1,100 reputation
113
bio website reedbeta.com
location Milpitas, CA
age 28
visits member for 1 year, 11 months
seen 20 hours ago

I'm a graphics programmer, an amateur physicist, and a sci-fi nerd. I teach computers how to make pretty pictures. I'm excited by beautiful, immersive, story-driven games and interactive fiction. I enjoy messing around with esoteric ideas. I like explaining things.

I currently work for NVIDIA DevTech. Previously, I worked for Sucker Punch Productions on the Infamous series of games for PS3 and PS4.

reedbeta.com - developer blog, OpenGL demos, and other projects. @reedbeta on Twitter.


1d
comment From affine space to a manifold?
@Heaviside If you have a geodesic curve that passes through Paris and New York, you can measure the distance along it (tracking it through multiple patches if necessary). And you can measure the angle of the geodesic relative to some reference frame at New York. So, you could say something like "Paris is 5800 km from New York at a heading of 30 degrees". In that sense you could locate Paris relative to New York. But depending on the spacetime there might or might not be such a geodesic, and it might or might not be unique.
2d
comment From affine space to a manifold?
@Heaviside In real life we can describe planes' positions and flight paths using just one patch, the usual latitude-longitude coordinates, because that covers almost the whole Earth. It only breaks down at the poles, and planes don't usually go too close to the poles. So it's in part a question of theoretical vs practical. :)
2d
comment From affine space to a manifold?
@Heaviside Well, I guess it depends what you mean by track a plane. If we lived in a complicated manifold with many patches we could certainly still describe the plane's path as it flies around. But in general we couldn't describe it by just one curve; we'd have to describe it by several curves, one in each patch, which match in the overlap regions.
Dec
16
comment From affine space to a manifold?
@Heaviside Sure you can, you just have to switch to the Atlantic Ocean patch at some point and then later switch to the Europe patch. (Presuming the patches overlap for a certain distance around their edges.)
Dec
15
comment From affine space to a manifold?
@Heaviside To describe events in some region you have to use a patch that covers that region. It doesn't matter if you imagine yourself as being located in some other patch. If there's a USA patch and a Europe patch, and I want to describe events in Europe, I have to use the Europe patch. It doesn't matter that I personally happen to be in the USA.
Dec
15
comment What affects the period and the frequency of a longitudinal vibration?
@CuriousOne You're right; I was thinking of a pendulum, in which case the mass doesn't matter. For mass-spring systems of course the ratio of mass and spring constant is what matters.
Dec
14
comment From affine space to a manifold?
@Heaviside Not sure I get what you're asking about "how to relate coordinates relative to a fixed reference to the "patch" coordinates". An affine space is kind of just a special-case manifold that has planar topology, so the whole thing can be covered by one coordinate patch, and is flat, so displacements add like vectors and thus there's a natural notion of the vector displacement between points.
Dec
14
comment From affine space to a manifold?
@Heaviside OK, if we forget about metrics and look only at topology, then AFAIK the reliance on patches is only present if you have non-planar topology. For instance, on a sphere you need at least two patches; a single patch is guaranteed to break down at at least one point (e.g. polar coordinates break down at the poles) due to the hairy ball theorem. I suppose more complicated topologies can require even more patches.
Dec
14
comment Does inflation predict a closed universe?
Inflation predicts that the size of the whole universe is many orders of magnitude greater than the observable part, so it could be spherical on the large scale but still appear perfectly flat to any measurement we could do.
Dec
14
comment What affects the period and the frequency of a longitudinal vibration?
In principle, for linear oscillations, the period should be independent of the mass and amplitude...but in real life, most oscillations are nonlinear, especially at too high of an amplitude. They are only approximately linear in the low-amplitude limit. Maybe that's affecting your data.
Dec
13
comment From affine space to a manifold?
@Heaviside The Euclidean metric is flat. If you start with that, you only ever get flat space, even if expressed in general curvilinear coordinates. Curved spaces have fundamentally different geometry, e.g. the angles in a triangle may not add up to 180° or the ratio of a circle's circumference and diameter may not be π. You can't get that from Euclidean space no matter what weird coordinates you use.
Dec
11
comment Why does room temperature water and metal feel almost as cool as each other?
Another effect that might be relevant is that when you dip your finger in water, the liquid conforms exactly to the shape of your finger and makes good thermal contact, while when you touch a solid metal surface you probably don't make such good contact.
Dec
11
comment Color Shift of Reflected Light
Computer graphics people have studied questions of how light reflects off surfaces for a long time, so you might benefit from reading some CG literature, such as the first talk of this course.
Dec
11
comment From affine space to a manifold?
@Heaviside Well, you have to have the metric as that's what lets you talk about physical distances and angles. Without that, you just have an abstract space with no connection to reality. Intrinsic curvature is encoded in the metric; the Riemann tensor is just made from a bunch of derivatives of the metric.
Dec
11
comment Does a body curve spacetime at higher velocities?
Also note that the values of $G_{\mu\nu}$ and $T_{\mu\nu}$ change in different reference frames too. They are no more or less "absolute" than the 4-momentum is.
Dec
11
comment Does a body curve spacetime at higher velocities?
I don't think the "relativistic mass" should be regarded as a true mass in any sense. It's simply the time component of the 4-momentum vector (divided by $c^2$). At relativistic speeds, that value is pretty meaningless without the other three components. At a guess, the relevant quantity for "amount of curvature" is likely to be the invariant magnitude of the 4-momentum...which is just the rest-mass.
Dec
11
comment Is there an error in Susskinds' derivation of Euler-Lagrange equations?
@MadScientist The $n = 7$ term only depends on $x_7$ and $x_6$, so it's irrelevant to $x_8$. And if you leave out the $n = 9$ term you don't capture all the dependence of the action on $x_8$.
Dec
11
revised Is there an error in Susskinds' derivation of Euler-Lagrange equations?
change i to n to match textbook
Dec
11
comment Is there an error in Susskinds' derivation of Euler-Lagrange equations?
@MadScientist No, the $n$th term depends on $x_n$ and $x_{n-1}$. So the $n = 8$ term depends on $x_8$ and $x_7$, while the $n = 9$ term depends on $x_9$ and $x_8$. Those are the only terms that depend on $x_8$. So to get the total dependence on $x_8$ he only needs to evaluate things at $n = 8$ and $n = 9$.
Dec
11
answered Is there an error in Susskinds' derivation of Euler-Lagrange equations?