@Ratman: I have to go I'm afraid. I started watching Schuller's first lecture, but it's slow going. I find I don't like watching videos I'm afraid, they're too slow. I can read much faster than a guy can lecture.
@Azmuth: see Born and Infeld’s 1935 paper on the quantization of the new field theory II. On page 12 they said this: “the inner angular momentum plays evidently a similar role to the spin in the usual theory of the electron. But it has some great advantages: it is an integral of the motion and has a real physical meaning as a property of the electromagnetic field, whereas the spin is defined as an angular momentum of an extensionless point, a rather mystical assumption”.
@MoreAnonymous Oh that's impossible! To become half of knowledgeable than him, you would have to cover whole of Physics, didn't I say that he's a professional programmer too! :P
Is it possible that this question about teaching torque is cross posted to the science educators stack exchange? As a question I think it's great just not fit for this particular site.
The question
@ACuriousMind Well, I'm watching some PCA videos (after building up some really basic linear algebra knowledge) and in there they fit a line on a 2D graph then rotate the line so to maximize the variance of the points projected on that line (or reducing the mean squared error will give the same result). Then that fitted line, PC1, has the most significance. But I don't understand what exactly is captured when the "points" are projected on the line.
@JingleBells I'm not sure what you mean by "captured". Mathematically, the projection is just taking the dot product of the point vector with the unit vector in the direction of the line
@ACuriousMind I'm not sure either. I guess I have to research it more. Maybe some linear transformation happens in the direction of the fitted line and then we transform the points as well and we just record their x1 and that's PC1.
well, one of the uses of PCA is that you can use the axes you get from it as a basis and then projecting onto the "most important" parts of your data is just projecting onto the first few components
uh small question, states in the hydrogen atom with the same $l$ value are invariant subspaces of the $\hat L^2$ operator and the $\hat L_z$ operator, but not the $\hat L_x$ and $\hat L_y$ operators right? My lecture notes imply they are invariant subspaces of all three angular momentum operators.
If I have the height of many humans and I plotted that data as a histogram (that captures the distribution), then the variance will be a number that tells us on average by how much each entry differs from the mean, right? How is that a measurement of spread? (by spreadness I understand 0 to 1 is less spread than 0 to 100)
@JingleBells for many nice distributions the variance corresponds nicely to what we'd intuitively call the "width" of the distribution
(see e.g. a Gaußian distribution)
And if you have a uniform distribution over 0-1 then your variance will be 1/12, but if you have a uniform distribution over 0-100 then your variance will be 10000/12, so it works there, too
Hmm, so high variance will mean higher "width" of the data? I guess it makes sense because a higher "width" will correspond to a larger sum of differences of the squares, right?
What does the square root in standard deviation do? I mean, if variance already measures spreadness, why introduce std?
I don't have any good reason except that it's sometimes the "nicer" quantity to work with, e.g. as it appears in the formula for a Gaußian distribution.
Alright then. Also, I get that PCA reduces dimensionality but in the end, we have a bunch of features PC1, PC2, PC3 that we don't know how they relate to our initial labeled features (height, head size, weight...). The only thing I can think of is to plug them into a neural network and predict something, but in any other case, how are those principal components useful when we don't know what they actually mean?
because it's one of the ways to deal with high-dimensional data, I guess? You don't necessarily need to use a neural net to build a predictive model on the largest components, and you might get lucky that they're mostly combinations of a few of the input variables
and I'm not sure it's "so famous" - you're just stumbling onto it because you're looking at ML stuff, right?
I've heard that the most widely used dim reduction technique is PCA
Well, I'm glad I learned about it. I guess it has its applications here and there but I've never stumbled upon a problem where it'll be really needed.
SVD seems much more useful as it literally finds patterns and "concepts" in your data.
Time to move to the "Probability and Information Theory" part of my deep learning book. I spent the last week exploring linear algebra and I think I have the core concepts down. I can't wait to see how I get to use linear algebra in ML.
I think even movies can be an important factor in the culture of a person, besides the fact that not everything must be done for learing something. If it makes you emotional is time well spent
I guess I don't have a movie addiction, and I've never had one. I've watched a lot of movies, and that has built me as a person and has introduced me to new concepts and ideas.
the manufacture of the brine needed for mozzarella production needs infrastructure to transport all the water and salt for it. More civil engineers, more infrastructure, more brine, more cheese.
Physics largely gets by without the notion of "causation", even if we often talk in terms of cause and effect, it's highly non-trivial to actually nail down what we actually mean by it (see e.g. Norton's dome and Norton's paper Causation as folk science)
Is it possible that this question about teaching torque is cross posted to the science educators stack exchange? As a question I think it's great just not fit for this particular site.
The question
