
New Math Proof Could Help Us Describe the Earth's Interior - selimthegrim
http://www.pbs.org/wgbh/nova/next/physics/math-proof-could-help-us-describe-the-earths-interior-like-never-before/
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DiabloD3
Not to insult this important work, but the headline makes this sound a lot
more important than it is, although "math proof" should have clued me in
otherwise.

I was expecting something that'd actually explain why our planet's core is
still hot, without using the thermonuclear crutch, given how it is nearly
solid iron (not liquid) at such temperatures; such as properly integrating
plasma physics (ie, Birkeland currents) into the math.

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thebooktocome
It's synonymous with the Nature headline: "Long-awaited mathematics proof
could help scan Earth's innards"

[http://www.nature.com/news/long-awaited-mathematics-proof-
co...](http://www.nature.com/news/long-awaited-mathematics-proof-could-help-
scan-earth-s-innards-1.21439)

I fail to see how either headline is not an accurate representation of the
result.

~~~
CJefferson
The problem is that it's unclear the maths result lines up exactly with
reality -- as I understand it, this is that a "perfect scan" lines up exactly
with one model of reality. What we want is that some kind of "nearly accurate
scan" produces a "nearly accurate reality". From my (limited) reading, the
proof doesn't seem to demonstrate that (maybe I scanned it too quickly)

~~~
thebooktocome
I agree that's a limitation of the proof, but this is a thread about
journalism tone. What alternative headline would you or the OP prefer? How
much weaker does it need to be? Is "could theoretically help" weak enough, or
do we need to go all the way to "could hypothetically, maybe, possibly help"?

Forgive me, but it's frustrating to see Monday morning quarterbacking on a
huge, important result that was the culmination of decades of work by the
authors. Prior to this, the most general result in boundary rigidity was
[https://arxiv.org/abs/1205.6425](https://arxiv.org/abs/1205.6425), which only
works on simple metrics.

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btilly
I am pretty sure that the work depends on the speed of sound being tied to
just density. But it isn't. Sound travels faster in some directions than
others.

[https://www.sciencedaily.com/releases/2017/02/170213124312.h...](https://www.sciencedaily.com/releases/2017/02/170213124312.htm)

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danra
Does this provide a new constructive way of mapping a space (which would be
exciting) or just a proff to a known conjecture which is already being used to
map spaces? (also cool but not as much)

~~~
tgb
I work in related areas of math but don't know anything about the applied side
of this stuff. The general rule of thumb though is that whatever algorithm the
mathematicians are proving correct is chosen so that it is easy to analyze and
isn't going to have the best convergence properties for actual use. After this
result, though, expect others to tackle questions like faster converging
algorithms, stability, etc. There are exceptions though: Newton's method was
both ridiculously fast and easy to work with mathematically and is still used
in both applied and pure contexts today.

