[FRIAM] from 5/15 virtual FRIAM

Sat May 16 21:47:09 EDT 2020

Jon-

While reading your essay I had several associations.  I recently read the
assertion that in developing axiomatic systems and proving the entailed
theorems mathematicians are writing for God as the authority.  So
mathematics, from that point of view is a conversation with God.

At the other extreme (?) I thought Reuben Hersh held a view similar to the
one you attribute to Nick:  that mathematics is the set of theorems that
mathematicians agree to by consensus.

I agree that Newtonian physics and differential calculus are the correct
model for objects moving in a vacuum.  I was given an $85 ticket by a
rookie police officer for rolling through a stop sign.  She said my wheels
never completely stopped turning  I don't think any experienced officer
would have given me a citation.  I had fantasies of writing to the judge
explaining that an object moving along a continuous path can stop for zero
seconds (unit of time irrelevant).  This happens when you throw an object
straight up (directly away from the center of the earth).  I don't know
about whether space and time have the Hausdorff property but for traffic
purposes it doesn't matter.

In the Woody Allen film "Sleeper", Allen's character wakes up 200 years in
the future.  He's getting in to know a stranger and he tells him that he
owned a health food store in Greenwich Village.  The stranger looked
puzzled and then said, "Oh, those were the days before scientists realized
that the ideal diet consists of steak and chocolate milkshakes".

I feel, without evidence, that mankind will not last long enough to see all
science as settled.  There is hope for pure math.

Is any of this responsive to your email?

Frank

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, May 16, 2020, 7:07 PM Jon Zingale <jonzingale at gmail.com> wrote:

> 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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