Totally with you on Ted Nelson, Stewart Brand, Martin Gardner and Vi Hart, who I know/knew well. Hadn't heard of Aubrey de Grey, enjoyed hearing his provocative rant about de-inevitabilizing aging. Another hero in this clan, for me, is The Domain of Science's Map of Mathematics <https://www.youtube.com/watch?v=OmJ-4B-mS-Y>, which implicitly characterizes what math is by diagramming the field's evolution and structure. And 4 million YouTube views show there is a hunger for this. I'm a funny mixture of firebrand and overly polite, so citing these iconoclasts is inspiring. So I'll stop being too polite and be proud of taking a radical stance. My stance is that mathematics suffers from self-inflicted poor public relations, and that this is not all inevitable or desirable. I want to spread the news that: - Mathematics is more than (just) calculation. Yeah that's old hat to mathematicians, but it persists as public misunderstanding. - Mathematics is about understanding patterns in the digital universe (meaning the universe of things that can be wholly described in symbols). Eugenia Cheng is all over this idea; I've hardly heard it expressed by others. I think the digital universe is a precursor idea to defining mathematics, and encompasses a few things outside the bounds of normal mathematics, such as taxonomies, computer science, and symbolic systems. - Mathematics is the language / tool / body of knowledge we use when we need to be precise (when there are big consequences for being slightly wrong), deal with complexity (because patterns are hard to see without abstraction), or deal with digital systems (like DNA, physics, or computers). This is a definition that deals with the edge of what is or isn't mathematics; most definitions I've seen do not help determine this distinction. - Research mathematicians are advance scouts who proactively look for patterns before we need them — a wildly adventurous thing to do. Thus the field of mathematics is a wildly unpruned bush, a bit like science, but far less tethered to modeling reality (though that influence remains a factor). - Research mathematicians (strongly) favor abstraction and generality, but that ain't the only kind of math. There's a big spectrum from concrete math (recreational math tends this direction) to abstract math (e.g. category theory). - These big ideas can and should be clearly taught to kids by (for instance), having them analyze and create games and puzzles, which are small formal systems. Well, that's my particular angle. On Thu, Aug 15, 2019 at 8:45 PM Steve Witham <sw@tiac.net> wrote:
Scott Kim wrote--
I think it's an occupational hazard of being an expert in any field, not just math, that it can be hard to explain what you do to an outsider. Nonetheless I think it's important to do, and not just for outsiders, but also for people inside the field. At least it's important to me — the dearth of mathematicians talking about what mathematics is I find intolerable, and makes me distrustful of mathematics as a field. Ted Nelson's _Computer Lib_ (1974) for me was a taste of what the good thing can be:
An enthusiastic insider in a field who is also a skeptical outsider without missing a beat.
There's the public-facing importance of that (especially with something commercial like computers), but also I like the way I oriented myself after reading that book.
Stewart Brand, Martin Gardner, Aubrey de Grey,
Vi Hart. https://youtu.be/v-pyuaThp-c "Doodling in Math Class: Connecting Dots" (talk about not missing beats)
--Steve
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun