
Start: 127
297
737
299
2643
21
93
14
1
1
----------------
Start: 141
1
1
----------------
Start: 165
238
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 169
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
----------------
Start: 180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
70
96
180
----------------
Start: 183
490
907
542
700
306
115
921
422
1839
9323
14
1
1
----------------
Start: 197
37
46
19
37
----------------
Start: 211
93
14
1
1
----------------
Start: 219
716
39
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 226
964
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
70
96
180
----------------
Start: 238
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 264
21
93
14
1
1
----------------
Start: 270
165
238
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 274
462
19
37
46
19
----------------
Start: 286
73
299
2643
21
93
14
1
1
----------------
Start: 297
737
299
2643
21
93
14
1
1
----------------
Start: 299
2643
21
93
14
1
1
----------------
Start: 306
115
921
422
1839
9323
14
1
1
----------------
Start: 326
274
462
19
37
46
19
----------------
Start: 333
1698
25318
33479
45671
88095
40332
4592
60
127
297
737
299
2643
21
93
14
1
1
----------------
Start: 356
615
1029
8196
197
37
46
19
37
----------------
Start: 375
46
19
37
46
----------------
Start: 394
526
612
219
716
39
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 399
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 406
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
70
----------------
Start: 422
1839
9323
14
1
1
----------------
Start: 433
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 440
511
394
526
612
219
716
39
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 459
60
127
297
737
299
2643
21
93
14
1
1
----------------
Start: 462
19
37
46
19
----------------
Start: 464
1159
921
422
1839
9323
14
1
1
----------------
Start: 490
907
542
700
306
115
921
422
1839
9323
14
1
1
----------------
Start: 495
464
1159
921
422
1839
9323
14
1
1
----------------
Start: 511
394
526
612
219
716
39
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 514
2117
93
14
1
1
----------------
Start: 526
612
219
716
39
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 542
700
306
115
921
422
1839
9323
14
1
1
----------------
Start: 545
4338
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 557
1101
2779
15008
15375
202762
107788
780706
96071
53594
141
1
1
----------------
Start: 607
286
73
299
2643
21
93
14
1
1
----------------
Start: 609
127
297
737
299
2643
21
93
14
1
1
----------------
Start: 612
219
716
39
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 615
1029
8196
197
37
46
19
37
----------------
Start: 648
226
964
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
70
96
180
----------------
Start: 656
514
2117
93
14
1
1
----------------
Start: 665
211
93
14
1
1
----------------
Start: 700
306
115
921
422
1839
9323
14
1
1
----------------
Start: 706
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
70
96
----------------
Start: 714
609
127
297
737
299
2643
21
93
14
1
1
----------------
Start: 716
39
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 737
299
2643
21
93
14
1
1
----------------
Start: 806
967
1400
4365
11353
127494
4220
2371
1925
1166
3993
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 819
197
37
46
19
37
----------------
Start: 872
648
226
964
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
70
96
180
----------------
Start: 874
1949
495
464
1159
921
422
1839
9323
14
1
1
----------------
Start: 902
714
609
127
297
737
299
2643
21
93
14
1
1
----------------
Start: 903
356
615
1029
8196
197
37
46
19
37
----------------
Start: 907
542
700
306
115
921
422
1839
9323
14
1
1
----------------
Start: 921
422
1839
9323
14
1
1
----------------
Start: 931
440
511
394
526
612
219
716
39
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 932
14
1
1
----------------
Start: 937
45
60
127
297
737
299
2643
21
93
14
1
1
----------------
Start: 943
399
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 964
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
70
96
180
----------------
Start: 967
1400
4365
11353
127494
4220
2371
1925
1166
3993
43
23
16
40
70
96
180
3664
24717
15492
84198
65489
3725
16974
41702
3788
5757
1958
14609
62892
44745
9385
169
40
----------------
Start: 996
459
60
127
297
737
299
2643
21
93
14
1
1

Snakeboy
02-24-2014, 10:31 PM
Impressive, Richard.

I have been doing this by hand, unfortunately, also cross-referencing them against some other things, so it's rather tedious.

I figured for a really complex analysis it would be a no-brainer to have a program do the looking, I unfortunately have not programmed since learning Basic on the Apple IIe

:D

I've not been able to find too much work in this area, aside from a little bit on the OEIS

http://oeis.org/A232013

Apparently these are called " orbits ", seems fitting.

Snakeboy
03-14-2014, 10:10 AM
Happy Pi day ! :yo:

Richard Amiel McGough
03-14-2014, 04:03 PM
And here's a Pi pie ...

