## The Best of Proto-Bytes Bits-n-Bytes, A Non-All-Inclusive Scientific Research Information and Idea Exchange

### Todays fun with numerical analysis and the number 23 and more….

Today I received a text mesage from a friend telling me they were celibrating thier 23rd anaversary of a special occasion.  So I decided to give a polite reply with some numerical analysis of 23.  I found a connection to the Fabannici Series and the Golden Ratio.  I thought how sweet, 23 = natural beauty for my friend on this special day.

While doing the research on the internet of the numbers I was crunching, I also found the following numerical series someone submitted and the site ask.com replied it was a phone number.  So I did my own analysis of it and here is what I was able to unravel.  My analysis is a little off of what some mathamiticians might seem is real inductive numerical analysis, however, the same method has always given me outstandingly high scores on my IQ tests so there must be something to the method of my maddness.

Any way I posted an entry on Face Book about my little morning exersize, which now has driven me into the after noon because ask deleted my detailed essay on the topic, and others wanted to see it and I send a tweet about it to see if anyone would like to reviwe my methods and have any comment.  Well, it’s taken me another 2 and 1/2 hours of recaculation and going even further to create this blog and do even more detailed research.  Hope you have fun reading the numerical methoda and conclusions I jump to…  They seem to entertain me…

Base Pairs: [5 2] [3 4] [2 3] 

[First order base pairs calculation on base pairs]

5-2=3

3-4=1 [1st Group 1: pairs {3,1}]

—–

[Second order base pairs  calculation on base pairs]

1-3=2 [Continue using the Group 1 base pair result]

3-4=1 [1st Group 2: pairs {2,1}]

—–

[Third order base pairs result all base pairs]

2-1=1 [1st Result Group: series terminator {1}]

[now reverse the process and revers the induction to add the First order Reslt Pairs]

3+1=4

2+1=3 [2nd Group: pairs {4,3}]

—–

[Again reverse the induction now subtract]

4-3=1 [2nd Result Group: {1}]

[Finally last subtraction of 1st result and 2nd result group {1,1}]

1-1=0 [Final Result: Absolute terminator {0}]

This is an interesting series.  The first group result yields mankind’s first logical number assignment 1 in the

counting system.  The second result group also yields 1 as the result, perhaps a mathematical logical expression

of trying to identify that if we both have ‘1’ and give it to a third who will have ‘2’ and we are both left with ‘0’

The addition of zero was never really introduced into mankind’s number system until this kind of calculation was necessary

mostly for book keeping, in small trade it was common knowledge that if you give it all away you walk away with nothing

but that is not how the barter system worked, which is what mankind used to assure that trade was fair and there was

never an deficiency of free trade.  So when these type of issues arose someone usually got hit over the head with a

blunt object to settle the dispute, and take what was rightfully theirs.  Okay, that was my analysis on inductive

addition and subtracting to achieve a derived absolute number result.  The same method could derive a formula that

would produce an endless series of number that conform to the it’s all equal to zero in the end, by correctly extending

the series.

The second analysis I performed was to see what the number add to and subtracted to:

23  [additive, which is a prime number (interesting)]

-13 [subtractive, also a prime number (equally interesting)]

in primes there is a great interest in finding what are called trans dental prime numbers, in which

the whole manifold of transcendental sets belonging to the absolute transcendental manifold is nearly infinite,

However it is believed that prime transcendental number belong to a set of number with an exact number of

possible transcenant primes.  So I looked for one:

23/13 = 1.7692307692307692307692307692308 [rational because it has real numbers which are divided]

then the inverse:

13/23 = 0.56521739130434782608695652173913

Correction: I used an on line Hugh number calculator to double check the math…  The number is not irrational at all

Okay nothing seemed too interesting here, so I subtracted:

0.56521739130434782608695652173913 – 1.7692307692307692307692307692308 =

-1.2040133779264214046822742474917 [this is irrational, perhaps a transcendental number also, not going to poof that]

and the positive if the sine is reversed:

1.2040133779264214046822742474917

Actually my x64 bit computer did not fully caculate the number so I thought it was irrational, however it is not:

1.204013377926421404682274247491638795986622073578595317725752508361204013377926421404682274247491

Well no search engine comes up with any answers on the above number,

however The Wolframalpha DB has some really close approximations for this number.

The best are:

[This is the exact ratio for the huge number calculation above]

360/299

and the linear continued fraction in form {1, 4, 1, 9, 6} “suppose this yields an exact continuation of

the infinite series.

http://www.wolframalpha.com/input/?i=1.2040133779264214046822742474917

The statistical data on the series is interesting on the alpha site:

mean                                    | 3.286

minimum                             | 2           (This is interesting)

first quartile                       | 2.25

median                                  | 3            (This is interesting)

third quartile                     | 4             (This is interesting)

maximum                            | 5             (This is interesting)

harmonic mean                | 2.958     (This is interesting)

geometric mean               | 3.12

root mean square           | 3.443

and…

sample standard deviation          | 1.113

sample variance                               | 1.238

interquartile range                          | 1.75

sample range                                      | 3

coefficient of variation                   | 0.3386

relative standard deviation         | 0.3386

population std. deviation             | 1.03

population variance                        | 1.061

mean deviation                                 | 0.898

median deviation                             | 1

quartile deviation                            | 0.875

standard error of the mean         | 0.4206

coef. of quartile variation            | 28 (This is interesting)

and a few more… (all very interesting, but require more time to investigate, esp. the pearsons number)

skewness                                                                 | 0.192

kurtosis                                                                    | 1.857

quartile skewness                                                | 0.1429

momental skewness                                            | 0.07143

Pearson’s second moment of skewness      | 0.7703

quartile skewness                                                | 0.1429

excess kurtosis                                                     | -1.143

This is the big wow of the statistical analysis for this series:

The confidence intervals of mean:

90% | 2.594 to 3.9775

95% | 2.4614 to 4.11

99% | 2.2024 to 4.369

Here is the link to the alpha site for just the series….

http://www.wolframalpha.com/input/?i=5+2+3+4+2+3+4

Further research:

Transcendental Number Theory

http://en.wikipedia.org/wiki/Transcendence_theory

http://en.wikipedia.org/wiki/Transcendental_number

http://en.wikipedia.org/wiki/Irrational_number

http://en.wikipedia.org/wiki/Champernowne_constant

http://en.wikipedia.org/wiki/Chaitin’s_constant

http://en.wikipedia.org/wiki/Schanuel’s_conjecture

Primes

http://en.wikipedia.org/wiki/Prime_number

http://en.wikipedia.org/wiki/Mersenne_prime

http://en.wikipedia.org/wiki/Fermat_prime

http://en.wikipedia.org/wiki/Euclid_number

http://en.wikipedia.org/wiki/Fibonacci_prime

Transcendental Primes

http://jlms.oxfordjournals.org/content/s1-39/1/405.extract

History of the number Zero

http://en.wikipedia.org/wiki/0_(number)

I’m done with this….  Send your comments…  If I have time I’ll use Audociacy to generate teh harmonic frequency I pointed out as ineresting.

@ProtoBytes

Advertisements