110 karma · joined November 24, 2021
the worst part is that i think this experience has completely tanked my confidence.
now id take a jr python dev job in a second.
"The way I read papers is by first reading the abstract. Then I try to state the results and prove them myself. When I get stuck I go to the paper to see what I got wrong."
Mileage may vary.
I certainly don't think of it this way.
There are many geometries and spaces that cannot be described fruitfully within the framework of algebraic geometry, much the same as how there are many functions that are not analytic.
It's so easy to make a free blog on github (like sub 5 minutes) with some version of jekyl. You should probably just do it.
Of course, for theoretical reasons, a heuristic is not guaranteed to be faster on all problem instances.
The general idea is to do some engineering and find a heuristic that works well for your problem. More sophisticated algorithms will try multiple heuristics at the same time (I believe OR tools has options that falll in this category). There is even research by now that aims to use ML to find good heuristics for a given family of problems (where the common characteristics of the problems might lend to a dominant heuristic).
These heuristics can still have guarantees of correctness. A good place to start is by looking up "branch and bound" algorithms, e.g., for ILP problems. The idea there is to narrow the search space while maintaining some theoretical guarantees.
(Not an expert but i did a project on this once. I'm sure someone more expert can come along and correct where I'm wrong.)
More importantly, it can be a dangerous business lapse.
By the end of that summer I was dreaming about moving back to north america where air conditioning is much more common in rental units.
> Despite all that, what I’m hoping for is that someone will come along and tell me that I got it all wrong. “When you do it as follows, the system works: $explanation” Because, you know, I’d really like to have static typing in Python.
I want X. Y (which is designed for somthing other than X) doesn't do X. Thus, I don't like Y.
To people out there writing educational blogs: do more research and find good, well written, timeless resources to point people to for the basics. Spend your energy writing something new that we haven't all already read.
https://www.kdd.org/kdd2018/accepted-papers/view/real-time-p...
I mean, this is a link to a pdf titled "chapter 3" buried deep in the directories of someone's academic homepage. There's no context about who the author is (is it a student project from a course? Part of a dissertation? notes for a draft of a book?), except that I think I can extract their name from the URL. It's pretty hard to tell, thus, who the desired audience is or what the aim of it is.
So whether one should expect one thing or another from this random pdf... I mean, without knowing more, what is there to reasonably expect?
For instance (and I can imagine this because I've taught an undergraduate course on graph theory, among other undergrad math courses), if these are notes from a course, then the instructor may have some good, context specific reasons for focusing on some topics while not going into details on others. But, as I said above, it's really impossible to know because this has just been plunked on HN with no context, as if that is somehow valuable.
Pardon my ignorance, is the spectrum of a graph something more than simply the set of it's eigenvalues?
> I do find the arguments around bad governance structures and oversight weird though, as those should have been known before they invested.
Likely they knew and saw an opportunity for their investment strategy.
If you learn 1 new skill each day for a year...
then you will be able to apply the 365 skills you've learned in
365! = 2510412867 5558732292 9294437488 1202770516 5520269876 0797668725 9519390110 6138220937 4196660180 0900025416 9376172314 3609823286 6070807112 3369979853 4453679106 5387238359 9704355532 7409376780 9149142944 0864316046 9250745101 3484702554 6014098005 9079655410 4119549610 5311886173 3734351455 1719328276 0847755882 2916902135 3912347918 6274701519 3968085049 4072260703 3001246328 3988005504 8742799987 6690416973 4378610781 8534466796 6871511049 6538881301 3683619901 0529180056 1258445494 8864861768 2915826347 5641489909 8413806780 9999604687 4881467348 3734069935 9838791124 9959575845 3887361666 1533093253 5512568450 5604638873 8129702951 3811518614 1368892298 6510005440 9439430146 9924411255 5755279140 7604927642 5374025041 0391056421 9790032896 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 000000000
different ways!
Obviously, how you should read dense technical material will differ greatly depending on your goal.
For instance, if you are looking only for an answer to a specific question, you might prefer to do a sort of DFS on the paper. Read the intro material to get an impression of where in the paper the answer might lie, then go read those parts (in descending order of likelihood of containing the answer). A similar approach might work if you already know the area and are simply looking to see if the paper contains a particular result. Sometimes this process will still require some investment in understanding notation and terminology, but time spent doing this should be kept to a minimum.
