One may find that philosophy taken as a whole is boring, tedious, monotonous, repetitive and lacking in creative intensity, with only a few exceptions. Even the exceptional cases (books, systems, concepts) can come to be banalised by their own creators, as they recite and organise their ideas over repeated use. Sometimes our own productions seem to be second hand copies of our few moments of learning or of inspiration.
Despite a sometimes euphoric rhetoric of de-anthropisation, individuation, conceptual creation, infinite intensities, pluralism, and the great outdoors, nothing seems to change and the old academic game seems to perpetuate itself.
Even Deleuze’s battle cry « philosophy is creation of concepts » has lost its provocative and political power, and can be found repeated unthinkingly as a self-evident formula. It has gone from strange provocation to marketing slogan to micro-social doxa in the space of a few years.
We have witnessed many attempts to break out from this impasse. The image of a « turn » has been invoked to proclaim, to describe and to incite to a radical change. The linguistic turn, the practice turn, the ontological turn, the ethical turn, the speculative turn, and the mathematical turn have succeeded or accompanied each other, provoking change within the academic microcosm but without changing its fundamental laws.
François Laruelle has felt this stifling aspect of philosophy intensely for decades, to the point of calling his own philosophy « non-philosophy », and « non-standard philosophy ». His solution is to take the image of the turn literally, mathematically and physically, and to take the mathematics and the physics imaginally, generically.
At this very general level, Laruelle is operating with the same sort of double crossover, or two way cross movement, as science fiction. An image (insight, affect, intensity, virtuality, quality, potential, speculation, intuition) is translated (literalised) into cognition, and this cognition is re-translated (estranged) into imagination.
More specifically, Laruelle employs the mathematics of complex numbers, comprising a « real » component (inscribed on the horizontal axis) and an « imaginary » component (the factor of a real number multiplied by √-1, thus forming an imaginary number (inscribed on the vertical axis). The two axes (real and imaginary) define the complex plane, and allow Laruelle to express his own non-philosophical turn as a « quarter turn », the result of multiplying standard philosophy (horizontal axis) by 90º, effecting a rotation onto the imaginary or vertical axis.
We can make several remarks at this point in our analysis
1) Laruelle is not always very clear on this point, but we must consider that the specific geometrical two way cross movement on the complex plane is only one possible analog of the generic conceptual double crossover.
2) Laruelle, at this stage of his argument, takes for granted the first movement, a quarter turn in which a speculative item on the imaginary axis is rotated into a cognitive content on the real axis. This first rotation is equivalent to the formation of standard, « sufficient » philosophy. The dissolution of this sufficiency requires the inverse movement, a rotation in which cognitive content is transposed onto the imaginary axis.
3) Laruelle seemingly considers only pure cases, sufficient philosophy limited to the real axis and non-standard philosophy confined to the imaginary axis. Despite vague talk of composites of philosophy and science under science, Laruelle does not make full use of the complex plane in its entirety.
AGENT SWARM 
I had only vaguely understood the quarter turn. I’m not sure if what I have read of his said very much about the quarter turn; it’s been a couple years since I’ve read anything of his.
So your explanation of it helps. And actually with your description, really kind of shows how his model lens itself to a difficult job. Lol. Like I understand what he means, or what you have described, as the quarter turn but then being able to speak about it in a way that makes sense seems like it would be pretty difficult to do to pull off.
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