Will to Truth

Please note that the post times of the following two posts were edited so that this post comes as part 1 of 3 in a large post.

Fractal (The Mandelbrot Set).

In mathematics, the Mandelbrot set is a set of points in the complex plane, the boundary of which forms a fractal.

When computed and graphed on the complex plane, the Mandelbrot Set is seen to have an elaborate boundary which does not simplify at any given magnification. This qualifies the boundary as a fractal.

The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and for being a complicated structure arising from a simple definition, and is one of the most well-known examples of mathematical visualization.

Fractals are often said to be the simplest demonstrations of beauty, paradoxically their simplicity makes them infinitely complicated and unending in design. Common fractals in nature are apparent in plants' branches, veins in leaves, skeletons of animals, branches of animals' veins and nerves, proportions of chemical compounds, lightning arcs, and the geometry of crystals.

Mathematical Symbols.

π = Pi, if you don't know, get the fhek off my blog. :-)

φ = The golden ratio, an irrational mathematical constant, (1+√5)/2, approximately 1.6180339887

It's a calculation for graphing logarithmic spirals and fractal sequences found in nature. The ratio created is also found universally in nature in relation to components of aesthetically pleasing subjects.

ƒ(x)=1/x is a mathematical singularity, where zero gives ±∞.

On a graph, given the value of zero, the function will explode as in the theoretical state of the Universe at the big bang. A physical paradox.

The Binary Star.

This design is about beauty and individuality. But please don't read that as pride. I am but a Debaser.

Read from the bottom point clockwise, following the longest lines (as you'd draw a star), and skipping over characters already crossed, ending with the top right point (which would then connect back to the bottom), the binary reads 1010011010, which, in decimal, is 666. Please trust, it's not satanic, though at a glance, it is nothing but. I don't, by any stretch of the imagination, even remotely have any inkling of any idea, not even any fickle, fleeting, or otherwise slightest belief in any character, entity, force, power, or emotion, that could be classified by any means as this "Satan." This drawing and theme is something I started working on when I was about 17, and is a reference to the all too common 'Semmelweis reflex' reaction to Atheism, agnosticism, and related topics, which is merrily depicted in this comic:
http://abstrusegoose.com/229


This number is called out in the Australian band Cog (one of my favorite bands and songs of all time) in 1010011010, about freedom, peace, and illusion, which references the George Orwell dystopian novel and film, 1984, wherein individuality is restricted by Big Brother, and the subjects are persecuted for their thoughtcrimes against the totalitarian, oligarchical collectivist society. This is also close to the theme of another favorite novella, Ayn Rand's Anthem. Thirdly, this systematic restriction of free will is referenced in another dystopian novel and film, A Clockwork Orange. Partially in thanks to a high school English teacher, my taste was fulfilled by experiencing these three brilliant pieces of literature. I will now never live without expressing myself and my satire in some way.


A very in-depth, two page description of the meaning behind the Binary Star design in its own rite can be found on my blog here (beware Semmelweists):
http://rcarhart.blogspot.com/2010/02/binary-star-defined.html


Truth?


So why tack "truth" on it; it's a pretty powerful message, especially on top of an otherwise deafening stamp; breakfast table in an otherwise empty room...


Because it's the Will to Truth.


This is beyond good and evil. There's no such consequence. It's math and it's physics. It's nature. It's all there is. It's a compilation of definition of pure aesthetic. It's the unguided, exposed, raw, natural, unending, sheer, blatant, pristine patent of reality as we know it. In all its glory and there for all to rejoice in.


So if that's absolute positivity, where's the balance? What's at the opposite end of that? Expecting unbridled fear, loathing, rage, grief, confusion, inadequacy? Those are only emotions. They exist only in the mind. It's the hidden secrets; the private thoughts of Einstein's God. The long forgotten drafts of the simplest, yet most complicated details of the Universe. And I can't imagine they'd be any less divine than what's revealed in the details.


This, the wonderment of the unknown, is what keeps the species motivated. Discovery through experimentation and exploration. Godsend confessions of the machine. Reverse engineering the alien technology within which we reside. We've acknowledged that our very growth as a planet is guided by Natural Law. We've been playing in the sandbox for millions of years. Hundreds of thousands of years by our calculation of our current particular self-defined species. We've seen our own invention shape our lives exponentially between generations, even unimaginably to our very recent ancestors. Yet we don't know what to strive for technologically, as our understanding of Natural Law is still juvenile. Perhaps even in its infancy. Aside from that, nor do we have any notion that we will behold any semblance of grasp on the inner workings of the Universe. So we continue to play in the sand! I don't know about you, but I am un chien that thinks that that is more than enough to live for, to die for, to strive for, to co-exist for; a solid basis of morality, conceivably fairer than any enforced conformity.


It's the curiosity I had as a little kid. I had no idea when I was seven, and thought about a question mark as a tattoo, that it would turn out to be so endlessly synchronous. So that finally lies at the very top.

Binary Star, Defined

Please note that the post time was edited so that this post comes as part 2 of 3 in a large post, and is displayed after its corresponding piece. This post is part one of a two part explanation of the Binary Star portion of the particular tattoo idea.

