Parabola is a quarterly magazine published by The Society for the Study of Myth and Tradition. Each issue centers around one topic, such as death, and is explored philosophically using many different view points. In each issue, you will find a short story, traditional myth or essay from an Indian (as in Native American), Eastern, Orthodox Christian or Classical Greek view point as often as you will see one from a Judeo-Christian perspective. It's expensive but if the topic being discussed interests you, very much worth the money.

One of the conic sections. In this vein, its relatives are the circle, the ellipse and the hyperbola. The generating equation for a parabola centered on the origin is y=ax2 for some constant a. Other parabolic shapes can be generated with the equation y=ax2n for some constant a in the real numbers and n in the natural numbers.

The defining characteristic of a parabola is that each point is equidistant from a point P and a line L which does not pass through the point. To this end, each point of a parabola is the center of a circle whose edge passes through the point P and touches the line L. The idea of a circle comes into play because each point on the edge of a circle is equidistant from the center.
Uses: mirrors in telescopes or headlights; parabolic surfaces in sound reflection; etc. The reason for these uses is that radiated energy from the focus of the parabola always ends up travelling in one direction. For example, a headlight contains a light source and a parabolic mirror. When any particular light beam from the light source hits the sides of the parabolic mirror, that beam is then directed in one direction (and only that direction, ignoring diffusion), parallel to all the other light beams which have bounced off the mirror. This is a partial laser effect; it is not complete since most light beams are significantly diffused at production, and few mirrors are "perfect".

Useful information about parabolas:

			Vertical axis		Horizontal axis		
Standard Form:		(x-h)²=4p(y-k)		(y-k)²=4p(x-h)
Eccentricity:		e=1			e=1
Length of latus rectum:	l=|4p|			l=|4p|
Directrix:		y=k-p			x=h-p
Vertex:			(h,k)			(h,k)
Focus:			(h,k+p)			(h+p,k)
Opening direction:	p<0 down, p>0 up	p<0 left, p>0 right
Parametric Form:	x′=2pt+h		x′=2pt²+h
			y′=2pt²+k		y′=2pt+k

See also:




We barely remember who or what came before this precious moment,
We are choosing to be here right now. Hold on, stay inside
This holy reality, this holy experience.
Choosing to be here in...


Parabola is the seventh track on Lateralus, Tool's 2001 offering. The album was the band's third, and was by all measurable standards their most complete, and most complex, production. Parabola was released as its own single in 2002 with Parabol included as the natural lead-in to the song. Parabol is the sixth track on Lateralus, and the two songs are undeniably and eternally linked to each other. Both songs feature lyrics by Maynard James Keenan, Adam Jones on guitar, Justin Chancellor on bass, and Danny Carey on percussion.

When Lateralus was first released, I was not a Tool fan. I had heard a few of their songs on the radio, or at parties, but nothing to the extent where I would say I could recognize their work. Then one day several of us were hanging out and someone put the new album on; it was good and I said so.

My friends shared a look, and said "Just wait."

"Wait for what?"

"The next song. It starts right... NOW."

And just like that I had my first toolgasm.

Not content with only allowing the first stanza of Parabola to mirror the last of Parabol, the band composed the two songs such that the last chord of Parabol is also the first chord of Parabola. A more seamless transition between tracks simply does not exist. The only hint that there has been a switch to a new song at all is the ferocity with which the bottom comes in. Whereas Parabol has very subdued percussion and no bass, both are immediately recognized in Parabola as the entire band savagely attacks the arpeggio theme laid down in the previous song.


This body. This body holding me. Be my reminder here that I am not alone in...
This body, this body holding me, feeling eternal
All this pain is an illusion.


Just as the musical themes of Parabola are an amplification of the same from Parabol, so are the lyrics an extension as well. After the first stanza, the meaning is still dangling near the obvious end of the spectrum, that the song is about love: either of the act between lovers or the moment of birth between a mother and child. The remainder of the song do not appear to support that claim. Rather the evidence seems to lean towards the moment of awareness. With multiple stanzas speaking to being "here in this body" we must acknowledge that on some level, the protagonist had a conscious independent of a body.

With this interpretation, Parabola could be construed to speak to all moments where a person gains awareness - either the literal awareness, or any significant recognizing of new ideas or self-actualization.


Alive... I...

In this holy reality, in this holy experience. Choosing to be here in...

This body. This body holding me. Be my reminder here that I am not alone in
This body, this body holding me, feeling eternal
All this pain is an illusion.


Parabola has an excellent video, which was directed by Adam Jones. The video includes both songs, Parabol and Parabola in one sweeping movement of art direction. The video opens with one humanoid figure carrying a case into a room with one large table. Two other humanoids meet him, and the first cuts open an apple shaped fruit such that the seeds are bisected perpendicular to the stem. The first figure holds the fruit up, the other humanoids appear to gasp, and one hold up his palm in recognition. An image which seems horribly normal, until we notice that there is a single flame burning at the tip of one of his fingers. All three figures lean over the square table, levitate themselves parallel to the ground, and begin to vomit a viscous black liquid as they hover in a perfect circle. The circle is closed, the image reverses contrast to a white circle and washed out black foreground, a multitude of hands enter the screen and pull the circle into a cat's cradle; this all happens at the exact moment that the band transitions from Parabol to Parabola. It is done exceptionally well.

The remainder of the video deals with a different humanoid character (this one with long antennas curling out of the corner of his eyelashes) and a small stop-motion creature. The small creature tries to call out to the humanoid for help just before a growing fullerene crushes it. The humanoid performs a brief autopsy, and then takes a walk through the forest. A leaf catches his eye, he picks it up, and the leaf transforms into a glowing eye which traces through the humanoids entire body, before coming to rest at the center of his forehead.


Twirling round with this familiar parabol.
Spinning, weaving round each new experience.
Recognize this as a holy gift and celebrate this chance to be alive and breathing.


The official video is great, really. I thought it was interesting to watch, and added an extra dimension to the song's analysis. However, there is a tour-de-force mashup video which blows the official music video out of the water. There are multiple copies floating around Youtube, many appearing to be copies, of The Fountain and Tool - Parabola. This is not a trailer for The Fountain. This is not a preview track of Parabola. It is, simply, a grand art-house interpretation of the entire Darren Aronofsky film told within the confines of the total runtime between Parabol and Parabola.

It was one of those videos where, upon finishing, you click on Replay without even thinking about it.

Since there is no film dialogue, and various key moments of the film are revealed in the mash-up, it is recommended to have viewed The Fountain before watching it set to Tool's masterpiece.


This body holding me reminds me of my own mortality.
Embrace this moment. Remember, we are eternal.
All this pain is an illusion.


Small text: Lyrics to Parabola by Tool
Official Parabol and Parabola video
The Fountain mashup video

Pa*rab"o*la (?), n.; pl. Parabolas (#). [NL., fr. Gr. ; -- so called because its axis is parallel to the side of the cone. See Parable, and cf. Parabole.] Geom.

(a) A kind of curve; one of the conic sections formed by the intersection of the surface of a cone with a plane parallel to one of its sides. It is a curve, any point of which is equally distant from a fixed point, called the focus, and a fixed straight line, called the directrix. See Focus.

(b) One of a group of curves defined by the equation y = axn where n is a positive whole number or a positive fraction. For the cubical parabola n = 3; for the semicubical parabola n = 3/2. See under Cubical, and Semicubical. The parabolas have infinite branches, but no rectilineal asymptotes.<

 

© Webster 1913.

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