So many of our logical systems in math and science
that are used for analysis are simple logical systems that are binary in
nature; either 0 or 1. That's it. There's no bending of the rules. It's
inflexible by nature. Kant believed that we don't learn math, one discovers
math. He believes that all are born with a logical system in their heads and
that reading mathematics is discovering a dormant language. It awakens the
logical system. If the logical system is accurately represented by, for
example, symbolic logic, then a logical system must be linear in nature. What is called Normative Logic is
characterized by parallel and perpendicular lines, but the logic one actually
uses in their daily lives has an inherent bending and declension in it.
Viking-Poets do not ride in perfectly straight lines nor take corners at
geometrically perfect angles, rather they ride in a flow of continual judgment
because of the never-ending bumps and imperfections along their path.
Nor does a Viking-Poet motorcyclist ride at a
constant speed. Instead there is a need to fill in the gaps and corners where
linear logic cannot go. They use intuition in their logic. So when cycling, one
must balance between the geometrically crisp logical model with a wise spatio-temporal
inflected logic. The decision-making process when riding is not rigid; it
takes into consideration the conceptual application of a linear system onto a
Kant 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 = 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.' So Kant
gets it. 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 zeitqualia. But this begs the
question: How can one see both duration and points in time? 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. 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. Kant writes 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.'
But Kant never undertook exploits. In fact he never
traveled more than forty miles from his home during his lifetime, so that's why
it was never revealed to him. But it has been revealed to the Viking-Poet from
empirical data: Kant's transcendental schema is that faculty in us that inflects
logic. If this transcendental schema is a product of the imagination, like
Kant says it is, then it could be that thing that bridges ones sense perception
and bends ones innate logical apparatus to understand the sense data in the
natural non-linear world.
So then what does inflection means precisely? Think
of the word ‘flex.' Inflection is an angle or bend, or a modulation in the
voice. It is a change in a plane curve from convex to concave. It's a pattern
of change in form undergone by words to express grammatical and syntactical
relations. To inflect is to vary the tone of pitch of the voice, or modulate.
It is to turn from a straight or usual course, and to bend. To inflect is to
give or recite the inflections of a word by conjugating or declining. It is to
alter the form of a word by inflection. Comes from the Latin inflectere,
meaning ‘to bend.'
bent lines in the Inflected Matrix of Mountainbike Logic sketch:
Kant, The Critique of Pure Reason