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I've always thought math would be much easier to learn if they used descriptive variable names. Or, at least in an interactive medium like the web, add some too

I've always thought math would be much easier to learn if they used descriptive variable names. Or, at least in an interactive medium like the web, add some tooltips at a bare minimum. Whenever I study math I spend 90% of the time looking up the symbols. 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

Waterluvian 3y ago
This was 90% of my problem with math. 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.
- bonoboTP 3y ago
  I agree but this is a surface level issue impacting the very beginner phase only. Once you get familiar with the vocabulary, the hard stuff will be the actual material, understanding the thing itself, not its description. This differentiates fields that have an actual subject matter from fields that are essentially terminology and categorizations all the way through, a self-referential map with no territory. 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).
  - Waterluvian 3y ago
    Oh definitely! Eventually you've spent so much time that the thetas and lambdas and Lorentzes and whatever become your close intimate friends. I've most recently experienced this with learning piano and how an ocean of white and black keys all developed these individual "identities." Like, "ah yes, <looks at A4> I won't forget you. We've had so many dramatic moments before, and remember that time I kept showing up at your neighbour's house instead?" ...Okay maybe I'm just weird.
shiandow 3y ago
People always seem to forget that mathematical notation is designed to make algebraic manipulations easier to follow. It's not really intended as something that makes sense on its own, it's mostly physicists who think something like E=mc^2 should have any meaning. 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.
- toxik 3y ago
  In computer science, we straddle this divide where the usual way to describe things in scientific literature is using algebraic notation, but the usual way to actually write up a program is to use meaningful variable names. It's not K_i, it's current_gains or something like that. It leads to a funny kind of style where especially computer science-related fields start writing K_{current} in scientific manuscripts, and are then chided because that is not how you use subscripts. The reverse is also true, theory-adjacent code tends to use a lot more terse naming conventions.
  - michaelrpeskin 3y ago
    I often work with a guy who's a pure computer scientist. He communicates in LaTeX and pseudocode only. I don't think he could find a compiler if he tried. What I've learned to do is keep his notation whenever I implement something. I start the function with a comment that says what paper I'm referencing when I implement it and then comment all of the one-letter variables. (In this case I would use K[i]). 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).
  - 3y ago
pinkmuffinere 3y ago
> 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 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
gromneer 3y ago
> 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 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.
- saulrh 3y ago
  Having written papers like this before, a large part of the problem is that almost all CS research is published in conferences, rather than journals, and conferences frequently have extremely strict length limits, on the order of three or five pages. If you have an even slightly complicated procedure it can be nightmarishly difficult to get even the core information into your paper, and you can forget about details or tangents.
foofie 3y ago
> I've always thought math would be much easier to learn if they used descriptive variable names. 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.
max_ 3y ago
I completely agree. And my insight similar to yours is that the greatest math book that no one has written is one where the meaning of notation, variables and a clear assortment of theorems across all topics are well curated.
- bonoboTP 3y ago
  Many math books nowadays come with Python code eg jupyter notebooks.
  - max_ 3y ago
    Python code is abit of an over kill. I was for example reading a cryptography book and it has symbols like a hamadad product.
deleted 3y ago
[deleted]
colechristensen 3y ago
I've always thought that code would be much easier to understand with shorter, less descriptive variable names. Whenever I look at new code most of the confusion involves searching through layers of abstraction for the part that actually does the thing as opposed to the layer upon layer of connections between abstractions which would be much less necessary if the entire behavior could be encoded in a single line. You can only have a small number of descriptive variables in an expression before it becomes entirely unreadable. That is opposed to single character with sub/superscripts where you can easily see what's happening with tens of variables in a single line of math. https://wikimedia.org/api/rest_v1/media/math/render/svg/a7d22d3c91ab780f2cfdf7eab2aff60850476e37 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 https://en.wikipedia.org/wiki/Oblique_shock )
malkia 3y ago
Check https://mitpress.ublish.com/ebook/structure-and-interpretation-classical-mechanics-0-preview/135/xiv https://mitpress.ublish.com/ebook/structure-and-interpretati...
o11c 3y ago
> trying to figure out what kind of order 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) 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.

