This vascillation is a 0-Sphere, it is how we imagine an object of the order, circle, sphere, simplex is expressed in 0 dimensions.
A 1-Sphere is a line. If you walk all the way from one end of the line to the other, you will end up at the beginning, much like the 2-Sphere, or the circle. The 3-Sphere is of course, a sphere proper, and 4-Sphere is called a simplex, and those are four spatial dimensions, for the sake of titillating the imagination.
The Earth is simplex-oid with one dimension in time. Of course, this is the expression of earth at any given point in time which not only contains its past, but predicts its future.
So, if scientists were given a snapshot of the soil of some random planet in our galaxy, they would be able to roughly guess most of the properties of the entire planet with just one simple clue.
The ability to envision this entire world from any given piece, necessitates that the rules that operate in this portion imply, are the same as or are derived from, in fact engaged within the same system as the part, and we know that this is not always the case.
A scientist with a clump of desert will have access to information, as it is contained within and refracted through the environment of the desert. We won't know anything about the nature of rainforests from a clump of desert even if we're clever enough to imply that they should exist with the clump of desert.
So Blake isn't really "at war" with science, or reductive logic, rather, he is at war with those who are trying to negate the imagination, in order to get to a truth. Blake understands this as confusing the map for the territory.
What Blake is trying to make us aware of is the infinite complexity of the information.
We have entered an either/or universe created out of the seven ages of corporeal concretization, demarcating time, as the remote functional God in the first pages of Genesis creates his vast Eden, part by part, in six consecutive days, resting on the seventh.
This story instantiates time. It is divided into seven segments and is geared toward revering the one day upon which God rested from His heavy labors; the one day on which God created nothing at all. This day, the Sabbath, is both the end and the beginning of a new cycle. This story of Creation is attributed, according the Documentary Theory to the Priestly tradition, a theory invented twenty years after Blake's death.
The Documentary Theory holds that the Torah proper is a composite of four earlier accounts of the Hebraic history and folklore, which are separated by ideas concerning God, and the sort of vision the other has of that God, calling Him at points by different names. Blake would have been aware of the different names, and as keen reader whose main concern was perspective, he would have recognized different visions of God. He uses the terms Jehovah, YHWH, and Elohim to evoke the sense of connection those terms have to their respective visions of God. Urizen is somewhat of a composite of these different visions, himself being at once an image of God and an agent of Creation, who himself represents the will of the Priest.
And unlike the God of the Elohist and Yahwist tradition, who is more or less anthropomorphic, being Himself capable of the sins He prohibits, the Priestly God is abstract and a functionary of the necessity to organize time; what in Blake could be called time-scraping because it represents the week cut into days, and then a day into hours, an hour into minutes and so forth, in both directions, toward millennia and nanoseconds, the aeon and the instant.
Likewise, this fall into organized time, instantiates routine, predictability, habits; the future as born out of the past. It is the beginning of the cycle. The seven ages of Urizen, in which his body materializes into a solid obstruction, occurs at precisely the same moment that time becomes carved out into the days of the week. The curse is this: the Vision, which is process of creation for Blake, has been reduced to the ocular, sensible world of matter, and the mathematical ratios which can be derived from measuring the length of the day, the shadows the Sun casts and, of course, the Architect's compass.
This is the future in some basic sense, being continually reborn out of the past. It resists change in favor of tradition, and identity. It instantiates self-hood, continuity, predictability all as the various forms and functions of Tradition in the absolute sense.
Tradition as an absolute principle, that is taken to its logical extreme; whose function is to preserve the self at all costs, and in a special sense, the past, the collected memories of the people; a shared sense of honor toward their principalities. Blake recognizes that the statehood, or the collective identity of the people was a prime target for deification, alongside the realms of nature, which had daemons, geniuses, or gods presiding over them as their powers. The gods are human reflections of the processes of nature, the cycling of the summers and winters are expressed in the liminal seasons of spring and fall, as when Persephone is taken into the underworld, or Tammuz must replace his bride Ishtar. In the case of Tammuz such a cycle was celebrated by the Sacred Marriage of the fertilizing goddess with leadership of the god-king. The union represented a harmonization of the powers of nature with kingship itself, and it was a community sacrament to be performed in the springtime.
The issue at play in Blake is the collective identity or selfhood, or more specifically, the nationalistic selfhood which prevents one from recognizing the Divine Vision. It is necessary to state that the selfhood Blake is critiquing is not necessarily nationalistic, but its system of religion was necessarily aimed toward providing a collective selfhood which could represent a city-state or an empire; and so by ritual, it becomes imbued with the power of the fertility/war goddess by observing Sacred Marriage in the springtime.
Back to the text; Los undergoes a transition in Chapter 5 and it is subtle yet significant. There is the sense (initially) that Los is either chained or conjoined to Urizen in some way. However, when Los' fires die and Urizen's world begins to cool and harden, Los is suddenly capable of beholding Urizen in his “abominable petrific chaos.” Suddenly, it is Urizen who is bound in chains while Los beholds him from afar, and Pities him.
