Strange Numerology: My Weird Arithmetical Leap and Some of Its Related Subjects--Part II
Created | Updated Nov 8, 2009
This Entry continues discussion of the Weird Arithmetical Leap with a long look at what happens when the number of 7's after the decimal point in its left-hand-side is allowed to vary. First let me briefly recapitulate and clarify certain things.
The first Entry in this sequence described how I mentioned that a specific calculator was used along with a specific encyclopedic source. The encyclopedia was named as Britannica 2001 on CD. The calculator--critical for its specific errors--is the version that came with Microsoft Works in 1998. I haven't yet looked at details of how the newer 2009 version I have here differs. In Part III I will get into my theory of the place of these two referrence sources in more detail. Right now it suffices to just treat them as providential. They just happened to be what I had available at the time.
This Entry focuses on a specific sequence of numbers for something of an analysis of historical dates. My Weird Arithmetical Leap produced the value of the fourth root of 17797577777.77777777777777777777 minus that of 17797577777 as equal to (in the calculator's way of representing scientific notation) 3.99047748332654274621776424874732e-9. This is actually not simply what the calculator says because there are two basic ways to make the calculation. I'll deal with that matter in Part III also. This Entry deals with the way I chose first.
What I'll henceforth call "The Second Huge Surprise" was also dealt with. That came about through looking at only the first part of the subtraction--the minuend--which calculates as 365.250000233886071957018637... for sixteen or more 7's after the decimal point. I'll probably be producing some research of interest on the sequence implied here in a later Part, and some surprising stuff will also be a major subject of Part II; but right now I'm just repeating the finding that pairing of the dates 1863 and 1957 in Britannica 2001 produced a subject I immediately looked up--Baha'i--because of its interest to me. Because the apostrophe was not read properly by the search engine, the search produced my 5-digit zip code by counting all instances of 'i' by itself. A couple of things that might interest people that I may not have reason to mention elsewhere (for a while, at least) are that the number of hits to search of simply 'Baha' is 42 (meaningful to hootooers who have been here for any length of time), and that search without the apostrophe (of Bahai) produces only one hit and that's to a significant Iranian mathematician and astronomer of the middle of the last millennium.
So, the situation I found myself in late 2008 was that there was significance to pairing dates and to noting what and how many hits came up. The rest of this Entry deals with the following sequence of strings of digits, where the twentieth (T) is what came out of the Weird Arithmetical Leap (multiplication by 10^41 removes the decimal point and exponent from scientific notation):
A) 359142973499977410591576151215843
B) 395057270849392473856631538710468
C) 398648700584328153405196202589402
D) 399007843557821663092273262750709
E) 399043757855171013478303172156007
F) 399047349284905948511079385487618
G) 399047708427879442014298739340673
H) 399047744342176791364620092250138
I) 399047747933606526299652222141233
J) 399047748292749499793155434507463
K) 399047748328663797142505755849039
L) 399047748332255226877440787079278
M) 399047748332614369850934291543726
N) 399047748332650284148283641489637
O) 399047748332653875578018575618945
P) 399047748332654234720992072586325
Q) 399047748332654270635289420821396
R) 399047748332654274226719164856657
S) 399047748332654274585862127762492
T) 399047748332654274621776424874732
U) 399047748332654274625367854911055
V) 399047748332654274625726996974463
W) 399047748332654274625762913801419
X) 399047748332654274625766502812177
Y) 399047748332654274625766863526507
Z) 399047748332654274625766899598687
The first thing you'll note is that I've stopped after exactly 26 terms of the sequence. The way the calculation was described, I really could only have twenty, but I adjusted the calculation process to accomplish further calculations beyond that. This will be quite significant in Part III, but only in the way the twenty-first term appeared was it oiginally significant in what follows. This significance is in the last eight digits of U. Consider also the last eight digits of S. I was essentially just experimenting by looking at the terms close to that of the Weird Arithmetical Leap, and these two were the ones I saw first beyond it. Here is the significance of these two as I saw it at the time: In regards to S first, since I saw it first, the last eight digits are a concatenation of the millennial years of 2776 and 2492; and in regards to U, the reverse-order of 1945 appears. This was all quite enough for me to have a need to look at the whole sequence in depth, a process that may be long in completing.
