northanger (northanger) wrote,

discrete combinatorial systems



This little war, this private fucking war of West’s, and you know what? I don’t think it’s ever going to end. Because I’m an American soldier, you know? I fought to liberate this country, and what we were told about that, then what West told us, those things weren’t the same. Maybe at first they might seem the same, but slowly, steadily, they drifted apart, further and further. West didn’t want the war to end, not ever. But he spoke to me, and I understand the special thing people feel for him. He’s not an ordinary man. He changed me. {Renomu}


7. O ye two Divine Hawks upon your Pinnacles!
Who keep watch over the Universe!
Ye who company the Bier to the House of Rest!
Who pilot the Ship of Ra advancing onwards to the heights of heaven!
Lord of the Shrine which standeth in the Centre of the Earth!
{Liber Israfel}


There cometh into the stone the great Angel whose name is Av2, and in him there are symbols which strive for mastery, --- Sulphur and the Pentagram, and they are harmonized by the Swastika3. These symbols are found both in the name of Av4 and in the name of the Aethyr. Thus he is neither Horus nor Osiris. He is called the radiance of Thoth; and this Aethyr is very hard to understand, for the images form and dissolve more rapidly than lightning. These images are the illusions made by the Ape of Thoth. And this I understand, that I am not worthy to receive the mysteries of this Aethyr. And all this which I have seen (being all the thoughts that I have ever thought) is, as it were, a guardian of the Aethyr5.

I seem quite helpless. I am trying all sorts of magical methods of piercing the veil: and the more I strive, the farther away I seem to get from success. But a voice comes now: Must not understanding lie open unto wisdom as the pyramids lie open to the stars?

Accordingly, I wait in a certain magical posture which it is not fitting to disclose, and above me appears the starry heaven6 of night, and one star greater than all the other stars. It is a star of eight rays. I recognize it as the star in the seventeenth key of the Tarot, as the Star of Mercury. And the light of it cometh from the path of Aleph. And the letter Cheth is also involved in the interpretation of this star, and the paths of he' and vau are the separations which this Star unites7. And in the heart of the star is an exceeding splendour, --- a god standing upon the moon, brilliant beyond imagining8. It is like unto the vision of the Universal Mercury. But this is the Fixed Mercury, and he' and vau are the perfected sulphur and salt. But now I come into the centre of the maze, and whirling dust of stars and great forgotten gods. It is the whirling Svastika which throws off all these things, for the Svastika is in aleph by the shape and number9, and in beth by the position of the arms of the Magician10, and in gimel11 because of the sign of the Mourning of Isis, and thus is the Crown defended by these three thunderbolts. Is not thrice seventeen fifty-one, that is, failure and pain?

Now I am shut out again by this black Svastika with a corona of fire about it.

And a voice cries: Cursed be he that shall uncover the nakedness of the Most High, for he is drunken upon the wine that is the blood of the adepts. And BABALON hath lulled him to sleep upon her breast, and she hath fled away, and left him naked, and she hath called her children together, saying: Come up with me, and let us make a mock of the nakedness of the Most High. {The Cry of the 6th Aethyr, Which is Called MAZ}


Most complex physical processes are blending processes. For example, if I mix some paints together, I get a blend that essentially averages the inputs into something homogenous. The alternative, and much more rare, combining process is called a discrete combinatorial process. In such processes the combination is not an average – each individual combination has perceptively unique qualities. This means a discrete combinatorial system can generate and infinite number of qualitatively different outputs. In other words, innovation in its broadest sense can really only be possible when discrete combinatorial systems are at work.

There are only two discrete combinatorial systems that we know of in the universe: DNA and human language (and by extension most of what we call “thinking”). It is no coincidence these are exactly the processes that we marvel at due to their ability to generate endless novelty. (See Steven Pinker’s book, “The Language Instinct”, for more discussion on grammar and mind as a discrete combinatorial system). These two systems have done pretty good so far -- the discrete combinatorics of DNA has resulted in the amazing natural world we live in, and the discrete combinatorics of our language system has created the fundamentally changed world we humans have wrought in the past 40,000 years or so. {Don’t Lose The Failures}

However, one point needs to be emphasized about DCSs: In the end result, you must be able to pick out the discrete parts, i.e. there still must be words or nucleotides. In blending systems (which contrast with discrete combinatorial systems), it works differently. Take color mixing as an example of a blending system. Combining red and white paint, you get pink, but there is no longer red or white paint left. So this is not a discrete system. If you were to make a bunch of tiny, alternating red and white dots on some paper, then from a distance, it would appear pink. This pink WOULD be an example of a discrete system, because you can still pick out the red and white parts. {Class Notes from 14 SEP 99}

Combination of Motor Primitives :: In the natural world some complex systems are discrete combinatorial systems - they utilize a finite number of discrete elements to create larger structures. The genetic code, language and perceptual phenomena are examples of systems in which discrete elements and a set of rules can generate a large number of meaningful entities that are quite distinct from those of their elements. A question of considerable importance is whether this fundamental characteristic of language and genetics is also a feature of the vertebrate motor system. In the last few years, my colleagues and I have asked this question: are there simple units (motor primitives) that can be flexibly combined to accomplish a variety of motor tasks? We have addressed this fundamental and long-standing question in experiments that utilize spinalized frogs, rats, and currently monkeys. With an array of approaches, such as microstimulation of the spinal cord, NMDA iontophoresis, cutaneous stimulation of the hindlimb, and vestibular activation, we have provided evidence for a modular organization of the frog's and rat's spinal cord. A "module" is a functional unit in the spinal cord that generates a specific motor output by selecting a specific pattern of muscle activation (a synergy). {Motor Control and Motor Learning}


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