@TedShifrin I know, my mom freaked out because the doctor kept mentioning I might be legally blind. I can see 20/20 with glasses though, so not that bad at the moment.
@AkivaWeinberger Isn't that a bit of an oversimplification? :/ Red, blue and green aren't three specific frequencies any way and there's sufficient overlap between those colors in the visual spectrum.
@CaptainAmerica16 Whether it's grad classes or undergrad classes, they only cover a fraction of a good book, and a good book only covers a fraction of the important stuff in a topic. So classes are just introductions to topics to enable you to get a paper qualification along the way.
@CaptainAmerica16 After you read Spivak's Calculus, you can read Shifrin's Multivariable Mathematics, which is essentially multivariable calculus with linear algebra.
Biology SE has a very nice discussion on the human color vision model. It's a bit more complicated than the RGB model we use for computers. The point here is that the L, M, S cone cell frequencies have considerable regions of overlap whereas the RGB model does not - so you can describe it as three independent coordinates (what Akiva calls a 3D subspace), whereas that simplistic model does not apply to cone cells but approximates it rather well.
Life would have been simpler if we could have described our vision in terms of "activations" of RGB cone cells with values ranging from 0 to 1 for each coordinate. Unfortunately, real physics sucks. :)
> A "physical color" is a combination of pure spectral colors (in the visible range). Since there are, in principle, infinitely many distinct spectral colors, the set of all physical colors may be thought of as an infinite-dimensional vector space, in fact a Hilbert space. We call this space $H_{\rm color}$.
> A humanly perceived color may be modeled as three numbers: the extents to which each of the 3 types of cones is stimulated. Thus a humanly perceived color may be thought of as a point in 3-dimensional Euclidean space. We call this space $\Bbb R^3_{\rm color}$.
In colorimetry, metamerism is a perceived matching of the colors with different (nonmatching) spectral power distributions. Colors that match this way are called metamers.
A spectral power distribution describes the proportion of total light given off (emitted, transmitted, or reflected) by a color sample at each visible wavelength; it defines the complete information about the light coming from the sample. However, the human eye contains only three color receptors (three types of cone cells), which means that all colors are reduced to three sensory quantities, called the tristimulus value...
> The term illuminant metameric failure or illuminant metamerism is sometimes used to describe situations where two material samples match when viewed under one light source but not another. Most types of fluorescent lights produce an irregular or peaky spectral emittance curve, so that two materials under fluorescent light might not match, even though they are a metameric match to an incandescent "white" light source with a nearly flat or smooth emittance curve.
> Normally, material attributes such as translucency, gloss or surface texture are not considered in color matching. However geometric metameric failure or geometric metamerism can occur when two samples match when viewed from one angle, but then fail to match when viewed from a different angle. A common example is the color variation that appears in pearlescent automobile finishes or "metallic" paper
Seems to have worked out well enough in any event. I had 3-4 backups in there, and 4 wishful thinking. The remaining 7 I classify as rough but hopefully I have a shot
Yeah, I ended up adding Notre Dame to it, I had a fee waiver because of the workshop I went to some time back and at least one guy there knows and seems to like me
So I'd like to think it's safe, and they have Behrens and Putnam who seem really interesting. Also two number theorists, though they're assistant professors so less sure bets
To make sure I was actually making progress, I split up the process to create the half-million vertices into 63 steps (one for each coordinate---you just need to ensure that each of them is nonnegative)
Hi all, a quick question. Suppose I know that $\int f \leq M$ for some $M$. Can anything be said about the integral $\int f \cdot g$ for some integrable function g?
Like can I put any bound on the integral of the product using M