I now focus on what the most basic results have been of the Britannica searches for all second millennium dates.
The first Entry in this sequence described how I mentioned that a specific calculator was used along with a specific encyclopedic source. The encyclopedia was named as Britannica 2001 on CD. The calculator--critical for its specific errors--is the version that came with Microsoft Works in 1998. I haven't yet looked at details of how the newer 2009 version I have here differs. In Part III I will get into my theory of the place of these two referrence sources in more detail. Right now it suffices to just treat them as providential. They just happened to be what I had available at the time.
This Entry focuses on a specific sequence of numbers for something of an analysis of historical dates. My Weird Arithmetical Leap produced the value of the fourth root of 17797577777.77777777777777777777 minus that of 17797577777 as equal to (in the calculator's way of representing scientific notation) 3.99047748332654274621776424874732e-9. This is actually not simply what the calculator says because there are two basic ways to make the calculation. I'll deal with that matter in Part III also. This Entry deals with the way I chose first.
What I'll henceforth call "The Second Huge Surprise" was also dealt with. That came about through looking at only the first part of the subtraction--the minuend--which calculates as 365.250000233886071957018637... for sixteen or more 7's after the decimal point. I'll probably be producing some research of interest on the sequence implied here in a later Part, and some surprising stuff will also be a major subject of Part II; but right now I'm just repeating the finding that pairing of the dates 1863 and 1957 in Britannica 2001 produced a subject I immediately looked up--Baha'i--because of its interest to me. Because the apostrophe was not read properly by the search engine, the search produced my 5-digit zip code by counting all instances of 'i' by itself. A couple of things that might interest people that I may not have reason to mention elsewhere (for a while, at least) are that the number of hits to search of simply 'Baha' is 42 (meaningful to hootooers who have been here for any length of time), and that search without the apostrophe (of Bahai) produces only one hit and that's to a significant Iranian mathematician and astronomer of the middle of the last millennium.
So, the situation I found myself in late 2008 was that there was significance to pairing dates and to noting what and how many hits came up. The rest of this Entry deals with the following sequence of strings of digits, where the twentieth (T) is what came out of the Weird Arithmetical Leap (multiplication by 10^41 removes the decimal point and exponent from scientific notation):
A) 359142973499977410591576151215843
B) 395057270849392473856631538710468
C) 398648700584328153405196202589402
D) 399007843557821663092273262750709
E) 399043757855171013478303172156007
F) 399047349284905948511079385487618
G) 399047708427879442014298739340673
H) 399047744342176791364620092250138
I) 399047747933606526299652222141233
J) 399047748292749499793155434507463
K) 399047748328663797142505755849039
L) 399047748332255226877440787079278
M) 399047748332614369850934291543726
N) 399047748332650284148283641489637
O) 399047748332653875578018575618945
P) 399047748332654234720992072586325
Q) 399047748332654270635289420821396
R) 399047748332654274226719164856657
S) 399047748332654274585862127762492
T) 399047748332654274621776424874732
U) 399047748332654274625367854911055
V) 399047748332654274625726996974463
W) 399047748332654274625762913801419
X) 399047748332654274625766502812177
Y) 399047748332654274625766863526507
Z) 399047748332654274625766899598687
The first thing you'll note is that I've stopped after exactly 26 terms of the sequence. The way the calculation was described, I really could only have twenty, but I adjusted the calculation process to accomplish further calculations beyond that. This will be quite significant in Part III, but only in the way the twenty-first term appeared was it oiginally significant in what follows. This significance is in the last eight digits of U. Consider also the last eight digits of S. I was essentially just experimenting by looking at the terms close to that of the Weird Arithmetical Leap, and these two were the ones I saw first beyond it. Here is the significance of these two as I saw it at the time: In regards to S first, since I saw it first, the last eight digits are a concatenation of the millennial years of 2776 and 2492; and in regards to U, the reverse-order of 1945 appears. This was all quite enough for me to have a need to look at the whole sequence in depth, a process that may be long in completing.
I now focus on what the most basic results have been of the Britannica searches for all second millennium dates.
