Even if they manage to avoid straight-up factual incorrectness, the writing is full of ambiguities and vagueness when you look closely. Meanwhile, space is wasted repeating the same claim in multiple ways, or explaining something simple.

They also seem unable to resist the hype/advertising tone, overselling the contribution while exaggerating the limitations of related work.

I would much rather read grammatically incorrect or awkward sentences.

While academic writing does have a few pointless historical conventions, the huge majority of "status quo writing style" is a logical consequence of 1) minimizing ambiguity, 2) organizing ideas coherently, 3) distinguishing opinion/interpretation from fact, and 4) providing enough detail to be reproducible.

Comments URL: https://news.ycombinator.com/item?id=45860588

Points: 2

# Comments: 0

An oblate spheroid is an example of a Riemannian manifold: a smooth object that looks like a plane (or, in general, any ℝ^n) locally, and has a way to measure angles between vectors in that local plane.

All Riemannian manifolds have an object called the Levi-Cevita connection, which defines how vectors in the local plane (tangent space) most naturally map to vectors in other tangent spaces in the immediate neighborhood.

Standing at a point on the Earth and looking in a certain direction gives us 1) a point on the manifold, and 2) a direction in that point's tangent space.

We then take an infinitesimally small step forward, and apply the Levi-Cevita connection to get from the old tangent space to the (infinitesimally nearby) new tangent space, and repeat. This defines an ordinary differential equation. Integrating the differential equation gives us a curve through the manifold.

Within some neighborhood of the initial point, this curve is a geodesic, i.e. the shortest path between the initial point and all subsequent points on the curve. This matches our typical intuition of "straight".

(Disclaimer: I am currently learning about this topic, but am not an expert.)

edit: https://en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid goes into some interesting specifics about the results of this process on ellipsoids.

I wish there was some way to do the same for programming. Imagine a classroom full of machines with no internet connection, just a compiler and some offline HTML/PDF documentation of languages and libraries.

https://www.science.org/doi/10.1126/scirobotics.abm6597

If you sample a random person with a math degree, the probability that they believe Erdos had more impact than Euler is 0. ;)

The application-submitting phase of the current cycle is over for TT positions, and some of the listings have been taken down. No idea if non-TT hiring follows the same cyclic pattern. But if the listings are looking thin, you should check again around November.

Not having a Ph.D. might disqualify you for some positions, but definitely not all of them. Teaching experience with positive evaluations will help a lot!

I wouldn't worry too much about laid-off developers/researchers. The huge majority of them will try to find another high-paying job.

Frank-Wolfe is a somewhat less well-known (compared to simplex, interior point, etc) convex optimization algorithm with many interesting properties [2, Section 3.3].

[1] https://roboticsproceedings.org/rss18/p039.html

[2] https://arxiv.org/abs/1405.4980

But once you get into something more sophisticated like using rotations in a dynamical system, statistical filtering, optimizing a rotation, etc., the abstractions begin to leak.

Often you realize that some parts of the original problem statement were adding complexity with no real benefit. And the techniques you use for the simple version are likely still relevant for the big version.

If the simplified version is still hopelessly difficult, it might be a good starting point for a counterexample/lower bound to convince yourself that the full problem is hard.