The Inflected Matrix:
When I opened my eyes I immediately felt the tightness of my skin. I reached for my water bottle and for food in my bag and feasted. For a moment I didn't know if it was dusk or dawn. Doppel was hunched over reading Kant's Critique of Pure Reason.
"Good to polish up on my Kant."
"Well, because the guy is such an intellect!"
"Maybe, but with purpose. Has some good ideas about time."
"He says that man has a natural intuition of time and space, and that time is quanta continua, meaning it must be looked at as continual because otherwise time and space would just be an empty point. An instant in the time continuum can only be a point, and a point in time by definition is void of any length of time. Therefore points of time would be 0 + 0 + 0 + 0. Time therefore must always be considered as duration. Kant says ‘the continuity of time is ordinarily designated by the term flowing or flowing away.' See, he's got it."
"But Kant never traveled more than 40 miles from his home over his entire lifetime. Not much a Viking-Poet."
"So a point in time becomes an instant merely at the beginning or end of a finite duration."
"The problem with that is that we are forced, it seems, to define the present as the end of the past and the beginning of the future."
"The now would then be void."
"So that's why it must be duration. And in that duration there should be qualia."
"How can we see both duration and points in time?"
"Ah! You put your finger on what I was just reading about. Kant calls it transcendental schema. It is the magical function we have in the imagination that bridges between instants in time and the sensibility of time as duration. He says this schema is the synthesis of perception with the representation of time. It is the filling in of time."
"What does the word schema mean outside of the world of Kant?"
"Schema is the orderly arrangement of parts, as in a philosophic system. It's the rover force that makes time, as defined as an infinite series of instants, intelligible as a quantum flow. He says of this that it is ‘art concealed in the depths of the human soul, whose real modes of activity nature is hardly likely to ever allow us to discover, and to have open to our gaze.'"
"That's some heavy stuff there maestro."
"Well, Kant never undertook exploits. That's why it was never revealed to him. But it has been to us. I think Kant's transcendental schema is that faculty in us that inflects logic, like I was talking about before. If this schema is a product of the imagination, like he says it is, then it could be that sensible thing that bridges our sense perception and bends our natural logical apparatus to that sense data in the natural world." I sat down and he sketched out what he meant on a piece of paper and handed it to me.
"See, this is what I mean. An inflected matrix."