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+Title: Communication and Reuse of Mathematical Models
+Author: bnewbold
+Date: 2020-06-28
+Tags: modelthing
+Status: draft
+
+This post describes the potential I see for collaborative infrastructure to
+agument group research and understanding of mathematical models. This type of
+model, consisting of symbolic equations than can be manupulated and computed by
+both humans and machines, have historically been surprisingly effective at
+describing the natural world. A prototype exploring some of these ideas is
+running at [modelthing.org](https://modelthing.org).
+
+After describing why this work is interesting and important to me personally, I
+will describe a vision of what augmentation systems might look like, describe
+some existing tools, then finally propose some specific tools to build and
+research questions to answer.
+
+Outline
+
+* personal backstory
+    => technologist essay
+    => my previous work
+* what would be better?
+* existing ecosystem
+    => latex, mathml
+    => modelica
+    => SBML
+* proposed system and research questions
+    => modelthing.org
+* reference list
+
+## Personal Backstory
+
+*Feel free to skip this section*
+
+Much of my university (undergraduate) time studying physics was spent exploring
+computational packages and computer algebra systems to automate math.  These
+included general purpose computer algebra or numerical computation systems like
+Mathematica, MATLAB, Numerical Recipies in C, SciPy, and Sage, as well as
+real-time data acquisition or simulation systems like LabView, ROOT, Geant4,
+and EPICS. I frequently used an online system called Hyperphysics to refresh my
+memory of basic physics and make quick calculations of things like Rayleigh
+scattering, and often wished I could contribute to and extend that website to
+more areas of math and physics.  In some cases these computational resources
+made it possible to skip over learning the underlying methods and math. A
+symptom of this was submitting problem set solutions typeset on a computer
+(with LaTeX), then failing to solve the same problems with pen and paper in
+exams.
+
+<div class="sidebar">
+<img src="/static/fig/sicm_cover.jpg" width="150px" alt="SICM book cover"><br>
+</div>
+
+A particularly influential experience late in my education was taking a course
+on classical mechanics using the Scheme programing language, taught by the
+authors of "Structure and Interpretation of Classical Mechanics" (SICM). The
+pedagogy of this course really struck a chord with me. Instead of learning how
+to operate a complex or even proprietary software black box, students learned
+to build up these systems almost from scratch. Writing and debugging equations
+and simulations in this framework was usually more about correcting our
+confusion or misunderstanding of the physics than computer science. I came to
+believe while teaching another human is the *best* way to demonstrate deep
+knowledge of a subject, teaching to a *computer* can be a pretty good start.
+
+<div class="sidebar">
+This isn't to say that computers as a pedagogical tool can replace
+human mentorship and interaction; the SICM course was also one of the most
+instructor-intensive and peer-interactive of any I took. And of course this
+learning format will not be best for everybody.
+</div>
+
+Some years later, I found myself at a junction in my career and looking for a
+larger project to dig in to. I think of myself as a narrative-motivated
+individual, and was struggling to make a connection between my specific skills
+and training with huge, abstract, world-level struggles and challenges
+confronting humanity. Bret Victor's "What Can A Technologist Do About Climate
+Change?" essay was full of connections between an inhumanly large and
+complicated planet-scale challenge and specific human-scale projects. The essay
+also makes the claim that systems modeling languages and tools have been
+under-invested in over time, and frames the question "What if there were an
+`npm` for scientific models?". The essay of course isn't a review or final word
+on this one subject, but it is encouraging to see somebody talking about
+similar ideas and finding the same state of research.
+
+Summary: computer math systems can be powerful for learning and understanding,
+but important that they are open, powerful, and well-designed for open
+exploration and unintended uses.
+
+TODO:
+
+* reinventing discovery
+    * web-era collaborative projects
+* explorable interactive web things
+    * really love these, but frustrated that the code/model is hard to get
+       out; even more so when creating new models interactively!
