Status Updates From Kant's Mathematical World: ...

General note on pictorial space representations: watch quick zooms on a windowed media player while you have a website with a lot of text open on the background or, even better, multiple notepads along with it.

Successive synthesis of a line based on indeterminate parts, as a condition of determinate thing with potential parts, sounds a lot like curves representing state space...He's reaching at modern linear algebra here, maybe!

What if mathematics, then, turns us into animals all the while expanding the proportion of the understanding? If you think about modern humans, they're not progressing towards the higher dimensions but instead they are in mathematical hyper-focus, jumping from quantity to quantity (the focus alternates but there is focus to a very isolated "this"). More and more like dogs, or flatlanders.

Mathematics, based on the concepts of the pure understanding, objectifies indeterminate quanta as determinate quantities. You actually never know the true properties of a spatial object because there's many but understanding demands a fixation to one object decomposible to parts. This sets the tone for science. While knowledge of quantity progresses, the intuition is degraded, and you "see" less.

The flatlander-human difference is located in the schemata..But it's funny: one would think humans have less intense schemata than flatlanders, since flatlanders reduce the indeterminate quanta more according to the categories, which is why they view the rotating cube as changing and twisting squares: reality more intensely categorized. Understanding would then be animalistic, while *seeing* is human, or higher.

Important point about intuition: pre-categorial intuition can represent *indeterminate* quanta out of the data of sensibility. I understand that these are basically different geometric forms not determined as to a certain "one" property of theirs: like circle as a flat object in flat space or floating in a 3D space. It's true that you can never think of it as both, but through categories you fix always on one.

The author first places the quantum in the realm of pre-categorial intuition, but now, dealing with intensive magnitudes, he says that determinate spaces are the quantum, their intensive qualities being the quantitas. Does it imply a sort of pancake model of categories? Categories of quantity applied to quanta of intuition would be the quanta to be schematized by categories of quality, in turn schematized by relation

Some shared properties of line, plane, cubic...All these objects presents themselves as so that no full definition can be given of their properties. Angles of the cubes can be turned inside out: surfaces of the planes can be construed as lower parts of an object pointing at the opposite direction, which would be the same object with its upper face visible: parts of lines could be either flat or deep, magnified to =

Kant's examples of synthesis of determinate space: drawing a line or sweeping out a line to generate surface. Is figurative synthesis of determinate space is always a generation of an n-dimensional object from a n-1 dimensional one? But then determination is based on a sizeless, zero-dimensional point: how is synthesis of a line explained then? Only if line, plane, and cube share properties(beyond having lines).

The relation of Kant's discursivity thesis to form/matter distinction: matter, previously the great unknown, becomes "the form of intuition", while conceptual determination is the form by which alone the matter or space in this case becomes knowable. Space is unknowable in itself without a type of conceptualization: here there is a possibility of different space concepts, like flatlanders and the like, within Kant