Waterluvian 3y ago

This was 90% of my problem with math. 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.

bonoboTP 3y ago
I agree but this is a surface level issue impacting the very beginner phase only. Once you get familiar with the vocabulary, the hard stuff will be the actual material, understanding the thing itself, not its description. This differentiates fields that have an actual subject matter from fields that are essentially terminology and categorizations all the way through, a self-referential map with no territory. 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).
- Waterluvian 3y ago
  Oh definitely! Eventually you've spent so much time that the thetas and lambdas and Lorentzes and whatever become your close intimate friends. I've most recently experienced this with learning piano and how an ocean of white and black keys all developed these individual "identities." Like, "ah yes, <looks at A4> I won't forget you. We've had so many dramatic moments before, and remember that time I kept showing up at your neighbour's house instead?" ...Okay maybe I'm just weird.

shiandow 3y ago

People always seem to forget that mathematical notation is designed to make algebraic manipulations easier to follow. It's not really intended as something that makes sense on its own, it's mostly physicists who think something like E=mc^2 should have any meaning. 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.

toxik 3y ago
In computer science, we straddle this divide where the usual way to describe things in scientific literature is using algebraic notation, but the usual way to actually write up a program is to use meaningful variable names. It's not K_i, it's current_gains or something like that. It leads to a funny kind of style where especially computer science-related fields start writing K_{current} in scientific manuscripts, and are then chided because that is not how you use subscripts. The reverse is also true, theory-adjacent code tends to use a lot more terse naming conventions.
- michaelrpeskin 3y ago
  I often work with a guy who's a pure computer scientist. He communicates in LaTeX and pseudocode only. I don't think he could find a compiler if he tried. What I've learned to do is keep his notation whenever I implement something. I start the function with a comment that says what paper I'm referencing when I implement it and then comment all of the one-letter variables. (In this case I would use K[i]). 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).
- 3y ago

pinkmuffinere 3y ago

> 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 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

gromneer 3y ago

> 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 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.

saulrh 3y ago
Having written papers like this before, a large part of the problem is that almost all CS research is published in conferences, rather than journals, and conferences frequently have extremely strict length limits, on the order of three or five pages. If you have an even slightly complicated procedure it can be nightmarishly difficult to get even the core information into your paper, and you can forget about details or tangents.

foofie 3y ago

> I've always thought math would be much easier to learn if they used descriptive variable names. 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.

max_ 3y ago

I completely agree. And my insight similar to yours is that the greatest math book that no one has written is one where the meaning of notation, variables and a clear assortment of theorems across all topics are well curated.

bonoboTP 3y ago
Many math books nowadays come with Python code eg jupyter notebooks.
- max_ 3y ago
  Python code is abit of an over kill. I was for example reading a cryptography book and it has symbols like a hamadad product.

deleted 3y ago

[deleted]

colechristensen 3y ago

I've always thought that code would be much easier to understand with shorter, less descriptive variable names. Whenever I look at new code most of the confusion involves searching through layers of abstraction for the part that actually does the thing as opposed to the layer upon layer of connections between abstractions which would be much less necessary if the entire behavior could be encoded in a single line. You can only have a small number of descriptive variables in an expression before it becomes entirely unreadable. That is opposed to single character with sub/superscripts where you can easily see what's happening with tens of variables in a single line of math. https://wikimedia.org/api/rest_v1/media/math/render/svg/a7d22d3c91ab780f2cfdf7eab2aff60850476e37 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 https://en.wikipedia.org/wiki/Oblique_shock )

malkia 3y ago

Check https://mitpress.ublish.com/ebook/structure-and-interpretation-classical-mechanics-0-preview/135/xiv https://mitpress.ublish.com/ebook/structure-and-interpretati...

o11c 3y ago

> trying to figure out what kind of order 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) 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.