The Atlas of Lie Groups and Representations

June 26, 2017 5:55 AM

Math Has No God Particle - "'Mathematicians are extremely reluctant to publicize what they do', Adams said. 'The immediate reaction from 90 percent of mathematicians is, 'It's too hard, there's no point in trying to write about this in the popular press.'' (Yet here we are.) ... About two months ago — 15 years after it began — the project was finally completed. Adams and his colleagues released Version 1.0 of their atlas software... Adams and his team haven't trumpeted this latest accomplishment at all. When I reached him at his home, he summarized the milestone plainly, but proudly, in the jargon of his field: 'We can now compute the Hermitian form on any irreducible representation.'"
posted by kliuless (24 comments total)

The asymmetry in storytelling between math and the other sciences may also be because the research has different start-up costs. You need billions of dollars to build an enormous tunnel to house a particle accelerator to discover evidence of the God particle, also known as the Higgs boson. A good story may secure you coverage, enthusiasm and, if you’re lucky, lots of cash. To map Lie groups, Vogan said, you just need a teaching load light enough to put in extra work on the weekends: “We can do these things with small amounts of money.”

".....and all I need is this yellow pad, some pencils, and a wastebasket".
And the philosophy professor says, "You need a wastebasket?"
posted by thelonius at 6:14 AM on June 26, 2017 [46 favorites]

in many ways, pure math is a lot like philosophy.. There's a great deal of underpinning, a lot of history, plenty of new ideas. Then, the person on the street will hear about it, and ask the usual "yeah, but what does it mean to me?"
posted by k5.user at 6:38 AM on June 26, 2017 [4 favorites]

We can now compute the Hermitian form on any irreducible representation.

Any sufficiently advanced mathematics is indistinguishable from communist propaganda.
posted by Naberius at 6:53 AM on June 26, 2017 [23 favorites]

Interesting question (ha general folks) posted recently in /r/math which seems like a very smart and reasonable crowd of mostly academics by a grad student "What is descriptive set theory, to a non-math person?"

The best answer seemed to be "classifying sets of reals by complexity.", now other than a subset of software folks that grok big e stuff and actual mathematicians the sentence is almost utterly meaningless. A bunch of comments like "You are correct that it's pretty much impossible to get into a discussion of descriptive set theory without being able to bring up Borel sets" (ok except for specialist in that disipline Borel sets is a wikipedia rat hole) there is some discussion of how hard it is to talk about serious abstract math but also a lot of 'just gotta read the proofs, here's a text to review after you get through topology and abstract algebra'.

And ya know, it's kinda true, for example, cohomology (a personal curiosity) is not an especially advanced topic but for a non-mathematician getting beyond "it's just counting holes", is a non trivial pursuit. A truly great math-science writer of the Asimov level would be a huge benefit to society
posted by sammyo at 7:04 AM on June 26, 2017 [6 favorites]

atlas offers installation instructions for Linux, Mac OS, Windows, and Solaris. Is that an artifact of its 15 year development history, or are there a lot of Solaris holdouts among abstract mathematicians?
posted by jedicus at 7:12 AM on June 26, 2017

(Solaris is still a big thing in a lot of large companies, owned data centers, etc. It's dying but isn't yet dead.)
posted by introp at 7:14 AM on June 26, 2017 [2 favorites]

atlas offers installation instructions for ... Solaris.

Pre-installation warning: do not install yourself onto Solaris if you often find yourself thinking about your deceased wife, lover or straw-hat-wearing child. Install yourself onto Windows instead: it's far less painful. I know you might not believe that, but Microsoft hasn't actually worked out how to construct your most painful memories out of immortal neutrino fuzz and glue them to your face until you go insane. Uh ... well, I haven't actually used Windows 10 yet, but I'm sure that ... no, look - just keep away from Solaris, for your own sake.

-- K. Kelvin.
posted by the quidnunc kid at 8:24 AM on June 26, 2017 [21 favorites]

An example of excellent mathematics communication (I believe I discovered it here on MetaFilter): Visualizing the Riemann zeta function and analytic continuation. I'm not (even close to being) a mathematician, but I found this extraordinarily easy to follow.

In general, though: I think that mathematics is just inherently and uniquely difficult to explain to non-specialists. In the other sciences, you're dealing with things that people experience in their everyday lives (however indirectly), things that can be seen and touched, and discoveries whose ramifications are often more concrete ("this new carbon lattice structure could lead to lightweight, stain-resistant dildos up to 100 times stronger than conventional acrylic dildos"). In mathematics, on the other hand, you're dealing with abstractions – and abstractions of abstractions. Sometimes those abstractions can be visualized or analogized (as in the Riemann-Zeta video), but sometimes they're just too complex or counterintuitive, especially for an audience who lacks familiarity with the foundational concepts.

(Also: I'm not sure that physics is doing any better at outreach when it uses gibberish terms such as "God particle". That's where all of the New Age "quantum" mumbo-jumbo comes from.)
posted by escape from the potato planet at 10:18 AM on June 26, 2017 [8 favorites]

That's an awesome Youtube channel.
posted by leotrotsky at 12:15 PM on June 26, 2017

Yeah...major financial institution here...still tons of Solaris running around here even though Oracle is trying hard to kill it. But the writing is on the wall, and soon we'll be down to AIX & Linux, with the occasional *BSD heretic.

