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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