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diff --git a/posts/modelthing-background.md b/posts/modelthing-background.md new file mode 100644 index 0000000..9234f70 --- /dev/null +++ b/posts/modelthing-background.md @@ -0,0 +1,194 @@ +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) + diff --git a/static/fig/sicm_cover.jpg b/static/fig/sicm_cover.jpg Binary files differnew file mode 100644 index 0000000..956a1b5 --- /dev/null +++ b/static/fig/sicm_cover.jpg |
