Also when this person says the subscript "denotes the order of the measurement" I'm trying to figure out what kind of order he's talking about. I guess that's the index? It's been a while since I did kalman filters:-p
The more pure the mathematics the shorter the scope of most variables. Typically a variable is defined just before it's used, with a scope no longer than the proof or derivation it's in.
Also some of the choices in this article are just plain silly. Such as using P as both variable and index, and then use it for the covariance matrix when the precision matrix is the exact inverse.
Usually the stuff I'm implementing is complicated enough that reading the code without reading the paper won't have much meaning. And if you're reading the paper, it's good to have as close to a 1-1 representation to help give confidence that I implemented it right.
I've had non-zero times where I took his pseudocode, pasted it into my IDE and did a search and replace of begin/end to braces and "<-" to "=" and it "just worked" on the first try. I always found that amazing that he could write this stuff without ever trying it (outside of his head).
* r,g,b,a
* h,s,l
* x,y,z
If you want people to understand, you skip the mathematical notation and use pseudocode, or at least you start with an explaination and once people know what they are looking at you go into the math notation.
I understand that mathematical notation can be very practical for describing a certain class of problems concisely, but especially if you teach or explain things, consider that being concise is meaningless if people don't understand what you describe.
Sometimes my feeling is that this is on purpose. People not understanding what you are doing (but you come across soo smart), is a feature to many. Even better: The layperson cannot tell whether you are talking utter gibberish or using the most precise language on earth.
I, however, think you can recognize real smart people by the phenomenon that every room they are in seems to become smarter in total, because they lift people up in their wake of understanding things so deeply, they can just break them down into their very simple, managable parts and translate obscure domain-specific languages into something people can grasp.
I too can go into deep domain specific lanuages, be it in philosophy, electrical regulation, film theory, programming lingo, music theory, control theory etc. But what is the point of doing that without making the person opposite understand what you're waffling on about? Because either you will seem like a knowledgeable person that has a total lack of self-perception or like a brick that doesn't care what message reaches the person opposite as long as rhey can hear themselves talk.
That being said: Domain-specific language can be okay if it is used between people within that domain. But I have met many physicists or mathematicians who also think math notation sucks, so maybe there could be something better.
I still haven't quite forgiven the writers of UMAP for writing a theorem that uses pi^n/2 / Gamma(n/2+1) instead of the more reasonable "volume of the unit sphere". It makes it so confusing that they fail to spot the theorem doesn't work for low dimensional objects embedded in high dimensional spaces, which is their exact use-case. Luckily their informal conclusion does work, mostly.
I hate that the most when reading papers. Authors trying to sound abstract and academic, but only accomplishing being frustratingly vague. AUTHORS YOU STILL HAVE TO INSERT THE SUBJECT INTO YOUR SENTENCES FOR THEM TO MAKE SENSE.
I'm so frustrated at this aspect in research papers more than anything else. You must disambiguate. Use absolute descriptors and do not use relative descriptors. Don't tell me to look right, because I'll look left. Use absolute descriptors! "then after spinning the prism the light cone blah blah blah" SPIN!? SPIN IN WHAT DIRECTION????? LEFT?RIGHT?! LATERAL? UP? DOWN???? How fast? How slow? You imagine all of these CRITICAL ASPECTS in your head when writing such ambiguous sentences, but the reader cannot read your mind.
I was for example reading a cryptography book and it has symbols like a hamadad product.
The order referred to is the index-in-time that a value correspond to. Eg, x_3 would be the state at the third time step. I think their subscript “p” stands for prediction. x_p at time 3 is the state we expect at time 4. But then when time 4 comes around, we incorporate new measurements and calculate x_4 including that new information. Just to be explicit, this x_4 will be different from the x_p we calculated at time 3, as our prediction is always a bit incorrect
I think the variable names are already picked to be descriptive. No one is picking them to be more obscure or harder to track. The problem is that those who are starting out still haven't picked up concepts or learned the standard notations for each problem domain, thus we are left with the pain of ramping up on a topic.
For reference, the Wikipedia page "Order (mathematics)" is a disambiguation page almost as long as the top-level disambiguation page "Order".
https://en.wikipedia.org/wiki/Order_(mathematics)
I generally don't have a problem with variable names, but creating syntax and terminology that conflicts with other mathematical use is a real problem.
Same when something is named descriptively: shield volcano, star dunes, vs. some person’s name like Rayleigh scattering.
It’s just an extra layer to memorize and parse.
In math/physics/engineering the terminology is unfamiliar at first but very precise and hence learnable. The vast majority of STEM textbooks (at least from good US university publishers) make their best effort in presenting the material understandably without any intentional obscurantism or additional fanciness. Academic joirnal/conference papers do sometimes intentionally confuse to game the publication metrics but intro materials are an earnest effort at educating. The subject matter has some inherent complexity, there's no need to prop it up artificially for prestige (that happens more in other fields that are insecure about their level of inherent complexity).
https://wikimedia.org/api/rest_v1/media/math/render/svg/a7d2...
Here's a formula for calculating the downstream Mach number in a certain kind of supersonic flow. I cannot imagine any way to write this in "descriptive variables" which makes the formula understandable at all, you just could not see the structure. (from https://en.wikipedia.org/wiki/Oblique_shock )