Forget traditional connotations of faith and luck for star tattoos. That's not really me. A star shape itself is a symbol of the obvious: a celestial star. This signifies my love for astrophysics. A desire to understand the Cosmos. All of my tattoos are/will be of my views and passions, and are related to philosophy and/or physics.

Celestial stars, from our perspective, are for the most part minuscule and insignificant, save the Sun, one of the primary ingredients in the very existence of our lives, which reminds us of their remarkable power, potential, and influence. Though we know that they aren't everlasting, that time is relative, and that their presence is constant for the most part as far as we are concerned, enough to trust and to navigate by. A symbol of eternal astonishing beauty, stars are however still insignificant in relation to each other and to further bodies. They beckon us to investigate deeper into the abyss of the heavens.

Having five points (as does any specific number) gives additional meaning to a star symbol. Apparent to us in nature almost exclusively to living organisms such as flowers and oceanic creatures, as well as the basic shape of the human body (think Vitruvian Man, another design I'm contemplating over), five points signifies the sacred occurrence of life as we know it. Five points represent a quest for Divine Knowledge and the secrets of life, a perfect reference to Einstein, who only claimed to wish to know the thoughts of God, in seeking a unifying theory. The rest... are details.

Further, Earth, water, air, fire, and spirit are often represented in the five points or angles of this star, and alternately, touch, sight, sound, taste, and smell. Both are curious lists that have deeper roots I'll speak of later in this blog.

Displaying the pentgram, or regular five pointed star outline, with one point directed downwards, is, yes, commonly associated with the devil, the devil's head, and frowned upon in sin. Fuck the devil. To be crystal clear, I don't believe in good, evil, Heaven or Hell. The significance in inverting my pentacle is as it has been since junior high, when I sewed one on a stocking cap: the goat's head.

I miss that hat.

The goat can still be thought to be demonic in nature, but you know this can't be true in my case.

Not to give credit to astrology and zodiacal mythology, but therein, a goat is shy, introverted, creative, has an aversion to making large decisions, is a dreamer, and is a perfectionist. Though a.) I don't believe in horoscopes or fortune telling, and b.) I wasn't born in the year of the goat, the goat does correspond to the Western Cancer sign, which is mine, and these attributes are exactly of my nature. The Cancer, or crab: can walk sideways, as the individual will take alternate paths in life; and, again, within its shell, is introverted; and is caring, sensitive, appreciative, and indirect. Again, however, I don't believe in this spiritual folly, and aim not to support it much. After all, I recognize that the main component in fortune, to make it seem credible, is ambiguity.

Though when circumscribed (not circumcised), as the symbol is in my hat pictured, the pentagram is considered a pentacle, which traditionally gives it concrete evidential mystical and/or satanic connotation, the only significance I hold when including the outlining circle is simplicity, symmetry, and perfection (ie: beauty), as does the star itself.

My reference to the goat is one that lies in opposition to the symbol of the sheep, the sheep being a blind follower, en masse; an unquestioning sacrifice; and a symbol of Christ. This I traditionally view as nonsense, as blasphemy. Yes, I see Christ as blasphemous. I don't believe in a personal god, nor do I believe that were there one he could justify such actions as personifying himself in such a manner. A goat, on the other hand, is either a leader of masses, or a follower of his lone path: even if it means rejecting traditional and modern edicts. Even if it means being rejected by the modern masses. And he couldn't care less. I'll be who I am, and say what I feel, for those who mind don't matter, and those who matter don't mind. That goat, not Satan, (is me).

Finally, but not last, I'd included an interweaving string of binary code to the design, and call this entire concept the Binary Star. A binary star, literally, is a stellar system consisting of two stars orbiting their center of mass. This phenomenon is precious in astrophysics, allowing specific measurements and predictions to be made in dealing with the systems themselves, as well as understanding star systems in general.

And last, the binary reads as 1010011010 in the design, which as mentioned before, translates into the decimal 666. I've explained why use binary, now why use the number of the beast, when I've just disproved my star's reference to Satan?

Another blog follows. If viewing this blog singly on the page:
http://rcarhart.blogspot.com/2010/02/1010011010-defined.html

1010011010, Defined

Please note that the post time was edited so that this post comes as part 3 of 3 in a large post, and is displayed after its corresponding piece.

First and foremost, the original negative connotation associated with the number 666 comes directly from the Bible. I don't hold any truth in anything contrived from said source. Sorry Mom, but it is, as all other history is, be it true or false, all hearsay, and one with a logical and curious mind such as mine must take it with a grain of salt... All other darkness is prescribed to the number as descendant to the same source of hearsay and, dare I say, ignorance.

I use the number because, growing up, when I first started to doubt that which was fed to me, I started to first research everything that directly went against what was suspiciously being preached to me. I therefore learned a lot about a lot of things, including this "evil" number, and I became inseparably attracted to it.