1075

Krakers
03-21-2014, 03:54 PM
Hi Snakeboy,

Been readin' some of yer mind numbin' numerologicals. I like the way you seriously play without playin' seriously.
Lookin' at the infinity of pi's digits fer patterns seems like a game fer immortals who just want to pass the time away
pleasantly. Carl Sagan, in the book "Contact", used the idea of findin' a really improbable pattern in that sequence as
a "signature of God".

I'm no mathematician, recreational or otherwise, and so I can still get those 'Eureka' moments when I come upon somethin' clever.
It passes when someone drains the water out of my tub by explainin' why it should be so. Anyway, I like playin' with the numbers
that others believe are religiously significant. It is as close as I get to worship.

http://davidbau.com/archives/2010/03/14/the_mystery_of_355113.html

The above web-site is a good beginning for understanding where the following folderol comes from.

If we perform the following transforms on the numbers 355 and 113 some curious stuff manifests.
Reverse the digits of either number and then add them.
355+311 = 666 = 553+113
Reverse both and add them yields 553+311 = 864.

3.14159265… = Pi
3.14159292… = 355/113
The pi approximation 355/113 has the first 7 digits of Pi in common
summing their squares: (3^2+ 1^2+ 4^2+ 1^2+ 5^2+ 9^2+ 2^2) = 137
multiplying them (3*1*4*1*5*9*2) = 1080
and adding them (3+1+4+1+5+9+2) = 25

Reverse the 7 digits common to both Pi and 355/113 and transform thusly:

(ln(2951413)^-1 / 10^8) +1 = 1.000000000671…

10^((6*86400)/66600) * (666+(1/2000))^-2 * (1+(671/10^11))^-1 = 137.0359990826...which is within error limits for the 2010 CODATA value for the fine structure constant.

Note: 86400 is the number of seconds in the nominal day and so 6 times that "represents" the 6 days of Genesis creation.
Note: 137 is Hebrew gematria for a word meaning "birth or genesis" (Mem 40, Vau 6, Tzaddi 90, Aleph 1)

Why multiply 666 by 100? The number 100 is the sum of (Yod 10, Mem 40, Yod, Mem) meaning "days"
What does 671 represent?
The last 2 words of Genesis chapter 1 (verse 1:31) are:
(Yod 10, Vau 6, mem 40, - He 5, Shin 300, Shin 300, Yod 10) sum = 671 meaning “the sixth day”
What is the rationale for (1/2000)?
The first letter of Genesis chapter 1 is Bet; its gematria value is 2. However, the qabbalists tell us that because it is writ
large; its value can be set at 2000.

I hope you find this interesting.
Krakers

Snakeboy
03-30-2014, 02:11 PM
Yes, very neat, indeed.

I had not noticed the sum of the squares of the first seven numbers after the digit in pi is 137

I had noticed the multiplicative expansions of pi can be used to produce 1080 and 540, although bringing this odd triviality up on a math forum immediately is met with " why would you want to do that ?! " ( lol ! ) Granted, it's not the regular process of a factorial calculation, but with that attitude of indignation , we might as well ask " why calculate anything at all " ?

As it turns out, tables of these " pi factorials ", for lack of a better term, used in conjunction with tables of standard factorials, can be used for calendar calculations, and more.

Plato and others didn't spend all that time in and around Egypt studying math for no reason, haha.

Plato's ever so mysterious statement in the Republic (8.546b):

" Now for divine begettings there is a period comprehended by a perfect number, and for mortal by the first in which augmentations dominating and dominated when they have attained to three distances and four limits of the assimilating and the dissimilating, the waxing and the waning, render all things conversable and commensurable with one another, whereof a basal four-thirds wedded to the pempad yields two harmonies at the third augmentation, the one the product of equal factors taken one hundred times, the other of equal length one way but oblong,-one dimension of a hundred numbers determined by the rational diameters of the pempad lacking one in each case, or of the irrational lacking two; the other dimension of a hundred cubes of the triad.

And this entire geometrical number is determinative of this thing, of better and inferior births. "

Hebrew " Molad " = " Birth " of the Moon.

Recall that Hipparchus also derived these Metatonic cycles for predicting things like eclipses, which he checked against the tables available from earlier astronomers.

Plato also named a " number of the tyrant ", which is also apparently part of calendar calculations, at least as far as I can tell so far.

Here are what would be the same crude approximate measurements made by the ancients:

1084

Those would be standard miles, and just rounded approximations, but I feel safe in assuming that that's where the NT numbers were derived in the first place.

144,000 / 666 = 1.62162162162162

I actually have about 50 pages of exhaustive tables that I have sat down and derived using all the ever so familiar biblical numbers, and so far, it would appear that they do indeed come from the calendar maths.