Maybe VMS will make a comeback, once they finish the x86-64 port...
posted by kjs3 at 2:27 PM on June 26, 2017 [2 favorites]

You think Solaris counts as a dinosaur in the sciences? I have a friend who's dad works doing climate physics, often with NOAA. They do the majority of their programming in FORTRAN.

I just about passed out when she told me that.
posted by lumpenprole at 4:04 PM on June 26, 2017 [1 favorite]

In general, though: I think that mathematics is just inherently and uniquely difficult to explain to non-specialists.

My dissertation is fairly straightforward to explain to be people with no math background (caveat: I did do combinatorics, which lends itself to examples particularly well). The hurdle tends to be either a) convincing people that they really will understand the core problem if they'd stop telling me how bad they are at math and let me explain or b) engineer types demanding an immediate application.
posted by hoyland at 4:46 PM on June 26, 2017 [4 favorites]

In my experience, the hurdles are rarely troublesome once you get past the starting gate: persuading somebody whose life would clearly be improved by investing 0.00001% of it in sufficiently concentrated attention on any aspect of mathematics to give a shit.
posted by flabdablet at 10:42 PM on June 26, 2017

An example of excellent mathematics communication (I believe I discovered it here on MetaFilter):

here :P

also, Piper Harron's PhD thesis! The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields: an Artist’s Rendering
posted by kliuless at 6:06 AM on June 27, 2017

You think Solaris counts as a dinosaur in the sciences? I have a friend who's dad works doing climate physics, often with NOAA. They do the majority of their programming in FORTRAN.


Heh, the craziest part about this, according to my grad school buddy who works on modeling Icebergs for one of the world's most complex climate models, is that they chose FORTRAN when the project started from scratch circa 2006! That's when I passed out.
posted by So You're Saying These Are Pants? at 2:58 PM on June 27, 2017 [1 favorite]

Lovely piece of maths writing just published by Quanta Magazine.
posted by roolya_boolya at 3:12 PM on June 27, 2017 [2 favorites]

Heh, the craziest part about this, according to my grad school buddy who works on modeling Icebergs for one of the world's most complex climate models, is that they chose FORTRAN when the project started from scratch circa 2006!

They likely have a dependency. I mean, pretty much everything numeric depends on BLAS or LAPACK somehow, so they're accessible from many languages, but there will likely be some specific library someone wrote in FORTRAN. Of course, it's also exactly the sort of thing people use FORTRAN for, so there's community norms as well.

The web developers gave me the most bizarre looks when I exclaimed "Crap, I need a FORTRAN compiler" at work one day, but, of course, even though I've never written FORTRAN in my life (see doing pure math and not physics), BLAS and LAPACK are always around and it's much less a dead language than people assume.
posted by hoyland at 4:48 AM on June 28, 2017 [1 favorite]

so there's community norms as well.

I think that's the biggest part of it. They're there to do math around climate, not learn programming. So they work with the tools that people have worked with before them.

After, I picked my jaw up off the floor, I went on a medium-dive into modern Fortran. And honestly, other than better tools, I couldn't find a compelling reason they shouldn't be using it.
posted by lumpenprole at 9:14 AM on June 29, 2017

I took a CS class from a grad student once, who told us that he found that FORTRAN was the best choice for his thesis work on, iirc, protein folding. I think it's mostly because there are lots of relevant and well-debugged numeric and scientific computation libraries, but there may have been other reasons, due to handling large data structures (not sure).
posted by thelonius at 9:43 AM on June 29, 2017

If the core of what you're doing boils down to performing vast amounts of fairly simple-minded arithmetic at high speed on huge arrays, FORTRAN's deficiencies for implementing fancy schmancy data structures and memory management don't get in your way, making FORTRAN no more annoying than anything newer (which will most likely have inherited its arithmetic expression syntax anyway).
posted by flabdablet at 11:42 AM on June 29, 2017 [1 favorite]

I very much understand the sentiment that it's too hard to explain - I did my dissertation in Lie theory/representation theory and have written papers about decompositions of irreducible representations, and I still only understand this project on the most basic of levels. (My research was on groups over algebraically closed fields; the real numbers did not enter into it. The representation of real Lie groups has a different flavor than complex Lie groups.)
posted by Frobenius Twist at 5:39 PM on June 29, 2017

I really wish I had an intuitive understanding of math. It would make doing physics much easier.
posted by runcibleshaw at 6:49 PM on July 2, 2017

-E8 from an icosahedral 'Big Bang'
-Sphere Packing Solved in Higher Dimensions
posted by kliuless at 4:56 AM on July 19, 2017

They do the majority of their programming in FORTRAN.

I just about passed out when she told me that.

There's a huge amount of Fortran work going on; pretty much anywhere lots of numbers are being crunched probably has something running written in Fortran. Intel ships a Fortran compiler along side it's C compiler to take advantage of the latest Intel SIMD instructions (AVX-512); IBM does the same for the latest Power SIMD instructions. Fortran is a natural here. Absoft has been selling their excellent Fortran compilers for 37 years. It's not like we're still programming in Fortran-77. The languages has continued to evolve incorporating modern language constructs. We've been through Fortran 90->95->2003 with Fortran 2008 as the latest ISO standard. Fortran 2015 due to be ratified next year.

I hate to think what you'd do if you knew how much COBOL is still being written. It could be fatal.
posted by kjs3 at 4:37 PM on July 25, 2017 [1 favorite]