Pity is a concept of enormous magnitude in Blake's Illuminated Texts, and likewise is one of four qualities attributed to the Divine Vision, the others being Mercy, Peace, and Love. Elsewhere, Pity plays a healing role, acting as a catalyst to some selfless action. Here, in Urizen, it merely “divides the Soul.”
Let's for the sake of argument assume that what Blake is describing is a personality experiencing a single internal reality. Los and Urizen are not separate autonomous beings, but rather parts of a divided whole. Los pitying Urizen would be something akin to “I pity myself.” “I” and “myself” explicitly refer to the same being, (the one who types this essay at his keyboard for you to read). It is no stretch to say that the subject and the object are then the same being, with different names referring to parts of the whole. The part of myself which does the pitying, has thus separated itself from the part of itself that it pities. To assert the statement “Pity divides the Soul” is to assert that there is only one certain kind of Pity, self-pity, for to Pity another is an entirely different affair in Blake, and to do so means to partake in Divinity. But here we have an instance, for example, of a Soul in lamentation over the turpitude of its Body, or more mundanely, the image of the Earth from the Sky.
Thus the Eternal Prophet was divided
Before the death-image of Urizen
For in changeable clouds and darkness
In a winterly night beneath,
The Abyss of Los stretch'd immense:
And now seen, now obscur'd, to the eyes
Of Eternals, the visions remote
Of the dark seperation appear'd.
As glasses discover Worlds
In the endless Abyss of space,
So the expanding eyes of Immortals
Beheld the dark visions of Los,
And the globe of life blood trembling
Blake is drawing a rather explicit connection between the way the Immortals behold Los' visions and the way Scientists peruse the sky with their telescopes. We are once again being shown a world which has been reduced to the ocular, visual representation; a type of knowing which has assumed a supremacy over other sorts of understanding, such as apprehension, imagination, aptitude, emotional intelligence. We have rational, systematic, and system bound reasoning asserting a sort of supremacy to the exclusion of the other types of knowing; a system which binds Reason into the observations capable of being made by the five senses; a system advanced by the empiricists and most notably, John Locke. It is built upon an observer/observed dichotomy. Einstein's Relativity would morph this dichotomy into obersever/observation, and Quantum Physics would further complicate Newton's Machine World by only being able to talk about probabilities.
So much of what scientists over the centuries have attempted to achieve has been based on territory generally reserved for the prophet. “What?” you say, laughing at my ignorance. But both the scientist and the prophet are concerned with accurately predicting the future; for if an experiment can be carried out once, but never duplicated, it proves nothing but an anomaly. It isn't good that an experiment work once, it must always work, over and over again. This ensures that the relation can be represented mathematically; thus “abstracted,” and can be worked with according the system of rules we agree constitute mathematics. Mathematics is a system, a machine, for analyzing the truth of its own assertions. If Newton's laws were universally accurate (that is, they applied to the Universe as a whole and were not just Earthbound approximations), then everything indeed would be predictable, and given a fast enough computer, one could predict the history of the entire Universe from the present. Blake knew better, and felt no need to prove it. Kurt Godel would do this for him with his Incompleteness Theorem. It is precisely our ability to break the rules, to use metasystemic logic, that allows us to fashion the rules of our system. Thus by assumption do we discover the truth, even when it runs contrary to our assumption. Thus by trial and error, experience, and experiment. The rules themselves cannot so much evaluate their own truth. The theory cannot assert its own correctness. They require an observer, an advocate, a mathematician, or a prophet.
How then does the Prophet predict? By seeing time as both cyclical and linear at once. Certain patterns keep repeating (though with infinite variety). There is the same rhythm to a song, and yet the words keep changing. As they do, the language becomes more and more opaque, until every every word is at a one to one correspondence with its referent. So constructed, the word, the thing itself, loses its connectivity to the world around it, becoming itself a solid thing in a universe of lonely monads. This superficial, sensory empiricism is only part of the story, according to Blake, whose argument goes something like this: if our senses alone dictate our knowledge of the world, then how could we perceive (say) Time? Without Time, we have no concept of Motion. Without Motion what becomes of Time?
The issue that comes into play for the mathematicians and empiricists alike who are in defense of their Machine World, is the undefinability of Truth itself, and the impossiblilty of constructing a system which can verify the truthfulness or falsity of all of its own statements. As Godel proved, even if it were possible to construct such a Machine, there would always be (at least) one question that the machine could not answer. In other words, there is always a base assumption at work within the system which is not provable within the system. For Blake the idea was simpler. Any idea which represented reality in accord merely with the five senses was bound to be a reduction of a greater whole. Such is Blake's critique on science. There is also the element to which Faith is antithetical to Demonstration, which plays a large role in Jerusalem.