While playing around with the Egyptian calendars, I happened to notice you can also derive a crude approximation of pi using rounded measurements from the Lunar calendar, although it is in a rather roundabout way...heh

When we plug the measurements of the Earth and Moon into the standard Pythagorean expression a2 + b2 = c2 the hypotenuse is 1.618

Where Earth = 1 , the proportionality is roughly

Radius of the Earth = 1
Radius of Earth and Moon = 1.272

Moon's mean radius is 1,079.6 miles / 2 = 539.8 miles
Moon's mass is ~ 1/81 of the Earth's mass, = ~1.2%

After a while of playing with all these numbers, I realized that we can simply write: 541/172 = 3.1453488...

This is naturally, not a very accurate value of pi, however, I noticed while playing with reoccurring periodic decimals, that we can get a little closer:

541.5454 / 172.2727 = 3.143535801087462

Which is closer, but using these takes us further from accurate pi

When we write it instead as:

541.4545 / 172.2727 = 3.143008149288889

We get a little closer still ( 4545 after the decimal instead of 5454 )

When we switch out 54 or 45 for 27, we can get a little closer:

541.2727 / 172.2727 = 3.141952845691743

Granted, as Rich points out, if we are even slightly adept with numbers, we can tease and prod any value we want to find out of any set of numbers, simply by exhaustive methods.

Exhaustive tables however, are how they made calculations for the three calendars ( Lunar, Solar, and Stellar ) in the first place.

Interestingly enough, while studying the semiosis of architecture, I noticed that the Washington monument seemed to make a vague reference ( you know how we love those, lol ) to the Lunar calendar.

At ground level the sides are 55.5 feet = 666 inches
The height is approximately 555.5 feet = 6666 inches

666/555 = 1.2
1.2*1.6182 = 3.1415088

Not so shocking, really, especially when we look at it from the top:

1086

As you can see, there seems to be some huge phallic object penetrating a Vesica Piscis , smack dab in the middle of the nation's capitol :eek:

Recall that the start of the repunit series in pi starts at the 153rd digit, with 111, whereas the rounded square root of 153 gives us the amount of New Moons in one calendar year

~ 12.369 New Moons

...is the " Lord a sun "...or is the " Lord a penis " ....or is it both ?:lol:

The phrase Novus ordo seclorum (Latin for "New order of the ages") appears on the reverse of the Great Seal of the United States.

The phrase is taken from the fourth Eclogue of Virgil, which contains a passage that reads:

Latin:

Ultima Cumaei venit iam carminis ætas;
Magnus ab integro sæclorum nascitur ordo.
iam redit et Virgo, redeunt Saturnia regna,
iam nova progenies cælo demittitur alto.

English:

Now comes the final era of the Sibyl's song;
The great order of the ages is born afresh.
And now justice returns, honored rules return;
now a new lineage is sent down from high heaven.

Those wacky Masons :lol:

Didn't want to veer too far into Woo-Woolandia, lol, but they were just some interesting things I noted, and after your notice of the possible Temurah (?) of that phrase " The Lord is a sun " ( 666 ) possibly also being " The Lord is a " penis "", it definitely raised my eyebrows a bit when I recalled the Washington Monument and the Eclogue of Virgil.

If I had to toss a guess, I would say that the " sign of Jonah " actually refers to this:

1085

Because, as per the Comma Johanneum, 1 John 5:7 , which bugged Newton so much, lol, there are " Three in heaven that bear witness ", which is where that 1080 value for the " holy spirit " in Greek came from. ( I am aware there are other values, however, I think I can also show that these are indeed from the calendar math )

Those " three in heaven that bear witness " seem uncannily similar to the three in the heavens that give us those lovely " signs of jonah "

There is much confusion surround all these things,...

Jonah was eaten by a fish....but he was actually eaten by the leviathan....but leviathan has been taken to mean everything from " ginzu knives " to " dinosaur "...to " satan ".......but...but...Moses was known in the Zohar as the " leviathan of the sea of the Torah.."..( According to some other opinions, he was also known as " the great fish "...to others, he was supposedly known by a name which referred to his tribal roots " Levi-Tanniyn ) ...But..but...the Moon has horns....but..but....we associate the Moon with Passover......but...but.....the Passover we associate with Jesus....but...but....Moses also was depicted as having horns......but...but... " Sin " was the eeeevil " Moon God "....but...but...." Shin " ( also pronounced " sin " ) is the letter of the Hebrew alphabet which according to some kabbalists, represents the three patriarchs of Israel......and a crown, which would belong to cheebus...but..but...." holy crown " = 666 in gematria...and 666 is eeeeevil.....but ...but.....dividing " god's number " 1080, by the " devil's number " 666...we get a ratio equivalent to approximations of Phi proportions on a circle...~ 137, ~222, ~ 360