On the other hand, if you intend to master the material and develop it further, then you might take a totally different approach where you prepare your own set of detailed notes on the paper (taking care to expand, in places where your own knowledge is lacking, techinical terms and concepts that are used in the paper but not explained using secondary references). This might also include working out many examples or thought experiments to help you internalize the logic and concepts. For a significant paper this process will take a long time, but it will be worthwhile if you truely want to understand the paper comprehensively and be able to build on it in a substantial way.
No matter your goal and approach, the point is that reading a paper productively is a systematic thing. Skimming technical papers lacksidasically is often a waste of time that doesn't produce value.
If you try to use a product of 3 rotation matrices that represent rotations around fixed axes to represent rotations in 3D, there will inevitably be gimbal lock because there cannot exist a covering map from a product of 3 circles to SO(3). (Gimbal lock happens at the points where the map locally fails to be a covering map)
SU(2) is the universal cover of SO(3). The unit quaternions are a faithful representation of SU(2). Conveniently, the double cover map from SU(2) to SO(3) is dead simple in this representation: a unit quaternion q in SU(2) act on a purely imaginary quaternion (thought of as a vector in R^3) by conjugation. This is the formula you wrote.
Since it is a covering map, there is no gimbal lock.
Edited to fix explanation.
a = dv /dt.
The issue with Euclidean geometry as an entrance to proofs and logic is two-fold. First, the definitions and axioms of Euclidean geometry are incomplete in many ways. Many definitions, such as that of a line, cannot be understood from what is written in Euclid but require a significant amount of intution pumping to be able to know how to properly work with them. Thus, the fundamental definitions in Euclidean geometry are bad examples of what a definition in math should be, and we are already starting on very rocky footing. Moreover, the axioms, as they are presented in Euclid or common modern educational sources, are not sufficient to do what is claimed. For example, the proof of postulate 1 already has a logical gap because there is no axiom which guarantees the existence of a point lying at the intersection of the two circles one has drawn. Again, the argument relies crucially on a figure, which is the intuition pump used in all of Euclid, but the picture is not based on any of the axioms, so it is reinforcing a bad way of thinking about proofs that is intuitive and not at all focused on carefully using definitions and axioms. (Of course, one can fix Euclidean geometry to be rigorous by adding many extra axioms, but the resulting axiomatic system is much more complex and is not at all suitable for highschool students, except possibly the brightest.)
The second, somewhat more minor, issue I have with Euclidean geometry, related to the first, is that the way arguments are phrased, and the use of figures to illustrate, often hides many logical steps that are only implicit. In particular, I am thinking of the implicit use of qunatifiers in statements that are proven in Euclidean geometry. This is an issue because as soon as one moves on to proofs in any other context encountered by students, e.g. in first year undergrad, it becomes much more difficult to do things correctly while only thinking about quantifiers implicitly.
It would be much more beneficial, in my opinion, to have the first introduction to proofs be a topic that is much, much simpler (such as integers) where the focus can be purely on how statements are formed with quantifiers, how strategies of proof are determined based on the form of the statement and which quantifiers are involved, and how the (much shorter and simpler, and not requiring an intuition pump to use correctly) definitions and basic properties of that topic can be applied in a proof.
The root of all of this is the importance in proofs of properly using the definitions and axioms. Students in highschool, except the most talented, just are not careful thinkers and will revert to their preferred lazy way of thinking (such as pictures and vague ideas) as soon as you give them the opening. In my experience, the only way to force students to understand how to properly prove things is to pull out the rug of their intuition, even briefly, for just long enough so that they learn how to do things without it. Then later, once they have properly adopted the mindset of using the definitions, you can let the intuition back in.
For context, I don't know if any of what I just said reflects how Euclidean geometry is taught in, say, Caifornia. I only know this from the perspective of having tried to incorporate Euclidean geometry in an undergraduate proofs course (in Canada where Euclidean geometry hasn't been part of the grade school curriculum for some time).
Does IC mean integrated chips? I have certainly read that modern farm equipment is less repairable, and I would not be surprised if they played a role. But I don't claim any knowledge about that. I may also have the time scales wrong.
But damn, those machines were a marvel sometimes. Here is a particularly fun one, the square bale picker/stacker. https://www.youtube.com/watch?v=TUWrNZaLttQ&ab_channel=Thoma...