+    *  eg, nytimes interactive, you can tweak parameters and interpret results
+       quickly, but can't tweak the model itself
+    *  "kill math"
+
+## Goals and Principles
+
+Core goal: advance the ability of humans to collaborate on large complex symbolic/computational models of natural systems
+
+* scale collaboration to more complex models
+* make digestion of knowledge faster/smoother: from primary source to
+  secondary/tertiary faster
+
+Some best practices:
+
+* **Free Software workflows**: the entire ecosystem does not need to be free
+  and open source software, but it is important that anybody can collaborate
+  using only open tools
+* **Transferability**: should be possible to move models from project to project,
+  even if using idfferent software platforms
+* **Versioning, typing, and forking**: lessons from sustainable distributed
+  software development (as opposed to large-scale projects within a single
+  organization) are that it must be possible to extend or make corrections to
+  individual components with as little disruption to other components as
+  possible. This means support for versioning, care about design of namespaces
+  (when references are by name), and automation to help detect "breaking
+  changes" and manage updates.
+* **Permissive licenses for content and metadata** to allow broad re-use.
+  More restrictive open licenses (eg, GPL, Non-Commercial, Share-Alike) are
+  acceptable (and often desirable) for software tools.
+* **Scale up and down**
+
+examples of applying core goal:
+-> "does veganism make sense"
+-> COVID-19 modeling
+-> understand equilibrium finances of large companies/institutions, for the people inside those institutions ("business model")
+
+## Existing Ecosystem
+
+Similar tools (in doc):
+
+* modelica
+* wolfram world: alpha, mathematica, system modeling
+* strong type systems
+* mathhml
+* SBML
+
+## Proposed System and Open Questions
+
+Proposed system to build:
+
+* simple intermediate format for math models
+    => limited in scope and semantics; like regex
+* transpilers to/from this format to general programming and computer algebra languages
+    => sort of like pandoc
+* tooling/systems to combine and build large compound models from components
+* public wiki-like catalog to collect and edit models
+
+Will mathematics continue to be "unreasonably effective" in the natural
+sciences as we try to understand larger and more complex systems?
+
+Will technical and resource limits constrain symbolic analysis of complex
+systems? Eg, will there be scaling problems with algorithms when working with
+large models?
+
+
+## References
+
+Structure and Interpretation of Classical Mechanics ("SICM") (book)
+[html](https://mitpress.mit.edu/sites/default/files/titles/content/sicm_edition_2/book.html)
+[wiki](https://openlibrary.org/works/OL16797774W/Structure_and_Interpretation_of_Classical_Mechanics)
+
+Functional Differential Geometry (book)
+[html](https://mitpress.mit.edu/books/functional-differential-geometry)
+
+Reinventing Discovery (book, Michael Nielsen)
+[openlibrary](https://openlibrary.org/works/OL15991453W/Reinventing_discovery)
+
+Hyperphysics (website)
+[url](http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/refr.html#c2)
+
+All Watched Over by Machines of Loving Grace (miniseries, Adam Curtis)
+[wiki](https://en.wikipedia.org/wiki/All_Watched_Over_by_Machines_of_Loving_Grace_(TV_series))
+
+What Can A Technologist Do About Climate Change? (essay, Bret Victor, Nov 2015)
+[html](http://worrydream.com/ClimateChange/)
+
+More is Different (paper, 1972)
+
+Distilling Free-Form Natural Laws from Experimental Data (paper, 2009)
+[pdf](https://www.isi.edu/~gil/diw2012/statements/lipson.pdf)
+
+Symbolic Mathematics Finally Yields to Neural Networks (article, 2020)
+[html](https://www.quantamagazine.org/symbolic-mathematics-finally-yields-to-neural-networks-20200520/)
+
+The Unreasonable Effectiveness of Mathematics in the Natural Sciences (article, 1960)
+[html](http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html)
+[wiki](https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences)
+