redvenom

Good thing I don't care at all what most people care about. If everyone had your attitude we'd all be listening to pop music instead of classical as well.

This highlights the difference between someone who cares about image quality and someone who just cares about reactions and likes.

In most situations that photographers actually care about (i.e. capturing beautiful, good light), ILCs already murder the iPhone. Computational photography may be cool but it is just helping the iPhone emulate ILCs.

The iPhone 12 may have some cool auto computational features, but in no way is it better than an ILC camera like a DSLR. If you actually compare image quality side by side, a DSLR typically will smoke an iPhone. Not to mention there is no way to go past ~100mm on even the best phones.

There's not much difference between the different formats in terms of engineering genius. The Raw data from a camera is basically a matrix of numbers...not too much innovation possible there. The fact that there are different formats is somewhat of a historical accident, and they preceded the DNG format. The format absolutely CAN be stored in a DNG, and in fact Pentax cameras have the option of either DNG or PEF.

Me too. For people on shared hosts (hundreds of small websites including small businesses), PHP is pretty much the only server-side language that you have access to (well, maybe aside from Perl).

It is a diagram whose vertices are mathematical objects and whose arrows are morphisms (often functions) between those objects such that any two paths between two vertices represent the same morphism/function. Typically it is used to infer information about one morphism or object using others, by keeping track of many properties at once in a graphical fashion.

I was thinking the title meant that I could sync an iPad with Linux...too bad. I was hoping that someone made it possible to sync music with the latest iOS.

Absolutely true, there is a lot to prove there. It's not an elementary explanation by any means, rather it is an outline that someone who knows Galois theory well could probably reconstruct.

The reason basically comes down to the fact that every time you perform a compass and straight-edge construction, you are constructing quadratic extensions of number fields, whereas trisection (in general) needs a cubic extension.

The 'in general' part is important: of course, you can trisect specific angles like a 90 degree angle.

(The construction of number field extensions is happening because let's say you construct a 90 degree angle, well that allows you to construct an isosceles triangle with equal sides length 1, and therefore you construct the square root of 2, so the extension Q(sqrt(2))

It does make you much better at formulating problems. In fact, from my experience as a mathematician and watching others do math, the vast majority of good problems comes after someone has solved a problem and then asked, "what if we change this instead?"

No, polygons in non-Euclidean space makes sense. Polygons and more generally, geometric simplicial complexes in other spaces is a branch of mathematics all by itself (geometric group theory), so you certainly shouldn't "throw it out the window".

The reason is because you want to be able to usefully talk about 'true vertices'. Another way to define a polygon is any convex hull of finitely many points in Euclidean 2-space with nonzero area. Then the 'real' vertices are those points on the boundary curve that are nondifferentiable ('pointy' or 'sharp').

Those are the special points you are interested in when you want to distinguish between vertices and other points on the boundary.

Work at a job so I can pursue my creative projects like writing blog posts and making documentaries.

Well, there are documented cases of evolution happening during our lifetimes.

But I would say as a mathematical process, pretty likely once you have the basic ingredients. Richard Dawkins has written some good popular science books like 'Climbing Mount Improbable' that talks about evolution in this light. His 'Selfish Gene' is also an excellent read. It is slightly more technical but definitely understandable without an immense technical background.