And wouldn't you know it, 144,000/666 = 216.2162162162162

Now, granted, some of these numbers I am playing around with are rounded or truncated in some cases, or in the case of pi, not incredibly accurate. However, all measurements are fundamentally approximations, where the increase in the precision of measurement simply decreases your error +/-, and for something like exhaustive repeated astronomical calculations, the first thing that would be obvious over time, are the fluctuations, which is why, ( I am guessing ) they started incorporating and or comparing larger and larger measurements, going from a Lunar calendar, to a Solar calendar, and finally a Stellar calendar that fairly accurately calculated how long it takes our solar system to make a rotation with the entire Milky Way.

I know it's going out on a limb, mathematically speaking, but if you can derive approximations of pi by dropping sticks over Gaussian curves, or averaging the sinuosity of rivers, it's not a far stretch to posit it can be derived by observing the movement of the " heavenly bodies ".

I think the biblical numbers, and system behind gematria values was all just borrowed............kind of like how NT writers simply took Plato's ideas about " Logos "..." rhema " which denotes actions,... and onoma , a mark set on those who do the actions........almost sounds like the ol mark of the derp...I mean...mark of the beast :eek:

No wonder people are so damn confused, hahahahah

Like I have stressed, if you put aside the words, and look solely at the math with all these biblical numbers, you'll find that while the words seem to weave stories that are logically inconsistent with each other, the numbers behind the words, and the numbers actually written, will produce these tables of calendar calculations, which are mathematically consistent with each other, and they agree with the bulk of ancient calculations for all three calendars, as far as I can tell.

I think as I become more familiar with combinatorics, trigonometry, algebra, ancient maths, etc, I will be able to provide some fairly convincing proof of my claims.

Pleasure speaking with you again :yo:

Krakers
03-30-2014, 06:18 PM
Greetings Snakeboy, fellow apopheniac! :winking0071:

Shall we continue to play?

Regardiing " Plato's ever so mysterious statement in the Republic (8.546b)"

And this entire geometrical number is determinative of this thing, of better and inferior births. "

Hebrew " Molad " = " Birth " of the Moon.

You said: Plato also named a "number of the tyrant ", which is also apparently part of calendar calculations, at least as far as I can tell so far.

Aye, Snakeboy, and ye’ll be happy ta hear that the number representin’ this tyrant be 729; and if ye look at it a certain way ye will get an erection!
For ye see, lad, 729 be 27^2 and 27 be the gematria value of (Vau Tet Yod Bet) meanin’ “penis” (Yehudah’s Dictionary).

You said: Recall that the start of the repunit series in pi starts at the 153rd digit, with 111, whereas the rounded square root of 153 gives us the amount of New Moons in one calendar year

~ 12.369 New Moons

365.24218967/29.53059 = 12.368… (call it 12.37) = sqrt(152.974)… and 12^2=144, 37^2 = 1369. A right angled triangle 12 length and 3 height has a hypotenuse of sqrt(153) and an area of 18; and 666+864 = 153*10.
365.24218967 = days in Earth’s tropical year and 29.53059 = days in the lunar cycle

So here is a formulation that “merges” the microcosm with the macrocosm.

(10^((6*86400)/(666*100))/666^2)/(1+(365.24218967/(365.24218967-365))/1000^3) = 137.035999100…
A very close approximation of the 2010 CODATA value of the fine structure constant.

1+(365.24218967/(365.24218967-365))/1000^3 = 1.00000150808…
1+(10^-3/(666-(29.53059/10))) using days in the lunar cycle. = 1.00000150818…
1+(10^-3/(666-(291/100))) where 291 via gematria is ARTz “Earth”. = 1.00000150809…

These can be divisors for (10^((6*86400)/(666*100))/666^2) that transform it into close values of alpha.

Regarding (10^((6*86400)/(666*100))/666^2): It is a variation on a formulation that I call Alpha666.
Alpha666 is derived from the magick square of the sun in the following way:
A = ((10^(222/(74*10)) / 10^(370^-1*(111+10*4)))*(10^4/666))^2 B = 1+(10^-3/(666-(296/100)))

A/B = 1087 = 137.035999084…

Where most of the numbers come from the occult artifact known as the:

1088

In the future this construction may be known (via anagram) either as: “Chief Magus’ quark stone.” or “A fuckin’ grotesque sham.”

May we play with it as a coded artifact designed to transmit key electromagnetic constants of nature to minds educated in modern science?
...is the " Lord a sun "...or is the " Lord a penis " ....or is it both?

Krakers
Steven Joseph Krakowski