Secondly, I have a habit, especially in discussing personal philosophies, or subjects that I have very intricate reason to display, to tend to show only a 'tip of the iceberg,' and to present a debased version of whatever meaning I initially intended. Some people get tattoos because they think they are pretty, and that's all you see. I get tattoos that dignify the ink running as deep into my skin as can be allowed, and you have to dig into me to grasp them. Even so, when the average stranger, client, aquaintence, or even friend inquires as to my underlying meaning, I don't care to share much further than a brief jaunt of what it means to me. But it's all here. I'll be who I am, and say what I feel, for those who mind don't matter, and those who matter don't mind. (As further discussed in regards to my arm tattoos.)

As a mathematical figure, 666 is a natural (1, 2, 3 ...), palindromic (ten animals I slam in a net; race car; dammit, I'm mad!; I, madam, I made radio! So I dared! Am I mad? Am I?, etc), repdigit (11, 444, etc; 666 is trips) number.

666 is abundant (the sum of its divisors is greater than two times itself):

The divisors of 666:

SUM(1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666) = 1482

2(666) = 1332

(interestingly, this is the sum of its palindromic/repdigit divisors, 111 + 222 + 333 + 666 = 1332)

The abundance of 666 is:

1482 - 1332

150

666 is triangular (think bowling pins, 1, 3, 6, 10, etc). This is because it is the sum of the first 36 natural numbers:

1 + 2 + 3 + ... + 34 + 35 + 36 = 666

Since 36 itself is both square and triangular, 666 is the sixth number of the form:

n^2(n^2 + 1) / 2

36(37) / 2

1332 / 2

666

and 666 is also the eighth number of the form of doubly triangular numbers:

n(n + 1)(n^2 + n + 2) / 8

8(9)(64 + 10) / 8

72(74) / 8

5328 / 8

666

666 is the magic total of the prime reciprocal magic square using 149.

I'll use an example, as this square would be 148 digits up and down.

Using 7, the repeating digits are as follows:

1 / 7 = .[1][4][2][8][5][7]

2 / 7 = .[2][8][5][7][1][4]

3 / 7 = .[4][2][8][5][7][1]

4 / 7 = .[5][7][1][4][2][8]

5 / 7 = .[7][1][4][2][8][5]

6 / 7 = .[8][5][7][1][4][2]

And the digits of each column, as well as each row, add up to 27, its magic total.

666 is a Smith number (composite number whose digits' sum is equal to the sum of the digits in its prime factorization):

6 + 6 + 6 = 18

2 * 3 * 3 * 37 = 666

2 + 3 + 3 + 3 + 7 = 18

Of the first million natural numbers, about 2.99% are Smith numbers. The more numbers you count to, the less percentage will be Smith numbers.

Using Roman numerals, 666 is represented as DCLXVI, which are in perfect consecutive descending order, once each:

D = 500

C = 100

L = 50

X = 10

V = 5

I = 1

But perhaps the most remarkable and beautiful of all properties of the number 666 is that it occurs as 13th prime in numbers following the Padovan sequence:

This is also the most complicated of the notable properties of 666:

P(0) = P(1) = P(2) = 1

and

P(n) = P(n − 2) + P(n − 3)

The first 13 values of P(n) are:

1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21

This is illustrated in the following diagram:

Also closely related is the Fibonacci sequence:

For me personally, the relationship between these two, and the relationship between the complicated, intricate almost unknowable patterns in the formulas, and the simplistic, breathtaking beauty of the spiraling forms that they create, and the fact that they are found in nature, is completely, utterly, fricking, dumbfounding.

Continuing yet deeper, this Fibonacci sequence is defined by the Golden ratio or φ (an irrational constant, included on this chest piece), and the Golden section, expressed as follows:

φ ≈ 1.6180339887

(a + b) / a = a / b = φ

This ratio describes the relationship between lengths of sides, when:

And so, this ratio, being used in the Vitruvian Man, as well as many other works of art, in accordance to geometric proportions found in nature, most notably between human body parts and human faces, especially as illustrated by da Vinci (among many), and, having also been used in works of music, can be found universally in nature, organic and inorganic. These self-similar, recurring patterns, described in simplest term as fractals, build the shapes defining the following examples:

branches in plants

veins in leaves

skeletons of animals

branches of their veins and nerves

proportions of chemical compounds
lightning arcs

geometry of crystals

Imitating the truest reality possible, it is said that obvious occurences of the Golden ratio in nature, and art forms using the Golden ratio as a basis of proportion, are the greatest performances of beauty.

The Golden ratio is also found in connection with 666, in the following expression:

-φ = sin 666^o + cos (6 * 6 * 6^o)

Sine and cosine, describing relationships between triangles and circles, gives yet another reason to incorporate a circle as I so desire. I've often thought of that for a tattoo, and/or the usage of the symbol for pi to recognize the awesomeness of the circle. Now I shall have that, and more.

Finally, the four lengths of line segments in a pentagram (shown in red, orange, green, and blue) are in Golden ratio to one another:

Pi, when written in binary, has several strings where the binary for 666 occur, naturally. The first instance of this is just after the 600th place after the decimal. It reads 1010011010 from the 601st to 610th places consecutively. There are 22 occurrences of this string in the first 32,768 digits.

Math. Nature. Beauty. Tell me how you get Satan out of that.