“The things that fascinate me the most about mathematics are logical
thought and the great importance attached to the correctness of
propositions. Every step made during calculations is conclusive and
mathematicians don’t like to make false statements. This is the reason why
people from this particular domain contemplate longer before they respond
to questions. Recently I read a sentence in a book which summarizes all
this fascinating stuff to me succinctly: ‘Mathematics is the purest form of
thought.’” —

Barbara Meier (via dauphinexvx <http://dauphinexvx.tumblr.com/>)

This is an interesting observation, and I don’t disagree that mathematics
is the purest form of thought, but what is thought? While we are at it,
what is a form?

In the first case, I have proposed that thought is meta-feeling. It is a
kind of trick within the interplay of intention and feeling to establish a
generalized neutral feeling which can be used like a variable in algebra. A
feeling like “I am angry and sad because a tiger ate my kids, but relieved
that it was only a dream” can sort of look at itself from a distance and
strike all kinds of other thought-like sparks. We can feel fear that dream
was a premonition. We can feel motivated to hunt tigers. These need not be
thoughts, but emotive dispositions. They don’t entail any awareness about
our state or our actions, only a desire for this or that response to a felt
condition.

The feeling need not be connected to a real event or a particular event,
but as we go up the ladder of meta-abstraction, the absence of immersive
personal feeling is replaced by formality and clarity. It is an echo of
decoherence, as the living wave of direct feeling ‘collapses’ into a
thermodynamically unambiguous state, the flow of participation is deferred
into analytical hindsight and strategic foresight.

On some level, it as if we are picking up the stylus from the universal
record and holding onto it while we deliberate our options. Thought is
born, in my view, as this kind of deferred meta entanglement…a feeling that
is whipped up into a frothy foam where it can be used to the sculpt air -
turning absence into a virtual presence through surface tension alone. The
thought bubble is hypothesis, and the ultimate thought bubble is
Mathematics because it seeks only to distill itself into its own purest
form. It is, however, still a form. There is still a thinker thinking the
thoughts, and the thoughts are still feelings of a living person, but these
facts are hidden from view within the mathematical context. The pretense is
toward a universal objectivity.

Indeed, it is not incorrect to say that ‘mathematics is the language of the
universe’, iff you define the universe to begin with as those forms which
can be publicly observed. In my view then, it is really tautological to say
that mathematics is the purest form of thought, since mathematics is only
the thought of purest forms. What then, are forms?

There are many ways to approach such a general term as form, but I prefer
the underlying sense which is shared with formality. A presented shape,
yes, but more like the logical essence of a presented shape. It is a
presentation of coherent qualities; stability and regularity, reducibility
to simpler, universal sub-forms, etc. Mathematics explores this aspect of
the universe while eschewing and denying all phenomena which seems exempt
from form. All things spontaneous and erratic, non-reducible and
proprietary are treated poorly. Emotions, free will, and the “I” to whom
they belong are not merely pushed to the back of the bus, but they are
pushed out the back door of the bus, to be paved over by the steam roller
in hot pursuit.

I sympathize with people who are unable to conceive of a concretely real
phenomenon which generates form intentionally rather than is defined by it,
but it is harder to be sympathetic when this disability is compounded by
the unwillingness to allow that it can be conceived. In my thousands of
hours arguing with STEM-minded people online I have found an overwhelming
bias against certain kinds of ideas and laughable acceptance of others.
Ridiculously grand abstractions like MWI, or replacing every atom in a
human brain roll off of the tongue easily, while ordinary terms like free
will are brought under Torquemadan hyper-scrutiny. The double standard is
tremendous, yet invisible to those who subscribe to it. Physics can be as
counter-intuitive and unexplainable as it wants to be, but if you bring up
intuition itself, then be prepared to hear a lot of ‘simply’ this and
‘merely’ that.

The good news though, is that through mathematical principles like
symmetry, we can move beyond these blind alleys. By applying all of what we
know about the public world, its forms and formulations in reverse we can
find where the private world of physics begins - not with numbers, but with
names; not with abstract thoughts but with sensory experience. To be a
living participant in a meaningful universe is to eventually put the stylus
down somewhere and let the music play.

The second post is shorter but it has pictures, so probably better to just