[FRIAM] from 5/15 virtual FRIAM

[Jon Zingale]

Disclaimers:
1. TLDR Warning
2. These opinions will be poorly founded and are subject to change.

Dave,

You write: `Nick raised the issue of being contrarian with regards science
and
could get no one to admit to anything beyond ignoring doctor's orders.`

Questions like the one Nick posed fill me with a sense of *aporia*.
I am left without an immediate response. Personally, I find it useful
to factor science into a number of modes or senses. The ultimate goal
for me is to sketch out the kind of space where I can investigate the
*shape*
of my own conception of science. Ultimately, whatever science is to me
cannot be a single consistent entity, but rather a kind of *eidetic
variation*.

* Science as institution. Science can be identified with its institutions:
STEM outreach after-school programs, publishing companies, research centers,
and the like. Here science is sometimes portrayed as a career with clear
delineations regarding who is *good* or *bad* at science. Its goals are set
by
commitees and participation is all but automated through bureaucratic
policy.
The authority we assert when we reference expertise, degrees and
associations
is one of institutional authority. While there is probably a lot for me to
pick
apart here, I will stick to two or three contrary beliefs I hold. For me,
the
notion of STEM is awkward exactly because mathematics is a liberal art and
not necessarily a science. Mathematics exists to describe relationships and
to
facilitate thought. It's home is not far from painting, drawing or the
activities of thespians. Another belief I hold is that any institution is
susceptible to *legitimation** crisis*. It is very possible, as is often
argued of
our news outlets, for scientific institutions to fail in their duty to
produce
science.

For anyone who is interested in these potential short-comings I recommend
reading the history of the Belousov-
<https://en.wikipedia.org/wiki/Belousov%E2%80%93Zhabotinsky_reaction>Zhabotinsky
reaction
<https://en.wikipedia.org/wiki/Belousov%E2%80%93Zhabotinsky_reaction>.
While the story ends
well, it leaves the critical reader wondering what *good science* has been
left to die.
Here, I hold the belief that there is very likely science, as legitimated
by other
scientific senses, which have been de-legitimated by science as institution.

Science as institution is not itself consistently decided. It is prone
to as-well-as open to inter-institutional disagreement. Putting aside for
the
moment that agreement will one day be reached (an ontological claim that
may itself not be amenable to scientific inquiry) any *active* area of
research
is riddled with competing theories. Extreme cases include cosmology and
string theory. A weaker example is the Feynman-Wheeler electron
<https://en.wikipedia.org/wiki/One-electron_universe>.

* Science as abstract authority. It is a personal pet peeve of mine when
someone forms a sentence like, "Well, science says X". It is a strange side-
effect of our culture that the notion of science can be lifted to the status
of abstract authority. The function of such a statement is to end
discussion,
to leave ideas stillborn. To the degree that I find this behavior appalling,
I hold beliefs contrary to science in this sense.

* Science as methodology. Science as the product of scientific methodology
has a great number of sub-topics whose surface I will barely ever get to
know.
Scientific method, peer-review publishing, description production,
explanation
production, Occam's Razor and the constructivists. Many scientific results
have at the core of their methodology useful but known-to-be troublesome
assumptions. The scientific method itself is a co-recursive algorithm and
therefore subject to limitations like NP-completeness and decidability.
At the root of our most trusted tools, like differentiation, hide the
uncertainties
of second-order logic. In an attempt to remedy perceived failings in the
tools of
formal logic, the constructivists (under the impetus of Brouwer, Heyting
and others)
proceeded to develop new logics which in turn were used to create new forms
of
analysis, non-standard analysis and synthetic differential geometry to name
two.

This proliferation of new tools, however, introduce new complexities.
Theorems which were abhorrent in one logical frame (Banach-Tarski) became
non-issues in another, but now in the new frame live other abhorrent
theorems <https://www.iep.utm.edu/con-math/#SH3a>
which didn't exist in the first (Specker's Theorem). I suspect it will not
be
possible for science as methodology to decide which logical frame is somehow
the *most correct*. As it stands I do value the predictions afforded by a
classically
founded differential calculus, even if its foundations are unresolvable.
Perhaps
less controversially, I hold space for the existence of Chaitin random
numbers.
In a Scientific American article
<http://www.owlnet.rice.edu/~km9/Randomness%20and%20Mathematical.pdf> Chaitin
writes:

'Although randomness can be precisely defined and can even be measured,
a given number cannot be proved to be random. This enigma establishes a
limit to what is possible in mathematics'.

Lastly on this point and just to bait Nick...
Nick often attributes to Peirce that, "Truth is what we will ultimately
come to agree upon". This idea is perhaps non-scientific in that it
may be a form of Ramsey statement (thanks Glen!) which falls on the side
of metaphysics. A truth-principle like this with Ramsey meta-physicality
would
suggest that truth is *here*, but we cannot *know* it, despite Nick's
deepest wishes.
Further, if we could *know* a thing in this way, we would only be able to
*verify*
it once *all of the ballots were in*.

* Science as metaphor. In a *very* *narrow* context, science can be
construed as
metaphor between mathematical model and physical observation. Nick often
points out that while *instantaneous velocity* is mathematical, we should
be leery
of calling it physical. When we apply the notion of an arc to the path of a
ball,
we are importing and projecting onto physical space the properties of a
model.
These properties almost invariably entail the continuity and smoothness of
time and of space. Arguably, even time and space are imported. I do believe
that time and space are *worth the import*, but I do not think of the
metaphor
as establishing truth.

* Science as culture. A biologist friend of mine asked me to validate his
claim that our universe is four dimensional. I took the opportunity to
elaborate
on the concept of dimension as I think of it, namely as an assertion about
linear independence. I attempted to move the conversation to a discussion
about models and what we intend to describe. I am ok with a four dimensional
time-space if we are discussing Einstein's relativity theory. Clearly, in
other
physical contexts I may wish to talk meaningfully about infinite dimensional
Hilbert spaces or six dimensional Calabi-Yau manifolds. He left the
conversation
miffed. Science has a cultural component, we argue and push and struggle to
define scientific contexts with each other. Imre Lakotos wrote a wonderful
book about this called "Conjectures and Refutations". It playfully covers,
in dialogue form, the development of modern topology from the perspective
of mathematics culture.

* Temporality in Science. Because Newton and Einstein held different
beliefs,
we cannot rely (nor should we) on science to be consistent in time. We can
hope,
along with Nick, that some scientific acquisition will meet the ultimate
gold-
standard, jump the limit of our methodologies and finally and gloriously be
classified as *known true*. While it would likely be the case that if Newton
were here today he would agree that Einstein's theory is better, there are
other
examples which exhibit oscillatory behavior. Is coffee good for you? Should
you avoid red meat? It is hard for me to keep up with the temporality of
science, and I suspect that we are capable of believing things which are
not-
now-but-will-one-day-satisfy the scientific criteria of one or many of the
senses above.

In many ways I feel that I am taking a bold risk in rambling here, so I hope
that it meets your (Dave) satisfaction. I also hope that it inspires others
to take a chance and spill some *e-ink*.

Full of it,
Jon
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